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Potassium humate is the potassium salt of humic acid . It is manufactured commercially by alkaline extraction of brown coal (lignite) leonardite and is used mainly as a soil conditioner . [ 1 ]
The extraction is performed in water with the addition of potassium hydroxide (KOH), sequestering agents, and hydrotropic surfactants . Heat is used to increase the solubility of humic acids and hence more potassium humate can be extracted. The resulting liquid is dried to produce the amorphous crystalline like product which can then be added as a granule to fertilizer. The potassium humate granules by way of chemical extraction lose their hydrophobic properties and are now soluble.
Depending on the source material, product quality varies. High quality oxidized lignite (brown coal), usually referred to as leonardite, is the best source material for extraction of large quantities of potassium humate. The less oxidized the coal, the less potassium humate extracted. Sources low in ash produce the best quality. Less oxidized brown coal contains a higher proportion of the insoluble humin fraction and along with peat which is lower in humic acid content and usually high in ash content requires separation by filtration or centrifugation to remove ash and humin. Peat is also high in non-humified organic matter that needs to be reduced to produce a high quality product. The benefit of peat is that it is usually 2-3 times higher in fulvic acid content, which are the low molecular weight fractions of humic acid that are high in oxygen containing functional groups and soluble at a low pH of <1. Fulvic acids have a higher cation exchange capacity and therefore have a higher chemical interaction with fertilizers and are able to form soluble chelates of trace metals.
Potassium humate is used in agriculture as a fertilizer additive to increase the efficiency of fertilizers especially nitrogen- and phosphorus-based fertilizer inputs. Other salts of humic acid are manufactured, mainly sodium humate, which is used in animal health supplements. It also can be used in aquaculture. | https://en.wikipedia.org/wiki/Potassium_humate |
Potassium hydroxide is an inorganic compound with the formula K OH , and is commonly called caustic potash .
Along with sodium hydroxide (NaOH), KOH is a prototypical strong base . It has many industrial and niche applications, most of which utilize its caustic nature and its reactivity toward acids . An estimated 700,000 to 800,000 tonnes were produced in 2005. KOH is noteworthy as the precursor to most soft and liquid soaps , as well as numerous potassium-containing chemicals. It is a white solid that is dangerously corrosive. [ 11 ]
KOH exhibits high thermal stability . Because of this high stability and relatively low melting point , it is often melt-cast as pellets or rods, forms that have low surface area and convenient handling properties. These pellets become tacky in air because KOH is hygroscopic . Most commercial samples are ca. 90% pure, the remainder being water and carbonates. [ 11 ] Its dissolution in water is strongly exothermic . Concentrated aqueous solutions are sometimes called potassium lyes . Even at high temperatures, solid KOH does not dehydrate readily. [ 12 ]
At higher temperatures, solid KOH crystallizes in the NaCl crystal structure . The OH − group is either rapidly or randomly disordered so that it is effectively a spherical anion of radius 1.53 Å (between Cl − and F − in size). At room temperature, the OH − groups are ordered and the environment about the K + centers is distorted, with K + −OH − distances ranging from 2.69 to 3.15 Å, depending on the orientation of the OH group. KOH forms a series of crystalline hydrates , namely the monohydrate KOH · H 2 O , the dihydrate KOH · 2 H 2 O and the tetrahydrate KOH · 4 H 2 O . [ 13 ]
About 112 g of KOH dissolve in 100 mL water at room temperature, which contrasts with 100 g/100 mL for NaOH. [ 14 ] Thus on a molar basis, KOH is slightly more soluble than NaOH. Lower molecular-weight alcohols such as methanol , ethanol , and propanols are also excellent solvents . They participate in an acid-base equilibrium. In the case of methanol the potassium methoxide (methylate) forms: [ 15 ]
Because of its high affinity for water, KOH serves as a desiccant in the laboratory. It is often used to dry basic solvents, especially amines and pyridines .
KOH, like NaOH, serves as a source of OH − , a highly nucleophilic anion that attacks polar bonds in both inorganic and organic materials. Aqueous KOH saponifies esters :
When R is a long chain, the product is called a potassium soap . This reaction is manifested by the "greasy" feel that KOH gives when touched; fats on the skin are rapidly converted to soap and glycerol .
Molten KOH is used to displace halides and other leaving groups . The reaction is especially useful for aromatic reagents to give the corresponding phenols . [ 16 ]
Complementary to its reactivity toward acids, KOH attacks oxides . Thus, SiO 2 is attacked by KOH to give soluble potassium silicates. KOH reacts with carbon dioxide to give potassium bicarbonate :
Historically, KOH was made by adding potassium carbonate to a strong solution of calcium hydroxide (slaked lime). The salt metathesis reaction results in precipitation of solid calcium carbonate , leaving potassium hydroxide in solution:
Filtering off the precipitated calcium carbonate and boiling down the solution gives potassium hydroxide ("calcinated or caustic potash"). This method of producing potassium hydroxide remained dominant until the late 19th century, when it was largely replaced by the current method of electrolysis of potassium chloride solutions. [ 11 ] The method is analogous to the manufacture of sodium hydroxide (see chloralkali process ):
Hydrogen gas forms as a byproduct on the cathode ; concurrently, an anodic oxidation of the chloride ion takes place, forming chlorine gas as a byproduct. Separation of the anodic and cathodic spaces in the electrolysis cell is essential for this process. [ 17 ]
KOH and NaOH can be used interchangeably for a number of applications, although in industry, NaOH is preferred because of its lower cost.
In industry, KOH is a good catalyst for hydrothermal gasification process. In this process, it is used to improve the yield of gas and amount of hydrogen in process. For example, production of coke (fuel) from coal often produces much coking wastewater. In order to degrade it, supercritical water is used to convert it to the syngas containing carbon monoxide , carbon dioxide , hydrogen and methane . Using pressure swing adsorption , we could separate various gases and then use power-to-gas technology to convert them to fuel. [ 18 ] On the other hand, the hydrothermal gasification process could degrade other waste such as sewage sludge and waste from food factories.
Many potassium salts are prepared by neutralization reactions involving KOH. The potassium salts of carbonate , cyanide , permanganate , phosphate , and various silicates are prepared by treating either the oxides or the acids with KOH. [ 11 ] The high solubility of potassium phosphate is desirable in fertilizers .
The saponification of fats with KOH is used to prepare the corresponding "potassium soaps ", which are softer than the more common sodium hydroxide -derived soaps. Because of their softness and greater solubility, potassium soaps require less water to liquefy, and can thus contain more cleaning agent than liquefied sodium soaps. [ 19 ]
Aqueous potassium hydroxide is employed as the electrolyte in alkaline batteries based on nickel - cadmium , nickel - hydrogen , and manganese dioxide - zinc . Potassium hydroxide is preferred over sodium hydroxide because its solutions are more conductive. [ 20 ] The nickel–metal hydride batteries in the Toyota Prius use a mixture of potassium hydroxide and sodium hydroxide. [ 21 ] Nickel–iron batteries also use potassium hydroxide electrolyte.
In food products, potassium hydroxide acts as a food thickener, pH control agent and food stabilizer. The FDA considers it generally safe as a direct food ingredient when used in accordance with Good Manufacturing Practices . [ 22 ] It is known in the E number system as E525 .
Like sodium hydroxide, potassium hydroxide attracts numerous specialized applications, virtually all of which rely on its properties as a strong chemical base with its consequent ability to degrade many materials. For example, in a process commonly referred to as "chemical cremation" or " resomation ", potassium hydroxide hastens the decomposition of soft tissues, both animal and human, to leave behind only the bones and other hard tissues. [ 23 ] Entomologists wishing to study the fine structure of insect anatomy may use a 10% aqueous solution of KOH to apply this process. [ 24 ]
In chemical synthesis, the choice between the use of KOH and the use of NaOH is guided by the solubility or keeping quality of the resulting salt .
The corrosive properties of potassium hydroxide make it a useful ingredient in agents and preparations that clean and disinfect surfaces and materials that can themselves resist corrosion by KOH. [ 17 ]
KOH is also used for semiconductor chip fabrication (for example anisotropic wet etching ).
Potassium hydroxide is often the main active ingredient in chemical "cuticle removers" used in manicure treatments.
Because aggressive bases like KOH damage the cuticle of the hair shaft, potassium hydroxide is used to chemically assist the removal of hair from animal hides. The hides are soaked for several hours in a solution of KOH and water to prepare them for the unhairing stage of the tanning process. This same effect is also used to weaken human hair in preparation for shaving. Preshave products and some shave creams contain potassium hydroxide to force open the hair cuticle and to act as a hygroscopic agent to attract and force water into the hair shaft, causing further damage to the hair. In this weakened state, the hair is more easily cut by a razor blade.
Potassium hydroxide is used to identify some species of fungi . A 3–5% aqueous solution of KOH is applied to the flesh of a mushroom and the researcher notes whether or not the color of the flesh changes. Certain species of gilled mushrooms , boletes , polypores , and lichens [ 25 ] are identifiable based on this color-change reaction. [ 26 ]
Potassium hydroxide is a caustic alkali and its solutions range from irritating to skin and other tissue in low concentrations, to highly corrosive in high concentrations. Eyes are particularly vulnerable, and dust or mist is severely irritating to lungs and can cause pulmonary edema . [ 27 ] Safety considerations are similar to those of sodium hydroxide .
The caustic effects arise from being highly alkaline, but if potassium hydroxide is neutralised with a non-toxic acid then it becomes a non-toxic potassium salt. It is approved as a food additive under the code E525. | https://en.wikipedia.org/wiki/Potassium_hydroxide |
Potassium hypochlorite is a chemical compound with the chemical formula K O Cl , also written as KClO. It is the potassium salt of hypochlorous acid . It consists of potassium cations ( K + ) and hypochlorite anions ( − OCl ). It is used in variable concentrations, often diluted in water solution. Its aqueous solutions are colorless liquids (light yellow when impure) that have a strong chlorine smell. [ 1 ] It is used as a biocide and disinfectant . [ 1 ]
Potassium hypochlorite is produced by the disproportionation reaction of chlorine with a solution of potassium hydroxide : [ 2 ]
This is the traditional method, first used by Claude Louis Berthollet in 1789. [ 3 ]
Another production method is electrolysis of potassium chloride solution.
With both methods, the reaction mixture must be kept cold to prevent formation of potassium chlorate .
Potassium hypochlorite is used for sanitizing surfaces as well as disinfecting drinking water . Because its degradation leaves behind potassium chloride rather than sodium chloride , its use has been promoted in agriculture , where addition of potassium to soil is desired. [ 4 ]
Potassium hypochlorite was first produced in 1789 by Claude Louis Berthollet in his laboratory located in Javel in Paris, France, by passing chlorine gas through a solution of potash lye . The resulting liquid, known as " Eau de Javel " ("Javel water"), was a weak solution of potassium hypochlorite. Due to production difficulties, the product was then modified using sodium instead of potassium , giving rise to sodium hypochlorite , widely used today as a disinfectant .
Like sodium hypochlorite , potassium hypochlorite is an irritant. It can cause severe damage on contact with the skin, eyes, and mucous membranes . [ 5 ] Inhalation of a mist of KOCl can cause bronchus and lung irritation, difficulty breathing, and in severe cases pulmonary edema . Ingestion of strong concentrations can be lethal. [ 6 ] Symptoms of contact or inhalation can be delayed. [ 1 ]
Potassium hypochlorite is not considered to cause a fire or explosive hazards by itself. [ 6 ] However, it can react explosively with numerous chemicals, including urea , ammonium salts , methanol , acetylene , and many organic compounds . Heating and acidification can produce toxic chlorine gas. [ 7 ] Containers may explode upon exposure to heat. [ 1 ] Potassium hypochlorite forms highly explosive NCl 3 upon contact with urea or ammonia . [ 1 ] | https://en.wikipedia.org/wiki/Potassium_hypochlorite |
Potassium is the main intracellular ion for all types of cells , while having a major role in maintenance of fluid and electrolyte balance. [ 1 ] [ 2 ] Potassium is necessary for the function of all living cells and is thus present in all plant and animal tissues. It is found in especially high concentrations within plant cells, and in a mixed diet, it is most highly concentrated in fruits. The high concentration of potassium in plants, associated with comparatively very low amounts of sodium there, historically resulted in potassium first being isolated from the ashes of plants ( potash ), which in turn gave the element its modern name. The high concentration of potassium in plants means that heavy crop production rapidly depletes soils of potassium, and agricultural fertilizers consume 93% of the potassium chemical production of the modern world economy.
The functions of potassium and sodium in living organisms are quite different. Animals, in particular, employ sodium and potassium differentially to generate electrical potentials in animal cells, especially in nervous tissue . Potassium depletion in animals, including humans, results in various neurological dysfunctions. Characteristic concentrations of potassium in model organisms are: 30–300 mM in E. coli , 300 mM in budding yeast, 100 mM in mammalian cell and 4 mM in blood plasma. [ 3 ]
The main role of potassium in plants is to provide the ionic environment for metabolic processes in the cytosol , and as such functions as a regulator of various processes including growth regulation. [ 4 ] Plants require potassium ions (K + ) for protein synthesis and for the opening and closing of stomata , which is regulated by proton pumps to make surrounding guard cells either turgid or flaccid . A deficiency of potassium ions can impair a plant's ability to maintain these processes. Potassium also functions in other physiological processes such as photosynthesis , protein synthesis , activation of some enzymes , phloem solute transport of photoassimilates into source organs , and maintenance of cation:anion balance in the cytosol and vacuole . [ 5 ]
Potassium is the major cation (K + , a positive ion) inside animal cells , while sodium (Na + ) is the major cation outside animal cells. The difference between the concentrations of these charged particles causes a difference in electric potential between the inside and outside of cells, known as the membrane potential . The balance between potassium and sodium is maintained by ion transporters in the cell membrane . All potassium ion channels are tetramers with several conserved secondary structural elements. A number of potassium channel structures have been solved including voltage gated , [ 6 ] [ 7 ] [ 8 ] ligand gated , [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] tandem-pore , [ 14 ] [ 15 ] [ 16 ] and inwardly rectifying channels, [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] from prokaryotes and eukaryotes . The cell membrane potential created by potassium and sodium ions allows the cell to generate an action potential —a "spike" of electrical discharge. The ability of cells to produce electrical discharge is critical for body functions such as neurotransmission , muscle contraction, and heart function. [ 22 ]
The U.S. National Academy of Medicine (NAM), on behalf of both the U.S. and Canada, sets Dietary Reference Intakes , including Estimated Average Requirements (EARs) and Recommended Dietary Allowances (RDAs), or Adequate Intakes (AIs) for when there is not sufficient information to set EARs and RDAs.
For both males and females under 9 years of age, the AIs for potassium are: 400 mg of potassium for 0 to 6-month-old infants, 860 mg of potassium for 7 to 12-month-old infants, 2,000 mg of potassium for 1 to 3-year-old children, and 2,300 mg of potassium for 4 to 8-year-old children.
For males 9 years of age and older, the AIs for potassium are: 2,500 mg of potassium for 9 to 13-year-old males, 3,000 mg of potassium for 14 to 18-year-old males, and 3,400 mg for males that are 19 years of age and older.
For females 9 years of age and older, the AIs for potassium are: 2,300 mg of potassium for 9 to 18-year-old females, and 2,600 mg of potassium for females that are 19 years of age and older.
For pregnant and lactating females, the AIs for potassium are: 2,600 mg of potassium for 14 to 18-year-old pregnant females, 2,900 mg for pregnant females that are 19 years of age and older; furthermore, 2,500 mg of potassium for 14 to 18-year-old lactating females, and 2,800 mg for lactating females that are 19 years of age and older. As for safety, the NAM also sets tolerable upper intake levels (ULs) for vitamins and minerals, but for potassium the evidence was insufficient, so no UL was established. [ 23 ] [ 24 ]
In 2019, the National Academies of Sciences, Engineering, and Medicine revised the Adequate Intake for potassium to 2,600 mg/day for females 19 years of age and older who are not pregnant or lactating, and 3,400 mg/day for males 19 years of age and older. [ 25 ] [ 26 ]
The European Food Safety Authority (EFSA) refers to the collective set of information as Dietary Reference Values, with Population Reference Intake (PRI) instead of RDA, and Average Requirement instead of EAR. AI and UL are defined the same as in the United States. For people ages 15 and older, the AI is set at 3,500 mg/day. AIs for pregnancy is 3,500 mg/day, for lactation 4,000 mg/day. For children ages 1–14 years, the AIs increase with age from 800 to 2,700 mg/day. These AIs are lower than the U.S. RDAs. [ 27 ] The EFSA reviewed the same safety question and decided that there was insufficient data to establish a UL for potassium. [ 28 ]
For U.S. food and dietary supplement labeling purposes, the amount in a serving is expressed as a percent of Daily Value (%DV). For potassium labeling purposes, 100% of the Daily Value was 3500 mg, but as of May 2016, it has been revised to 4700 mg. [ 29 ] [ 30 ] A table of the old and new adult Daily Values is provided at Reference Daily Intake .
20 mEq (781 mg) potassium from potassium gluconate (4680 mg), or potassium citrate (2040 mg), mixed with a half-cup (1.12 dL) water, taken two to four times a day, may be used on a daily basis. [ 31 ] [ 32 ]
Because of the risk of small-bowel lesions, the US FDA requires some potassium salts (for example potassium chloride ) containing more than 99 mg (about 1.3 mEq) to be labeled with a warning. [ 33 ]
Eating a variety of foods that contain potassium is the best way to get an adequate amount.
Foods with high sources of potassium include kiwifruit , orange juice , potatoes , coconut , avocados , apricots , parsnips and turnips , although many other fruits , vegetables , legumes, and meats contain potassium.
Common foods very high in potassium: [ 34 ]
Foods containing the highest concentration: [ 34 ]
Diets low in potassium increase risk of hypertension, stroke and cardiovascular disease. [ 36 ] [ 37 ]
A severe shortage of potassium in body fluids may cause a potentially fatal condition known as hypokalemia . Hypokalemia typically results from loss of potassium through diarrhea , diuresis , or vomiting. Symptoms are related to alterations in membrane potential and cellular metabolism. Symptoms include muscle weakness and cramps, paralytic ileus , ECG abnormalities, intestinal paralysis, decreased reflex response and (in severe cases) respiratory paralysis, alkalosis and arrhythmia .
In rare cases, habitual consumption of large amounts of black licorice has resulted in hypokalemia. Licorice contains a compound ( glycyrrhizin ) that increases urinary excretion of potassium. [ 38 ]
Adult women in the United States consume on average half the AI, for men two-thirds. For all adults, fewer than 5% exceed the AI. [ 39 ] Similarly, in the European Union , insufficient potassium intake is widespread. [ 40 ]
Gastrointestinal symptoms are the most common side effects of potassium supplements, including nausea, vomiting, abdominal discomfort, and diarrhea. Taking potassium with meals or taking a microencapsulated form of potassium may reduce gastrointestinal side effects.
Hyperkalemia is the most serious adverse reaction to potassium. Hyperkalemia occurs when potassium builds up faster than the kidneys can remove it. It is most common in individuals with renal failure . Symptoms of hyperkalemia may include tingling of the hands and feet, muscular weakness, and temporary paralysis. The most serious complication of hyperkalemia is the development of an abnormal heart rhythm ( arrhythmia ), which can lead to cardiac arrest.
Although hyperkalemia is rare in healthy individuals, oral doses greater than 18 grams taken at one time in individuals not accustomed to high intakes can lead to hyperkalemia. | https://en.wikipedia.org/wiki/Potassium_in_biology |
Potassium iodate ( K I O 3 ) is an ionic inorganic compound with the formula KIO 3 . It is a white salt that is soluble in water. [ 1 ]
It can be prepared by reacting a potassium-containing base such as potassium hydroxide with iodic acid , for example: [ 1 ]
It can also be prepared by adding iodine to a hot, concentrated solution of potassium hydroxide: [ 1 ]
Or by fusing potassium iodide with potassium chlorate , bromate or perchlorate , the melt is extracted with water and potassium iodate is isolated from the solution by crystallization: [ 2 ]
The analogous reaction with potassium hypochlorite is also possible: [ 3 ]
KI + 3KOCl → 3KCl + KIO 3
Conditions/substances to avoid include: heat , shock , friction , [ 4 ] combustible materials, [ 1 ] reducing materials, aluminium , [ 4 ] organic compounds , [ 1 ] carbon , hydrogen peroxide and sulfides . [ 4 ]
Potassium iodate is sometimes used for iodination of table salt to prevent iodine deficiency . In the US, iodized salt contains antioxidants , because atmospheric oxygen can oxidize wet iodide to iodine; other countries simply use potassium iodate instead. [ 5 ] Salt mixed with ferrous fumarate and potassium iodate, "double fortified salt", are used to address both iron and iodine deficiencies. [ 6 ] Potassium iodate is also used to provide iodine in some baby formula . [ 7 ]
Like potassium bromate , potassium iodate is occasionally used as a maturing agent in baking. [ 8 ]
Potassium iodate may be used to protect against accumulation of radioactive iodine in the thyroid by saturating the body with a stable source of iodine prior to exposure. [ 9 ] Approved by the World Health Organization for radiation protection, potassium iodate (KIO 3 ) is an alternative to potassium iodide (KI) , which has poor shelf life in hot and humid climates . [ 10 ] The UK , Singapore , United Arab Emirates , and the U.S. states Idaho and Utah all maintain potassium iodate tablets towards this end. [ citation needed ] Following the September 11 attacks , the government of Ireland issued potassium iodate tablets to all households for a similar purpose. [ 11 ]
Potassium iodate is not approved by the U.S. Food and Drug Administration (FDA) for use as a thyroid blocker , and the FDA has taken action against US websites that promote this use. [ 13 ] [ 14 ]
Potassium iodate is an oxidizing agent and as such it can form explosive mixtures when combined with organic compounds. [ 1 ] | https://en.wikipedia.org/wiki/Potassium_iodate |
Potassium iodide is a chemical compound , medication , and dietary supplement . [ 3 ] [ 4 ] It is a medication used for treating hyperthyroidism , in radiation emergencies , and for protecting the thyroid gland when certain types of radiopharmaceuticals are used. [ 5 ] It is also used for treating skin sporotrichosis and phycomycosis . [ 5 ] [ 6 ] It is a supplement used by people with low dietary intake of iodine . [ 4 ] It is administered orally. [ 5 ]
Common side effects include vomiting, diarrhea, abdominal pain, rash, and swelling of the salivary glands . [ 5 ] Other side effects include allergic reactions , headache , goitre , and depression . [ 6 ] While use during pregnancy may harm the baby, its use is still recommended in radiation emergencies. [ 5 ] Potassium iodide has the chemical formula K I . [ 7 ] Commercially it is made by mixing potassium hydroxide with iodine. [ 8 ] [ 9 ]
Potassium iodide has been used medically since at least 1820. [ 10 ] It is on the World Health Organization's List of Essential Medicines . [ 11 ] Potassium iodide is available as a generic medication and over the counter . [ 12 ] Potassium iodide is also used for the iodization of salt . [ 4 ]
Potassium iodide is a nutritional supplement in animal feeds and also in the human diet. In humans it is the most common additive used for iodizing table salt (a public health measure to prevent iodine deficiency in populations that get little seafood). The oxidation of iodide causes slow loss of iodine content from iodised salts that are exposed to excess air. The alkali metal iodide salt, over time and exposure to excess oxygen and carbon dioxide, slowly oxidizes to metal carbonate and elemental iodine, which then evaporates. [ 13 ] Potassium iod ate ( K I O 3 ) is used to iodize some salts so that the iodine is not lost by oxidation. Dextrose or sodium thiosulfate are often added to iodized table salt to stabilize potassium iodide thus reducing loss of the volatile chemical. [ 14 ]
Thyroid iodine uptake blockade with potassium iodide is used in nuclear medicine scintigraphy and therapy with some radioiodinated compounds that are not targeted to the thyroid, such as iobenguane ( MIBG ), which is used to image or treat neural tissue tumors, or iodinated fibrinogen , which is used in fibrinogen scans to investigate clotting. These compounds contain iodine, but not in the iodide form. Since they may be ultimately metabolized or break down to radioactive iodide, it is common to administer non-radioactive potassium iodide to ensure that iodide from these radiopharmaceuticals is not sequestered by the normal affinity of the thyroid for iodide.
The World Health Organization (WHO) provides guidelines for potassium iodide use following a nuclear accident. The dosage of potassium iodide is age-dependent: neonates (<1 month) require 16 mg/day; children aged 1 month to 3 years need 32 mg/day; those aged 3-12 years need 65 mg/day; and individuals over 12 years and adults require 130 mg/day. [ 15 ] These dosages list mass of potassium iodide rather than elemental iodine. [ 16 ] [ 15 ] Potassium iodide can be administered as tablets or as Lugol's iodine solution. [ 15 ] The same dosage is recommended by the US Food and Drug Administration . [ 17 ] A single daily dose is typically sufficient for 24-hour protection. [ 15 ] However, in cases of prolonged or repeated exposure, health authorities may recommend multiple daily doses. [ 15 ] Priority for prophylaxis is given to the most sensitive groups: pregnant and breastfeeding women, infants, and children under 18 years. [ 15 ] The recommended doses of potassium iodide, which contains a stable isotope of iodine, only protect the thyroid gland from radioactive iodine. [ 15 ] It does not offer protection against other radioactive substances. [ 15 ] Some sources recommend alternative dosing regimens. [ specify ] [ 18 ]
Not all sources are in agreement on the necessary duration of thyroid blockade, although agreement appears to have been reached about the necessity of blockade for both scintigraphic and therapeutic applications of iobenguane. Commercially available iobenguane is labeled with iodine-123 , and product labeling recommends administration of potassium iodide 1 hour prior to administration of the radiopharmaceutical for all age groups, [ 19 ] while the European Association of Nuclear Medicine recommends (for iobenguane labeled with either isotope), that potassium iodide administration begin one day prior to radiopharmaceutical administration, and continue until the day following the injection, with the exception of new-borns, who do not require potassium iodide doses following radiopharmaceutical injection. [ 18 ] [ 20 ]
Product labeling for diagnostic iodine-131 iobenguane recommends potassium iodide administration one day before injection and continuing 5 to 7 days following administration, in keeping with the much longer half-life of this isotope and its greater danger to the thyroid. [ 21 ] Iodine-131 iobenguane used for therapeutic purposes requires a different pre-medication duration, beginning 24–48 hours prior to iobenguane injection and continuing 10–15 days following injection. [ 22 ]
In 1982, the U.S. Food and Drug Administration approved potassium iodide to protect thyroid glands from radioactive iodine involving accidents or fission emergencies. In an accidental event or attack on a nuclear power plant , or in nuclear bomb fallout , volatile fission product radionuclides may be released. Of these products, 131 I (Iodine-131) is one of the most common and is particularly dangerous to the thyroid gland because it may lead to thyroid cancer . [ 24 ] By saturating the body with a source of stable iodide prior to exposure, inhaled or ingested 131 I tends to be excreted, which prevents radioiodine uptake by the thyroid. According to one 2000 study "KI administered up to 48 h before 131 I exposure can almost completely block thyroid uptake and therefore greatly reduce the thyroid absorbed dose. However, KI administration 96 h or more before 131 I exposure has no significant protective effect. In contrast, KI administration after exposure to radioiodine induces a smaller and rapidly decreasing blockade effect." [ 25 ] According to the FDA, KI should not be taken as a preventative before radiation exposure. Since KI protects for approximately 24 hours, it must be dosed daily until a risk of significant exposure to radioiodine no longer exists. [ 26 ]
Emergency 130 milligrams potassium iodide doses provide 100 mg iodide (the other 30 mg is the potassium in the compound), [ 16 ] which is roughly 700 times larger than the normal nutritional need (see recommended dietary allowance ) for iodine, which is 150 micrograms (0.15 mg) of iodine (as iodide) per day for an adult. A typical tablet weighs 160 mg, with 130 mg of potassium iodide and 30 mg of excipients , such as binding agents . [ 16 ]
Potassium iodide cannot protect against any other mechanisms of radiation poisoning , nor can it provide any degree of protection against dirty bombs that produce radionuclides other than those of iodine. [ 15 ]
The potassium iodide in iodized salt is insufficient for this use. [ 27 ] A likely lethal dose of salt (more than a kilogram [ 28 ] ) would be needed to equal the potassium iodide in one tablet. [ 29 ]
The World Health Organization does not recommend KI prophylaxis for adults over 40 years, unless the radiation dose from inhaled radioiodine is expected to threaten thyroid function, because the KI side effects increase with age and may exceed the KI protective effects; "...unless doses to the thyroid from inhalation rise to levels threatening thyroid function, that is of the order of about 5 Gy . Such radiation doses will not occur far away from an accident site." [ 23 ] [ 15 ]
The U.S. Department of Health and Human Services restated these two years later as "The downward KI (potassium iodide) dose adjustment by age group, based on body size considerations, adheres to the principle of minimum effective dose. The recommended standard (daily) dose of KI for all school-age children is the same (65 mg). However, adolescents approaching adult size (i.e., >70 kg [154 lbs]) should receive the full adult dose (130 mg) for maximal block of thyroid radioiodine uptake. Neonates ideally should receive the lowest dose (16 mg) of KI." [ 30 ]
There is reason for caution with prescribing the ingestion of high doses of potassium iodide and iodate, because their unnecessary use can cause conditions such as the Jod-Basedow phenomena , trigger and/or worsen hyperthyroidism and hypothyroidism , and then cause temporary or even permanent thyroid conditions.
It can also cause sialadenitis (an inflammation of the salivary gland), gastrointestinal disturbances, and rashes.
Potassium iodide is also not recommended for people with dermatitis herpetiformis and hypocomplementemic vasculitis – conditions that are linked to a risk of iodine sensitivity. [ 31 ]
There have been some reports of potassium iodide treatment causing swelling of the parotid gland (one of the three glands that secrete saliva ), due to its stimulatory effects on saliva production. [ 32 ]
A saturated solution of KI (SSKI) is typically given orally in adult doses several times a day (5 drops of SSKI assumed to be 1 ⁄ 3 mL) for thyroid blockade (to prevent the thyroid from excreting thyroid hormone) and occasionally this dose is also used, when iodide is used as an expectorant (the total dose is about one gram KI per day for an adult). The anti-radioiodine doses used for 131 I uptake blockade are lower, and range downward from 100 mg a day for an adult, to less than this for children (see table). All of these doses should be compared with the far lower dose of iodine needed in normal nutrition, which is only 150 μg per day (150 micrograms, not milligrams).
At maximal doses, and sometimes at much lower doses, side effects of iodide used for medical reasons, in doses of 1000 times the normal nutritional need, may include: acne, loss of appetite, or upset stomach (especially during the first several days, as the body adjusts to the medication). More severe side effects that require notification of a physician are: fever, weakness, unusual tiredness, swelling in the neck or throat, [ citation needed ] mouth sores, skin rash, nausea, vomiting, stomach pains, irregular heartbeat, [ citation needed ] numbness or tingling of the hands or feet, or a metallic taste in the mouth. [ 33 ] [ citation needed ]
In the event of a radioiodine release the ingestion of prophylaxis potassium iodide, if available, or even iodate, would rightly take precedence over perchlorate administration, and would be the first line of defence in protecting the population from a radioiodine release. However, in the event of a radioiodine release too massive and widespread to be controlled by the limited stock of iodide and iodate prophylaxis drugs, then the addition of perchlorate ions to the water supply, or distribution of perchlorate tablets would serve as a cheap, efficacious, second line of defense against carcinogenic radioiodine bioaccumulation.
The ingestion of goitrogen drugs is, much like potassium iodide also not without its dangers, such as hypothyroidism . In all these cases however, despite the risks, the prophylaxis benefits of intervention with iodide, iodate or perchlorate outweigh the serious cancer risk from radioiodine bioaccumulation in regions where radioiodine has sufficiently contaminated the environment.
KI is used with silver nitrate to make silver iodide (AgI), an important chemical in film photography. KI is a component in some disinfectants and hair treatment chemicals. KI is also used as a fluorescence quenching agent in biomedical research, an application that takes advantage of collisional quenching of fluorescent substances by the iodide ion. However, for several fluorophores addition of KI in μM-mM concentrations results in increase of fluorescence intensity, and iodide acts as fluorescence enhancer. [ 34 ]
Potassium iodide is a component in the electrolyte of dye sensitised solar cells (DSSC) along with iodine.
Potassium iodide finds its most important applications in organic synthesis mainly in the preparation of aryl iodides in the Sandmeyer reaction , starting from aryl amines. Aryl iodides are in turn used to attach aryl groups to other organics by nucleophilic substitution, with iodide ion as the leaving group.
Potassium iodide is an ionic compound which is made of the following ions : K + I − . It crystallises in the sodium chloride structure. It is produced industrially by treating KOH with iodine. [ 35 ]
It is a white salt , which is the most commercially significant iodide compound, with approximately 37,000 tons produced in 1985. It absorbs water less readily than sodium iodide , making it easier to work with.
Aged and impure samples are yellow because of the slow oxidation of the salt to potassium carbonate and elemental iodine . [ 35 ]
Since the iodide ion is a mild reducing agent , I − is easily oxidised to iodine ( I 2 ) by powerful oxidising agents such as chlorine :
This reaction is employed in the isolation of iodine from natural sources. Air will oxidize iodide, as evidenced by the observation of a purple extract when aged samples of KI are rinsed with dichloromethane . As formed under acidic conditions, hydriodic acid (HI) is a stronger reducing agent. [ 36 ] [ 37 ] [ 38 ]
Like other iodide salts, KI forms triiodide ( I − 3 ) when combined with elemental iodine .
Unlike I 2 , I − 3 salts can be highly water-soluble. Through this reaction, iodine is used in redox titrations . Aqueous KI 3 ( Lugol's iodine ) solution is used as a disinfectant and as an etchant for gold surfaces.
Potassium iodide and silver nitrate are used to make silver(I) iodide , which is used for high speed photographic film and for cloud seeding :
KI serves as a source of iodide in organic synthesis . A useful application is in the preparation of aryl iodides from arenediazonium salts . [ 39 ] [ 40 ]
KI, acting as a source of iodide, may also act as a nucleophilic catalyst for the alkylation of alkyl chlorides , bromides , or mesylates .
Potassium iodide has been used medically since at least 1820. [ 10 ] Some of the earliest uses included cures for syphilis , [ 10 ] lead and mercury poisoning .
Potassium iodide's (KI) value as a radiation protective (thyroid blocking) agent was demonstrated following the Chernobyl nuclear reactor disaster in April 1986. A saturated solution of potassium iodide (SSKI) was administered to 10.5 million children and 7 million adults in Poland [ 30 ] [ 41 ] as a preventative measure against accumulation of radioactive 131 I in the thyroid gland.
Reports differ concerning whether people in the areas immediately surrounding Chernobyl itself were given the supplement. [ 42 ] [ 20 ] However the US Nuclear Regulatory Commission (NRC) reported, "thousands of measurements of I-131 (radioactive iodine) activity...suggest that the observed levels were lower than would have been expected had this prophylactic measure not been taken. The use of KI...was credited with permissible iodine content in 97% of the evacuees tested." [ 20 ]
With the passage of time, people living in irradiated areas where KI was not available have developed thyroid cancer at epidemic levels, which is why the US Food and Drug Administration (FDA) reported "The data clearly demonstrate the risks of thyroid radiation... KI can be used [to] provide safe and effective protection against thyroid cancer caused by irradiation." [ 43 ]
Chernobyl also demonstrated that the need to protect the thyroid from radiation was greater than expected. Within ten years of the accident, it became clear that thyroid damage caused by released radioactive iodine was virtually the only adverse health effect that could be measured. As reported by the NRC, studies after the accident showed that "As of 1996, except for thyroid cancer, there has been no confirmed increase in the rates of other cancers, including leukemia, among the... public, that have been attributed to releases from the accident." [ 44 ]
But equally important to the question of KI is the fact that radioactivity releases are not "local" events. Researchers at the World Health Organization accurately located and counted the residents with cancer from Chernobyl and were startled to find that "the increase in incidence [of thyroid cancer] has been documented up to 500 km from the accident site... significant doses from radioactive iodine can occur hundreds of kilometers from the site, beyond emergency planning zones." [ 23 ] Consequently, far more people than anticipated were affected by the radiation, which caused the United Nations to report in 2002 that "The number of people with thyroid cancer... has exceeded expectations. Over 11,000 cases have already been reported." [ 45 ]
The Chernobyl findings were consistent with studies of the effects of previous radioactivity releases. In 1945, several hundreds of thousands of people working and residing in the Japanese cities of Hiroshima and Nagasaki were exposed to high levels of radiation after atomic bombs were detonated over the two cities by the United States. Survivors of the A-bombings, also known as hibakusha , have markedly high rates of thyroid disease; a 2006 study of 4091 hibakusha found nearly half the participants (1833; 44.8%) had an identifiable thyroid disease. [ 46 ]
An editorial in The Journal of the American Medical Association regarding thyroid diseases in both hibakusha and those affected by the Chernobyl disaster reports that "[a] straight line adequately describes the relationship between radiation dose and thyroid cancer incidence" and states "it is remarkable that a biological effect from a single brief environmental exposure nearly 60 years in the past is still present and can be detected." [ 47 ]
The development of thyroid cancer among residents in the North Pacific from radioactive fallout following the United States' nuclear weapons testing in the 1950s (on islands nearly 200 miles downwind of the tests) were instrumental in the 1978 decision by the FDA to issue a request for the availability of KI for thyroid protection in the event of a release from a commercial nuclear power plant or weapons-related nuclear incident. Noting that KI's effectiveness was "virtually complete" and finding that iodine in the form of KI was substantially superior to other forms including iodate (KIO 3 ) in terms of safety, effectiveness, lack of side effects, and speed of onset, the FDA invited manufacturers to submit applications to produce and market KI. [ 48 ]
It was reported on 16 March 2011, that potassium iodide tablets were given preventively to U.S. Naval air crew members flying within 70 nautical miles of the Fukushima Daiichi Nuclear Power Plant damaged in the earthquake (8.9/9.0 magnitude) and ensuing tsunami on 11 March 2011. The measures were seen as precautions, and the Pentagon said no U.S. forces have shown signs of radiation poisoning. By 20 March, the US Navy instructed personnel coming within 100 miles of the reactor to take the pills. [ 49 ]
In the Netherlands, the central storage of iodine-pills is located in Zoetermeer , near The Hague . In 2017, the Dutch government distributed pills to hundreds of thousands of residents who lived within a certain distance of nuclear power plants and met some other criteria. [ 50 ] [ 51 ]
By 2020, potassium iodide tablets are made available free of charge for all residents in all pharmacies throughout the country. [ 52 ]
Three companies (Anbex, Inc., Fleming Co, and Recipharm of Sweden) have met the strict FDA requirements for manufacturing and testing of KI, and they offer products (IOSAT, ThyroShield, and ThyroSafe, [ 53 ] respectively) which are available for purchase. In 2012, Fleming Co. sold all its product rights and manufacturing facility to other companies and no longer exists. ThyroShield is currently not in production.
Tablets of potassium iodide are supplied for emergency purposes related to blockade of radioiodine uptake, a common form of radiation poisoning due to environmental contamination by the short-lived fission product 131 I . [ 54 ] Potassium iodide may also be administered pharmaceutically for thyroid storm .
For reasons noted above, therapeutic drops of SSKI, or 130 mg tablets of KI as used for nuclear fission accidents, are not used as nutritional supplements, since an SSKI drop or nuclear-emergency tablet provides 300 to 700 times more iodine than the daily adult nutritional requirement. Dedicated nutritional iodide tablets containing 0.15 mg (150 micrograms (μg)) of iodide, from KI or from various other sources (such as kelp extract) are marketed as supplements, but they are not to be confused with the much higher pharmaceutical dose preparations.
Potassium iodide can be conveniently prepared in a saturated solution, abbreviated SSKI. This method of delivering potassium iodide doesn't require a method to weigh out the potassium iodide, thus allowing it to be used in an emergency situation. KI crystals are simply added to water until no more KI will dissolve and instead sits at the bottom of the container. With pure water, the concentration of KI in the solution depends only on the temperature. Potassium iodide is highly soluble in water thus SSKI is a concentrated source of KI. At 20 degrees Celsius the solubility of KI is 140-148 grams per 100 grams of water. [ 55 ] Because the volumes of KI and water are approximately additive, the resulting SSKI solution will contain about 1.00 gram (1000 mg) KI per milliliter (mL) of solution. This is 100% weight/volume (note units of mass concentration ) of KI (one gram KI per mL solution), which is possible because SSKI is significantly more dense than pure water—about 1.67 g/mL. [ 56 ] Because KI is about 76.4% iodide by weight, SSKI contains about 764 mg iodide per mL. This concentration of iodide allows the calculation of the iodide dose per drop, if one knows the number of drops per milliliter. For SSKI, a solution more viscous than water, there are assumed to be 15 drops per mL; the iodide dose is therefore approximately 51 mg per drop. It is conventionally rounded to 50 mg per drop.
The term SSKI is also used, especially by pharmacists, to refer to a U.S.P. pre-prepared solution formula, made by adding KI to water to prepare a solution containing 1000 mg KI per mL solution (100% wt/volume KI solution), to closely approximate the concentration of SSKI made by saturation. This is essentially interchangeable with SSKI made by saturation, and also contains about 50 mg iodide per drop. | https://en.wikipedia.org/wiki/Potassium_iodide |
Potassium nitrate is an oxidizer so storing it near fire hazards or reducing agents should be avoided to minimise risk in case of a fire.
Synonyms : Saltpetre; Niter/Nitre; Nitric acid potassium salt; Salt Peter CAS No. : 7757-79-1 Molecular Weight : 101.1 Chemical Formula : K N O 3 [ 1 ]
Emergency Overview Danger - oxidizer. Contact with some materials may cause fire. Harmful if swallowed, inhaled or absorbed through the skin. Causes irritation to skin, eyes and respiratory tract.
SAF-T-DATA Ratings
Health Rating : 1 - Minimal Flammability Rating : 0 - None Reactivity Rating : 2 - Moderate (Oxidizer) Contact Rating : 1 - Minimal (Life) Lab Protective Equip : Safety goggles and surgical face mask (If you are planning to encounter this material close up for a period of time). Gloves optional. Storage Color Code : Yellow (Reactive)
Potential Health Effects
Inhalation : Causes irritation to the respiratory tract. Symptoms may include coughing, shortness of breath . Ingestion : Causes irritation to the gastrointestinal tract. Symptoms may include nausea, vomiting and diarrhea. May cause gastroenteritis and abdominal pains. Purging and diuresis can be expected. Rare cases of nitrates being converted to the more toxic nitrites have been reported, mostly with infants. Skin Contact : Causes irritation to skin. Symptoms include redness, itching, and pain. Eye Contact : Causes irritation, redness, and pain. Chronic Exposure : Under some circumstances methemoglobinemia occurs in individuals when the nitrate is converted by bacteria in the stomach to nitrite. Nausea, vomiting, dizziness, rapid heart beat, irregular breathing, convulsions, coma, and death can occur should this conversion take place. Chronic exposure to nitrites may cause anemia and adverse effects to kidney.
Inhalation :none Skin Contact : none Eye Contact : Flush eyes with water, lifting lower and upper eyelids occasionally.
Fire : Not combustible itself but substance is a strong oxidizer and its heat of reaction with reducing agents or combustibles may accelerate burning. Explosion : No danger of explosion. KNO 3 is an oxidising agent, so will accelerate combustion of combustibles. Fire Extinguishing Media : Dry chemical, carbon dioxide, Halon, water spray, or fog. If water is used, apply from as far a distance as possible. Water spray may be used to keep fire exposed containers cool. Do not allow water runoff to enter sewers or waterways. Special Information : Wear full protective clothing and breathing equipment for high-intensity fire or potential explosion conditions. This oxidizing material can increase the flammability of adjacent combustible materials.
Remove all sources of ignition. Ventilate area of leak or spill. Wear appropriate personal protective equipment as specified in Section 8. Spills: Clean up spills in a manner that does not disperse dust into the air. Use non-sparking tools and equipment. Reduce airborne dust and prevent scattering by moistening with water. Pick up spill for recovery or disposal and place in a closed container.
Keep in a tightly closed container, stored in a cool, dry, ventilated area. Protect against physical damage and moisture. Isolate from any source of heat or ignition. Avoid storage on wood floors. Separate from incompatibles, combustibles, organic or other readily oxidizable materials.
Ventilation System : A system of local and/or general exhaust is recommended to keep employee exposures as low as possible. Local exhaust ventilation is generally preferred because it can control the emissions of the contaminant at its source, preventing dispersion of it into the general work area. Please refer to the ACGIH document, Industrial Ventilation, A Manual of Recommended Practices, most recent edition, for details. Personal Respirators (NIOSH Approved) : For conditions of use where exposure to dust or mist is apparent and engineering controls are not feasible, a particulate respirator (NIOSH type N95 or better filters) may be worn. If oil particles (e.g. lubricants, cutting fluids, glycerine, etc.) are present, use a NIOSH type R or P filter. For emergencies or instances where the exposure levels are not known, use a full-face positive-pressure, air-supplied respirator. Skin Protection : Not required. Eye Protection : Not required. Optionally use chemical safety goggles where dusting or splashing of solutions is possible.
Appearance : White crystals. Odor : sour or salty. Solubility : 36 gm/100 ml water Specific Gravity : 2.1 pH : ca. 7 % Volatiles by volume @ 21C (70F) : 0 Boiling Point : 400 °C (752 °F) Melting Point : 333 °C (631 °F) Vapor Density (Air=1) : 3.00 Vapor Pressure (mm Hg) : Negligible @ 20 °C
Stability : Stable under ordinary conditions of use and storage. Hazardous Decomposition Products : Oxides of nitrogen and toxic metal fumes may form when heated to decomposition. Hazardous Polymerization : Will not occur. Incompatibilities : Heavy metals, phosphites, organic compounds, carbonaceous materials, strong acids, and many other substances. Conditions to Avoid : Heat, flames, ignition sources and incompatibles.
Whatever cannot be saved for recovery or recycling should be handled as hazardous waste and sent to a RCRA approved waste facility. Processing, use or contamination of this product may change the waste management options. State and local disposal regulations may differ from federal disposal regulations. Dispose of container and unused contents in accordance with federal, state and local requirements. | https://en.wikipedia.org/wiki/Potassium_nitrate_(data_page) |
Potassium nitrite (distinct from potassium nitrate ) is the inorganic compound with the chemical formula K N O 2 . It is an ionic salt of potassium ions K + and nitrite ions NO 2 − , which forms a white or slightly yellow, hygroscopic crystalline powder that is soluble in water. [ 1 ]
It is a strong oxidizer and may accelerate the combustion of other materials. Like other nitrite salts such as sodium nitrite , potassium nitrite is toxic if swallowed, and laboratory tests suggest that it may be mutagenic or teratogenic . Gloves and safety glasses are usually used when handling potassium nitrite.
Nitrite is present at trace levels in soil, natural waters, plant and animal tissues, and fertilizer. [ 2 ] The pure form of nitrite was first made by the Swedish chemist Carl Wilhelm Scheele working in the laboratory of his pharmacy in the market town of Köping . He heated potassium nitrate at red heat for half an hour and obtained what he recognized as a new “salt.” The two compounds (potassium nitrate and nitrite) were characterized by Péligot and the reaction was established as:
Potassium nitrite can be obtained by the reduction of potassium nitrate. The production of potassium nitrite by absorption of nitrogen oxides in potassium hydroxide or potassium carbonate is not employed on a large scale because of the high price of these alkalies. Furthermore, the fact that potassium nitrite is highly soluble in water makes the solid difficult to recover.
The mixing of cyanamide and KNO 2 produces changes from white solids to yellow liquid and then to orange solid, forming cyanogen and ammonia gases. No external energy is used and the reactions are carried out with a small amount of O 2 . [ 3 ]
Potassium nitrite forms potassium nitrate when heated in the presence of oxygen from 550 °C to 790 °C. The rate of reaction increases with temperature, but the extent of reaction decreases. At 550 °C and 600 °C the reaction is continuous and eventually goes to completion. From 650 °C to 750 °C, as the case of decomposition of potassium nitrate is, the system attains equilibrium . At 790 °C, a rapid decrease in volume is first observed, followed by a period of 15 minutes during which no volume changes occur. This is then followed by an increase in volume due primarily to the evolution of nitrogen, which is attributed to the decomposition of potassium nitrite. [ 4 ]
Potassium nitrite reacts at an extremely slow rate with a liquid ammonia solution of potassium amide at room temperatures, and in the presence of ferric oxide or cobaltic oxide , to form nitrogen and potassium hydroxide .
Interest in a medical role for inorganic nitrite was first aroused because of the spectacular success of organic nitrites and related compounds in the treatment of angina pectoris . While working with Butter at the Edinburgh Royal Infirmary in the 1860s, Brunton noted that the pain of angina could be lessened by venesection and wrongly concluded that the pain must be due to elevated blood pressure. As a treatment for angina, the reduction of circulating blood by venesection was inconvenient. Therefore, he decided to try the effect on a patient of inhaling amyl nitrite , a recently synthesized compound and one that his colleague had shown lowered blood pressure in animals. Pain associated with an anginal attack disappeared rapidly, and the effect lasted for several minutes, generally long enough for the patient to recover by resting. For a time, amyl nitrite was the favored treatment for angina, but due to its volatility, it was replaced by chemically related compounds that had the same effect. [ 2 ]
The effect of potassium nitrite on the nervous system, brain, spinal cord, pulse, arterial blood pressure, and respiration of healthy human volunteers was noted, as was the variability between individuals. The most significant observation was that even a small dose of <0.5 grains (≈30 mg) given by mouth caused, at first, an increase in arterial blood pressure , followed by a moderate decrease. With larger doses, pronounced hypotension ensued. They also noted that potassium nitrite, however administered, had a profound effect on the appearance and oxygen-carrying capacity of the blood. They compared the biological action of potassium nitrite with that of amyl and ethyl nitrites and concluded that the similarity of action depends on the conversion of organic nitrites to nitrous acid . [ 2 ]
Solutions of acidified nitrite have been used successfully to generate NO and to induce vasorelaxation in isolated blood vessel studies, and the same reaction mechanism has been proposed to explain the biological action of nitrite . [ 2 ]
Potassium nitrite is used in the manufacturing of heat transfer salts. As food additive E249 , potassium nitrite is a preservative similar to sodium nitrite and is approved for usage in the EU, [ 5 ] USA, [ 6 ] Australia and New Zealand [ 7 ] (where it is listed under its INS number 249).
Potassium nitrite is also used by modern luthiers to darken the tone and possibly improve the acoustic characteristics of violins , used after completing the box and before varnishing . The KNO2 is applied then exposed to sunlight .
When reacting with acids, potassium nitrite forms toxic nitrous oxides. Fusion with ammonium salts results in effervescence and ignition . Reactions with reducing agents can result in fires and explosions. [ 8 ]
Potassium nitrite is stored with other oxidizing agents but separated from flammables, combustibles, reducing agents , acids, cyanides , ammonium compounds, amides, and other nitrogenous salts in a cool, dry, well ventilated location. [ 8 ] | https://en.wikipedia.org/wiki/Potassium_nitrite |
Potassium oxide ( K 2 O ) is an ionic compound of potassium and oxygen . It is a base . This pale yellow solid is the simplest oxide of potassium. It is a highly reactive compound that is rarely encountered. Some industrial materials, such as fertilizers and cements, are assayed assuming the percent composition that would be equivalent to K 2 O.
Potassium oxide is produced from the reaction of oxygen and potassium; this reaction affords potassium peroxide , K 2 O 2 . Treatment of the peroxide with potassium produces the oxide: [ 5 ]
Alternatively and more conveniently, K 2 O is synthesized by heating potassium nitrate with metallic potassium:
Other possibility is to heat potassium peroxide at 500 °C which decomposes at that temperature giving pure potassium oxide and oxygen.
Potassium hydroxide cannot be further dehydrated to the oxide but it can react with molten potassium to produce it, releasing hydrogen as a byproduct.
K 2 O crystallises in the antifluorite structure . In this motif the positions of the anions and cations are reversed relative to their positions in CaF 2 , with potassium ions coordinated to 4 oxide ions and oxide ions coordinated to 8 potassium. [ 6 ] [ 7 ] K 2 O is a basic oxide and reacts with water violently to produce the caustic potassium hydroxide . It is deliquescent and will absorb water from the atmosphere, initiating this vigorous reaction.
The chemical formula K 2 O (or simply 'K') is used in several industrial contexts: the N-P-K numbers for fertilizers , in cement formulas , and in glassmaking formulas . Potassium oxide is often not used directly in these products, but the amount of potassium is reported in terms of the K 2 O equivalent for whatever type of potash was used, such as potassium carbonate . For example, potassium oxide is about 83% potassium by weight, while potassium chloride is only 52%. Potassium chloride provides less potassium than an equal amount of potassium oxide. Thus, if a fertilizer is 30% potassium chloride by weight, its standard potassium rating, based on potassium oxide, would be only 18.8%.
Media related to Potassium oxide at Wikimedia Commons | https://en.wikipedia.org/wiki/Potassium_oxide |
Potassium pentasulfide is the inorganic compound with the formula K 2 S 5 . It is a red-orange solid that dissolves in water. The salt decomposes rapidly in air.
It is one of several polysulfide salts with the general formula M 2 S n , where M = Li, Na, K and n = 2, 3, 4, 5, 6. [ 1 ] The polysulfide salts of potassium and sodium are similar.
The salt is prepared by the addition of elemental sulfur to potassium sulfide . An idealized equation is shown for potassium hydrosulfide:
The structure consists of zigzag chains of S 2− 5 paired with K + ions. [ 2 ]
Various polysulfides K 2 S 2 - K 2 S 6 are components of liver of sulfur . Polysulfides, like sulfides, can induce stress corrosion cracking in carbon steel and stainless steel . | https://en.wikipedia.org/wiki/Potassium_pentasulfide |
Potassium periodate is an inorganic salt with the molecular formula KIO 4 . It is composed of a potassium cation and a periodate anion and may also be regarded as the potassium salt of periodic acid . Note that the pronunciation is per-iodate, not period-ate.
Unlike other common periodates, such as sodium periodate and periodic acid , it is only available in the meta periodate form; the corresponding potassium ortho periodate (K 5 IO 6 ) has never been reported.
Potassium periodate can be prepared by the oxidation of an aqueous solution of potassium iodate by chlorine and potassium hydroxide . [ 1 ]
It can also be generated by the electrochemical oxidation of potassium iodate , however the low solubility of KIO 3 makes this approach of limited use.
Potassium periodate decomposes at 582 °C to form potassium iodate and oxygen .
The low solubility of KIO 4 makes it useful for the determination of potassium [ citation needed ] and cerium . [ 2 ]
It is slightly soluble in water (one of the less soluble of potassium salts, owing to a large anion), giving rise to a solution that is slightly alkaline . On heating (especially with manganese(IV) oxide as catalyst), it decomposes to form potassium iodate, releasing oxygen gas.
KIO 4 forms tetragonal crystals of the Scheelite type ( space group I 4 1 / a ). [ 3 ] | https://en.wikipedia.org/wiki/Potassium_periodate |
Potassium permanganate is an inorganic compound with the chemical formula KMnO 4 . It is a purplish-black crystalline salt, which dissolves in water as K + and MnO − 4 ions to give an intensely pink to purple solution.
Potassium permanganate is widely used in the chemical industry and laboratories as a strong oxidizing agent , and also as a medication for dermatitis , for cleaning wounds , and general disinfection . It is on the World Health Organization's List of Essential Medicines . [ 5 ] In 2000, worldwide production was estimated at 30,000 tons. [ 5 ]
Potassium permanganate is the potassium salt of the tetrahedral transition metal oxo complex permanganate , in which four O 2− ligands are bound to a manganese(VII) center. [ citation needed ]
KMnO 4 forms orthorhombic crystals with constants: a = 910.5 pm , b = 572.0 pm, c = 742.5 pm. The overall motif is similar to that for barium sulfate , with which it forms solid solutions . [ 6 ] In the solid (as in solution), each MnO − 4 centre is tetrahedral. The Mn–O distances are 1.62 Å. [ 7 ]
The purplish-black color of solid potassium permanganate, and the intensely pink to purple color of its solutions, is caused by its permanganate anion, which gets its color from a strong charge-transfer absorption band caused by excitation of electrons from oxo ligand orbitals to empty orbitals of the manganese(VII) center. [ 8 ]
Potassium permanganate functions as a strong oxidising agent . [ 9 ] Through this mechanism it results in disinfection , astringent effects, and decreased smell. [ 9 ]
Potassium permanganate is used for a number of skin conditions . [ 10 ] This includes fungal infections of the foot , impetigo , pemphigus , superficial wounds, dermatitis , and topical ulcers. [ 11 ] [ 10 ] Radioactive contamination of the skin can be cleaned with potassium permanganate and vigorous scrubbing. For topical ulcers it is used together with procaine benzylpenicillin . [ 10 ] Typically it is used in skin conditions that produce a lot of liquid. [ 11 ] It can be applied as a soaked dressing or a bath. [ 12 ] It can be used in children and adults. [ 13 ] Petroleum jelly may be used on the nails before soaking to prevent their discoloration. [ 14 ] For treating eczema, it is recommended using for only a few days at a time due to the possibility of it irritating the skin. [ 15 ]
The U.S. Food and Drug Administration does not recommend its use in the crystal or tablet form. It should only be used in a diluted liquid form. [ 16 ]
Potassium permanganate was first made in the 1600s and came into common medical use at least as early as the 1800s. [ 17 ] During World War I Canadian soldiers were given potassium permanganate (to be applied mixed with an ointment) in an effort to prevent sexually transmitted infections . [ 18 ] Some have attempted to bring about an abortion by putting it in the vagina, though this is not effective. [ 19 ] [ 20 ] [ 16 ] Other historical uses have included an effort to wash out the stomach in those with strychnine or picrotoxin poisoning. [ 21 ]
Side effects from topical use may include irritation of the skin and discoloration of clothing. [ 22 ] A harsh burn on a child from an undissolved tablet has been reported. [ 15 ] Higher concentration solutions can result in chemical burns . [ 23 ] Therefore, the British National Formulary recommends 100 mg be dissolved in a liter of water before use to form a 1:10,000 (0.01%) solution. [ 15 ] [ 24 ] [ 13 ] Wrapping the dressings soaked with potassium permanganate is not recommended. [ citation needed ]
Potassium permanganate is toxic if taken by mouth. [ 25 ] Side effects may include nausea, vomiting, and shortness of breath may occur. [ 26 ] If a sufficiently large amount (about 10 grams) is eaten death may occur. [ 26 ]
Concentrated solutions when drunk have resulted in acute respiratory distress syndrome or swelling of the airway. [ 27 ] Recommended measures for those who have ingested potassium permanganate include gastroscopy . [ 27 ] Activated charcoal or medications to cause vomiting are not recommended. While medications like ranitidine and acetylcysteine may be used in toxicity, evidence for this use is poor. [ 27 ]
In the United States the FDA requires tablets of the medication to be sold by prescription . [ 16 ] Potassium permanganate, however, does not have FDA approved uses and therefore non medical grade potassium permanganate is sometimes used for medical purposes. [ citation needed ]
It is available under a number of brand names including Permasol, Koi Med Tricho-Ex, and Kalii permanganas RFF. [ 28 ] It is occasionally called "Condy's crystals". [ 29 ]
Potassium permanganate may be used to prevent the spread of glanders among horses. [ 30 ]
Almost all applications of potassium permanganate exploit its oxidizing properties. [ 31 ] As a strong oxidant that does not generate toxic byproducts, KMnO 4 has many niche uses. [ citation needed ]
Potassium permanganate is used extensively in the water treatment industry. It is used as a regeneration chemical to remove iron and hydrogen sulfide (rotten egg smell) from well water via a "manganese greensand" filter. "Pot-Perm" is also obtainable at pool supply stores and is used additionally to treat wastewater. Historically it was used to disinfect drinking water [ 32 ] [ 33 ] and can turn the water pink. [ 34 ] Modern hiking and survivalist guides advise against using potassium permanganate in the field because it is difficult to dose correctly. [ 35 ] It currently finds application in the control of nuisance organisms such as zebra mussels in fresh water collection and treatment systems. [ 36 ]
A major application of KMnO 4 is as a reagent for the synthesis of organic compounds. [ 37 ] Significant amounts are required for the synthesis of ascorbic acid , chloramphenicol , saccharin , isonicotinic acid , and pyrazinoic acid . [ 31 ]
KMnO 4 is used in qualitative organic analysis to test for the presence of unsaturation . It is sometimes referred to as Baeyer's reagent after the German organic chemist Adolf von Baeyer . The reagent is an alkaline solution of potassium permanganate. Reaction with double or triple bonds ( R 2 C=CR 2 or R−C≡C−R ) causes the color to fade from purplish-pink to brown. Aldehydes and formic acid (and formates ) also give a positive test. [ 38 ] The test is antiquated.
KMnO 4 solution is a common thin layer chromatography (TLC) stain for the detection of oxidizable functional groups, such as alcohols, aldehydes, alkenes, and ketones. Such compounds result in a white to orange spot on TLC plates. [ 39 ] [ 40 ] [ 41 ]
Potassium permanganate can be used to quantitatively determine the total oxidizable organic material in an aqueous sample. The value determined is known as the permanganate value. In analytical chemistry , a standardized aqueous solution of KMnO 4 is sometimes used as an oxidizing titrant for redox titrations ( permanganometry ). As potassium permanganate is titrated, the solution becomes a light shade of purple, which darkens as excess of the titrant is added to the solution. In a related way, it is used as a reagent to determine the Kappa number of wood pulp. For the standardization of KMnO 4 solutions, reduction by oxalic acid is often used. [ 42 ] In agricultural chemistry, it is used for estimation of active carbon in soil. [ 43 ]
Aqueous, acidic solutions of KMnO 4 are used to collect gaseous mercury in flue gas during stationary source emissions testing. [ 44 ]
In histology , potassium permanganate was used as a bleaching agent. [ 45 ] [ 46 ]
Ethylene absorbents extend storage time of bananas even at high temperatures. This effect can be exploited by packing bananas in polyethylene together with potassium permanganate. By removing ethylene by oxidation, the permanganate delays the ripening, increasing the fruit's shelf life up to 4 weeks without the need for refrigeration. [ 47 ] [ 48 ] [ 49 ]
The chemical reaction, in which ethylene (C 2 H 4 ) is oxidised by potassium permanganate (KMnO 4 ) to carbon dioxide (CO 2 ), manganese oxide (MnO 2 ) and potassium hydroxide (KOH), in the presence of water, is presented as follows: [ 50 ]
3 C 2 H 4 + 12 KMnO 4 + 2 H 2 O → 6 CO 2 + 2 H 2 O + 12 MnO 2 + 12 KOH
Potassium permanganate is sometimes included in survival kits: as a hypergolic fire starter (when mixed with glycerol antifreeze from a car radiator); [ 51 ] [ 52 ] [ 53 ] as a water sterilizer; and for creating distress signals on snow. [ 54 ]
Potassium permanganate is added to "plastic sphere dispensers" to create backfires, burnouts, and controlled burns . Polymer spheres resembling ping-pong balls containing small amounts of permanganate are injected with ethylene glycol and projected towards the area where ignition is desired, where they spontaneously ignite seconds later. [ 55 ] [ 56 ] Both handheld [ 56 ] helicopter- [ 55 ] unmanned aircraft systems (UAS) or boat-mounted [ 56 ] plastic sphere dispensers are used.
Potassium permanganate is one of the principal chemicals used in the film and television industries to "age" props and set dressings. Its ready conversion to brown MnO 2 creates "hundred-year-old" or "ancient" looks on hessian cloth (burlap), ropes, timber and glass. [ 57 ]
Potassium permanganate can be used to oxidize cocaine paste to purify it and increase its stability. This led to the Drug Enforcement Administration launching Operation Purple in 2000, with the goal of monitoring the world supply of potassium permanganate; however, potassium permanganate derivatives and substitutes were soon used thereafter to avoid the operation. [ 58 ]
Potassium permanganate is used as an oxidizing agent in the synthesis of cocaine and methcathinone . [ 59 ]
Potassium permanganate is one of a number of possible treatments for Ichthyophthirius multifiliis (commonly known as "ich"), a parasite that infects and usually kills freshwater aquarium fish.
In 1659, Johann Rudolf Glauber fused a mixture of the mineral pyrolusite (manganese dioxide, MnO 2 ) and potassium carbonate to obtain a material that, when dissolved in water, gave a green solution ( potassium manganate ) which slowly shifted to violet and then finally red. [ 60 ] The reaction that produced the color changes that Glauber observed in his solution of potassium permanganate and potassium manganate (K 2 MnO 4 ) is now known as the " chemical chameleon ". [ 61 ] This report represents the first description of the production of potassium permanganate. [ 62 ] Just under 200 years later, London chemist Henry Bollmann Condy had an interest in disinfectants; he found that fusing pyrolusite with sodium hydroxide (NaOH) and dissolving it in water produced a solution with disinfectant properties. He patented this solution, and marketed it as 'Condy's Fluid'. Although effective, the solution was not very stable. This was overcome by using potassium hydroxide (KOH) rather than NaOH. This was more stable, and had the advantage of easy conversion to the equally effective potassium permanganate crystals. This crystalline material was known as 'Condy's crystals' or 'Condy's powder'. Potassium permanganate was comparatively easy to manufacture, so Condy was subsequently forced to spend considerable time in litigation to stop competitors from marketing similar products. [ 63 ] According to Varlam Shalamov , potassium permanganate solution was used as a catch-all treatment for dysentery, frostbite and ulcers in the Gulag camps of Kolyma.
Early photographers used it as a component of flash powder . It is now replaced with other oxidizers, due to the instability of permanganate mixtures. [ citation needed ]
Potassium permanganate is produced industrially from manganese dioxide , which also occurs as the mineral pyrolusite . In 2000, worldwide production was estimated at 30,000 tonnes. [ 31 ] The MnO 2 is fused with potassium hydroxide and heated in air or with another source of oxygen, like potassium nitrate or potassium chlorate . [ 31 ] This process gives potassium manganate :
With sodium hydroxide, the end product is not sodium manganate but a Mn(V) compound, which is one reason why the potassium permanganate is more commonly used than sodium permanganate . Furthermore, the potassium salt crystallizes better. [ 31 ]
The potassium manganate is then converted into permanganate by electrolytic oxidation in alkaline media:
Although of no commercial importance, potassium manganate can be oxidized by chlorine or by disproportionation under acidic conditions. [ 64 ] The chlorine oxidation reaction is
and the acid-induced disproportionation reaction may be written as
A weak acid such as carbonic acid is sufficient for this reaction:
Permanganate salts may also be generated by treating a solution of Mn 2+ ions with strong oxidants such as lead dioxide (PbO 2 ), sodium bismuthate (NaBiO 3 ), or peroxydisulfate . Tests for the presence of manganese exploit the vivid violet color of permanganate produced by these reagents.
Dilute solutions of KMnO 4 convert alkenes into diols . This behaviour is also used as a qualitative test for the presence of double or triple bonds in a molecule, since the reaction decolorizes the initially purple permanganate solution and generates a brown precipitate (MnO 2 ). In this context, it is sometimes called Baeyer's reagent . However, bromine serves better in measuring unsaturation (double or triple bonds) quantitatively, since KMnO 4 , being a very strong oxidizing agent , can react with a variety of groups.
Under acidic conditions, the alkene double bond is cleaved to give the appropriate carboxylic acid : [ 65 ]
Potassium permanganate oxidizes aldehydes to carboxylic acids, illustrated by the conversion of n - heptanal to heptanoic acid: [ 66 ]
Even an alkyl group (with a benzylic hydrogen) on an aromatic ring is oxidized, e.g. toluene to benzoic acid . [ 67 ]
Glycols and polyols are highly reactive toward KMnO 4 . For example, addition of potassium permanganate to an aqueous solution of sugar and sodium hydroxide produces the chemical chameleon reaction, which involves dramatic color changes associated with the various oxidation states of manganese . A related vigorous reaction is exploited as a fire starter in survival kits. For example, a mixture of potassium permanganate and glycerol or pulverized glucose ignites readily. [ 51 ] Its sterilizing properties are another reason for inclusion of KMnO 4 in a survival kit. [ citation needed ]
Treating a mixture of aqueous potassium permanganate with a quaternary ammonium salt results in ion exchange, precipitating the quat salt of permanganate. Solutions of these salts are sometimes soluble in organic solvents: [ 68 ]
Similarly, addition of a crown ether also gives a lipophilic salt. [ 69 ]
Permanganate reacts with concentrated hydrochloric acid to give chlorine and manganese(II):
In neutral solution, permanganate slowly reduces to manganese dioxide (MnO 2 ). This is the material that stains one's skin when handling KMnO 4 .
KMnO 4 reduces in alkaline solution to give green K 2 MnO 4 : [ 70 ]
This reaction illustrates the relatively rare role of hydroxide as a reducing agent.
Addition of concentrated sulfuric acid to potassium permanganate gives Mn 2 O 7 . [ 71 ] Although no reaction may be apparent, the vapor over the mixture will ignite paper impregnated with alcohol. Potassium permanganate and sulfuric acid react to produce some ozone , which has a high oxidizing power and rapidly oxidizes the alcohol, causing it to combust. As the reaction also produces explosive Mn 2 O 7 , this should only be attempted with great caution. [ 72 ] [ 73 ]
Solid potassium permanganate decomposes when heated:
It is a redox reaction.
Potassium permanganate poses risks as an oxidizer . [ 74 ] Contact with skin can cause skin irritation and in some cases severe allergic reaction. It can also result in discoloration and clothing stains. [ 75 ] | https://en.wikipedia.org/wiki/Potassium_permanganate |
Potassium peroxide is an inorganic compound with the molecular formula K 2 O 2 . It is formed as potassium reacts with oxygen in the air, along with potassium oxide (K 2 O) and potassium superoxide (KO 2 ).
Potassium peroxide reacts with water to form potassium hydroxide and oxygen :
Potassium peroxide is a highly reactive, oxidizing white to yellowish solid which, while not flammable itself, reacts violently with flammable materials. It decomposes violently on contact with water . [ 1 ]
The standard enthalpy of formation of potassium peroxide is ΔH f 0 = −496 kJ/mol.
Potassium peroxide is used as an oxidizing agent and bleach (due to the peroxide ), and to purify air. | https://en.wikipedia.org/wiki/Potassium_peroxide |
Potassium peroxymonosulfate is widely used as an oxidizing agent , for example, in pools and spas (usually referred to as monopersulfate or "MPS"). It is the potassium salt of peroxymonosulfuric acid . Potassium peroxymonosulfate per se is rarely encountered. It is often confused with the triple salt 2KHSO 5 ·KHSO 4 ·K 2 SO 4 , known as Oxone .
The standard electrode potential for potassium peroxymonosulfate is +1.81 V with a half reaction generating the hydrogen sulfate ( pH = 0 ): [ 3 ]
Potassium peroxymonosulfate per se is a relatively obscure salt, but its derivative called Oxone is of commercial value. Oxone refers to the triple salt 2KHSO 5 ·KHSO 4 ·K 2 SO 4 . As such about one third by weight is potassium peroxymonosulfate. Oxone has a longer shelf life than does potassium peroxymonosulfate. A white, water-soluble solid, Oxone loses <1% of its oxidizing power per month. [ 4 ]
Oxone, which is commercially available, is produced from peroxysulfuric acid, which is generated in situ by combining oleum and hydrogen peroxide . Careful neutralization of this solution with potassium hydroxide allows the crystallization of the triple salt.
Oxone is used widely for cleaning. It whitens dentures, [ 5 ] oxidizes organic contaminants in swimming pools, [ 6 ] and cleans chips for the manufacture of microelectronics. [ 5 ] [ 7 ] [ 8 ]
Oxone is a versatile oxidant in organic synthesis. It oxidizes aldehydes to carboxylic acids ; in the presence of alcoholic solvents, the esters may be obtained. [ 9 ] Internal alkenes may be cleaved to two carboxylic acids (see below), while terminal alkenes may be epoxidized . Sulfides give sulfones , tertiary amines give amine oxides , and phosphines give phosphine oxides .
Further illustrative of the oxidative power of this salt is the conversion of an acridine derivative to the corresponding acridine- N-oxide . [ 10 ]
Oxone oxidizes sulfides to sulfoxides and then to sulfones . [ 11 ]
Oxone converts ketones to dioxiranes , which are used for diverse oxidations in organic synthesis. The dominant reagent dimethyldioxirane (DMDO) forms upon treatment of acetone with oxone. Dioxiranes are versatile, especially for the epoxidation of olefins . [ 12 ] Dioxiranes are also oxidize other unsaturated functionality, heteroatoms, and alkane C-H bonds. [ 13 ]
Oxone is used in the production of some organic periodinanes , notably the oxidation of 2-iodobenzoic acid to 2-iodoxybenzoic acid (IBX). [ 14 ]
Oxone has been investigated for the delignification of wood. [ 15 ]
Ammonium , sodium , and potassium salts of HSO − 5 are used in the plastics industry as radical initiators for polymerization . They are also used as etchants , oxidative desizing agents for textile fabrics, and for decolorizing and deodorizing oils. | https://en.wikipedia.org/wiki/Potassium_peroxymonosulfate |
Potassium persulfate is the inorganic compound with the formula K 2 S 2 O 8 . Also known as potassium peroxydisulfate , it is a white solid that is sparingly soluble in cold water, but dissolves better in warm water. This salt is a powerful oxidant, commonly used to initiate polymerizations .
The sodium and potassium salts are very similar. In the potassium salt, the O-O distance is 1.495 Å. The individual sulfate groups are tetrahedral, with three short S-O distances near 1.43 and one long S-O bond at 1.65 Å. [ 3 ]
Potassium persulfate can be prepared by electrolysis of a cold solution potassium bisulfate in sulfuric acid at a high current density. [ 1 ] [ 4 ]
It can also be prepared by adding potassium bisulfate (KHSO 4 ) to a solution of the more soluble salt ammonium peroxydisulfate (NH 4 ) 2 S 2 O 8 . In principle it can be prepared by chemical oxidation of potassium sulfate using fluorine . Several million kilograms of the ammonium, sodium, and potassium salts of peroxydisulfate are produced annually.
This salt is used to initiate polymerization of various alkenes leading to commercially important polymers such as styrene-butadiene rubber and polytetrafluoroethylene and related materials. In solution, the dianion dissociates to give radicals: [ 5 ]
It is used in organic chemistry as an oxidizing agent , [ 6 ] for instance in the Elbs persulfate oxidation of phenols and the Boyland–Sims oxidation of anilines .
As a strong yet stable bleaching agent it also finds use in various hair bleaches and lighteners. Such brief and non-continuous use is normally hazard free, however prolonged contact can cause skin irritation. [ 7 ] It has been used as an improving agent for flour with the E number E922, although it is no longer approved for this use within the EU.
The salt is a strong oxidant and is incompatible with organic compounds. Prolonged skin contact can result in irritation. [ 7 ] | https://en.wikipedia.org/wiki/Potassium_persulfate |
Potassium picrate , or potassium 2,4,6-trinitrophenolate , is an organic chemical, a picrate of potassium . It is a reddish yellow or green crystalline material. It is a primary explosive . Anhydrous potassium picrate forms orthorhombic crystals.
Potassium picrate was first prepared in impure form in the mid 17th century by Johann Rudolf Glauber by dissolving wood in nitric acid and neutralizing with potassium carbonate . It is commonly made by neutralizing picric acid with potassium carbonate. It has been used in industry since the 1860s. [ 1 ]
Potassium Picrate and picric acid were formerly used in pyrotechnics to produce whistle effects, but since mixes that don't involve primary explosives have since been developed it is no longer used in that industry. Its chief applications were as a component of explosives (with potassium nitrate and charcoal), propellants (with the same substances in the poudre Dessignole of the 1870s French Navy), and in explosive primers (with lead picrate and potassium chlorate). [ 1 ] : 27
Potassium picrate is not a very powerful explosive. It is somewhat shock-sensitive. In contact with flame it deflagrates with a loud sound. [ clarification needed ] If ignited in confined space, it will detonate . It is more sensitive than picric acid . [ 1 ] : 27
In contact with metals (e.g. lead, calcium, iron), potassium picrate, like ammonium picrate and picric acid , forms picrates of said metals. These are often more dangerous and more sensitive explosives. Contact with such materials therefore should be prevented.
Potassium picrate is used to determine the concentration of nonionic surfactants in water; materials detectable by this method are called potassium picrate active substances ( PPAS ).
As with other picrates, potassium picrate may be produced by the neutralization of picric acid with the corresponding carbonate.
As picric acid is barely soluble in water the reaction must be done in an appropriate solvent like methanol.
First dissolving the picric acid in methanol and then adding potassium carbonate will result in potassium picrate. Temperature control is important to prevent detonation or excessive methanol evaporation.
According to Urbanski, Potassium picrate detonated 10% of the time when struck by a mass of 2kg dropped from the height of 21cm.
By comparison, the more sensitive anhydrous lead picrate detonated 10% of the time when struck by the same mass dropped from the height of 2cm. | https://en.wikipedia.org/wiki/Potassium_picrate |
Potassium sodium tartrate tetrahydrate , also known as Rochelle salt , is a double salt of tartaric acid first prepared (in about 1675) by an apothecary , Élie Seignette [ fr ] , of La Rochelle , France. Potassium sodium tartrate and monopotassium phosphate were the first materials discovered to exhibit piezoelectricity . [ 3 ] This property led to its extensive use in crystal phonograph cartridges , microphones and earpieces during the post-World War II consumer electronics boom of the mid-20th century. Such transducers had an exceptionally high output with typical pick-up cartridge outputs as much as 2 volts or more. Rochelle salt is deliquescent so any transducers based on the material deteriorated if stored in damp conditions.
It has been used medicinally as a laxative . It has also been used in the process of silvering mirrors. It is an ingredient of Fehling's solution (reagent for reducing sugars). It is used in electroplating , in electronics and piezoelectricity , and as a combustion accelerator in cigarette paper (similar to an oxidizer in pyrotechnics ). [ 2 ]
In organic synthesis, it is used in aqueous workups to break up emulsions , particularly for reactions in which an aluminium-based hydride reagent was used. [ 4 ] Sodium potassium tartrate is also important in the food industry. [ 5 ]
It is a common precipitant in protein crystallography and is also an ingredient in the Biuret reagent which is used to measure protein concentration. This ingredient maintains cupric ions in solution at an alkaline pH.
The starting material is tartar with a minimum 68% tartaric acid content. This is first dissolved in water or in the mother liquor of a previous batch. It is then basified with hot saturated sodium hydroxide solution to pH 8, decolorized with activated charcoal , and chemically purified before being filtered. The filtrate is evaporated to 42 °Bé at 100 °C, and passed to granulators in which Seignette's salt crystallizes on slow cooling. The salt is separated from the mother liquor by centrifugation, accompanied by washing of the granules, and is dried in a rotary furnace and sieved before packaging. Commercially marketed grain sizes range from 2000 μm to < 250 μm (powder). [ 2 ]
Larger crystals of Rochelle salt have been grown under conditions of reduced gravity and convection on board Skylab . [ 6 ] Rochelle salt crystals will begin to dehydrate when the relative humidity drops to about 30% and will begin to dissolve at relative humidities above 84%. [ 7 ]
In 1824, Sir David Brewster demonstrated piezoelectric effects using Rochelle salts, [ 8 ] which led to him naming the effect pyroelectricity . [ 9 ]
In 1919, Alexander McLean Nicolson worked with Rochelle salt, developing audio-related inventions like microphones and speakers at Bell Labs. [ 10 ]
Rochelle salt-based composites have gained renewed interest for their applications in impact energy absorption and smart sensing technologies. [ 11 ] [ 12 ] Recent research has demonstrated the growth of Rochelle salt crystals within 3D-printed cuttlebone -inspired structures, resulting in multifunctional composites that combine mechanical robustness with piezoelectric properties. The chambered microstructure inspired by cuttlefish bone provides high stiffness and energy absorption capacity, making these composites suitable for protective equipment and structural health monitoring. [ 13 ] The developed composites exhibit remarkable mechanical performance, with enhanced fracture toughness and resistance to impact. Under cyclic loading, they maintain consistent piezoelectric output for up to 7000 cycles. Impact tests show voltage outputs peaking at approximately 8 V, and a piezoelectric coefficient (d33) around 30 pC/N. [ 13 ] These properties enable real-time sensing of impact forces, making the material suitable for use in wearable protective gear, such as smart armor for athletes and fall detection devices for the elderly.
Sustainability and recyclability are notable advantages of this material. The Rochelle salt crystals can be dissolved and re-grown within the structure, allowing the composite to be repaired after damage. Recycled samples retain up to 95% of their original mechanical and piezoelectric performance. [ 13 ] Potential applications extend to sports safety equipment, aerospace structures, military armor, and biomedical monitoring devices, highlighting the versatility and functionality of Rochelle salt composites in modern material science. [ 13 ] | https://en.wikipedia.org/wiki/Potassium_sodium_tartrate |
Potassium spatial buffering is a mechanism for the regulation of extracellular potassium concentration by astrocytes . Other mechanisms for astrocytic potassium clearance are carrier-operated or channel-operated potassium chloride uptake. [ 1 ] The repolarization of neurons tends to raise potassium concentration in the extracellular fluid. If a significant rise occurs, it will interfere with neuronal signaling by depolarizing neurons. Astrocytes have large numbers of potassium ion channels facilitating the removal of potassium ions from the extracellular fluid. They are taken up at one region of the astrocyte and then distributed throughout the cytoplasm of the cell, and further to its neighbors via gap junctions . This keeps extracellular potassium at levels that prevent interference with the normal propagation of an action potential .
Glial cells, once believed to have a passive role in CNS, are active regulators of numerous functions in the brain, including clearance of the neurotransmitter from the synapses, guidance during neuronal migration, control of neuronal synaptic transmission, and maintaining an ideal ionic environment for active communications between neurons in central nervous system. [ 2 ]
Neurons are surrounded by extracellular fluid rich in sodium ions and poor in potassium ions. The concentrations of these ions are reversed inside the cells. Due to the difference in concentration, there is a chemical gradient across the cell membrane, which leads to sodium influx and potassium efflux. When the action potential takes place, a considerable change in extracellular potassium concentration occurs due to the limited volume of the CNS extracellular space. The change in potassium concentration in the extracellular space impacts a variety of neuronal processes, such as maintenance of membrane potential, activation and inactivation of voltage gated channels, synaptic transmission, and electrogenic transport of neurotransmitters. Change of extracellular potassium concentration of from 3mM can affect neural activity. Therefore, there are diverse cellular mechanisms for tight control of potassium ions, the most widely accepted mechanism being K+ spatial buffering mechanism. Orkand and his colleagues who first theorized spatial buffering stated “if a Glial cell becomes depolarized by K+ that has accumulated in the clefts, the resulting current carries K+ inward in the high [K+] region and out again, through electrically coupled Glial cells in low [K+] regions”
In the model presented by Orkand and his colleagues, glial cells intake and traverse potassium ions from region of high concentrations to region of low concentration maintaining potassium concentration to be low in extracellular space. Glial cells are well suited for transportation of potassium ions since it has unusually high permeability to potassium ions and traverse long distance by its elongated shape or by being coupled to one another. [ 3 ] [ 4 ]
Potassium buffering can be broadly categorized into two categories: Potassium uptake and Potassium spatial buffering. For potassium uptake, excess potassium ions are temporarily taken into glial cells through transporters, or potassium channels. In order to preserve electroneutrality, potassium influxes into glial cells are accompanied by influx of chlorine or efflux of sodium. It is expected that when potassium accumulates within glial cells, water influx and swelling occurs. For potassium spatial buffering, functionally coupled glial cells with high potassium permeability transfer potassium ions from regions of elevated potassium concentration to regions of lower potassium concentration. The potassium current is driven by the difference in glial syncytium membrane potential and local potassium equilibrium potential. When one region of potassium concentration increases, there is a net driving force causing potassium to flow into the glial cells. The entry of potassium causes a local depolarization that propagates electrotonically through the glial cell network which causes net driving force of potassium out of the glial cells. This process causes dispersion of local potassium with little net gain of potassium ions within the glial cells, which in turn prevents swelling. Glial cell depolarization caused by neuronal activity releases potassium onto bloodstream, which was once widely hypothesized to be cause of vessel relaxation, was found to have little effect on neurovascular coupling. [ 5 ] Despite the efficiency of potassium spatial buffering mechanisms, in certain regions of CNS, potassium buffering seems more dependent on active uptake mechanisms rather than spatial buffering. Therefore, the exact role of glial potassium spatial buffering in the various regions of our brain still remains uncertain. [ 6 ]
The high permeability of glial cell membranes to potassium ions is a result of expression of high densities of potassium-selective channels with high open-probability at resting membrane potentials . Kir channels, potassium inward-rectifying channels , allow passage of potassium ions inward much more readily than outward. They also display a variable conductance that positively correlates with extracellular potassium concentration: the higher the potassium concentration outside the cell, the higher the conductance.
Kir channels are categorized into seven major subfamilies, Kir1 to Kir7, with a variety of gating mechanisms. Kir3 and Kir6 are primarily activated by intracellular G-proteins . Because they have a relatively low open-probability compared to the other families, they have little impact on potassium buffering. Kir1 and Kir7 are mainly expressed in epithelial cells , such as those in the kidney, choroid plexus, or retinal pigment epithelium, and have no impact on spatial buffering. Kir2, however, are expressed in brain neurons and glial cells. Kir4 and Kir5 are, along with Kir2, located in Muller glia and play important roles in potassium siphoning. There are some discrepancies among studies on expression of these channels in the stated locations. [ 7 ] [ 8 ]
The panglial syncytium is a large network of interconnected glial cells, which are extensively linked by gap junctions. The panglial syncytium spreads through central nervous system where it provides metabolic and osmotic support, as well as ionic regulation of myelinated axons in white matter tracts. The three types of macroglial cells within network of panglial syncytium are astrocytes , oligodendrocytes , and ependymocytes. Originally it was believed that there was homologous gap junction between oligodendrocytes. It was later found through untrastructural analysis that gap junctions do not directly link adjacent oligodendrocytes, rather it gap junctions with adjacent astrocytes, providing secondary pathway to nearby oligodendrocytes. With direct gap junction between myelin sheaths to surrounding astrocytes, excess potassium and osmotic water directly enters astrocyte syncytium, where it passively spreads downstream to astrocyte endfeet processes at capillaries and the glia limitans . [ 9 ]
Potassium spatial buffering that occurs in the retina is called potassium siphoning, where the Muller cell is the principal glial cell type. Muller cells have important role in retinal physiology. It maintains retinal cell metabolism and are critical in maintaining potassium homeostasis in extracellular space during neuronal activity. Like cells responsible for spatial buffering, Muller cells are distinctively permeable to potassium ions through Kir channels. Like other glial cells, the high selectivity of Muller cell membranes to potassium ions is due to the high density of Kir channels. Potassium conductance is unevenly distributed in Muller cells. [ 10 ] By focally increasing potassium ions along amphibian Muller cells and recording the resulting depolarization, the observed potassium conductance was concentrated in the endfoot process of 94% of the total potassium conductance localized to the small subcellular domain. The observation lead to hypothesis that excess potassium in extracellular space is “siphoned” by the Muller cells to the vitreous humor. Potassium siphoning is a specialized form of spatial buffering mechanisms where large reservoir of potassium ions is emptied into vitreous humor. Similar distribution pattern of Kir channels could be found in amphibians. [ 11 ] [ 12 ] [ 13 ]
Existence of potassium siphoning was first reported in 1966 study by Orkand et al. In the study, optic nerve of Necturus was dissected to document the long-distance movement of potassium after the nerve stimulation. Following the low frequency stimulation of .5 Hz at the retinal end of the dissected optic nerve, depolarization 1-2mV was measured at astrocytes at the opposite end of the nerve bundle, which was up to several millimeters from the electrode. With higher frequency stimulation, higher plateau of depolarization was observed. Therefore, they hypothesized that the potassium released to extracellular compartment during axonal activity entered and depolarized nearby astrocytes, where it was transported away by unfamiliar mechanism, which caused depolarization on astrocytes distant from site of stimulation. The proposed model was actually inappropriate since at the time neither gap junctions nor syncytium among glial cells were known, and optic nerve of Necturus are unmyelinated, which means that potassium efflux occurred directly into the periaxonal extracellular space, where potassium ions in extracellular space would be directly absorbed into the abundant astrocytes around axons. [ 14 ]
In patients with Tuberous Sclerosis Complex (TSC), abnormalities occur in astrocyte, which leads to pathogenesis of neurological dysfunction in this disease. TSC is a multisystem genetic disease with mutation in either TSC1 or TSC2 gene. It results in disabling neurological symptoms such as mental retardation, autism, and seizures. Glial cells have important physiological roles of regulating neuronal excitability and preventing epilepsy. Astrocytes maintain homeostasis of excitatory substances, such as extracellular potassium, by immediate uptake through specific potassium channels and sodium potassium pumps. It is also regulated by potassium spatial buffering via astrocyte networks where astrocytes are coupled through gap junctions. Mutations in TSC1 or TSC2 gene often results in decreased expression of the astrocytic connexin protein, Cx43 . [ 15 ] With impairment in gap junction coupling between astrocytes, myriad of abnormalities in potassium buffering occurs which results in increased extracellular potassium concentration and may predispose to neuronal hyperexcitability and seizures. According to a study done on animal model, connexin43-deficient mice showed decreased threshold for the generation of epileptiform events. The study also demonstrated role of gap junction in accelerating potassium clearance, limiting potassium accumulation during neuronal firing, and relocating potassium concentrations. [ 16 ]
Demyelinating Diseases of the central nervous system, such as Neuromyelitis Optica, often leads to molecular components of the panglial syncytium being compromised, which leads to blocking of potassium spatial buffering. Without mechanism of potassium buffering, potassium induced osmotic swelling of myelin occurs where myelins are destroyed and axonal salutatory conduction ceases. [ 17 ] | https://en.wikipedia.org/wiki/Potassium_spatial_buffering |
Potassium sulfide is an inorganic compound with the formula K 2 S . The colourless solid is rarely encountered, because it reacts readily with water, a reaction that affords potassium hydrosulfide (KSH) and potassium hydroxide (KOH). Most commonly, the term potassium sulfide refers loosely to this mixture, not the anhydrous solid.
It adopts an antifluorite structure , which means that the small K + ions occupy the tetrahedral (F − ) sites in fluorite , and the larger S 2− centers occupy the eight-coordinate sites. Li 2 S , Na 2 S , and Rb 2 S crystallize similarly. [ 3 ]
It can be produced by heating K 2 SO 4 with carbon ( coke ):
In the laboratory, pure K 2 S may be prepared by the reaction of potassium and sulfur in anhydrous ammonia. [ 4 ]
Sulfide is highly basic, consequently K 2 S completely and irreversibly hydrolyzes in water according to the following equation:
For many purposes, this reaction is inconsequential since the mixture of SH − and OH − behaves as a source of S 2− . Other alkali metal sulfides behave similarly. [ 3 ]
Potassium sulfides are formed when black powder is burned and are important intermediates in many pyrotechnic effects, such as senko hanabi and some glitter formulations. [ 5 ] | https://en.wikipedia.org/wiki/Potassium_sulfide |
Potassium superoxide is an inorganic compound with the formula K O 2 . [ 6 ] It is a yellow paramagnetic solid that decomposes in moist air. It is a rare example of a stable salt of the superoxide anion. It is used as a CO 2 scrubber, H 2 O dehumidifier, and O 2 generator in rebreathers , spacecraft , submarines , and spacesuits .
Potassium superoxide is produced by burning molten potassium in an atmosphere of excess oxygen . [ 7 ]
The salt consists of K + and O − 2 ions, linked by ionic bonding. The O–O distance is 1.28 Å. [ 2 ]
Potassium superoxide is a source of superoxide, which is an oxidant and a nucleophile, depending on its reaction partner. [ 8 ]
Upon contact with water, it undergoes disproportionation to potassium hydroxide , oxygen, and hydrogen peroxide:
It reacts with carbon dioxide, releasing oxygen:
Theoretically, 1 kg of KO 2 absorbs 0.310 kg of CO 2 while releasing 0.338 kg of O 2 . One mole of KO 2 absorbs 0.5 moles of CO 2 and releases 0.75 moles of oxygen.
Potassium superoxide finds only niche uses as a laboratory reagent. Because it reacts with water, KO 2 is often studied in organic solvents. Since the salt is poorly soluble in nonpolar solvents, crown ethers are typically used. The tetraethylammonium salt is also known. Representative reactions of these salts involve using superoxide as a nucleophile , e.g., in converting alkyl bromides to alcohols and acyl chlorides to diacyl peroxides . [ 10 ]
Ion exchange with tetramethylammonium hydroxide gives tetramethylammonium superoxide, a yellow solid. [ 11 ]
The Russian Space Agency has successfully used potassium superoxide in chemical oxygen generators for its spacesuits and Soyuz spacecraft . Potassium superoxide was also used in a rudimentary life support system for five mice as part of the Biological Cosmic Ray Experiment on Apollo 17. [ 12 ]
KO 2 has also been used in canisters for rebreathers for firefighting and mine rescue , and in cartridges for chemical oxygen generators on submarines. A flash fire caused by dropping such a cartridge into seawater contributed to the Kursk disaster . This highly exothermic reaction with water is also the reason why potassium superoxide has had only limited use in scuba rebreathers . | https://en.wikipedia.org/wiki/Potassium_superoxide |
Potassium tert -butoxide (or potassium t -butoxide ) is a chemical compound with the formula [(CH 3 ) 3 COK] n (abbr. KOtBu). This colourless solid is a strong base (pKa of conjugate acid is 17 in H 2 O), [ 3 ] which is useful in organic synthesis . The compound is often depicted as a salt, and it often behaves as such, but its ionization depends on the solvent. [ 1 ]
Potassium t -butoxide is commercially available as a solution and as a solid, but it is often generated in situ for laboratory use because samples are so moisture- sensitive and older samples are often of low purity. It is prepared by the reaction of dry tert -butyl alcohol with potassium metal. [ 4 ] The solid is obtained by evaporating these solutions followed by heating the solid. The solid can be purified by sublimation.
It crystallizes as a tetrameric cubane-type cluster . It crystallises from tetrahydrofuran / pentane at −20 °C as [tBuOK·tBuOH] ∞ , which consists of straight chains linked by hydrogen bonding . Sublimation of [tBuOK·tBuOH] ∞ affords the tetramer [tBuOK] 4 , which adopts a cubane-like structure. Mildly Lewis basic solvents such as THF and diethyl ether do not break up the tetrameric structure, which persists in the solid, in solution and even in the gas phase. [ 5 ]
Many modifications have been reported that influence the reactivity of this reagent . The compound adopts a complex cluster structure (the adjacent picture is a simplified cartoon), and additives that modify the cluster affect the reactivity of the reagent. For example, DMF , DMSO , hexamethylphosphoramide (HMPA), and 18-crown-6 interact with the potassium center, yielding solvent separated ion pairs such as K(DMSO) x + and tert -BuO − . Whereas in benzene, on the other hand, the compound remains as a cluster structure, which is less basic. [ 1 ] Even in polar solvents, it is not as strong as amide bases, e.g., lithium diisopropylamide , but stronger than potassium hydroxide. Its steric bulk inhibits the group from participating in nucleophilic addition, such as in a Williamson ether synthesis or related S N 2 reactions. [ citation needed ]
Substrates that are deprotonated by potassium t -butoxide include terminal acetylenes and active methylene compounds . It is useful in dehydrohalogenation reactions. Illustrating the latter behavior, potassium tert -butoxide reacts with chloroform yielding dichlorocarbene , which is useful for dichloro cyclopropanations . [ 6 ] [ 7 ] Potassium tert -butoxide can abstract a beta-proton from alkylammonium cations, leading to the Hofmann product via an elimination reaction .
Potassium tert -butoxide catalyzes the reaction of hydrosilanes and heterocyclic compounds to give the silyl derivatives, with release of H 2 . [ 8 ]
Potassium tert -butoxide is a very strong base that rapidly attacks living tissue.
Potassium tert -butoxide forms explosive mixtures when treated with dichloromethane . [ 9 ] [ 10 ] | https://en.wikipedia.org/wiki/Potassium_tert-butoxide |
Potassium tetraiodomercurate(II) is an inorganic compound with the chemical formula K 2 [ Hg I 4 ] . It consists of potassium cations and tetraiodomercurate(II) anions. It is the active agent in Nessler's reagent, used for detection of ammonia . [ 2 ]
The compound crystallizes from a heated solution of mercuric iodide , potassium iodide , and precisely 2% water in acetone . Attempted synthesis in concentrated aqueous solution will give the pale orange monohydrate K[Hg(H 2 O)I 3 ] instead. [ 3 ]
K 2 [HgI 4 ] is a precursor to analogous copper and silver salts M 2 [HgI 4 ] (M=Cu, Ag). [ 4 ]
Nessler's reagent , named after Julius Neßler (Nessler), is a 0.09 mol/L solution of potassium tetraiodomercurate(II) in 2.5 mol/L potassium hydroxide . This pale solution becomes deeper yellow in the presence of ammonia ( NH 3 ). At higher concentrations, a brown precipitate derivative of Millon's base ( HgO·Hg(NH 2 )Cl ) may form. The sensitivity as a spot test is about 0.3 μg NH 3 in 2 μL. [ 5 ]
The brown precipitate is not fully characterized and may vary from HgO·Hg(NH 2 )I to 3HgO·Hg(NH 3 ) 2 I 2 . [ 6 ] | https://en.wikipedia.org/wiki/Potassium_tetraiodomercurate(II) |
Potassium peroxochromate , potassium tetraperoxochromate(V) , or simply potassium perchromate , is an inorganic compound having the chemical formula K 3 [ Cr ( O 2 ) 4 ] . It is a red-brown paramagnetic solid. It is the potassium salt of tetraperoxochromate(V), one of the few examples of chromium in the +5 oxidation state and one of the rare examples of a complex stabilized only by peroxide ligands. [ 2 ] This compound is used as a source of singlet oxygen . [ 1 ]
Potassium peroxochromate is prepared by treating potassium chromate with hydrogen peroxide at 0 °C:
The intermediate tetraperoxochromate(VI) is reduced by hydrogen peroxide, forming tetraperoxochromate(V): [ 3 ] [ 4 ]
Thus, the overall reaction is:
The compound decomposes spontaneously at higher temperatures. | https://en.wikipedia.org/wiki/Potassium_tetraperoxochromate(V) |
Potassium thioacetate is an organosulfur compound and a salt with the formula CH 3 COS − K + . This white, water-soluble solid is used as a reagent for preparing thioacetate esters and other derivatives. [ 1 ]
Potassium thioacetate, which is commercially available, can be prepared by combining acetyl chloride and potassium hydrogen sulfide :
It arises also by the neutralization of thioacetic acid with potassium hydroxide .
In a common application, potassium thioacetate is combined with alkylating agents to give thioacetate esters (X = halide ):
Hydrolysis of these esters affords thiols :
The thioacetate esters can also be cleaved with methanethiol in the presence of stoichiometric base, as illustrated in the preparation of pent-4-yne-1-thiol: [ 2 ] | https://en.wikipedia.org/wiki/Potassium_thioacetate |
Potato root nematodes or potato cyst nematodes ( PCN ) are 1-mm long roundworms belonging to the genus Globodera , which comprises around 12 species. They live on the roots of plants of the family Solanaceae , such as potatoes and tomatoes . PCN cause growth retardation and, at very high population densities, damage to the roots and early senescence of plants. The nematode is not indigenous to Europe but originates from the Andes. Fields are free from PCN until an introduction occurs, after which the typical patches, or hotspots, occur on the farmland. These patches can become full field infestations when unchecked. Yield reductions can average up to 60% at high population densities.
The eggs hatch in the presence of Solanoeclepine A , a substance secreted by the roots of host plants otherwise known as root exudates. The nematodes hatch when they grow into a second-stage juvenile (J2). At this stage, the J2 nematodes find host cells to feed off of. The potato cyst nematodes are endoparasites meaning they go completely into the root to feed. Access to the root cells is gained through piercing through the cell wall using the nematode’s stylet. After a feeding tube has been established, a syncytium begins to form through the breakdown of multiple cell walls adjacent to each other. J2 nematodes continue to feed until they grow into third-stage juveniles (J3), then fourth-stage juveniles (J4), and finally reach the adult stage. The shape of the J3 females begins to appear more like a sac as the female grows into a J4 nematode. At the J4 stage, the body of the female nematode lies outside of the root while the head remains inside the cell. During this stage, the male nematodes become motile again and are then able to fertilize the female nematodes leading to embryos developing inside the female body. Once the female is fertilized, the female dies and leaves a protective cyst containing 200-500 eggs. [ 1 ] Once the cysts detach from the original hosts, they remain in the soil until they find another suitable host beginning the cycle again. Cyst nematodes are monocyclic because they have one life cycle per season. Potato cyst nematodes can be detected by their patchy distribution in the field. The specific distribution is caused by the limited spread of these nematodes. Most potato cyst nematodes don’t migrate very far across a field because of their feeding patterns. [ 2 ] Both susceptible and resistant potato varieties will suffer from growth retardation at low and medium populations densities. At very high population densities mechanical damage of the root system will occur. [ 3 ] The female individuals swell up and appear as cysts on the surface of the roots, each containing up to 400 eggs. In temperate zones only one generation per year will occur. In the Mediterranean countries sometimes a second generation is reported. Cysts can then also be found on the skin of the tubers. Each year without host a certain fraction of the eggs will hatch (spontaneous hatch). The eggs can survive for up to 20 years inside these cysts. [ citation needed ]
The speed of spread of the nematodes from field to field can be reduced by cleaning equipment of possibly infested soil before changing location and by using only certified PCN-free seed tubers. If possible, ask for seed potatoes grown on fields which were declared free of the potato cyst nematode. Pesticides can be used, but they will not get a field free of nematodes. They will increase yields and are only profitable at high population densities, when the financial profit of the extra yield will surpass the cost of the pesticide application. Crop rotation with at least 6 years between planting of a susceptible crop is an effective means to reduce nematode population densities to below damage threshold. However, the best way to manage potato cyst nematodes is the use of (partial) resistant potato varieties. During the last 10 years [ when? ] a number of varieties have been developed which can keep both potato cyst nematode species below damage and detection threshold, without the use of pesticides.
Other methods of pest control include nematicides such as fosthiazate (Nemathorin), aldicarb (Temik), oxamyl (Vydate) and fluopyram which are applied to the soil. [ 4 ] [ 5 ] The level of toxicity is important to consider when applying and depends on the manufacturer and the specific instructions of application. The use of certified disease free seed will also assure that potato cyst nematodes are not present due to planting infected tubers. Soil testing for potato cyst nematodes is also crucial in keeping track of the prevalence of the nematodes. Controlling the quantity of the nematodes allows the prevention of an epidemic. Lastly, resistance to potato cyst nematode has been found in Solanum acaule . [ 4 ] The downside is that Solanum acaule is a wild potato species containing high glycoalkaloid content making it toxic for consumers. The use of trap crops such as Solanum sisymbriifolium has been shown to reduce the density of PCN in soil by up to 80%, reducing the need for pesticide application [ 6 ]
Potato cyst nematodes have the ability to cause a large scale devastation in crops due to the massive amounts of nematode embryos in each cyst. Many continents across the world such as Australia, North America, Asia, Europe, and Africa have had many epidemics of potato cyst nematodes that continue to persist year after year. [ 7 ] Potato cyst nematodes are important economically due to the fact that they can substantially reduce crop yields. Globodera pallida are able to cause 80% yield loss in a potato field if left untreated. [ 8 ] On a more global scale, the Australian potato industry is worth about AUD$500 million yearly which equates to $340 million U.S. dollars. [ 7 ] [ 9 ] | https://en.wikipedia.org/wiki/Potato_cyst_nematode |
The potato paradox is a mathematical calculation that has a result which seems counter-intuitive to many people. The Universal Book of Mathematics states the problem as such: [ 1 ]
Fred brings home 100 kg of potatoes, which (being purely mathematical potatoes) consist of 99% water. He then leaves them outside overnight so that they consist of 98% water. What is their new weight? The surprising answer is 50 kg. [ 2 ]
In Quine's classification of paradoxes , the potato paradox is a veridical paradox.
If the potatoes are 99% water, the dry mass is 1%. This means that the 100 kg of potatoes contains 1 kg of dry mass, which does not change, as only the water evaporates.
In order to make the potatoes be 98% water, the dry mass must become 2% of the total weight—double what it was before. The amount of dry mass, 1 kg, remains unchanged, so this can only be achieved by reducing the total mass of the potatoes. Since the proportion that is dry mass must be doubled, the total mass of the potatoes must be halved, giving the answer 50 kg.
Originally, 1% of the 100kg was dry matter, that is to say 1kg. After they dried, the dry mass of the potatoes made up 2%, or one fiftieth, of the total, which must therefore be 50 × 1kg = 50kg.
The potato paradox was a "Puzzler" on the Car Talk radio show. [ 3 ] | https://en.wikipedia.org/wiki/Potato_paradox |
A potential energy surface ( PES ) or energy landscape describes the energy of a system , especially a collection of atoms, in terms of certain parameters , normally the positions of the atoms. The surface might define the energy as a function of one or more coordinates; if there is only one coordinate, the surface is called a potential energy curve or energy profile . An example is the Morse/Long-range potential .
It is helpful to use the analogy of a landscape: for a system with two degrees of freedom (e.g. two bond lengths), the value of the energy (analogy: the height of the land) is a function of two bond lengths (analogy: the coordinates of the position on the ground). [ 1 ]
The PES concept finds application in fields such as physics , chemistry and biochemistry , especially in the theoretical sub-branches of these subjects. It can be used to theoretically explore properties of structures composed of atoms, for example, finding the minimum energy shape of a molecule or computing the rates of a chemical reaction . It can be used to describe all possible conformations of a molecular entity , or the spatial positions of interacting molecules in a system, or parameters and their corresponding energy levels, typically Gibbs free energy . Geometrically, the energy landscape is the graph of the energy function across the configuration space of the system. The term is also used more generally in geometric perspectives to mathematical optimization , when the domain of the loss function is the parameter space of some system.
The geometry of a set of atoms can be described by a vector, r , whose elements represent the atom positions. The vector r could be the set of the Cartesian coordinates of the atoms, or could also be a set of inter-atomic distances and angles.
Given r , the energy as a function of the positions, E ( r ) , is the value of E ( r ) for all r of interest. Using the landscape analogy from the introduction, E gives the height on the "energy landscape" so that the concept of a potential energy surface arises.
To study a chemical reaction using the PES as a function of atomic positions, it is necessary to calculate the energy for every atomic arrangement of interest. Methods of calculating the energy of a particular atomic arrangement of atoms are well described in the computational chemistry article, and the emphasis here will be on finding approximations of E ( r ) to yield fine-grained energy-position information.
For very simple chemical systems or when simplifying approximations are made about inter-atomic interactions, it is sometimes possible to use an analytically derived expression for the energy as a function of the atomic positions. An example is the London - Eyring - Polanyi -Sato potential [ 2 ] [ 3 ] [ 4 ] for the system H + H 2 as a function of the three H-H distances.
For more complicated systems, calculation of the energy of a particular arrangement of atoms is often too computationally expensive for large scale representations of the surface to be feasible. For these systems a possible approach is to calculate only a reduced set of points on the PES and then use a computationally cheaper interpolation method, for example Shepard interpolation , to fill in the gaps. [ 5 ]
A PES is a conceptual tool for aiding the analysis of molecular geometry and chemical reaction dynamics . Once the necessary points are evaluated on a PES, the points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature . Stationary points (or points with a zero gradient) have physical meaning: energy minima correspond to physically stable chemical species and saddle points correspond to transition states , the highest energy point on the reaction coordinate (which is the lowest energy pathway connecting a chemical reactant to a chemical product).
The term is useful when examining protein folding ; while a protein can theoretically exist in a nearly infinite number of conformations along its energy landscape, in reality proteins fold (or "relax") into secondary and tertiary structures that possess the lowest possible free energy . The key concept in the energy landscape approach to protein folding is the folding funnel hypothesis.
In catalysis , when designing new catalysts or refining existing ones, energy landscapes are considered to avoid low-energy or high-energy intermediates that could halt the reaction or demand excessive energy to reach the final products. [ 6 ]
In glassing models, the local minima of an energy landscape correspond to metastable low temperature states of a thermodynamic system . [ 7 ] [ 8 ]
In machine learning , artificial neural networks may be analyzed using analogous approaches. [ 9 ] For example, a neural network may be able to perfectly fit the training set , corresponding to a global minimum of zero loss, but overfitting the model ("learning the noise" or "memorizing the training set"). Understanding when this happens can be studied using the geometry of the corresponding energy landscape. [ 10 ]
Potential energy surfaces for chemical reactions can be classified as attractive or repulsive by comparing the extensions of the bond lengths in the activated complex relative to those of the reactants and products. [ 11 ] [ 12 ] For a reaction of type A + B—C → A—B + C, the bond length extension for the newly formed A—B bond is defined as R* AB = R AB − R 0 AB , where R AB is the A—B bond length in the transition state and R 0 AB in the product molecule. Similarly for the bond which is broken in the reaction, R* BC = R BC − R 0 BC , where R 0 BC refers to the reactant molecule. [ 13 ]
For exothermic reactions , a PES is classified as attractive (or early-downhill ) if R* AB > R* BC , so that the transition state is reached while the reactants are approaching each other. After the transition state, the A—B bond length continues to decrease, so that much of the liberated reaction energy is converted into vibrational energy of the A—B bond. [ 13 ] [ 14 ] An example is the harpoon reaction K + Br 2 → K—Br + Br, in which the initial long-range attraction of the reactants leads to an activated complex resembling K + •••Br − •••Br. [ 13 ] The vibrationally excited populations of product molecules can be detected by infrared chemiluminescence . [ 15 ] [ 16 ]
In contrast the PES for the reaction H + Cl 2 → HCl + Cl is repulsive (or late-downhill ) because R* HCl < R* ClCl and the transition state is reached when the products are separating. [ 13 ] [ 14 ] For this reaction in which the atom A (here H) is lighter than B and C, the reaction energy is released primarily as translational kinetic energy of the products. [ 13 ] For a reaction such as F + H 2 → HF + H in which atom A is heavier than B and C, there is mixed energy release, both vibrational and translational, even though the PES is repulsive. [ 13 ]
For endothermic reactions , the type of surface determines the type of energy which is most effective in bringing about reaction. Translational energy of the reactants is most effective at inducing reactions with an attractive surface, while vibrational excitation (to higher vibrational quantum number v) is more effective for reactions with a repulsive surface. [ 13 ] As an example of the latter case, the reaction F + HCl(v=1) → Cl + HF is about five times faster than F + HCl(v=0) → Cl + HF for the same total energy of HCl. [ 17 ]
The concept of a potential energy surface for chemical reactions was first suggested by the French physicist René Marcelin in 1913. [ 18 ] The first semi-empirical calculation of a potential energy surface was proposed for the H + H 2 reaction by Henry Eyring and Michael Polanyi in 1931. Eyring used potential energy surfaces to calculate reaction rate constants in the transition state theory in 1935.
Potential energy surfaces are commonly shown as three-dimensional graphs, but they can also be represented by two-dimensional graphs, in which the advancement of the reaction is plotted by the use of isoenergetic lines.
The collinear system H + H 2 is a simple reaction that allows a two-dimension PES to be plotted in an easy and understandable way.
In this reaction, a hydrogen atom (H) reacts with a dihydrogen molecule (H 2 ) by forming a new bond with one atom from the molecule, which in turn breaks the bond of the original molecule. This is symbolized as H a + H b –H c → H a –H b + H c . The progression of the reaction from reactants (H+H₂) to products (H-H-H), as well as the energy of the species that take part in the reaction, are well defined in the corresponding potential energy surface.
Energy profiles describe potential energy as a function of geometrical variables (PES in any dimension are independent of time and temperature).
We have different relevant elements in the 2-D PES:
Schön, J. C. (5 August 2024). "Energy landscapes—Past, present, and future: A perspective" . Journal of Chemical Physics . 161 (5): 050901. Bibcode : 2024JChPh.161e0901S . doi : 10.1063/5.0212867 . Retrieved 17 December 2024 . | https://en.wikipedia.org/wiki/Potential_energy_surface |
In fluid dynamics , potential flow or irrotational flow refers to a description of a fluid flow with no vorticity in it. Such a description typically arises in the limit of vanishing viscosity , i.e., for an inviscid fluid and with no vorticity present in the flow.
Potential flow describes the velocity field as the gradient of a scalar function: the velocity potential . As a result, a potential flow is characterized by an irrotational velocity field , which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero.
In the case of an incompressible flow the velocity potential satisfies Laplace's equation , and potential theory is applicable. However, potential flows also have been used to describe compressible flows and Hele-Shaw flows . The potential flow approach occurs in the modeling of both stationary as well as nonstationary flows.
Applications of potential flow include: the outer flow field for aerofoils , water waves , electroosmotic flow , and groundwater flow . For flows (or parts thereof) with strong vorticity effects, the potential flow approximation is not applicable. In flow regions where vorticity is known to be important, such as wakes and boundary layers , potential flow theory is not able to provide reasonable predictions of the flow. [ 1 ] However, there are often large regions of a flow in which the assumption of irrotationality is valid, allowing the use of potential flow for various applications; these include flow around aircraft , groundwater flow , acoustics , water waves , and electroosmotic flow . [ 2 ]
In potential or irrotational flow, the vorticity vector field is zero, i.e.,
ω ≡ ∇ × v = 0 , {\displaystyle {\boldsymbol {\omega }}\equiv \nabla \times \mathbf {v} =0,}
where v ( x , t ) {\displaystyle \mathbf {v} (\mathbf {x} ,t)} is the velocity field and ω ( x , t ) {\displaystyle {\boldsymbol {\omega }}(\mathbf {x} ,t)} is the vorticity field. Like any vector field having zero curl, the velocity field can be expressed as the gradient of certain scalar, say φ ( x , t ) {\displaystyle \varphi (\mathbf {x} ,t)} which is called the velocity potential , since the curl of the gradient is always zero. We therefore have [ 3 ]
v = ∇ φ . {\displaystyle \mathbf {v} =\nabla \varphi .}
The velocity potential is not uniquely defined since one can add to it an arbitrary function of time, say f ( t ) {\displaystyle f(t)} , without affecting the relevant physical quantity which is v {\displaystyle \mathbf {v} } . The non-uniqueness is usually removed by suitably selecting appropriate initial or boundary conditions satisfied by φ {\displaystyle \varphi } and as such the procedure may vary from one problem to another.
In potential flow, the circulation Γ {\displaystyle \Gamma } around any simply-connected contour C {\displaystyle C} is zero. This can be shown using the Stokes theorem ,
Γ ≡ ∮ C v ⋅ d l = ∫ ω ⋅ d f = 0 {\displaystyle \Gamma \equiv \oint _{C}\mathbf {v} \cdot d\mathbf {l} =\int {\boldsymbol {\omega }}\cdot d\mathbf {f} =0}
where d l {\displaystyle d\mathbf {l} } is the line element on the contour and d f {\displaystyle d\mathbf {f} } is the area element of any surface bounded by the contour. In multiply-connected space (say, around a contour enclosing solid body in two dimensions or around a contour enclosing a torus in three-dimensions) or in the presence of concentrated vortices, (say, in the so-called irrotational vortices or point vortices, or in smoke rings), the circulation Γ {\displaystyle \Gamma } need not be zero. In the former case, Stokes theorem cannot be applied and in the later case, ω {\displaystyle {\boldsymbol {\omega }}} is non-zero within the region bounded by the contour. Around a contour encircling an infinitely long solid cylinder with which the contour loops N {\displaystyle N} times, we have
Γ = N κ {\displaystyle \Gamma =N\kappa }
where κ {\displaystyle \kappa } is a cyclic constant. This example belongs to a doubly-connected space. In an n {\displaystyle n} -tuply connected space, there are n − 1 {\displaystyle n-1} such cyclic constants, namely, κ 1 , κ 2 , … , κ n − 1 . {\displaystyle \kappa _{1},\kappa _{2},\dots ,\kappa _{n-1}.}
In case of an incompressible flow — for instance of a liquid , or a gas at low Mach numbers ; but not for sound waves — the velocity v has zero divergence : [ 3 ]
∇ ⋅ v = 0 , {\displaystyle \nabla \cdot \mathbf {v} =0\,,}
Substituting here v = ∇ φ {\displaystyle \mathbf {v} =\nabla \varphi } shows that φ {\displaystyle \varphi } satisfies the Laplace equation [ 3 ]
∇ 2 φ = 0 , {\displaystyle \nabla ^{2}\varphi =0\,,}
where ∇ 2 = ∇ ⋅ ∇ is the Laplace operator (sometimes also written Δ ). Since solutions of the Laplace equation are harmonic functions , every harmonic function represents a potential flow solution. As evident, in the incompressible case, the velocity field is determined completely from its kinematics : the assumptions of irrotationality and zero divergence of flow. Dynamics in connection with the momentum equations, only have to be applied afterwards, if one is interested in computing pressure field: for instance for flow around airfoils through the use of Bernoulli's principle .
In incompressible flows, contrary to common misconception, the potential flow indeed satisfies the full Navier–Stokes equations , not just the Euler equations , because the viscous term
μ ∇ 2 v = μ ∇ ( ∇ ⋅ v ) − μ ∇ × ω = 0 {\displaystyle \mu \nabla ^{2}\mathbf {v} =\mu \nabla (\nabla \cdot \mathbf {v} )-\mu \nabla \times {\boldsymbol {\omega }}=0}
is identically zero. It is the inability of the potential flow to satisfy the required boundary conditions, especially near solid boundaries, makes it invalid in representing the required flow field. If the potential flow satisfies the necessary conditions, then it is the required solution of the incompressible Navier–Stokes equations.
In two dimensions, with the help of the harmonic function φ {\displaystyle \varphi } and its conjugate harmonic function ψ {\displaystyle \psi } (stream function), incompressible potential flow reduces to a very simple system that is analyzed using complex analysis (see below).
Potential flow theory can also be used to model irrotational compressible flow. The derivation of the governing equation for φ {\displaystyle \varphi } from Eulers equation is quite straightforward. The continuity and the (potential flow) momentum equations for steady flows are given by
ρ ∇ ⋅ v + v ⋅ ∇ ρ = 0 , ( v ⋅ ∇ ) v = − 1 ρ ∇ p = − c 2 ρ ∇ ρ {\displaystyle \rho \nabla \cdot \mathbf {v} +\mathbf {v} \cdot \nabla \rho =0,\quad (\mathbf {v} \cdot \nabla )\mathbf {v} =-{\frac {1}{\rho }}\nabla p=-{\frac {c^{2}}{\rho }}\nabla \rho }
where the last equation follows from the fact that entropy is constant for a fluid particle and that square of the sound speed is c 2 = ( ∂ p / ∂ ρ ) s {\displaystyle c^{2}=(\partial p/\partial \rho )_{s}} . Eliminating ∇ ρ {\displaystyle \nabla \rho } from the two governing equations results in
c 2 ∇ ⋅ v − v ⋅ ( v ⋅ ∇ ) v = 0. {\displaystyle c^{2}\nabla \cdot \mathbf {v} -\mathbf {v} \cdot (\mathbf {v} \cdot \nabla )\mathbf {v} =0.}
The incompressible version emerges in the limit c → ∞ {\displaystyle c\to \infty } . Substituting here v = ∇ φ {\displaystyle \mathbf {v} =\nabla \varphi } results in [ 4 ] [ 5 ]
( c 2 − φ x 2 ) φ x x + ( c 2 − φ y 2 ) φ y y + ( c 2 − φ z 2 ) φ z z − 2 ( φ x φ y φ x y + φ y φ z φ y z + φ z φ x ϕ z x ) = 0 {\displaystyle (c^{2}-\varphi _{x}^{2})\varphi _{xx}+(c^{2}-\varphi _{y}^{2})\varphi _{yy}+(c^{2}-\varphi _{z}^{2})\varphi _{zz}-2(\varphi _{x}\varphi _{y}\varphi _{xy}+\varphi _{y}\varphi _{z}\varphi _{yz}+\varphi _{z}\varphi _{x}\phi _{zx})=0}
where c = c ( v ) {\displaystyle c=c(v)} is expressed as a function of the velocity magnitude v 2 = ( ∇ ϕ ) 2 {\displaystyle v^{2}=(\nabla \phi )^{2}} . For a polytropic gas , c 2 = ( γ − 1 ) ( h 0 − v 2 / 2 ) {\displaystyle c^{2}=(\gamma -1)(h_{0}-v^{2}/2)} , where γ {\displaystyle \gamma } is the specific heat ratio and h 0 {\displaystyle h_{0}} is the stagnation enthalpy . In two dimensions, the equation simplifies to
( c 2 − φ x 2 ) φ x x + ( c 2 − φ y 2 ) φ y y − 2 φ x φ y φ x y = 0. {\displaystyle (c^{2}-\varphi _{x}^{2})\varphi _{xx}+(c^{2}-\varphi _{y}^{2})\varphi _{yy}-2\varphi _{x}\varphi _{y}\varphi _{xy}=0.}
Validity: As it stands, the equation is valid for any inviscid potential flows, irrespective of whether the flow is subsonic or supersonic (e.g. Prandtl–Meyer flow ). However in supersonic and also in transonic flows, shock waves can occur which can introduce entropy and vorticity into the flow making the flow rotational. Nevertheless, there are two cases for which potential flow prevails even in the presence of shock waves, which are explained from the (not necessarily potential) momentum equation written in the following form
∇ ( h + v 2 / 2 ) − v × ω = T ∇ s {\displaystyle \nabla (h+v^{2}/2)-\mathbf {v} \times {\boldsymbol {\omega }}=T\nabla s}
where h {\displaystyle h} is the specific enthalpy , ω {\displaystyle {\boldsymbol {\omega }}} is the vorticity field, T {\displaystyle T} is the temperature and s {\displaystyle s} is the specific entropy. Since in front of the leading shock wave, we have a potential flow, Bernoulli's equation shows that h + v 2 / 2 {\displaystyle h+v^{2}/2} is constant, which is also constant across the shock wave ( Rankine–Hugoniot conditions ) and therefore we can write [ 4 ]
v × ω = − T ∇ s {\displaystyle \mathbf {v} \times {\boldsymbol {\omega }}=-T\nabla s}
1) When the shock wave is of constant intensity, the entropy discontinuity across the shock wave is also constant i.e., ∇ s = 0 {\displaystyle \nabla s=0} and therefore vorticity production is zero. Shock waves at the pointed leading edge of two-dimensional wedge or three-dimensional cone ( Taylor–Maccoll flow ) has constant intensity. 2) For weak shock waves, the entropy jump across the shock wave is a third-order quantity in terms of shock wave strength and therefore ∇ s {\displaystyle \nabla s} can be neglected. Shock waves in slender bodies lies nearly parallel to the body and they are weak.
Nearly parallel flows: When the flow is predominantly unidirectional with small deviations such as in flow past slender bodies, the full equation can be further simplified. Let U e x {\displaystyle U\mathbf {e} _{x}} be the mainstream and consider small deviations from this velocity field. The corresponding velocity potential can be written as φ = x U + ϕ {\displaystyle \varphi =xU+\phi } where ϕ {\displaystyle \phi } characterizes the small departure from the uniform flow and satisfies the linearized version of the full equation. This is given by
( 1 − M 2 ) ∂ 2 ϕ ∂ x 2 + ∂ 2 ϕ ∂ y 2 + ∂ 2 ϕ ∂ z 2 = 0 {\displaystyle (1-M^{2}){\frac {\partial ^{2}\phi }{\partial x^{2}}}+{\frac {\partial ^{2}\phi }{\partial y^{2}}}+{\frac {\partial ^{2}\phi }{\partial z^{2}}}=0}
where M = U / c ∞ {\displaystyle M=U/c_{\infty }} is the constant Mach number corresponding to the uniform flow. This equation is valid provided M {\displaystyle M} is not close to unity. When | M − 1 | {\displaystyle |M-1|} is small (transonic flow), we have the following nonlinear equation [ 4 ]
2 α ∗ ∂ ϕ ∂ x ∂ 2 ϕ ∂ x 2 = ∂ 2 ϕ ∂ y 2 + ∂ 2 ϕ ∂ z 2 {\displaystyle 2\alpha _{*}{\frac {\partial \phi }{\partial x}}{\frac {\partial ^{2}\phi }{\partial x^{2}}}={\frac {\partial ^{2}\phi }{\partial y^{2}}}+{\frac {\partial ^{2}\phi }{\partial z^{2}}}}
where α ∗ {\displaystyle \alpha _{*}} is the critical value of Landau derivative α = ( c 4 / 2 υ 3 ) ( ∂ 2 υ / ∂ p 2 ) s {\displaystyle \alpha =(c^{4}/2\upsilon ^{3})(\partial ^{2}\upsilon /\partial p^{2})_{s}} [ 6 ] [ 7 ] and υ = 1 / ρ {\displaystyle \upsilon =1/\rho } is the specific volume. The transonic flow is completely characterized by the single parameter α ∗ {\displaystyle \alpha _{*}} , which for polytropic gas takes the value α ∗ = α = ( γ + 1 ) / 2 {\displaystyle \alpha _{*}=\alpha =(\gamma +1)/2} . Under hodograph transformation, the transonic equation in two-dimensions becomes the Euler–Tricomi equation .
The continuity and the (potential flow) momentum equations for unsteady flows are given by
∂ ρ ∂ t + ρ ∇ ⋅ v + v ⋅ ∇ ρ = 0 , ∂ v ∂ t + ( v ⋅ ∇ ) v = − 1 ρ ∇ p = − c 2 ρ ∇ ρ = − ∇ h . {\displaystyle {\frac {\partial \rho }{\partial t}}+\rho \nabla \cdot \mathbf {v} +\mathbf {v} \cdot \nabla \rho =0,\quad {\frac {\partial \mathbf {v} }{\partial t}}+(\mathbf {v} \cdot \nabla )\mathbf {v} =-{\frac {1}{\rho }}\nabla p=-{\frac {c^{2}}{\rho }}\nabla \rho =-\nabla h.}
The first integral of the (potential flow) momentum equation is given by
∂ φ ∂ t + v 2 2 + h = f ( t ) , ⇒ ∂ h ∂ t = − ∂ 2 φ ∂ t 2 − 1 2 ∂ v 2 ∂ t + d f d t {\displaystyle {\frac {\partial \varphi }{\partial t}}+{\frac {v^{2}}{2}}+h=f(t),\quad \Rightarrow \quad {\frac {\partial h}{\partial t}}=-{\frac {\partial ^{2}\varphi }{\partial t^{2}}}-{\frac {1}{2}}{\frac {\partial v^{2}}{\partial t}}+{\frac {df}{dt}}}
where f ( t ) {\displaystyle f(t)} is an arbitrary function. Without loss of generality, we can set f ( t ) = 0 {\displaystyle f(t)=0} since φ {\displaystyle \varphi } is not uniquely defined. Combining these equations, we obtain
∂ 2 φ ∂ t 2 + ∂ v 2 ∂ t = c 2 ∇ ⋅ v − v ⋅ ( v ⋅ ∇ ) v . {\displaystyle {\frac {\partial ^{2}\varphi }{\partial t^{2}}}+{\frac {\partial v^{2}}{\partial t}}=c^{2}\nabla \cdot \mathbf {v} -\mathbf {v} \cdot (\mathbf {v} \cdot \nabla )\mathbf {v} .}
Substituting here v = ∇ φ {\displaystyle \mathbf {v} =\nabla \varphi } results in
φ t t + ( φ x 2 + φ y 2 + φ z 2 ) t = ( c 2 − φ x 2 ) φ x x + ( c 2 − φ y 2 ) φ y y + ( c 2 − φ z 2 ) φ z z − 2 ( φ x φ y φ x y + φ y φ z φ y z + φ z φ x ϕ z x ) . {\displaystyle \varphi _{tt}+(\varphi _{x}^{2}+\varphi _{y}^{2}+\varphi _{z}^{2})_{t}=(c^{2}-\varphi _{x}^{2})\varphi _{xx}+(c^{2}-\varphi _{y}^{2})\varphi _{yy}+(c^{2}-\varphi _{z}^{2})\varphi _{zz}-2(\varphi _{x}\varphi _{y}\varphi _{xy}+\varphi _{y}\varphi _{z}\varphi _{yz}+\varphi _{z}\varphi _{x}\phi _{zx}).}
Nearly parallel flows: As in before, for nearly parallel flows, we can write (after introudcing a recaled time τ = c ∞ t {\displaystyle \tau =c_{\infty }t} )
∂ 2 ϕ ∂ τ 2 + 2 M ∂ 2 ϕ ∂ x ∂ τ = ( 1 − M 2 ) ∂ 2 ϕ ∂ x 2 + ∂ 2 ϕ ∂ y 2 + ∂ 2 ϕ ∂ z 2 {\displaystyle {\frac {\partial ^{2}\phi }{\partial \tau ^{2}}}+2M{\frac {\partial ^{2}\phi }{\partial x\partial \tau }}=(1-M^{2}){\frac {\partial ^{2}\phi }{\partial x^{2}}}+{\frac {\partial ^{2}\phi }{\partial y^{2}}}+{\frac {\partial ^{2}\phi }{\partial z^{2}}}}
provided the constant Mach number M {\displaystyle M} is not close to unity. When | M − 1 | {\displaystyle |M-1|} is small (transonic flow), we have the following nonlinear equation [ 4 ]
∂ 2 ϕ ∂ τ 2 + 2 ∂ 2 ϕ ∂ x ∂ τ = − 2 α ∗ ∂ ϕ ∂ x ∂ 2 ϕ ∂ x 2 + ∂ 2 ϕ ∂ y 2 + ∂ 2 ϕ ∂ z 2 . {\displaystyle {\frac {\partial ^{2}\phi }{\partial \tau ^{2}}}+2{\frac {\partial ^{2}\phi }{\partial x\partial \tau }}=-2\alpha _{*}{\frac {\partial \phi }{\partial x}}{\frac {\partial ^{2}\phi }{\partial x^{2}}}+{\frac {\partial ^{2}\phi }{\partial y^{2}}}+{\frac {\partial ^{2}\phi }{\partial z^{2}}}.}
Sound waves: In sound waves, the velocity magntiude v {\displaystyle v} (or the Mach number) is very small, although the unsteady term is now comparable to the other leading terms in the equation. Thus neglecting all quadratic and higher-order terms and noting that in the same approximation, c {\displaystyle c} is a constant (for example, in polytropic gas c 2 = ( γ − 1 ) h 0 {\displaystyle c^{2}=(\gamma -1)h_{0}} ), we have [ 8 ] [ 4 ]
∂ 2 φ ∂ t 2 = c 2 ∇ 2 φ , {\displaystyle {\frac {\partial ^{2}\varphi }{\partial t^{2}}}=c^{2}\nabla ^{2}\varphi ,}
which is a linear wave equation for the velocity potential φ . Again the oscillatory part of the velocity vector v is related to the velocity potential by v = ∇ φ , while as before Δ is the Laplace operator , and c is the average speed of sound in the homogeneous medium . Note that also the oscillatory parts of the pressure p and density ρ each individually satisfy the wave equation, in this approximation.
Potential flow does not include all the characteristics of flows that are encountered in the real world. Potential flow theory cannot be applied for viscous internal flows , [ 1 ] except for flows between closely spaced plates . Richard Feynman considered potential flow to be so unphysical that the only fluid to obey the assumptions was "dry water" (quoting John von Neumann). [ 9 ] Incompressible potential flow also makes a number of invalid predictions, such as d'Alembert's paradox , which states that the drag on any object moving through an infinite fluid otherwise at rest is zero. [ 10 ] More precisely, potential flow cannot account for the behaviour of flows that include a boundary layer . [ 1 ] Nevertheless, understanding potential flow is important in many branches of fluid mechanics. In particular, simple potential flows (called elementary flows ) such as the free vortex and the point source possess ready analytical solutions. These solutions can be superposed to create more complex flows satisfying a variety of boundary conditions. These flows correspond closely to real-life flows over the whole of fluid mechanics; in addition, many valuable insights arise when considering the deviation (often slight) between an observed flow and the corresponding potential flow. Potential flow finds many applications in fields such as aircraft design. For instance, in computational fluid dynamics , one technique is to couple a potential flow solution outside the boundary layer to a solution of the boundary layer equations inside the boundary layer. The absence of boundary layer effects means that any streamline can be replaced by a solid boundary with no change in the flow field, a technique used in many aerodynamic design approaches. Another technique would be the use of Riabouchinsky solids . [ dubious – discuss ]
Potential flow in two dimensions is simple to analyze using conformal mapping , by the use of transformations of the complex plane . However, use of complex numbers is not required, as for example in the classical analysis of fluid flow past a cylinder. It is not possible to solve a potential flow using complex numbers in three dimensions. [ 11 ]
The basic idea is to use a holomorphic (also called analytic ) or meromorphic function f , which maps the physical domain ( x , y ) to the transformed domain ( φ , ψ ) . While x , y , φ and ψ are all real valued , it is convenient to define the complex quantities
z = x + i y , and w = φ + i ψ . {\displaystyle {\begin{aligned}z&=x+iy\,,{\text{ and }}&w&=\varphi +i\psi \,.\end{aligned}}}
Now, if we write the mapping f as [ 11 ]
f ( x + i y ) = φ + i ψ , or f ( z ) = w . {\displaystyle {\begin{aligned}f(x+iy)&=\varphi +i\psi \,,{\text{ or }}&f(z)&=w\,.\end{aligned}}}
Then, because f is a holomorphic or meromorphic function, it has to satisfy the Cauchy–Riemann equations [ 11 ]
∂ φ ∂ x = ∂ ψ ∂ y , ∂ φ ∂ y = − ∂ ψ ∂ x . {\displaystyle {\begin{aligned}{\frac {\partial \varphi }{\partial x}}&={\frac {\partial \psi }{\partial y}}\,,&{\frac {\partial \varphi }{\partial y}}&=-{\frac {\partial \psi }{\partial x}}\,.\end{aligned}}}
The velocity components ( u , v ) , in the ( x , y ) directions respectively, can be obtained directly from f by differentiating with respect to z . That is [ 11 ]
d f d z = u − i v {\displaystyle {\frac {df}{dz}}=u-iv}
So the velocity field v = ( u , v ) is specified by [ 11 ]
u = ∂ φ ∂ x = ∂ ψ ∂ y , v = ∂ φ ∂ y = − ∂ ψ ∂ x . {\displaystyle {\begin{aligned}u&={\frac {\partial \varphi }{\partial x}}={\frac {\partial \psi }{\partial y}},&v&={\frac {\partial \varphi }{\partial y}}=-{\frac {\partial \psi }{\partial x}}\,.\end{aligned}}}
Both φ and ψ then satisfy Laplace's equation : [ 11 ]
Δ φ = ∂ 2 φ ∂ x 2 + ∂ 2 φ ∂ y 2 = 0 , and Δ ψ = ∂ 2 ψ ∂ x 2 + ∂ 2 ψ ∂ y 2 = 0 . {\displaystyle {\begin{aligned}\Delta \varphi &={\frac {\partial ^{2}\varphi }{\partial x^{2}}}+{\frac {\partial ^{2}\varphi }{\partial y^{2}}}=0\,,{\text{ and }}&\Delta \psi &={\frac {\partial ^{2}\psi }{\partial x^{2}}}+{\frac {\partial ^{2}\psi }{\partial y^{2}}}=0\,.\end{aligned}}}
So φ can be identified as the velocity potential and ψ is called the stream function . [ 11 ] Lines of constant ψ are known as streamlines and lines of constant φ are known as equipotential lines (see equipotential surface ).
Streamlines and equipotential lines are orthogonal to each other, since [ 11 ]
∇ φ ⋅ ∇ ψ = ∂ φ ∂ x ∂ ψ ∂ x + ∂ φ ∂ y ∂ ψ ∂ y = ∂ ψ ∂ y ∂ ψ ∂ x − ∂ ψ ∂ x ∂ ψ ∂ y = 0 . {\displaystyle \nabla \varphi \cdot \nabla \psi ={\frac {\partial \varphi }{\partial x}}{\frac {\partial \psi }{\partial x}}+{\frac {\partial \varphi }{\partial y}}{\frac {\partial \psi }{\partial y}}={\frac {\partial \psi }{\partial y}}{\frac {\partial \psi }{\partial x}}-{\frac {\partial \psi }{\partial x}}{\frac {\partial \psi }{\partial y}}=0\,.}
Thus the flow occurs along the lines of constant ψ and at right angles to the lines of constant φ . [ 11 ]
Δ ψ = 0 is also satisfied, this relation being equivalent to ∇ × v = 0 . So the flow is irrotational. The automatic condition ∂ 2 Ψ / ∂ x ∂ y = ∂ 2 Ψ / ∂ y ∂ x then gives the incompressibility constraint ∇ · v = 0 .
Any differentiable function may be used for f . The examples that follow use a variety of elementary functions ; special functions may also be used. Note that multi-valued functions such as the natural logarithm may be used, but attention must be confined to a single Riemann surface .
In case the following power -law conformal map is applied, from z = x + iy to w = φ + iψ : [ 12 ]
w = A z n , {\displaystyle w=Az^{n}\,,}
then, writing z in polar coordinates as z = x + iy = re iθ , we have [ 12 ]
φ = A r n cos n θ and ψ = A r n sin n θ . {\displaystyle \varphi =Ar^{n}\cos n\theta \qquad {\text{and}}\qquad \psi =Ar^{n}\sin n\theta \,.}
In the figures to the right examples are given for several values of n . The black line is the boundary of the flow, while the darker blue lines are streamlines, and the lighter blue lines are equi-potential lines. Some interesting powers n are: [ 12 ]
The constant A is a scaling parameter: its absolute value | A | determines the scale, while its argument arg( A ) introduces a rotation (if non-zero).
If w = Az 1 , that is, a power law with n = 1 , the streamlines (i.e. lines of constant ψ ) are a system of straight lines parallel to the x -axis. This is easiest to see by writing in terms of real and imaginary components:
f ( x + i y ) = A ( x + i y ) = A x + i A y {\displaystyle f(x+iy)=A\,(x+iy)=Ax+iAy}
thus giving φ = Ax and ψ = Ay . This flow may be interpreted as uniform flow parallel to the x -axis.
If n = 2 , then w = Az 2 and the streamline corresponding to a particular value of ψ are those points satisfying
ψ = A r 2 sin 2 θ , {\displaystyle \psi =Ar^{2}\sin 2\theta \,,}
which is a system of rectangular hyperbolae . This may be seen by again rewriting in terms of real and imaginary components. Noting that sin 2 θ = 2 sin θ cos θ and rewriting sin θ = y / r and cos θ = x / r it is seen (on simplifying) that the streamlines are given by
ψ = 2 A x y . {\displaystyle \psi =2Axy\,.}
The velocity field is given by ∇ φ , or
( u v ) = ( ∂ φ ∂ x ∂ φ ∂ y ) = ( + ∂ ψ ∂ y − ∂ ψ ∂ x ) = ( + 2 A x − 2 A y ) . {\displaystyle {\begin{pmatrix}u\\v\end{pmatrix}}={\begin{pmatrix}{\frac {\partial \varphi }{\partial x}}\\[2px]{\frac {\partial \varphi }{\partial y}}\end{pmatrix}}={\begin{pmatrix}+{\partial \psi \over \partial y}\\[2px]-{\partial \psi \over \partial x}\end{pmatrix}}={\begin{pmatrix}+2Ax\\[2px]-2Ay\end{pmatrix}}\,.}
In fluid dynamics, the flowfield near the origin corresponds to a stagnation point . Note that the fluid at the origin is at rest (this follows on differentiation of f (z) = z 2 at z = 0 ). The ψ = 0 streamline is particularly interesting: it has two (or four) branches, following the coordinate axes, i.e. x = 0 and y = 0 . As no fluid flows across the x -axis, it (the x -axis) may be treated as a solid boundary. It is thus possible to ignore the flow in the lower half-plane where y < 0 and to focus on the flow in the upper halfplane. With this interpretation, the flow is that of a vertically directed jet impinging on a horizontal flat plate. The flow may also be interpreted as flow into a 90 degree corner if the regions specified by (say) x , y < 0 are ignored.
If n = 3 , the resulting flow is a sort of hexagonal version of the n = 2 case considered above. Streamlines are given by, ψ = 3 x 2 y − y 3 and the flow in this case may be interpreted as flow into a 60° corner.
If n = −1 , the streamlines are given by
ψ = − A r sin θ . {\displaystyle \psi =-{\frac {A}{r}}\sin \theta .}
This is more easily interpreted in terms of real and imaginary components: ψ = − A y r 2 = − A y x 2 + y 2 , x 2 + y 2 + A y ψ = 0 , x 2 + ( y + A 2 ψ ) 2 = ( A 2 ψ ) 2 . {\displaystyle {\begin{aligned}\psi ={\frac {-Ay}{r^{2}}}&={\frac {-Ay}{x^{2}+y^{2}}}\,,\\x^{2}+y^{2}+{\frac {Ay}{\psi }}&=0\,,\\x^{2}+\left(y+{\frac {A}{2\psi }}\right)^{2}&=\left({\frac {A}{2\psi }}\right)^{2}\,.\end{aligned}}}
Thus the streamlines are circles that are tangent to the x-axis at the origin. The circles in the upper half-plane thus flow clockwise, those in the lower half-plane flow anticlockwise. Note that the velocity components are proportional to r −2 ; and their values at the origin is infinite. This flow pattern is usually referred to as a doublet , or dipole , and can be interpreted as the combination of a source-sink pair of infinite strength kept an infinitesimally small distance apart. The velocity field is given by
( u , v ) = ( ∂ ψ ∂ y , − ∂ ψ ∂ x ) = ( A y 2 − x 2 ( x 2 + y 2 ) 2 , − A 2 x y ( x 2 + y 2 ) 2 ) . {\displaystyle (u,v)=\left({\frac {\partial \psi }{\partial y}},-{\frac {\partial \psi }{\partial x}}\right)=\left(A{\frac {y^{2}-x^{2}}{\left(x^{2}+y^{2}\right)^{2}}},-A{\frac {2xy}{\left(x^{2}+y^{2}\right)^{2}}}\right)\,.}
or in polar coordinates:
( u r , u θ ) = ( 1 r ∂ ψ ∂ θ , − ∂ ψ ∂ r ) = ( − A r 2 cos θ , − A r 2 sin θ ) . {\displaystyle (u_{r},u_{\theta })=\left({\frac {1}{r}}{\frac {\partial \psi }{\partial \theta }},-{\frac {\partial \psi }{\partial r}}\right)=\left(-{\frac {A}{r^{2}}}\cos \theta ,-{\frac {A}{r^{2}}}\sin \theta \right)\,.}
If n = −2 , the streamlines are given by
ψ = − A r 2 sin 2 θ . {\displaystyle \psi =-{\frac {A}{r^{2}}}\sin 2\theta \,.}
This is the flow field associated with a quadrupole . [ 13 ]
A line source or sink of strength Q {\displaystyle Q} ( Q > 0 {\displaystyle Q>0} for source and Q < 0 {\displaystyle Q<0} for sink) is given by the potential
w = Q 2 π ln z {\displaystyle w={\frac {Q}{2\pi }}\ln z}
where Q {\displaystyle Q} in fact is the volume flux per unit length across a surface enclosing the source or sink. The velocity field in polar coordinates are
u r = Q 2 π r , u θ = 0 {\displaystyle u_{r}={\frac {Q}{2\pi r}},\quad u_{\theta }=0}
i.e., a purely radial flow.
A line vortex of strength Γ {\displaystyle \Gamma } is given by
w = Γ 2 π i ln z {\displaystyle w={\frac {\Gamma }{2\pi i}}\ln z}
where Γ {\displaystyle \Gamma } is the circulation around any simple closed contour enclosing the vortex. The velocity field in polar coordinates are
u r = 0 , u θ = Γ 2 π r {\displaystyle u_{r}=0,\quad u_{\theta }={\frac {\Gamma }{2\pi r}}}
i.e., a purely azimuthal flow.
For three-dimensional flows, complex potential cannot be obtained.
The velocity potential of a point source or sink of strength Q {\displaystyle Q} ( Q > 0 {\displaystyle Q>0} for source and Q < 0 {\displaystyle Q<0} for sink) in spherical polar coordinates is given by
ϕ = − Q 4 π r {\displaystyle \phi =-{\frac {Q}{4\pi r}}}
where Q {\displaystyle Q} in fact is the volume flux across a closed surface enclosing the source or sink. The velocity field in spherical polar coordinates are
u r = Q 4 π r 2 , u θ = 0 , u ϕ = 0. {\displaystyle u_{r}={\frac {Q}{4\pi r^{2}}},\quad u_{\theta }=0,\quad u_{\phi }=0.} | https://en.wikipedia.org/wiki/Potential_flow |
In mathematics , potential flow around a circular cylinder is a classical solution for the flow of an inviscid , incompressible fluid around a cylinder that is transverse to the flow. Far from the cylinder, the flow is unidirectional and uniform. The flow has no vorticity and thus the velocity field is irrotational and can be modeled as a potential flow . Unlike a real fluid, this solution indicates a net zero drag on the body, a result known as d'Alembert's paradox .
A cylinder (or disk) of radius R is placed in a two-dimensional, incompressible, inviscid flow. The goal is to find the steady velocity vector V and pressure p in a plane, subject to the condition that far from the cylinder the velocity vector (relative to unit vectors i and j ) is: [ 1 ]
where U is a constant, and at the boundary of the cylinder
where n̂ is the vector normal to the cylinder surface. The upstream flow is uniform and has no vorticity. The flow is inviscid, incompressible and has constant mass density ρ . The flow therefore remains without vorticity, or is said to be irrotational , with ∇ × V = 0 everywhere. Being irrotational, there must exist a velocity potential φ :
Being incompressible, ∇ · V = 0 , so φ must satisfy Laplace's equation :
The solution for φ is obtained most easily in polar coordinates r and θ , related to conventional Cartesian coordinates by x = r cos θ and y = r sin θ . In polar coordinates, Laplace's equation is (see Del in cylindrical and spherical coordinates ):
The solution that satisfies the boundary conditions is [ 2 ]
The velocity components in polar coordinates are obtained from the components of ∇ φ in polar coordinates:
and
Being inviscid and irrotational, Bernoulli's equation allows the solution for the pressure field to be obtained directly from the velocity field:
where the constants U and p ∞ appear so that p → p ∞ far from the cylinder, where V = U . Using V 2 = V 2 r + V 2 θ ,
In the figures, the colorized field referred to as "pressure" is a plot of
On the surface of the cylinder, or r = R , pressure varies from a maximum of 1 (shown in the diagram in red ) at the stagnation points at θ = 0 and θ = π to a minimum of −3 (shown in blue ) on the sides of the cylinder, at θ = π / 2 and θ = 3π / 2 . Likewise, V varies from V = 0 at the stagnation points to V = 2 U on the sides, in the low pressure. [ 1 ]
The flow being incompressible, a stream function can be found such that
It follows from this definition, using vector identities ,
Therefore, a contour of a constant value of ψ will also be a streamline, a line tangent to V . For the flow past a cylinder, we find:
Laplace's equation is linear, and is one of the most elementary partial differential equations . This simple equation yields the entire solution for both V and p because of the constraint of irrotationality and incompressibility. Having obtained the solution for V and p , the consistency of the pressure gradient with the accelerations can be noted.
The dynamic pressure at both the upstream and the downstream stagnation point has a value of 1 / 2 ρU 2 . This value is needed to decelerate the free stream flow of speed U to zero speed at both these points. This symmetry arises only because the flow is completely frictionless.
The low pressure on the lateral sides of the cylinder is needed to provide the centripetal acceleration of the flow:
where L is the radius of curvature of the flow. [ 3 ] But L ≈ R , and V ≈ U . The integral of the equation for centripetal acceleration over a distance Δ r ≈ R will thus yield
The exact solution has, for the lowest pressure,
The low pressure, which must be present to provide the centripetal acceleration, will also increase the flow speed as the fluid travels from higher to lower values of pressure. Thus we find the maximum speed in the flow, V = 2 U , in the low pressure on the sides of the cylinder.
A value of V > U is consistent with conservation of the volume of fluid. With the cylinder blocking some of the flow, V must be greater than U somewhere in the plane through the center of the cylinder and transverse to the flow.
The symmetry of this ideal solution has a stagnation point on the rear side of the cylinder, as well as on the front side. The pressure distribution over the front and rear sides are identical, leading to the peculiar property of having zero drag on the cylinder, a property known as d'Alembert's paradox . Unlike an ideal inviscid fluid, a viscous flow past a cylinder, no matter how small the viscosity, will acquire a thin boundary layer adjacent to the surface of the cylinder. Boundary layer separation will occur, and a trailing wake will exist in the flow behind the cylinder. The pressure at each point on the wake side of the cylinder will be lower than on the upstream side, resulting in a drag force in the downstream direction.
The problem of potential compressible flow over circular cylinder was first studied by O. Janzen in 1913 [ 4 ] and by Lord Rayleigh in 1916 [ 5 ] with small compressibility effects. Here, the small parameter is the square of the Mach number M 2 = U 2 / c 2 ≪ 1 {\displaystyle \mathrm {M} ^{2}=U^{2}/c^{2}\ll 1} , where c is the speed of sound . Then the solution to first-order approximation in terms of the velocity potential is
where a {\displaystyle a} is the radius of the cylinder.
Regular perturbation analysis for a flow around a cylinder with slight perturbation in the configurations can be found in Milton Van Dyke (1975). [ 6 ] In the following, ε will represent a small positive parameter and a is the radius of the cylinder. For more detailed analyses and discussions, readers are referred to Milton Van Dyke 's 1975 book Perturbation Methods in Fluid Mechanics . [ 6 ]
Here the radius of the cylinder is not r = a , but a slightly distorted form r = a (1 − ε sin 2 θ ) . Then the solution to first-order approximation is
Here the radius of the cylinder varies with time slightly so r = a (1 + ε f ( t )) . Then the solution to first-order approximation is
In general, the free-stream velocity U is uniform, in other words ψ = Uy , but here a small vorticity is imposed in the outer flow.
Here a linear shear in the velocity is introduced.
where ε is the small parameter. The governing equation is
Then the solution to first-order approximation is
Here a parabolic shear in the outer velocity is introduced.
Then the solution to the first-order approximation is
where χ is the homogeneous solution to the Laplace equation which restores the boundary conditions.
Let C ps represent the surface pressure coefficient for an impermeable cylinder:
where p s is the surface pressure of the impermeable cylinder. Now let C pi be the internal pressure coefficient inside the cylinder, then a slight normal velocity due to the slight porousness is given by
but the zero net flux condition
requires that C pi = −1 . Therefore,
Then the solution to the first-order approximation is
If the cylinder has variable radius in the axial direction, the z -axis, r = a ( 1 + ε sin z / b ) , then the solution to the first-order approximation in terms of the three-dimensional velocity potential is
where K 1 ( r / b ) is the modified Bessel function of the first kind of order one. | https://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder |
In physics , chemistry and biology , a potential gradient is the local rate of change of the potential with respect to displacement , i.e. spatial derivative , or gradient . This quantity frequently occurs in equations of physical processes because it leads to some form of flux .
The simplest definition for a potential gradient F in one dimension is the following: [ 1 ]
where ϕ ( x ) is some type of scalar potential and x is displacement (not distance ) in the x direction, the subscripts label two different positions x 1 , x 2 , and potentials at those points, ϕ 1 = ϕ ( x 1 ), ϕ 2 = ϕ ( x 2 ) . In the limit of infinitesimal displacements, the ratio of differences becomes a ratio of differentials :
The direction of the electric potential gradient is from x 1 {\displaystyle x_{1}} to x 2 {\displaystyle x_{2}} .
In three dimensions , Cartesian coordinates make it clear that the resultant potential gradient is the sum of the potential gradients in each direction:
where e x , e y , e z are unit vectors in the x, y, z directions. This can be compactly written in terms of the gradient operator ∇ ,
although this final form holds in any curvilinear coordinate system , not just Cartesian.
This expression represents a significant feature of any conservative vector field F , namely F has a corresponding potential ϕ . [ 2 ]
Using Stokes' theorem , this is equivalently stated as
meaning the curl , denoted ∇×, of the vector field vanishes.
In the case of the gravitational field g , which can be shown to be conservative, [ 3 ] it is equal to the gradient in gravitational potential Φ :
There are opposite signs between gravitational field and potential, because the potential gradient and field are opposite in direction: as the potential increases, the gravitational field strength decreases and vice versa.
In electrostatics , the electric field E is independent of time t , so there is no induction of a time-dependent magnetic field B by Faraday's law of induction :
which implies E is the gradient of the electric potential V , identical to the classical gravitational field: [ 4 ]
In electrodynamics , the E field is time dependent and induces a time-dependent B field also (again by Faraday's law), so the curl of E is not zero like before, which implies the electric field is no longer the gradient of electric potential. A time-dependent term must be added: [ 5 ]
where A is the electromagnetic vector potential . This last potential expression in fact reduces Faraday's law to an identity.
In fluid mechanics , the velocity field v describes the fluid motion. An irrotational flow means the velocity field is conservative, or equivalently the vorticity pseudovector field ω is zero:
This allows the velocity potential to be defined simply as:
In an electrochemical half-cell , at the interface between the electrolyte (an ionic solution ) and the metal electrode , the standard electric potential difference is: [ 6 ]
where R = gas constant , T = temperature of solution, z = valency of the metal, e = elementary charge , N A = Avogadro constant , and a M +z is the activity of the ions in solution. Quantities with superscript ⊖ denote the measurement is taken under standard conditions . The potential gradient is relatively abrupt, since there is an almost definite boundary between the metal and solution, hence the interface term. [ clarification needed ]
In biology , a potential gradient is the net difference in electric charge across a cell membrane . [ dubious – discuss ] [ citation needed ]
Since gradients in potentials correspond to physical fields , it makes no difference if a constant is added on (it is erased by the gradient operator ∇ which includes partial differentiation ). This means there is no way to tell what the "absolute value" of the potential "is" – the zero value of potential is completely arbitrary and can be chosen anywhere by convenience (even "at infinity"). This idea also applies to vector potentials, and is exploited in classical field theory and also gauge field theory .
Absolute values of potentials are not physically observable, only gradients and path-dependent potential differences are. However, the Aharonov–Bohm effect is a quantum mechanical effect which illustrates that non-zero electromagnetic potentials along a closed loop (even when the E and B fields are zero everywhere in the region) lead to changes in the phase of the wave function of an electrically charged particle in the region, so the potentials appear to have measurable significance.
Field equations , such as Gauss's laws for electricity , for magnetism , and for gravity , can be written in the form:
where ρ is the electric charge density , monopole density (should they exist), or mass density and X is a constant (in terms of physical constants G , ε 0 , μ 0 and other numerical factors).
Scalar potential gradients lead to Poisson's equation :
A general theory of potentials has been developed to solve this equation for the potential. The gradient of that solution gives the physical field, solving the field equation. | https://en.wikipedia.org/wiki/Potential_gradient |
In mathematical logic and in particular in model theory , a potential isomorphism is a collection of finite partial isomorphisms between two models which satisfies certain closure conditions. Existence of a partial isomorphism entails elementary equivalence , however the converse is not generally true, but it holds for ω-saturated models .
A potential isomorphism between two models M and N is a non-empty collection F of finite partial isomorphisms between M and N which satisfy the following two properties:
A notion of Ehrenfeucht-Fraïssé game is an exact characterisation of elementary equivalence and potential isomorphism can be seen as an approximation of it. Another notion that is similar to potential isomorphism is that of local isomorphism . | https://en.wikipedia.org/wiki/Potential_isomorphism |
In ecology , potential natural vegetation ( PNV ), also known as Kuchler potential vegetation, is the vegetation that would be expected given environmental constraints ( climate , geomorphology , geology ) without human intervention or a hazard event.
The concept was developed in the mid 1950s by phytosociologist Reinhold Tüxen , partly expanding on the concept of climax vegetation .
PNV is widely used in modern conservation and renaturation projects to predict the most adapted species for a definite ecotope . Native species being considered having optimum ecological resilience for their native environment, and the best potential to enhance biodiversity .
To determine "natural" vegetation, scientists research the original vegetation of a land through retrospective ecology .
Study of past ecosystems allowed to demonstrate, for instance, that numerous contemporary biotopes (like the " wild " Slovenian forests for instance), supposedly largely untouched, were in fact very remote from their natural vegetation . [ citation needed ]
In Japan, Akira Miyawaki demonstrated after study that, on the one hand, long supposed "native species" had in fact been introduced on account of human intervention since over 1000 years (especially, coniferous being privileged over deciduous ). On the other hand, that reforestation with "original" species gives good and often spectacular results. [ citation needed ]
Maps of potential natural vegetation [ 1 ] are used worldwide for improved ecosystem comprehension and management .
However the concept is subject to debate, [ 2 ] [ 3 ] on similar grounds as for the climax theory . Critics argue that ecosystems are not static but ever dynamic: as bioclimatic conditions constantly evolve, it is illusory to define either a final or a primary stage of vegetation. | https://en.wikipedia.org/wiki/Potential_natural_vegetation |
When examining a system computationally one may be interested in knowing how the free energy changes as a function of some inter- or intramolecular coordinate (such as the distance between two atoms or a torsional angle). The free energy surface along the chosen coordinate is referred to as the potential of mean force (PMF). If the system of interest is in a solvent, then the PMF also incorporates the solvent effects. [ 1 ]
The PMF can be obtained in Monte Carlo or molecular dynamics simulations to examine how a system's energy changes as a function of some specific reaction coordinate parameter. For example, it may examine how the system's energy changes as a function of the distance between two residues, or as a protein is pulled through a lipid bilayer. It can be a geometrical coordinate or a more general energetic (solvent) coordinate. Often PMF simulations are used in conjunction with umbrella sampling , because typically the PMF simulation will fail to adequately sample the system space as it proceeds. [ 2 ]
The Potential of Mean Force [ 3 ] of a system with N particles is by construction the potential that gives the average force over all the configurations of all the n+1...N particles acting on a particle j at any fixed configuration keeping fixed a set of particles 1...n
Above, − ∇ j w ( n ) {\displaystyle -\nabla _{j}w^{(n)}} is the averaged force, i.e. "mean force" on particle j . And w ( n ) {\displaystyle w^{(n)}} is the so-called potential of mean force. For n = 2 {\displaystyle n=2} , w ( 2 ) ( r ) {\displaystyle w^{(2)}(r)} is the average work needed to bring the two particles from infinite separation to a distance r {\displaystyle r} . It is also related to the radial distribution function of the system, g ( r ) {\displaystyle g(r)} , by: [ 4 ]
The potential of mean force w ( 2 ) {\displaystyle w^{(2)}} is usually applied in the Boltzmann inversion method as a first guess for the effective pair interaction potential that ought to reproduce the correct radial distribution function in a mesoscopic simulation. [ 5 ] Lemkul et al. have used steered molecular dynamics simulations to calculate the potential of mean force to assess the stability of Alzheimer's amyloid protofibrils. [ 6 ] Gosai et al. have also used umbrella sampling simulations to show that potential of mean force decreases between thrombin and its aptamer (a protein-ligand complex) under the effect of electrical fields. [ 7 ]
This physical chemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Potential_of_mean_force |
Potential renal acid load (PRAL) is a measure of the acid that the body produces after ingesting a food. This is different from pH, which is the acidity of a food before being consumed. [ 1 ] [ 2 ] PRAL is a different acidity measure than the food ash measurement. [ 3 ]
Some acidic foods actually have a negative PRAL measurement, meaning they reduce acidity in the stomach. [ 4 ] [ 5 ]
A low PRAL diet (not to be confused with an alkaline diet ) can lower acidity in the stomach, which can be helpful for people suffering GERD or Acid Reflux. However, it does not lower the pH of blood and therefore cannot treat osteoporosis or other conditions. [ 6 ]
This medical article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Potential_renal_acid_load |
In anatomy , a potential space is a space between two adjacent structures that are normally pressed together (directly apposed). Many anatomic spaces are potential spaces, which means that they are potential rather than realized (with their realization being dynamic according to physiologic or pathophysiologic events). In other words, they are like an empty plastic bag that has not been opened (two walls collapsed against each other; no interior volume until opened) or a balloon that has not been inflated. The pleural space , between the visceral and parietal pleura of the lung , is a potential space. [ 1 ] Though it only contains a small amount of fluid normally, it can sometimes accumulate fluid or air that widens the space. [ 2 ] The pericardial space is another potential space that may fill with fluid (effusion) in certain disease states (e.g. pericarditis ; a large pericardial effusion may result in cardiac tamponade ).
This anatomy article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Potential_space |
A potential well is the region surrounding a local minimum of potential energy . Energy captured in a potential well is unable to convert to another type of energy ( kinetic energy in the case of a gravitational potential well) because it is captured in the local minimum of a potential well. Therefore, a body may not proceed to the global minimum of potential energy, as it would naturally tend to do due to entropy .
Energy may be released from a potential well if sufficient energy is added to the system such that the local maximum is surmounted. In quantum physics , potential energy may escape a potential well without added energy due to the probabilistic characteristics of quantum particles ; in these cases a particle may be imagined to tunnel through the walls of a potential well.
The graph of a 2D potential energy function is a potential energy surface that can be imagined as the Earth's surface in a landscape of hills and valleys. Then a potential well would be a valley surrounded on all sides with higher terrain, which thus could be filled with water (e.g., be a lake ) without any water flowing away toward another, lower minimum (e.g. sea level ).
In the case of gravity , the region around a mass is a gravitational potential well, unless the density of the mass is so low that tidal forces from other masses are greater than the gravity of the body itself.
A potential hill is the opposite of a potential well, and is the region surrounding a local maximum .
Quantum confinement can be observed once the diameter of a material is of the same magnitude as the de Broglie wavelength of the electron wave function . [ 1 ] When materials are this small, their electronic and optical properties deviate substantially from those of bulk materials. [ 2 ]
A particle behaves as if it were free when the confining dimension is large compared to the wavelength of the particle. During this state, the bandgap remains at its original energy due to a continuous energy state. However, as the confining dimension decreases and reaches a certain limit, typically in nanoscale, the energy spectrum becomes discrete . As a result, the bandgap becomes size-dependent. As the size of the particles decreases, the electrons and electron holes come closer, and the energy required to activate them increases, which ultimately results in a blueshift in light emission .
Specifically, the effect describes the phenomenon resulting from electrons and electron holes being squeezed into a dimension that approaches a critical quantum measurement, called the exciton Bohr radius . In current application, a quantum dot such as a small sphere confines in three dimensions, a quantum wire confines in two dimensions, and a quantum well confines only in one dimension. These are also known as zero-, one- and two-dimensional potential wells, respectively. In these cases they refer to the number of dimensions in which a confined particle can act as a free carrier. See external links , below, for application examples in biotechnology and solar cell technology.
The electronic and optical properties of materials are affected by size and shape. Well-established technical achievements including quantum dots were derived from size manipulation and investigation for their theoretical corroboration on quantum confinement effect. [ 3 ] The major part of the theory is the behaviour of the exciton resembles that of an atom as its surrounding space shortens. A rather good approximation of an exciton's behaviour is the 3-D model of a particle in a box . [ 4 ] The solution of this problem provides a sole [ clarification needed ] mathematical connection between energy states and the dimension of space. Decreasing the volume or the dimensions of the available space, increases the energy of the states. Shown in the diagram is the change in electron energy level and bandgap between nanomaterial and its bulk state.
The following equation shows the relationship between energy level and dimension spacing:
Research results [ 5 ] provide an alternative explanation of the shift of properties at nanoscale. In the bulk phase, the surfaces appear to control some of the macroscopically observed properties. However, in nanoparticles , surface molecules do not obey the expected configuration [ which? ] in space. As a result, surface tension changes tremendously.
The Young–Laplace equation can give a background on the investigation of the scale of forces applied to the surface molecules:
Under the assumption of spherical shape R 1 = R 2 = R {\displaystyle R_{1}=R_{2}=R} and resolving the Young–Laplace equation for the new radii R {\displaystyle R} (nm), we estimate the new Δ P {\displaystyle \Delta P} (GPa). The smaller the radii, the greater the pressure is present. The increase in pressure at the nanoscale results in strong forces toward the interior of the particle. Consequently, the molecular structure of the particle appears to be different from the bulk mode, especially at the surface. These abnormalities at the surface are responsible for changes of inter-atomic interactions and bandgap . [ 6 ] [ 7 ] | https://en.wikipedia.org/wiki/Potential_well |
A potentially hazardous object ( PHO ) is a near-Earth object – either an asteroid or a comet – with an orbit that can make close approaches to the Earth and which is large enough to cause significant regional damage in the event of impact . [ 1 ] They are conventionally defined as having a minimum orbit intersection distance with Earth of less than 0.05 astronomical units (19.5 lunar distances ) and an absolute magnitude of 22 or brighter, the latter of which roughly corresponds to a size larger than 140 meters. [ 2 ] More than 99% of the known potentially hazardous objects are no impact threat over the next 100 years. [ 3 ] As of February 2025 [update] , just 21 of the known potentially hazardous objects listed on the Sentry Risk Table could not be excluded as potential threats over the next hundred years. [ 4 ] Over hundreds if not thousands of years though, the orbits of some "potentially hazardous" asteroids can evolve to live up to their namesake.
Most of these objects are potentially hazardous asteroids ( PHAs ), and a few are comets . As of November 2022 [update] there are 2,304 known PHAs (about 8% of the total near-Earth population), of which 153 are estimated to be larger than one kilometer in diameter (see list of largest PHAs below) . [ 5 ] [ 6 ] [ a ] Most of the discovered PHAs are Apollo asteroids (1,965) and fewer belong to the group of Aten asteroids (185). [ 7 ] [ 8 ]
A potentially hazardous object can be known not to be a threat to Earth for the next 100 years or more, if its orbit is reasonably well determined. Potentially hazardous asteroids with some threat of impacting Earth in the next 100 years are listed on the Sentry Risk Table. As of September 2022 [update] , only 17 potentially hazardous asteroids are listed on the Sentry Risk Table. [ 4 ] Most potentially hazardous asteroids are ruled out as hazardous to at least several hundreds of years when their competing best orbit models are sufficiently constrained, but recent discoveries whose orbital constraints are little-known have divergent or incomplete mechanical models until observation yields further data. After several astronomical surveys , the number of known PHAs has increased tenfold since the end of the 1990s (see bar charts below) . [ 5 ] The Minor Planet Center 's website List of the Potentially Hazardous Asteroids also publishes detailed information for these objects. [ 9 ]
In May 2021, NASA astronomers reported that 5 to 10 years of preparation may be needed to avoid a potential impactor , as most recently based on a simulated exercise conducted by the 2021 Planetary Defense Conference. [ 10 ] [ 11 ] [ 12 ]
An object is considered a PHO if its minimum orbit intersection distance (MOID) with respect to Earth is less than 0.05 AU (7,500,000 km ; 4,600,000 mi ) – approximately 19.5 lunar distances – and its absolute magnitude is brighter than 22, approximately corresponding to a diameter above 140 meters (460 ft). [ 1 ] [ 2 ] This is big enough to cause regional devastation to human settlements unprecedented in human history in the case of a land impact, or a major tsunami in the case of an ocean impact. Such impact events occur on average around once per 10,000 years. NEOWISE data estimates that there are 4,700 ± 1,500 potentially hazardous asteroids with a diameter greater than 100 meters. [ 13 ]
The two main scales used to categorize the impact hazards of asteroids are the Palermo scale and the Torino scale.
A potentially hazardous comet ( PHC ) is a short-period comet which currently has an Earth- MOID less than 0.05 AU. Known PHCs include: 109P/Swift-Tuttle , 55P/Tempel–Tuttle , 15P/Finlay , 289P/Blanpain , 255P/Levy , 206P/Barnard–Boattini , 21P/Giacobini–Zinner , and 73P/Schwassmann–Wachmann . Halley's Comet fit the criteria before AD 837, when it passed the earth at a distance of 0.033 AU. It now has an MOID of 0.075 AU.
In 2012 NASA estimated 20 to 30 percent of these objects have been found. [ 13 ] During an asteroid's close approaches to another planet it will be subject to gravitational perturbation , modifying its orbit, and potentially changing a previously non-threatening asteroid into a PHA or vice versa. This is a reflection of the dynamic character of the Solar System.
Several astronomical survey projects such as Lincoln Near-Earth Asteroid Research , Catalina Sky Survey and Pan-STARRS continue to search for more PHOs. Each one found is studied by various means, including optical, radar , and infrared to determine its characteristics, such as size, composition, rotation state, and to more accurately determine its orbit. Both professional and amateur astronomers participate in such observation and tracking.
Asteroids larger than approximately 35 meters across can pose a threat to a town or city. [ 14 ] However the diameter of most small asteroids is not well determined, as it is usually only estimated based on their brightness and distance, rather than directly measured, e.g. from radar observations. For this reason NASA and the Jet Propulsion Laboratory use the more practical measure of absolute magnitude ( H ). Any asteroid with an absolute magnitude of 22.0 or brighter is assumed to be of the required size. [ 2 ]
Only a coarse estimation of size can be found from the object's magnitude because an assumption must be made for its albedo which is also not usually known for certain. The NASA near-Earth object program uses an assumed albedo of 0.14 for this purpose. In May 2016, the asteroid size estimates arising from the Wide-field Infrared Survey Explorer and NEOWISE missions have been questioned. [ 15 ] [ 16 ] [ 17 ] Although the early original criticism had not undergone peer review, [ 18 ] a more recent peer-reviewed study was subsequently published. [ 19 ] [ 20 ]
With a mean diameter of approximately 7 kilometers, Apollo asteroid (53319) 1999 JM 8 is likely the largest known potentially hazardous object, despite its fainter absolute magnitude of 15.2, compared to other listed objects in the table below (note: calculated mean-diameters in table are inferred from the object's brightness and its (assumed) albedo. They are only an approximation.) .
Below is a list of the largest PHAs (based on absolute magnitude H ) discovered in a given year. Historical data of the cumulative number of discovered PHA since 1999 are displayed in the bar charts—one for the total number and the other for objects larger than one kilometer. [ 5 ] PHAs brighter than absolute magnitude 17.75 are likely larger than 1 km in size.
Solar System → Local Interstellar Cloud → Local Bubble → Gould Belt → Orion Arm → Milky Way → Milky Way subgroup → Local Group → Local Sheet → Virgo Supercluster → Laniakea Supercluster → Local Hole → Observable universe → Universe Each arrow ( → ) may be read as "within" or "part of". | https://en.wikipedia.org/wiki/Potentially_hazardous_object |
In clinical terms, a potentiator is a reagent that enhances sensitization of an antigen . Potentiators are used in the clinical laboratory for performing blood banking procedures that require enhancement of agglutination to detect the presence of antibodies or antigens in a patient's blood sample. Examples of potentiators include albumin , LISS (low ionic-strength saline) and PEG ( polyethylene glycol ). [ 1 ] Potentiators are also known as enhancement reagents.
Albumin acts as a potentiator by reducing the zeta potential around the suspended red blood cells, thus dispersing the repulsive negative charges and enhancing agglutination. Low ionic strength saline (LISS) is a potentiator that acts by not only reducing the zeta potential , but also by increasing the amount of antibody taken up by the red blood cell during sensitization. LISS is a solution of glycine and albumin. Polyethylene glycol (PEG) in a LISS solution removes water from the system and thus concentrates the antibodies present. PEG can cause non-specific aggregation of cells, thus eliminating the necessity for centrifugation after 37 °C (99 °F) incubation. PEG is not appropriate for use in samples from patients with increased plasma protein , such as patients with multiple myeloma . False-positive results may occur more frequently with the use of polyethylene glycol due to its strong agglutination capabilities.
In clinical pharmacology, a potentiator is a drug, herb, or chemical that intensifies the effects of a given drug. For example, hydroxyzine or dextromethorphan is used to get more pain relief and anxiolysis out of an equal dose of an opioid medication. The potentiation can take place at any part of the liberation, absorption, distribution, metabolism and elimination of the drug. | https://en.wikipedia.org/wiki/Potentiator |
A potentiometer is an instrument for measuring voltage or 'potential difference' by comparison of an unknown voltage with a known reference voltage . If a sensitive indicating instrument is used, very little current is drawn from the source of the unknown voltage. Since the reference voltage can be produced from an accurately calibrated voltage divider , a potentiometer can provide high precision in measurement. The method was described by Johann Christian Poggendorff around 1841 and became a standard laboratory measuring technique. [ 1 ]
In this arrangement, a fraction of a known voltage from a resistive slide wire is compared with an unknown voltage by means of a galvanometer . The sliding contact or wiper of the potentiometer is adjusted and the galvanometer briefly connected between the sliding contact and the unknown voltage. The deflection of the galvanometer is observed and the sliding tap adjusted until the galvanometer no longer deflects from zero. At that point the galvanometer draws no current from the unknown source, and the magnitude of voltage can be calculated from the position of the sliding contact.
This null balance measuring method is still important in electrical metrology and standards work and is also used in other areas of electronics.
Measurement potentiometers are divided into four main classes listed below.
The principle of a potentiometer is that the potential dropped across a segment of a wire of uniform cross-section carrying a constant current is directly proportional to its length. The potentiometer is a simple device used to measure the electrical potentials (or compare the e.m.f of a cell). One form of potentiometer is a uniform high-resistance wire attached to an insulating support, marked with a linear measuring scale. In use, an adjustable regulated voltage source E, of greater magnitude than the potential to be measured, is connected across the wire so as to pass a steady current through it.
Between the end of the wire and any point along it will be a potential proportional to the length of wire to that point. By comparing the potential at points along the wire with an unknown potential, the magnitude of the unknown potential can be determined. The instrument used for comparison must be sensitive, but need not be particularly well-calibrated or accurate so long as its deflection from zero position can be easily detected.
In this circuit, the ends of a uniform resistance wire R 1 are connected to a regulated DC supply V S for use as a voltage divider. The potentiometer is first calibrated by positioning the wiper (arrow) at the spot on the R 1 wire that corresponds to the voltage of a standard cell so that R 2 R 1 = cell voltage V S {\displaystyle {R_{2} \over R_{1}}={{\mbox{cell voltage}} \over V_{\mathrm {S} }}}
A standard electrochemical cell is used whose emf is known (e.g. 1.0183 volts for a Weston standard cell ). [ 2 ] [ 3 ]
The supply voltage V S is then adjusted until the galvanometer shows zero, indicating the voltage on R 2 is equal to the standard cell voltage.
An unknown DC voltage, in series with the galvanometer, is then connected to the sliding wiper, across a variable-length section R 3 of the resistance wire. The wiper is moved until no current flows into or out of the source of unknown voltage, as indicated by the galvanometer in series with the unknown voltage. The voltage across the selected R 3 section of wire is then equal to the unknown voltage. The final step is to calculate the unknown voltage from the fraction of the length of the resistance wire that was connected to the unknown voltage.
The galvanometer does not need to be calibrated, as its only function is to read zero or not zero. When measuring an unknown voltage and the galvanometer reads zero, no current is drawn from the unknown voltage and so the reading is independent of the source's internal resistance, as if by a voltmeter of infinite resistance.
Because the resistance wire can be made very uniform in cross-section and resistivity, and the position of the wiper can be measured easily, this method can be used to measure unknown DC voltages greater than or less than a calibration voltage produced by a standard cell without drawing any current from the standard cell.
If the potentiometer is attached to a constant voltage DC supply such as a lead–acid battery , then a second variable resistor (not shown) can be used to calibrate the potentiometer by varying the current through the R 1 resistance wire.
If the length of the R 1 resistance wire is AB, where A is the (-) end and B is the (+) end, and the movable wiper is at point X at a distance AX on the R 3 portion of the resistance wire when the galvanometer gives a zero reading for an unknown voltage, the distance AX is measured or read from a pre-printed scale next to the resistance wire. The unknown voltage can then be calculated: V U = ( C a l i b r a t i o n C e l l V o l t a g e ) A X A B {\displaystyle V_{U}=(Calibration\ Cell\ Voltage){AX \over AB}}
The constant resistance potentiometer is a variation of the basic idea in which a variable current is fed through a fixed resistor. These are used primarily for measurements in the millivolt and microvolt range.
This is a form of the constant resistance potentiometer described above but designed to minimize the effects of contact resistance and thermal emf. This equipment is satisfactorily used down to readings of 1000 nV or so.
Another development of the standard types was the 'thermocouple potentiometer' especially adapted for temperature measurement with thermocouples . [ 4 ] Potentiometers for use with thermocouples also measure the temperature at which the thermocouple wires are connected, so that cold-junction compensation may be applied to correct the apparent measured EMF to the standard cold-junction temperature of 0 degrees C.
To make a potentiometric determination of an analyte in a solution, the potential of the cell is measured. This measurement must be corrected for the reference and junction potentials. It can also be used in standardisation methods. The concentration of the analyte can then be calculated from the Nernst Equation . Many varieties of this basic principle exist for quantitative measurements.
A metre bridge is a simple type of potentiometer which may be used in school science laboratories to demonstrate the principle of resistance measurement by potentiometric means. A resistance wire is laid along the length of a metre rule and contact with the wire is made through a galvanometer by a slider. When the galvanometer reads zero, the ratio between the lengths of wire to the left and right of the slider is equal to the ratio between the values of a known and an unknown resistor in a parallel circuit. [ 5 ] | https://en.wikipedia.org/wiki/Potentiometer_(measuring_instrument) |
A potentiometric sensor is a type of chemical sensor that may be used to determine the analytical concentration of some components of the analyte gas or solution . These sensors measure the electrical potential of an electrode when no current is present.
The signal is measured as the potential difference (voltage) between the working electrode and the reference electrode. The working electrode's potential must depend on the concentration of the analyte in the gas or solution phase. The reference electrode is needed to provide a defined reference potential.
Potentiometric solid state gas sensors have been generally classified into three broad groups.
This electrochemistry -related article is a stub . You can help Wikipedia by expanding it .
This article about analytical chemistry is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Potentiometric_sensor |
A potentiometric surface is the imaginary plane where a given reservoir of fluid will "equalize out to" if allowed to flow. A potentiometric surface is based on hydraulic principles. For example, two connected storage tanks with one full and one empty will gradually fill/drain to the same level. This is because of atmospheric pressure and gravity. This idea is heavily used in city water supplies - a tall water tower containing the water supply has a great enough potentiometric surface to provide flowing water at a decent pressure to the houses it supplies.
For groundwater "potentiometric surface" is a synonym of "piezometric surface" which is an imaginary surface that defines the level to which water in a confined aquifer would rise were it completely pierced with wells . [ 1 ] If the potentiometric surface lies above the ground surface, a flowing artesian well results. Contour maps and profiles of the potentiometric surface can be prepared from the well data.
This classical mechanics –related article is a stub . You can help Wikipedia by expanding it .
This water supply –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Potentiometric_surface |
In analytical chemistry , potentiometric titration is a technique similar to direct titration of a redox reaction. It is a useful means of characterizing an acid . No indicator is used; instead the electric potential is measured across the analyte , typically an electrolyte solution. To do this, two electrodes are used, an indicator electrode (the glass electrode and metal ion indicator electrode) and a reference electrode . Reference electrodes generally used are hydrogen electrodes, calomel electrodes, and silver chloride electrodes . The indicator electrode forms an electrochemical half-cell with the ions of interest in the test solution. The reference electrode forms the other half-cell.
The overall electric potential is calculated as
E sol is the potential drop over the test solution between the two electrodes. E cell is recorded at intervals as the titrant is added. A graph of potential against volume added can be drawn and the end point of the reaction is halfway between the jump in voltage. E cell depends on the concentration of the ions of interest with which the indicator electrode is in contact. For example, the electrode reaction may be
As the concentration of M n + changes, the E cell changes correspondingly. Thus the potentiometric titration involve measurement of E cell with the addition of titrant. Types of potentiometric titration include acid–base titration (total alkalinity and total acidity), redox titration (HI/HY and cerate), precipitation titration (halides), and complexometric titration (free EDTA and Antical #5).
The first potentiometric titration was carried out in 1893 by Robert Behrend at Ostwald's Institute in Leipzig. He titrated mercurous solution with potassium chloride , potassium bromide , and potassium iodide . He used a mercury electrode along with a mercury/ mercurous nitrate reference electrode. He found that in a cell composed of mercurous nitrate and mercurous nitrate/mercury, the initial voltage is 0. If potassium chloride is added to mercurous nitrate on one side, mercury (I) chloride is precipitated. This decreased the osmotic pressure of mercury (I) ions on the side and creates a potential difference. This potential difference increases slowly as additional potassium chloride is added, but then increases more rapidly. He found the greatest potential difference is achieved once all of the mercurous nitrate has been precipitated. This was used to discern end points of titrations. [ 1 ]
Wilhelm Böttger then developed the tool of potentiometric titration while working at Ostwald's Institute. [ 2 ] He used potentiometric titration to observe the differences in titration between strong and weak acids, as well as the behavior of polybasic acids. He introduced the idea of using potentiometric titrations for acids and bases that could not be titrated in conjunction with a colorimetric indicator [ 1 ]
Potentiometric titrations were first used for redox titrations by Crotogino. He titrated halide ions with potassium permanganate using a shiny platinum electrode and a calomel electrode . He said that if an oxidizing agent is added to a reducing solution then the equilibrium between the reducing substance and reaction product will shift towards the reaction product. This changes the potential very slowly until the amount of reducing substance becomes very small. A large change in potential will occur then once a small addition of the titrating solution is added, as the final amounts of reducing agent are removed and the potential corresponds solely to the oxidizing agent. This large increase in potential difference signifies the endpoint of the reaction. [ 1 ] | https://en.wikipedia.org/wiki/Potentiometric_titration |
A potentiostat is the electronic hardware required to control a three electrode cell and run most electroanalytical experiments. A Bipotentiostat and polypotentiostat are potentiostats capable of controlling two working electrodes and more than two working electrodes, respectively. [ 1 ] [ 2 ] [ 3 ] [ 4 ]
The system functions by maintaining the potential of the working electrode at a constant level with respect to the reference electrode by adjusting the current at an auxiliary electrode . The heart of the different potentiostatic electronic circuits is an operational amplifier (op amp). [ 5 ] It consists of an electric circuit which is usually described in terms of simple op amps .
This equipment is fundamental to modern electrochemical studies using three electrode systems for investigations of reaction mechanisms related to redox chemistry and other chemical phenomena. The dimensions of the resulting data depend on the experiment. In voltammetry , electric current in amps is plotted against electric potential in voltage . In a bulk electrolysis total coulombs passed (total electric charge ) is plotted against time in seconds even though the experiment measures electric current ( amperes ) over time. This is done to show that the experiment is approaching an expected number of coulombs.
Most early potentiostats could function independently, providing data output through a physical data trace. Modern potentiostats are designed to interface with a personal computer and operate through a dedicated software package. The automated software allows the user rapidly to shift between experiments and experimental conditions. The computer allows data to be stored and analyzed more effectively, rapidly, and accurately than the earlier standalone devices.
A potentiostat is a control and measuring device. It comprises an electric circuit which controls the potential across the cell by sensing changes in its resistance , varying accordingly the current supplied to the system: a higher resistance will result in a decreased current, while a lower resistance will result in an increased current, in order to keep the voltage constant as described by Ohm's law .
As a result, the variable system resistance and the controlled current are inversely proportional
Since 1942, when the English electrochemist Archie Hickling ( University of Leicester ) built the first three electrode potentiostat, [ 6 ] substantial progress has been made to improve the instrument. Hickling's device used a third electrode, the reference electrode to control the cell potential automatically. Up until the present day his principle has remained in use. At a glance, a potentiostat measures the potential difference between the working and the reference electrode, applies the current through the counter electrode and measures the current as an i {\displaystyle i} R {\displaystyle R} voltage drop over a series resistor ( R m {\displaystyle R_{\textrm {m}}} in Fig. 1).
The control amplifier (CA) is responsible for maintaining the voltage between the reference and the working electrode as closely as possible to the voltage of the input source E i {\displaystyle E_{\textrm {i}}} . It adjusts its output to automatically control the cell current so that a condition of equilibrium is satisfied. The theory of operation is best understood using the equations below.
Prior to observing the following equations, one may note that, from an electrical point of view, the electrochemical cell and the current measurement resistor R m {\displaystyle R_{\textrm {m}}} may be regarded as two impedances (Fig. 2). Z 1 {\displaystyle Z_{1}} includes R m {\displaystyle R_{\textrm {m}}} in series with the interfacial impedance of the counter electrode and the solution resistance between the counter and the reference. Z 2 {\displaystyle Z_{2}} represents the interfacial impedance of the working electrode in series with the solution resistance between the working and the reference
electrodes.
The role of the control amplifier is to amplify the potential difference between the positive (or noninverting) input and the negative (or inverting) input. This may be translated mathematically into the following equation:
where A {\displaystyle A} is the amplification factor of the CA. At this point the assumption may be made that a negligible amount of current is flowing through the reference electrode. This correlates to physical phenomenon since the reference electrode is connected to a high impedance electrometer. Thus, the cell current may be described in two ways:
and
Combining Eqs. (2) and (3) yields Eq. (4):
where β {\displaystyle \beta } is the fraction of the output voltage of the control amplifier returned to its negative input; namely the feedback factor:
Combining Eqs. (1) and (4) yields Eq. (6):
When the quantity β {\displaystyle \beta } A {\displaystyle A} becomes very large with respect to one, Eq. (6) reduces to Eq. (7), which is one of the negative feedback equations:
Eq. (7) proves that the control amplifier works to keep the voltage between the reference and the working close to the input source voltage.
Replacing the CA, a control algorithm can maintain a constant voltage E c {\displaystyle E_{\textrm {c}}} between the reference electrode and the working electrode. [ 7 ] This algorithm is based on the rule of proportion :
If the measurement intervals of Eq. (8) are kept constant, the control algorithm sets the cell voltage U m {\displaystyle U_{\textrm {m}}} so to keep E c {\displaystyle E_{\textrm {c}}} as close as possible to the setpoint E SP {\displaystyle E_{\textrm {SP}}} . The algorithm requires software-controllable hardware such as a digital multimeter , a power supply , and a double-pole double-throw relay . The relay is necessary to switch polarity.
In electrochemical experiments the electrodes are the pieces of equipment that comes in immediate contact with the analyte . For this reason the electrodes are very important for determining the experimental result. The electrode surface may or may not catalyze chemical reactions. The size of the electrodes affects the magnitude of the currents passed which can affect signal to noise. But electrodes are not the only limiting factor for electrochemical experiments, the potentiostat also has a limited range of operation. The following are a few significant features that vary between instruments. | https://en.wikipedia.org/wiki/Potentiostat |
A pothole is a pot-shaped depression in a road surface , [ 1 ] usually asphalt pavement , where traffic has removed broken pieces of the pavement. It is usually the result of water in the underlying soil structure and traffic passing over the affected area. Water first weakens the underlying soil; traffic then fatigues and breaks the poorly supported asphalt surface in the affected area. Continued traffic action ejects both asphalt and the underlying soil material to create a hole in the pavement. [ 2 ]
According to the US Army Corps of Engineers 's Cold Regions Research and Engineering Laboratory , pothole formation requires two factors to be present at the same time: water and traffic. Water weakens the soil beneath the pavement while traffic applies the loads that stress the pavement past the breaking point. Potholes form progressively from fatigue of the road surface which can lead to a precursor failure pattern known as crocodile (or alligator) cracking . [ 3 ] Eventually, chunks of pavement between the fatigue cracks gradually work loose, and may then be plucked or forced out of the surface by continued wheel loads to create a pothole. [ 4 ]
In areas subject to freezing and thawing, frost heaving can damage a pavement and create openings for water to enter. In the spring , thaw of pavements accelerates this process when the thawing of upper portions of the soil structure in a pavement cannot drain past still-frozen lower layers, thus saturating the supporting soil and weakening it. [ 4 ]
Potholes can grow to several feet in width, though they usually only develop to depths of a few inches. If they become large enough, damage to tires, wheels, and vehicle suspensions is liable to occur. Serious road accidents can occur as a direct result, especially on those roads where vehicle speeds are greater. [ 4 ]
Potholes may result from four main causes: [ 4 ]
The following steps can be taken to avoid pothole formation in existing pavements: [ 4 ]
At-risk pavement are more often local roads with lower structural standards and more complicating factors, like underground utilities, than major arteries. Pavement condition monitoring can lead to timely preventive action. Surveys address pavement distresses, which both diminishes the strength of the asphalt layer and admits water into the pavement, and effective drainage of water from within and around the pavement structure. [ 4 ]
Drainage structures, including ditching and storm sewers are essential for removing water from pavements. Avoiding other risk factors with good construction includes well-draining base and sub-base soils that avoid frost action and promote drying of the soil structure. Adequate crowns promote drainage to the sides. Good crack control prevents water penetration into the pavement soil structure. [ 4 ]
Preventive maintenance adds maintaining pavement structural integrity with thickness and continuity to the mix of preventing water penetration and promoting water migration away from the roadway. [ 4 ]
Eaton, et al., advocate a permitting process for utility cuts with specifications that avoid loss of structural continuity of pavements and flaws or failures that allow water penetration. [ 4 ]
Some municipalities require contractors to install utility repair tags to identify responsible parties of the deteriorated patches. [ 5 ]
A US Air Force manual advocates semiannual inspection of pavement cracks with crack sealing commencing on cracks that exceed 6.4 millimetres (0.25 in) [ 6 ]
Pothole patching methods may be either temporary or semi-permanent. Temporary patching is reserved for weather conditions that are not favorable to a more permanent solution and usually uses a cold mix asphalt patching compound placed in an expedient manner to temporarily restore pavement smoothness. Semi-permanent patching uses more care in reconstructing the perimeter of the failed area to blend with the surrounding pavement and usually employs a hot-mix asphalt fill above replacement of appropriate base materials. [ 4 ]
The Federal Highway Administration (FHWA) offers an overview of best practices which includes several repair techniques; throw-and-roll, semi-permanent, spray injection, and edge seal. [ 2 ] The FHWA suggests the best patching techniques, at times other than winter, are spray injection, throw-and-roll, semi-permanent, or edge seal procedures. In winter, the throw-and-roll technique may be the only available option. The Council for Scientific and Industrial Research in South Africa offers similar methods for the repair of potholes. [ 7 ]
Asphaltic patch materials consist of a binder and aggregate that come in two broad categories, hot mix and cold mix. Hot mixes are used by some agencies, they are produced at local asphalt plants. [ 4 ] The FHWA manual cites three types of cold mixes, those produced by a local asphalt plant, either 1) using the available aggregate and binder or 2) according to specifications set by the agency that will use the mix. The third type is a proprietary cold mix, which is manufactured to an advertised standard. [ 2 ]
The FHWA manual [ 2 ] cites the throw-and-roll method as the most basic method, best used as a temporary repair under conditions when it is difficult to control the placement of material, such as winter-time. It consists of:
This method is widely used due to its simplicity and speed, especially as an expedient method when the material is placed under unfavorable conditions of water or temperature. It can also be employed at times when the pothole is dry and clean with more lasting results. [ 8 ] Eaton, et al., noted that the failure rate of expedient repairs is high and that they can cost as much as five times the cost of properly done repairs. They advocate this type of repair only when weather conditions prevent proper techniques. [ 4 ]
Researchers from the University of Minnesota Duluth have tested mixing asphalt with iron ore containing magnetite which is then heated using ferromagnetic resonance (using microwaves at a specific frequency) to heat the mixed asphalt. The mixture used a compound of between 1% and 2% magnetite. The group discovered that material could be heated for a patch to 100 °C (212 °F) in approximately ten minutes which then applied a more effective repair and drove out moisture which improved adhesion. [ 9 ]
The FHWA manual [ 2 ] cites the semi-permanent repair method as one of the best for repairing potholes, short of full-depth roadway replacement. It consists of:
While this repair procedure provides durable results, it requires more labor and is more equipment-intensive than the throw-and-roll or the spray-injection procedure.
The FHWA manual [ 2 ] cites the spray-injection procedure as an efficient alternative to semi-permanent repair. It requires specialized equipment, however. It consists of:
This procedure requires no compaction after the cover aggregate has been placed.
The FHWA manual [ 2 ] cites the edge seal method as an alternative to the above techniques. It consists of:
In this procedure, waiting for any water to dry may require a second visit to place the tack coat. The tack material prevents water from getting through the edge of the patch and helps bond the patch to the surrounding pavement.
An FHWA-sponsored study determined that the "throw-and-roll technique proved as effective as the semi-permanent procedure when the two procedures were compared directly, using similar materials". It also found the throw-and-roll procedure to be generally more cost-effective when using quality materials. It further found that spray-injection repairs were as effective as control patches, depending on the expertise of the equipment operator. [ 8 ]
The American Automobile Association estimated in the five years prior to 2016 that 16 million drivers in the United States have suffered damage from potholes to their vehicle including tire punctures , bent wheels , and damaged suspensions with a cost of $3 billion a year. In India, between 2015 and 2017, an average of 3,000 people per year were killed in accidents involving potholes. [ 10 ] Britain has estimated that the cost of fixing all roads with potholes in the country would cost £12 billion. [ 9 ] 255 cyclists in Britain were killed or seriously injured because of road defects between 2017 and 2023. [ 11 ]
Some jurisdictions offer websites or mobile apps for pothole-reporting. These allow citizens to report potholes and other road hazards , optionally including a photograph and GPS coordinates. [ 12 ] [ 13 ] It is estimated there are 55 million potholes in the United States. [ 14 ] The self-proclaimed pothole capital, Edmonton , Alberta, Canada reportedly spends $4.8 million on 450,000 potholes annually, as of 2015. [ 15 ]
India has historically lost over 3,000 people per year to accidents caused by potholes. [ 10 ] This situation has engendered citizen movement to address the problem. [ 16 ]
In the United Kingdom , more than half a million pot holes were reported in 2017, an increase of 44% on the 2015 figure. There are processes in place to report potholes at different levels of jurisdiction. The process for claiming compensation varies by jurisdiction. [ 17 ]
Potholes have been commented on both in various media.
Two artists, Jim Bachor of Chicago and Baadal Nanjundaswamy of Bangalore , India, have used artwork as a commentary on potholes by placing mosaics (depicting ice cream in various manifestations) [ 18 ] or sculpture (in the form of a crocodile) in potholes. [ 19 ] Elsewhere, activists in Russia used painted caricatures of local officials with their mouths as potholes, to show their anger about the poor state of the roads. [ 20 ] In Manchester, England , a graffiti artist painted images of penises around potholes, which often resulted in them being repaired within 48 hours. [ 21 ]
The Beatles song " A Day in the Life " references potholes. John Lennon wrote the song's final verse inspired by a Far & Near news brief, in the same 17 January edition of the Daily Mail that had inspired the first two verses. [ 22 ] Under the headline "The holes in our roads", the brief stated: "There are 4,000 holes in the road in Blackburn, Lancashire, or one twenty-sixth of a hole per person, according to a council survey. If Blackburn is typical, there are two million holes in Britain's roads and 300,000 in London." [ 23 ]
In the Seinfeld episode The Pothole , George discovers that he has lost his keys, including a commemorative Phil Rizzuto keychain that says "Holy Cow" when activated. He then retraces his steps, and returns to a street where he had jumped over a pothole, which is now filled in with asphalt. The "Holy Cow" phrase is heard when a car runs over it. | https://en.wikipedia.org/wiki/Pothole |
A potion is a liquid "that contains medicine , poison , or something that is supposed to have magic powers." [ 1 ] It derives from the Latin word potio which refers to a drink or the act of drinking. [ 2 ] The term philtre is also used, often specifically to describe a love potion , a potion that is believed to induce feelings of love or attraction in the one who drinks it. [ 3 ] Throughout history, there have been several types of potions for a range of purposes. [ 4 ] Reasons for taking potions have included curing an illness, securing immortality , and trying to inspire love. These potions, while often ineffective or poisonous, occasionally had some degree of medicinal benegits depending on what they sought to fix and the type and amount of ingredients used. [ 5 ] Common ingredients in historical potions included Spanish fly , [ 6 ] nightshade plants , cannabis , and opium . [ 7 ]
During the 17th to 19th century, it was common in Europe to see peddlers offering potions for ailments ranging from heartbreak to the plague. These were eventually dismissed as quackery . [ 8 ] Prostitutes, courtesans, enchanters and midwives were also known to distribute potions. [ 9 ]
The word potion has its origins in the Latin word potus , an irregular past participle of potare , meaning "to drink". This evolved to the word potionem (nominative potio ) meaning either "a potion, a drinking" or a "poisonous draught, magic potion". [ 2 ] In Ancient Greek, the word for both drugs and potions was "pharmaka" or "pharmakon". [ 10 ] In the 12th century, the French had the word pocion , meaning "potion", "draught", or "medicine". By the 13th century, this word became pocioun , referring to either a medicinal drink, or a dose of liquid medicine (or poison).
The word "potion" is also cognate with the Spanish words pocion with the same meaning, and ponzoña , meaning "poison"; The word pozione was originally the same word for both "poison" and "potion" in Italian, but by the early 15th century in Italy, potion began to be known specifically as a magical or enchanted drink. [ 2 ]
The practice of administering potions has had a long history of being illegalised. Despite these laws, there have been several different administrators of potions across history. [ 5 ]
Quacks or charlatans are people who sell "medical methods that do not work and are only intended to make money". [ 11 ] In Europe in the 15th century it was also common to see long-distance peddlers , who sold supposedly magical healing potions and elixirs . [ 9 ] During the Great Plague of London in the 17th century, quacks sold many fake potions promising either cures or immunity. [ 12 ] Because pills looked less trustworthy to the public, potions were often the top sellers of quacks. [ 13 ] These potions often included bizarre ingredients such as floral pomanders and the smoke of fragrant woods. [ 14 ] The well known Wessex quack Vilbert was known to sell love potions made of pigeon hearts. [ 5 ] By the 18th century in England, it was common for middle class households to stock potions that claimed to solve a variety of ailments. Quackery grew to its height in the 19th century. [ 8 ]
In 18th- and 19th-century Britain, pharmacies or apothecaries were often a cheaper, more accessible option for medical treatment than doctors. [ 15 ] Potions distributed by chemists for illnesses were often derived from herbs and plants, and based on old beliefs and remedies. [ 16 ]
Prior to the Pharmacy Act 1868 anybody could become a pharmacist or chemist. Since the practice was unregulated, potions were often made from scratch. [ 17 ]
Potions were additionally used to cure illness in livestock. One potion found in a 19th-century pharmacist's recipe book was to be used for "lambs of about 7 years old" and contains chalk, pomegranate and opium. [ 17 ]
There was a strict hierarchy in the medical community of Europe during the 12th to 15th centuries. Male doctors were the most respected and paid followed by female apothecaries, barber-surgeons and surgeons. [ 18 ] Women were often the main way that individuals who could not afford doctors or apothecaries could gain medical treatment [ citation needed ] Potions, in addition to calming teas or soup, were a common homemade treatment made by women. When unable to go to a female house member, early modern people would often go to the wise women of their village. [ citation needed ] Wise women (who were often supposed witches ) were knowledgeable in health care [ 19 ] and could administer potions, lotions or salves in addition to performing prayers or chants. This was often free of charge or significantly less expensive than the potions of apothecaries. [ citation needed ]
The limited jobs available to women during the 17th to 18th century in Europe often involved a knowledge of potions as an additional way to gain a financial income. [ 20 ] Jobs that often involved the selling of love potions included prostitutes, courtesans, enchanters and midwives. [ 20 ] These practices varied by region. In Rome, up until the period of the civil wars , the only physicians were drug-sellers, enchanters and midwives. [ 21 ] In Greece, retired courtesans often both created potions and worked as midwives. [ 22 ] Prostitutes in Europe were often expected to be an expert in magic and administer love potions. [ 21 ] [ failed verification ]
In the Middle Ages and the early modern period, using potions to induce sterility and abortion was widely practiced in Europe. The majority of abortive potions were made using emmenagogue herbs (herbs used to stimulate menstruation) which were intended to cause a period and end a pregnancy. [ 23 ] Additionally abortive potions could also be prepared by infusion of herbs or other plants. For example, the willow tree was a common ingredient in these potions, as it was fabled to cause sterility. [ 24 ] Several key theological and legal literature of the time condemned this practice, including Visigothic law and the Church. [ 24 ]
Many herbal potions containing emmenagogues did not contain abortifacients (substances that induce abortion) and were instead used to cure amenorrhoea (a lack of period). There are several different types of literature in the humoral tradition that propose the use of herbal potions or suppositories to provoke menstruation. [ 23 ]
Giulia Tofana (1581-1651) was an Italian poisoner, known as the inventor of the famous poison Aqua Tofana . Born in Sicily, she invented and started to sell the poison in Palermo in Sicily. [ 25 ] She later established herself in Rome , where she continued the business, specialising in selling to women in abusive marriages who wanted to become widows. [ 25 ] She died peacefully in 1651 and left the business to her stepdaughter Gironima Spana , who expanded it to a substantial business in the 1650s. The organization was exposed in 1659 and resulted in the famous Spana Prosecution , which became a subject of sensationalistic mythologization for centuries. [ 25 ]
Paula de Eguiluz was born into slavery in Santo Domingo, Dominican Republic in the 17th century. Within the area in which she lived, sickness and disease ravaged the towns and major cities. Paula de Eguiluz decided to research and find her own cures to these maladies. Because of this, she is widely known for being involved in health care and healing.
Once her healing and health care practice took off, she started to sell potions and serums to clients. de Eguiluz's business attracted a following and slowly got her into a bit of trouble.
Due to Paula's healing accomplishments, she was arrested approximately 3 times. During these inquisitions, she was forced to tell the jury that she performed witchcraft. In response to these false confessions, she was imprisoned and whipped several times.
Catherine Monvoisin , better known to some as La Voisin, was born within the year 1640 in France.
Catherine Monvoisin married Antoine Monvoisin who was a jeweler in Paris. His business plummeted and Catherine had to find work in order for her and her family to survive. She had a knack for reading people very accurately coupled with chiromancy and utilized her skills in order to make money.
La Voisin would read people's horoscopes and perform abortions, but she also sold potions and poisons to her clients. Her work quickly became well known throughout France and people would quickly become her clients. Around the year 1665, her fortune telling was questioned by Saint Vincent de Paul's Order, but she was quick to dismiss the allegations of witchcraft.
Catherine would then begin making potions whether it be for love, murder, or everyday life. Her love potion consisted of bones, the teeth of moles, human blood, Spanish fly beetles, and even small amounts of human remains. Her predecessor and major influence was Giulia Tofana .
On March 12, 1679, Catherine was arrested Notre- Dame Bonne- Nouvelle due to a string of incidents involving her and her potions. She confessed her crimes of murder and told authorities a majority of everything they needed to know about the people she knowingly murdered.
On February 22, 1680, La Voisin was sentenced to a public death wherein she was to be burned as the stake for witchcraft.
Jacqueline Felice de Almania was tried in Italy in 1322 for the unlicensed practice of medicine. She was mainly accused of doing a learned male physicians job and accepting a fee. [ 26 ] This job involved "examining urine by its physical appearance; touching the body; and prescribing potions, digestives, and laxatives." [ 18 ] Eight witnesses testified to her medical experience and wisdom. However, as she had not attended university, her knowledge was dismissed. Jacqueline Felice was then found guilty and fined and excommunicated from the church. [ 18 ]
Emotions such as anger, fear, and sadness are universal [ 27 ] and as such potions have been created across history and cultures in response to these human emotions. [ 4 ]
Love potions have been used throughout history and cultures. [ 6 ] Scandinavians often used love-philtres, which is documented in the Norse poem The Lay of Gudrun . [ 5 ]
In 17th-century Cartagena , Afro-Mexican curer ( curanderos/as ) and other Indigenous healers could gain an income and status from selling spells and love potions to women trying to secure men and financial stability. [ 28 ] These love potions were sold to women of all social classes, who often wished to gain sexual agency. [ 28 ]
In the early 9th century, Arab physician Yuhanna ̄ Ibn Masawaih used the dye kermes to create a potion called Confectio Alchermes . The potion was "intended for the caliph and his court and not for commoners." [ 29 ] The potion was intended to cure heart palpitations, restore strength and cure madness and depression. [ 29 ]
During the Renaissance in Europe, Confectio Alchermes was used widely. Recipes for the potion appeared in the work of the popular English apothecary Nicholas Culpeper and the official pharmacopoeia handbooks of London and Amsterdam. Queen Elizabeth 's French ambassador was even treated with the remedy; however, the recipe was altered to include a "unicorn's horn" (possibly a ground-up narwhal tusk ) in addition to the traditional ingredients. [ 29 ] The ingredients for the potion mainly included ambergris, cinnamon, aloes, gold leaf, musk, pulverized lapis lazuli, and white pearls. [ 29 ]
St Paul's potion was intended to cure epilepsy, catalepsy and stomach problems. Many ingredients used in the potion had medicinal value. According to Toni Mount the list of ingredients included "liquorice, sage, willow, roses, fennel, cinnamon, ginger, cloves, cormorant blood, mandrake, dragon's blood and three kinds of pepper". [ 30 ]
Many of these ingredients still have medicinal value in the 21st century. Liquorice can be used to treat coughs and bronchitis. Sage can help memory and improve blood flow to the brain. Willow contains salicylic acid, which is a component of aspirin. Fennel , cinnamon and ginger are all carminatives, which help relieve gas in the intestines. The cormorant blood adds iron to treat anemia. If used in small doses, Mandrake is a good sleeping draught (though in large doses Mandrake can be poisonous.) Dragon's blood refers to the bright red resin of the tree Dracaena draco . According to Toni Mount "it has antiseptic, antibiotic, anti-viral and wound-healing properties, and it is still used in some parts of the world to treat dysentery." [ 30 ]
Creating a potion for immortality, was a common pursuit of alchemists throughout history. [ 31 ] The Elixir of Life is a famous potion that aimed to create eternal youth . [ 32 ] During the Chinese dynasties , this elixir of life was often recreated and drunk by emperors, nobles and officials. [ citation needed ] In India, there is a myth of the potion amrita , a drink of immortality made out of nectar. [ 33 ]
Ayahuasca , is a hallucinogenic plant-based potion used in many parts of the world. It was first created by indigenous South Americans from the Amazon basin as a spiritual medicine. [ 34 ] The potion was often administered by a shaman during a ceremony. The potion contains the boiled stems of the ayahuasca vine and leaves from the chacruna plant. Chacruna contains dimethyltryptamine (also known as DMT), a psychedelic drug. The potion caused users to vomit or 'purge' and induced hallucinations. [ 35 ]
Potions or mixtures are common within many of local mythologies. In particular, references to love potions are common in many cultures. [ 36 ] Yusufzai witches, for example, would bathe a recently deceased leatherworker and sell the water to those seeking a male partner; this practice is said to exist in a modified form in modern times. [ 36 ]
Potions have played a critical role in many pieces of literature. Shakespeare wrote potions into many of his plays including a love potion in A Midsummer Night's Dream , poison in Hamlet , and Juliet takes a potion to fake her death in Romeo and Juliet . [ 37 ]
In the fairytale " The Little Mermaid " by Hans Christian Andersen , the Little Mermaid wishes to become human and have an immortal soul. She visits the Sea Witch who sells her a potion, in exchange for which she cuts out the Little Mermaid's tongue. The Sea Witch makes the potion using her own blood that she cuts from her breast. She warns the Little Mermaid that it will feel as if she had been cut with a sword when her fin becomes legs, that she will never be able to become a mermaid again, and risks turning into seafoam and not having an immortal soul if she fails to win the Prince's love. The Little Mermaid decides to take the potion which successfully turns her into a human so that she can try to win the love of the Prince and an immortal soul. [ 38 ]
In the novella The Strange Case of Dr. Jekyll and Mr. Hyde by Robert Louis Stevenson, Dr. Henry Jekyll creates a potion that transforms him into an evil version of himself called Edward Hyde. Dr. Jekyll does not explain how he created this potion because he felt his "discoveries were incomplete," he only indicates that it requires a "particular salt." He uses the potion successfully to go back and forth between his normal self, Dr. Jekyll, and his evil self, Mr. Hyde.
In the Harry Potter series, potions also play a main role. [ citation needed ] The students are required to attend potion classes, taught by Severus Snape and Horace Slughorn and knowledge of potions often becomes a factor for many of the characters. Throughout the course of the story, several characters take Polyjuice Potion to impersonate other characters, while the use of Felix Felicus potion in Book 6 helps Harry Potter gain vital information about horcruxes.
In the 11th century, plants belonging to the nightshade family Solanaceae were often used as an ingredients in the potions - aphrodisiac or otherwise - and flying ointments of witches. The specific nightshades used in such concoctions were usually tropane alkaloid -containing species belonging to the Old World tribes Hyoscyameae and Mandragoreae . [ 4 ] These potions were known as pharmaka diabolika ("devilish drugs"). [ 4 ]
The root of Mandragora officinarum , the celebrated mandrake, fabled in legend to shriek when uprooted, was often used to prepare sleeping potions, although it could prove poisonous in excess, due to its tropane alkaloid content. [ 39 ] M. officinarum is native to the Mediterranean region . Administered in small doses mandrake root has been used in folk medicine as an analgesic , an aphrodisiac and a remedy for infertility. Larger doses act as an entheogen of the deliriant class, having the potential to cause profound confusion and dysphoria characterised by realistic hallucinations of an unpleasant character. Classical and Renaissance authors have left certain accounts of the use of the plant by witches in the preparation of potions intended variously to excite love, cause insanity or even kill. Scopolamine , a toxic, deliriant alkaloid present in (and named after) Scopolia carniolica and also present in Mandragora , Hyoscyamus and other Solanaceae, was used by the infamous Dr. Crippen to kill his wife. [ 40 ]
In ancient Greece, the Spanish fly (also known as cantharides) was crushed with herbs and used in love potions. It was believed to be effective due to the bodily warmth that resulted from ingesting it. However, this was actually a result of inflammation from toxins in the tissues of the beetle. Ferdinand II of Aragon drank many potions and elixir contains the Spanish fly. [ 41 ]
Cochineal , another type of dye, replaced kermes as an ingredient in Confectio Alchermes in the 17th and 18th centuries. Cochineal was also heavily used as an ingredient in potions for jaundice . Jaundice potions were a mix of Cochineal, cream of tartar and Venetian soap and patients were directed to take it three times a day. [ 42 ]
Cannabis and opium has been used in potions throughout human history. [ 7 ] Potions containing cannabis and/or opium were particularly popular in Arabia, Persia, and Muslim India after the arrival of the drugs around the 9th century. [ 43 ] Cannabis and opium were a common ingredient used in potions and tinctures sold by apothecaries in 19th-century Europe, as the ingredients made patients feel better, and the addictive nature of the drug meant it sold well. [ 16 ] Nepenthes pharmakon is a famous type of magical potion recorded in Homer's Odyssey, intended to cure sorrow. In Ancient Greek Pharmakon was the word for medicine and Nepenthes meant no ( ne) sorrow ( penthes). Since the 18th century it is believed to be made from opium. [ 7 ] | https://en.wikipedia.org/wiki/Potion |
Potocytosis is a type of receptor-mediated endocytosis in which small molecules are transported across the plasma membrane of a cell . The molecules are transported by caveolae (rather than clathrin -coated vesicles) and are deposited directly into the cytosol . [ 1 ]
Like other types of receptor-mediated endocytosis, potocytosis typically begins when an extracellular ligand binds to a receptor protein on the surface of a cell, thus beginning the formation of an endocytotic vesicle . The ligand is usually of low molecular mass (e.g. vitamins ), but some larger molecules (such as lipids ) can also act as ligands. [ 1 ] [ 2 ]
Lipid rafts in the plasma membrane act as membrane microdomains. They are enriched in cholesterol and sphingolipids and are involved potocytosis as the lateral compartmentalization of molecules. Caveolae are caveolin-1-enriched smooth invaginations found on these lipid rafts that contribute to transportation of molecules. [ 3 ] Potocytosis works by taking up material into caveolae at the surface of the cell. Glycosylphosphatidylinositol -anchored class of membrane proteins generate high concentrations of molecules. This may either be by releasing a receptor bound molecule, by converting molecules enzymatically or by releasing them from a carrier protein. [ 4 ] | https://en.wikipedia.org/wiki/Potocytosis |
A potometer' (from Greek ποτό = drunken, and μέτρο = measure), sometimes known as transpirometer , is a device used for measuring the rate of water uptake of a leafy shoot which is almost equal to the water lost through transpiration. The causes of water uptake are photosynthesis and transpiration . [ 1 ]
The rate of transpiration can be estimated in two ways:
There are two main types of potometers: the bubble potometer (as detailed below), and the mass potometer. The mass potometer consists of a plant with its root submerged in a beaker. This beaker is then placed on a digital balance; readings can be made to determine the amount of water lost by the plant.
Potometers come in a variety of designs, but all follow the same basic principle.
When a twig is cut from a plant, it should be immediately put under water (only the cut portion). Then, a small part is cut under water. This prevents entry of air into the xylem vessels.
The conditions of the potometer, other than the alteration that is being tested, should not be changed during a test, as outside conditions (such as temperature) determine water uptake.
Everything must be completely watertight so that no leakage occurs.
A potometer measures rate of water uptake, which is distinct from transpiration itself. This is because not all of the water that is taken by the plant is used for transpiration (water taken might be used for photosynthesis or by the cells to maintain turgidity ). To measure transpiration rate directly, rather than the rate of water uptake, utilize a scientific instrument which quantifies water transfer at the leaves. However, in general the water retained by the plant is so minute that it can be neglected. | https://en.wikipedia.org/wiki/Potometer |
PottersWheel is a MATLAB toolbox for mathematical modeling of time-dependent dynamical systems that can be expressed as chemical reaction networks or ordinary differential equations (ODEs). [ 1 ] It allows the automatic calibration of model parameters by fitting the model to experimental measurements. CPU-intensive functions are written or – in case of model dependent functions – dynamically generated in C. Modeling can be done interactively using graphical user interfaces or based on MATLAB scripts using the PottersWheel function library. The software is intended to support the work of a mathematical modeler as a real potter's wheel eases the modeling of pottery.
The basic use of PottersWheel covers seven phases from model creation to the prediction of new
experiments.
The dynamical system is formalized into a set of reactions or differential equations using a visual model designer or a text editor. The model is stored as a MATLAB *.m ASCII file. Modifications can therefore be tracked using a version control system like subversion or git . Model import and export is supported for SBML . Custom import-templates may be used to import custom model structures. Rule-based modeling is also supported, where a pattern represents a set of automatically generated reactions.
Example for a simple model definition file for a reaction network A → B → C → A with observed species A and C:
External data saved in *.xls or *.txt files can be added to a model creating a model-data-couple . A mapping dialog allows to connect data column names to observed species names. Meta information in the data files comprise information about the experimental setting. Measurement errors are either stored in the data files, will be calculated using an error model, or are estimated automatically.
To fit a model to one or more data sets, the corresponding model-data-couples are combined into a fitting-assembly . Parameters like initial values, rate constants, and scaling factors can be fitted in an experiment-wise or global fashion. The user may select from several numerical integrators, optimization algorithms, and calibration strategies like fitting in normal or logarithmic parameter space.
The quality of a fit is characterized by its chi-squared value. As a rule of thumb, for N fitted data points and p calibrated parameters, the chi-squared value should have a similar value
as N − p or at least N . Statistically, this is expressed using a chi-squared test resulting in a p-value above a significance threshold of e.g. 0.05. For lower p-values, the model is
Apart from further chi-squared based characteristics like AIC and BIC , data-model-residual analyses exist, e.g. to investigate whether the residuals follow a Gaussian distribution . Finally, parameter confidence intervals may be estimated using either the Fisher information matrix approximation or based on the profile-likelihood function , if parameters are not unambiguously identifiable.
If the fit is not acceptable, the model has to be refined and the procedure continues with step 2. Else, the dynamic model properties can be examined and predictions calculated.
If the model structure is not able to explain the experimental measurements, a set of physiologically reasonable alternative models should be created. In order to avoid redundant model paragraphs and copy-and-paste errors, this can be done using a common core-model which is the same for all variants. Then, daughter -models are created and fitted to the data, preferably using batch processing strategies based on MATLAB scripts. As a starting point to envision suitable model variants, the PottersWheel equalizer may be used to understand the dynamic behavior of the original system.
A mathematical model may serve to display the concentration time-profile of unobserved species, to determine sensitive parameters representing potential targets within a clinical setting, or to calculate model characteristics like the half-life of a species.
Each analysis step may be stored into a modeling report, which may be exported as a Latex-based PDF.
An experimental setting corresponds to specific characteristics of driving input functions and
initial concentrations. In a signal transduction pathway model the concentration of a ligand
like EGF may be controlled experimentally. The driving input designer allows investigating the effect of a continuous, ramp, or pulse stimulation in combination with varying initial concentrations using the equalizer. In order to discriminate competing model hypotheses, the designed experiment should have as different observable time-profiles as possible.
Many dynamical systems can only be observed partially, i.e. not all system species are accessible experimentally. For biological applications the amount and quality of experimental data is often limited. In this setting parameters can be structurally or practically non-identifiable. Then, parameters may compensate each other and fitted parameter values strongly depend on initial guesses. In PottersWheel non-identifiability can be detected using the Profile Likelihood Approach . [ 2 ] For characterizing functional relationships between the non-identifiable parameters PottersWheel applies random and systematic fit sequences. [ 3 ] | https://en.wikipedia.org/wiki/PottersWheel |
In statistical mechanics , the Potts model , a generalization of the Ising model , is a model of interacting spins on a crystalline lattice . [ 1 ] By studying the Potts model, one may gain insight into the behaviour of ferromagnets and certain other phenomena of solid-state physics . The strength of the Potts model is not so much that it models these physical systems well; it is rather that the one-dimensional case is exactly solvable , and that it has a rich mathematical formulation that has been studied extensively.
The model is named after Renfrey Potts , who described the model near the end of his 1951 Ph.D. thesis. [ 2 ] The model was related to the "planar Potts" or " clock model ", which was suggested to him by his advisor, Cyril Domb . The four-state Potts model is sometimes known as the Ashkin–Teller model , [ 3 ] after Julius Ashkin and Edward Teller , who considered an equivalent model in 1943.
The Potts model is related to, and generalized by, several other models, including the XY model , the Heisenberg model and the N-vector model . The infinite-range Potts model is known as the Kac model . When the spins are taken to interact in a non-Abelian manner, the model is related to the flux tube model , which is used to discuss confinement in quantum chromodynamics . Generalizations of the Potts model have also been used to model grain growth in metals, coarsening in foams , and statistical properties of proteins . [ 4 ] A further generalization of these methods by James Glazier and Francois Graner , known as the cellular Potts model , [ 5 ] has been used to simulate static and kinetic phenomena in foam and biological morphogenesis .
The Potts model consists of spins that are placed on a lattice ; the lattice is usually taken to be a two-dimensional rectangular Euclidean lattice, but is often generalized to other dimensions and lattice structures.
Originally, Domb suggested that the spin takes one of q {\displaystyle q} possible values [ citation needed ] , distributed uniformly about the circle , at angles
where s = 0 , 1 , . . . , q − 1 {\displaystyle s=0,1,...,q-1} and that the interaction Hamiltonian is given by
with the sum running over the nearest neighbor pairs ⟨ i , j ⟩ {\displaystyle \langle i,j\rangle } over all lattice sites, and J c {\displaystyle J_{c}} is a coupling constant, determining the interaction strength. This model is now known as the vector Potts model or the clock model . Potts provided the location in two dimensions of the phase transition for q = 3 , 4 {\displaystyle q=3,4} . In the limit q → ∞ {\displaystyle q\to \infty } , this becomes the XY model .
What is now known as the standard Potts model was suggested by Potts in the course of his study of the model above and is defined by a simpler Hamiltonian:
where δ ( s i , s j ) {\displaystyle \delta (s_{i},s_{j})} is the Kronecker delta , which equals one whenever s i = s j {\displaystyle s_{i}=s_{j}} and zero otherwise.
The q = 2 {\displaystyle q=2} standard Potts model is equivalent to the Ising model and the 2-state vector Potts model, with J p = − 2 J c {\displaystyle J_{p}=-2J_{c}} . The q = 3 {\displaystyle q=3} standard Potts model is equivalent to the three-state vector Potts model, with J p = − 3 2 J c {\displaystyle J_{p}=-{\frac {3}{2}}J_{c}} .
A generalization of the Potts model is often used in statistical inference and biophysics, particularly for modelling proteins through direct coupling analysis . [ 4 ] [ 6 ] This generalized Potts model consists of 'spins' that each may take on q {\displaystyle q} states: s i ∈ { 1 , … , q } {\displaystyle s_{i}\in \{1,\dots ,q\}} (with no particular ordering). The Hamiltonian is,
where J i j ( k , k ′ ) {\displaystyle J_{ij}(k,k')} is the energetic cost of spin i {\displaystyle i} being in state k {\displaystyle k} while spin j {\displaystyle j} is in state k ′ {\displaystyle k'} , and h i ( k ) {\displaystyle h_{i}(k)} is the energetic cost of spin i {\displaystyle i} being in state k {\displaystyle k} . Note: J i j ( k , k ′ ) = J j i ( k ′ , k ) {\displaystyle J_{ij}(k,k')=J_{ji}(k',k)} . This model resembles the Sherrington-Kirkpatrick model in that couplings can be heterogeneous and non-local. There is no explicit lattice structure in this model.
Despite its simplicity as a model of a physical system, the Potts model is useful as a model system for the study of phase transitions . For example, for the standard ferromagnetic Potts model in 2 d {\displaystyle 2d} , a phase transition exists for all real values q ≥ 1 {\displaystyle q\geq 1} , [ 7 ] with the critical point at β J = log ( 1 + q ) {\displaystyle \beta J=\log(1+{\sqrt {q}})} . The phase transition is continuous (second order) for 1 ≤ q ≤ 4 {\displaystyle 1\leq q\leq 4} [ 8 ] and discontinuous (first order) for q > 4 {\displaystyle q>4} . [ 9 ]
For the clock model, there is evidence that the corresponding phase transitions are infinite order BKT transitions , [ 10 ] and a continuous phase transition is observed when q ≤ 4 {\displaystyle q\leq 4} . [ 10 ] Further use is found through the model's relation to percolation problems and the Tutte and chromatic polynomials found in combinatorics. For integer values of q ≥ 3 {\displaystyle q\geq 3} , the model displays the phenomenon of 'interfacial adsorption' [ 11 ] with intriguing critical wetting properties when fixing opposite boundaries in two different states [ clarification needed ] .
The Potts model has a close relation to the Fortuin- Kasteleyn random cluster model , another model in statistical mechanics . Understanding this relationship has helped develop efficient Markov chain Monte Carlo methods for numerical exploration of the model at small q {\displaystyle q} , and led to the rigorous proof of the critical temperature of the model. [ 7 ]
At the level of the partition function Z p = ∑ { s i } e − H p {\displaystyle Z_{p}=\sum _{\{s_{i}\}}e^{-H_{p}}} , the relation amounts to transforming the sum over spin configurations { s i } {\displaystyle \{s_{i}\}} into a sum over edge configurations ω = { ( i , j ) | s i = s j } {\displaystyle \omega ={\Big \{}(i,j){\Big |}s_{i}=s_{j}{\Big \}}} i.e. sets of nearest neighbor pairs of the same color. The transformation is done using the identity [ 12 ]
This leads to rewriting the partition function as
where the FK clusters are the connected components of the union of closed segments ∪ ( i , j ) ∈ ω [ i , j ] {\displaystyle \cup _{(i,j)\in \omega }[i,j]} . This is proportional to the partition function of the random cluster model with the open edge probability p = v 1 + v = 1 − e − J p {\displaystyle p={\frac {v}{1+v}}=1-e^{-J_{p}}} . An advantage of the random cluster formulation is that q {\displaystyle q} can be an arbitrary complex number, rather than a natural integer.
Alternatively, instead of FK clusters, the model can be formulated in terms of spin clusters , using the identity
A spin cluster is the union of neighbouring FK clusters with the same color: two neighbouring spin clusters have different colors, while two neighbouring FK clusters are colored independently.
The one dimensional Potts model may be expressed in terms of a subshift of finite type , and thus gains access to all of the mathematical techniques associated with this formalism. In particular, it can be solved exactly using the techniques of transfer operators . (However, Ernst Ising used combinatorial methods to solve the Ising model , which is the "ancestor" of the Potts model, in his 1924 PhD thesis). This section develops the mathematical formalism, based on measure theory , behind this solution.
While the example below is developed for the one-dimensional case, many of the arguments, and almost all of the notation, generalizes easily to any number of dimensions. Some of the formalism is also broad enough to handle related models, such as the XY model , the Heisenberg model and the N-vector model .
Let Q = {1, ..., q } be a finite set of symbols, and let
be the set of all bi-infinite strings of values from the set Q . This set is called a full shift . For defining the Potts model, either this whole space, or a certain subset of it, a subshift of finite type , may be used. Shifts get this name because there exists a natural operator on this space, the shift operator τ : Q Z → Q Z , acting as
This set has a natural product topology ; the base for this topology are the cylinder sets
that is, the set of all possible strings where k +1 spins match up exactly to a given, specific set of values ξ 0 , ..., ξ k . Explicit representations for the cylinder sets can be gotten by noting that the string of values corresponds to a q -adic number , however the natural topology of the q-adic numbers is finer than the above product topology.
The interaction between the spins is then given by a continuous function V : Q Z → R on this topology. Any continuous function will do; for example
will be seen to describe the interaction between nearest neighbors. Of course, different functions give different interactions; so a function of s 0 , s 1 and s 2 will describe a next-nearest neighbor interaction. A function V gives interaction energy between a set of spins; it is not the Hamiltonian, but is used to build it. The argument to the function V is an element s ∈ Q Z , that is, an infinite string of spins. In the above example, the function V just picked out two spins out of the infinite string: the values s 0 and s 1 . In general, the function V may depend on some or all of the spins; currently, only those that depend on a finite number are exactly solvable.
Define the function H n : Q Z → R as
This function can be seen to consist of two parts: the self-energy of a configuration [ s 0 , s 1 , ..., s n ] of spins, plus the interaction energy of this set and all the other spins in the lattice. The n → ∞ limit of this function is the Hamiltonian of the system; for finite n , these are sometimes called the finite state Hamiltonians .
The corresponding finite-state partition function is given by
with C 0 being the cylinder sets defined above. Here, β = 1/ kT , where k is the Boltzmann constant , and T is the temperature . It is very common in mathematical treatments to set β = 1, as it is easily regained by rescaling the interaction energy. This partition function is written as a function of the interaction V to emphasize that it is only a function of the interaction, and not of any specific configuration of spins. The partition function, together with the Hamiltonian, are used to define a measure on the Borel σ-algebra in the following way: The measure of a cylinder set, i.e. an element of the base, is given by
One can then extend by countable additivity to the full σ-algebra. This measure is a probability measure ; it gives the likelihood of a given configuration occurring in the configuration space Q Z . By endowing the configuration space with a probability measure built from a Hamiltonian in this way, the configuration space turns into a canonical ensemble .
Most thermodynamic properties can be expressed directly in terms of the partition function. Thus, for example, the Helmholtz free energy is given by
Another important related quantity is the topological pressure , defined as
which will show up as the logarithm of the leading eigenvalue of the transfer operator of the solution.
The simplest model is the model where there is no interaction at all, and so V = c and H n = c (with c constant and independent of any spin configuration). The partition function becomes
If all states are allowed, that is, the underlying set of states is given by a full shift , then the sum may be trivially evaluated as
If neighboring spins are only allowed in certain specific configurations, then the state space is given by a subshift of finite type . The partition function may then be written as
where card is the cardinality or count of a set, and Fix is the set of fixed points of the iterated shift function:
The q × q matrix A is the adjacency matrix specifying which neighboring spin values are allowed.
The simplest case of the interacting model is the Ising model , where the spin can only take on one of two values, s n ∈ {−1, 1} and only nearest neighbor spins interact. The interaction potential is given by
This potential can be captured in a 2 × 2 matrix with matrix elements
with the index σ, σ′ ∈ {−1, 1}. The partition function is then given by
The general solution for an arbitrary number of spins, and an arbitrary finite-range interaction, is given by the same general form. In this case, the precise expression for the matrix M is a bit more complex.
The goal of solving a model such as the Potts model is to give an exact closed-form expression for the partition function and an expression for the Gibbs states or equilibrium states in the limit of n → ∞, the thermodynamic limit .
The Potts model has applications in signal reconstruction. Assume that we are given noisy observation of a piecewise constant signal g in R n . To recover g from the noisy observation vector f in R n , one seeks a minimizer of the corresponding inverse problem, the L p -Potts functional P γ ( u ), which is defined by
The jump penalty ‖ ∇ u ‖ 0 {\displaystyle \|\nabla u\|_{0}} forces piecewise constant solutions and the data term ‖ u − f ‖ p p {\displaystyle \|u-f\|_{p}^{p}} couples the minimizing candidate u to the data f . The parameter γ > 0 controls the tradeoff between regularity and data fidelity . There are fast algorithms for the exact minimization of the L 1 and the L 2 -Potts functional. [ 13 ]
In image processing, the Potts functional is related to the segmentation problem. [ 14 ] However, in two dimensions the problem is NP-hard. [ 15 ] | https://en.wikipedia.org/wiki/Potts_model |
In physics and chemical engineering , the term Pouillet effect refers to an exothermic reaction that takes place when a liquid is added to a powder. Strictly speaking, the heat generated is caused by adhesion of the liquid to the surface of the particles rather than by a chemical reaction. [ 1 ] It was first observed in 1802 by physicist John Leslie , who noted that heat was evolved when dry sawdust was wetted with water. [ 2 ] Claude Pouillet later described this phenomenon in 1822, and it subsequently became known as the Pouillet effect in France, and then elsewhere. [ 3 ] [ 4 ]
Under certain conditions, a negative Pouillet effect is possible, i.e., heat can be absorbed instead of being released. G. Schwalbe showed that in the case of water below 4 degrees Celsius, the temperature of the system decreases. [ 5 ] Joseph Mellor argued that this is due to the negative thermal expansion coefficient of water between 0 and 4 degrees Celsius, [ 6 ] with the temperature change Δ T {\displaystyle \Delta T} given by
Δ T = α T C p D Δ P {\displaystyle \Delta T={{\alpha T} \over {C_{p}D}}\Delta P}
where α {\displaystyle \alpha } is the thermal expansion coefficient, C P {\displaystyle C_{P}} is the specific heat , D {\displaystyle D} is the specific gravity , and Δ P {\displaystyle \Delta P} is the applied pressure due to the addition of the liquid. According to this formula, any liquid with a negative thermal expansion coefficient would be expected to exhibit a drop in temperature. | https://en.wikipedia.org/wiki/Pouillet_effect |
Poul Jørgensen (born 2 March 1944 in Silkeborg , Denmark) is professor of chemistry at the Department of Chemistry, Aarhus University (AU), Denmark and director of the qLEAP Center for Theoretical Chemistry at AU, [ 1 ] which was established in April 2012.
Jørgensen has made seminal contributions to the field of electronic structure theory. He is also one of the main authors of the DALTON program and a member of the International Academy of Quantum Molecular Science .
Jørgensen's list of peer-reviewed publications contains numerous self-contained articles which, in many cases, have become central sources within the field of electronic structure theory. His areas of research have been diverse and include work on:
Jørgensen has written more than 350 publications in peer-reviewed international journals, in addition to four books (3 co-authored and 1 edited),
He had more than 19,000 citations and a h-index of 68 (according to ISI Web of Knowledge database). [ citation needed ]
He has also organized the "Sostrup Summer School - Quantum Chemistry and Molecular Properties" alongside Trygve Helgaker and Jeppe Olsen biannually since 1990.
Jørgensen's career has been outlined in a Special Issue of Advances in Quantum Chemistry [ 14 ] | https://en.wikipedia.org/wiki/Poul_Jørgensen_(chemist) |
The pour point of a liquid is the temperature below which the liquid loses its flow characteristics.
It is defined as the minimum temperature in which the oil has the ability to pour down from a beaker. [ 1 ] [ 2 ] In crude oil a high pour point is generally associated with a high paraffin content, typically found in crude deriving from a larger proportion of plant material. That type of crude oil is mainly derived from a kerogen Type III.
ASTM D97, Standard Test Method for Pour Point of Crude Oils. The specimen is cooled inside a cooling bath to allow the formation of paraffin wax crystals. At about 9 °C (16 °F) above the expected pour point, and for every subsequent 3 °C (5.4 °F), the test jar is removed and tilted to check for surface movement. When the specimen does not flow when tilted, the jar is held horizontally for 5 seconds. If it does not flow, 3 °C is added to the corresponding temperature and the result is the pour point temperature.
It is also useful to note that failure to flow at the pour point may also be due to the effect of viscosity or the previous thermal history of the specimen. Therefore, the pour point may give a misleading view of the handling properties of the oil. Additional fluidity tests may also be undertaken. An approximate range of pour point can be observed from the specimen's upper and lower pour point.
ASTM D5949, Standard Test Method for Pour Point of Petroleum Products (Automatic Pressure Pulsing Method) is an alternative to the manual test procedure. It uses automatic apparatus and yields pour point results in a format similar to the manual method (ASTM D97) when reporting at a 3 °C. [ 3 ]
The D5949 test method determines the pour point in a shorter period of time than manual method D97. Less operator time is required to run the test using this automatic method. Additionally, no external chiller bath or refrigeration unit is needed. D5949 is capable of determining pour point within a temperature range of −57 to 51 °C (−71 to 124 °F). Results can be reported at 1 °C (1.8 °F) or 3 °C testing intervals. This test method has better repeatability and reproducibility than manual method D97.
Under ASTM D5949, the test sample is heated and then cooled by a Peltier device at a rate of 1.5±0.1 °C/min. At either 1 °C or 3 °C intervals, a pressurized pulse of compressed gas is imparted onto the surface of the sample. Multiple optical detectors continuously monitor the sample for movement. The lowest temperature at which movement is detected on the sample surface is determined to be the pour point.
Two pour points can be derived which can give an approximate temperature window depending on its thermal history. Within this temperature range, the sample may appear liquid or solid. This happens because wax crystals form less readily when it has been heated within the past 24 hours and contributes to the lower pour point.
The upper pour point is measured by pouring the test sample directly into a test jar. The sample is then cooled and inspected for pour point as per the usual pour point method. The method usually gives higher pour point because the thermal history has not been cancelled by a prolonged thermal treatment.
The lower pour point is measured by first pouring the sample into a stainless steel pressure vessel . The vessel is then screwed tight and heated to above 102 °C (216 °F) in an oil bath. After a specified time, the vessel is removed and cooled for a short while. The sample is then poured into a test jar and immediately closed with a cork carrying the thermometer . The sample is then cooled and then inspected for pour point as per the usual pour point method. | https://en.wikipedia.org/wiki/Pour_point |
In electrochemistry , and more generally in solution chemistry, a Pourbaix diagram , also known as a potential/pH diagram , E H –pH diagram or a pE/pH diagram , is a plot of possible thermodynamically stable phases ( i.e. , at chemical equilibrium ) of an aqueous electrochemical system. Boundaries (50 %/50 %) between the predominant chemical species (aqueous ions in solution, or solid phases) are represented by lines. As such a Pourbaix diagram can be read much like a standard phase diagram with a different set of axes. Similarly to phase diagrams, they do not allow for reaction rate or kinetic effects. Beside potential and pH, the equilibrium concentrations are also dependent upon, e.g., temperature, pressure, and concentration. Pourbaix diagrams are commonly given at room temperature, atmospheric pressure, and molar concentrations of 10 −6 and changing any of these parameters will yield a different diagram.
The diagrams are named after Marcel Pourbaix (1904–1998), the Belgian engineer who invented them.
Pourbaix diagrams are also known as E H -pH diagrams due to the labeling of the two axes.
The vertical axis is labeled E H for the voltage potential with respect to the standard hydrogen electrode (SHE) as calculated by the Nernst equation . The "H" stands for hydrogen, although other standards may be used, and they are for room temperature only.
For a reversible redox reaction described by the following chemical equilibrium :
With the corresponding equilibrium constant K :
The Nernst equation is:
sometimes formulated as:
or, more simply directly expressed numerically as:
where:
The horizontal axis is labeled pH for the −log function of the H + ion activity.
The lines in the Pourbaix diagram show the equilibrium conditions, that is, where the activities are equal, for the species on each side of that line. On either side of the line, one form of the species will instead be said to be predominant. [ 3 ]
In order to draw the position of the lines with the Nernst equation, the activity of the chemical species at equilibrium must be defined. Usually, the activity of a species is approximated as equal to the concentration (for soluble species) or partial pressure (for gases). The same values should be used for all species present in the system. [ 3 ]
For soluble species, the lines are often drawn for concentrations of 1 M or 10 −6 M. Sometimes additional lines are drawn for other concentrations.
If the diagram involves the equilibrium between a dissolved species and a gas, the pressure is usually set to P 0 = 1 atm = 101 325 Pa , the minimum pressure required for gas evolution from an aqueous solution at standard conditions. [ 3 ]
In addition, changes in temperature and concentration of solvated ions in solution will shift the equilibrium lines in accordance with the Nernst equation.
The diagrams also do not take kinetic effects into account, meaning that species shown as unstable might not react to any significant degree in practice.
A simplified Pourbaix diagram indicates regions of "immunity", "corrosion" and "passivity", instead of the stable species. They thus give a guide to the stability of a particular metal in a specific environment. Immunity means that the metal is not attacked, while corrosion shows that general attack will occur. Passivation occurs when the metal forms a stable coating of an oxide or other salt on its surface, the best example being the relative stability of aluminium because of the alumina layer formed on its surface when exposed to air.
While such diagrams can be drawn for any chemical system, it is important to note that the addition of a metal binding agent ( ligand ) will often modify the diagram. For instance, carbonate ( CO 2− 3 ) has a great effect upon the diagram for uranium. (See diagrams at right). The presence of trace amounts of certain species such as chloride ions can also greatly affect the stability of certain species by destroying passivating layers.
Even though Pourbaix diagrams are useful for a metal corrosion potential estimation they have, however, some important limitations: [ 4 ] : 111
The E h {\displaystyle E_{h}} and pH of a solution are related by the Nernst equation as commonly represented by a Pourbaix diagram ( E h {\displaystyle E_{h}} – pH plot) . E h {\displaystyle E_{h}} explicitly denotes E red {\displaystyle E_{\text{red}}} expressed versus the standard hydrogen electrode (SHE). For a half cell equation, conventionally written as a reduction reaction ( i.e. , electrons accepted by an oxidant on the left side):
The equilibrium constant K of this reduction reaction is:
where curly braces { } indicate activities ( a ), rectangle braces [ ] denote molar or molal concentrations ( C ), γ {\displaystyle \gamma } represent the activity coefficients , and the stoichiometric coefficients are shown as exponents.
Activities correspond to thermodynamic concentrations and take into account the electrostatic interactions between ions present in solution. When the concentrations are not too high, the activity ( a i {\displaystyle a_{i}} ) can be related to the measurable concentration ( C i {\displaystyle C_{i}} ) by a linear relationship with the activity coefficient ( γ i {\displaystyle \gamma _{i}} ):
The half-cell standard reduction potential E red ⊖ {\displaystyle E_{\text{red}}^{\ominus }} is given by
where Δ G ⊖ {\displaystyle \Delta G^{\ominus }} is the standard Gibbs free energy change, z is the number of electrons involved, and F is the Faraday's constant . The Nernst equation relates pH and E h {\displaystyle E_{h}} as follows:
In the following, the Nernst slope (or thermal voltage ) V T = R T / F {\displaystyle V_{T}=RT/F} is used, which has a value of 0.02569... V at STP . When base-10 logarithms are used, V T λ = 0.05916... V at STP where λ = ln[10] = 2.3026.
This equation is the equation of a straight line for E red {\displaystyle E_{\text{red}}} as a function of pH with a slope of − 0.05916 ( h z ) {\displaystyle -0.05916\,\left({\frac {h}{z}}\right)} volt (pH has no units).
This equation predicts lower E red {\displaystyle E_{\text{red}}} at higher pH values. This is observed for the reduction of O 2 into H 2 O, or OH − , and for reduction of H + into H 2 . E red {\displaystyle E_{\text{red}}} is then often noted as E h {\displaystyle E_{h}} to indicate that it refers to the standard hydrogen electrode (SHE) whose E red {\displaystyle E_{\text{red}}} = 0 by convention under standard conditions (T = 298.15 K = 25 °C = 77 F, P gas = 1 atm (1.013 bar), concentrations = 1 M and thus pH = 0).
When the activities ( a i {\displaystyle a_{i}} ) can be considered as equal to the molar , or the molal , concentrations ( C i {\displaystyle C_{i}} ) at sufficiently diluted concentrations when the activity coefficients ( γ i {\displaystyle \gamma _{i}} ) tend to one, the term regrouping all the activity coefficients is equal to one, and the Nernst equation can be written simply with the concentrations ( C i {\displaystyle C_{i}} ) denoted here with square braces [ ]:
There are three types of line boundaries in a Pourbaix diagram: Vertical, horizontal, and sloped. [ 5 ] [ 6 ]
When no electrons are exchanged ( z = 0), the equilibrium between A , B , C , and D only depends on [H + ] and is not affected by the electrode potential. In this case, the reaction is a classical acid-base reaction involving only protonation /deprotonation of dissolved species. The boundary line will be a vertical line at a particular value of pH. The reaction equation may be written:
and the energy balance is written as Δ G ∘ = − R T ln K {\displaystyle \Delta G^{\circ }=-RT\ln K} , where K is the equilibrium constant :
Thus:
or, in base-10 logarithms,
which may be solved for the particular value of pH.
For example [ 5 ] consider the iron and water system, and the equilibrium line between the ferric ion Fe 3+ ion and hematite Fe 2 O 3 . The reaction equation is:
which has Δ G ∘ = − 8242.5 J / m o l {\displaystyle \Delta G^{\circ }=-8242.5\,\mathrm {J/mol} } . [ 5 ] The pH of the vertical line on the Pourbaix diagram can then be calculated:
Because the activities (or the concentrations) of the solid phases and water are equal to unity: [Fe 2 O 3 ] = [H 2 O] = 1, the pH only depends on the concentration in dissolved Fe 3+ :
At STP, for [Fe 3+ ] = 10 −6 , this yields pH = 1.76.
When H + and OH − ions are not involved in the reaction, the boundary line is horizontal and independent of pH. The reaction equation is thus written:
As, the standard Gibbs free energy Δ G ∘ = − R T ln K {\displaystyle \Delta G^{\circ }=-RT\ln K} :
Using the definition of the electrode potential ∆G = -zFE , where F is the Faraday constant , this may be rewritten as a Nernst equation:
or, using base-10 logarithms:
For the equilibrium Fe 2+ / Fe 3+ , taken as example here, considering the boundary line between Fe 2+ and Fe 3+ , the half-reaction equation is:
Since H + ions are not involved in this redox reaction, it is independent of pH. E o = 0.771 V with only one electron involved in the redox reaction. [ 7 ] The potential E h is a function of temperature via the thermal voltage V T {\displaystyle V_{T}} and directly depends on the ratio of the concentrations of the Fe 2+ and Fe 3+ ions:
For both ionic species at the same concentration (e.g., 10 − 6 M {\displaystyle 10^{-6}\mathrm {M} } ) at STP, log 1 = 0, so, E h = E ∘ = 0.771 V {\displaystyle E_{h}=E^{\circ }=0.771\,\mathrm {V} } , and the boundary will be a horizontal line at E h = 0.771 volts. The potential will vary with temperature.
In this case, both electrons and H + ions are involved and the electrode potential is a function of pH. The reaction equation may be written:
Using the expressions for the free energy in terms of potentials, the energy balance is given by a Nernst equation:
For the iron and water example, considering the boundary line between the ferrous ion Fe 2+ and hematite Fe 2 O 3 , the reaction equation is:
The equation of the boundary line, expressed in base-10 logarithms is:
As, the activities, or the concentrations, of the solid phases and water are always taken equal to unity by convention in the definition of the equilibrium constant K : [Fe 2 O 3 ] = [H 2 O] = 1.
The Nernst equation thus limited to the dissolved species Fe 2+ and H + is written as:
For, [Fe 2+ ] = 10 −6 M, this yields:
Note the negative slope (−0.1775) of this line in a E h –pH diagram.
In many cases, the possible conditions in a system are limited by the stability region of water. In the Pourbaix diagram for uranium presented here above, the limits of stability of water are marked by the two dashed green lines, and the stability region for water falls between these two lines. It is also depicted here beside by the two dashed red lines in the simplified Pourbaix diagram restricted to the water stability region only.
Under highly reducing conditions (low E H ), water is reduced to hydrogen according to: [ 3 ]
and,
Using the Nernst equation, setting E 0 = 0 V as defined by convention for the standard hydrogen electrode (SHE, serving as reference in the reduction potentials series) and the hydrogen gas fugacity (corresponding to chemical activity for a gas) at 1, the equation for the lower stability line of water in the Pourbaix diagram at standard temperature and pressure is:
Below this line, water is reduced to hydrogen, and it will usually not be possible to pass beyond this line as long as there is still water present in the system to be reduced.
Correspondingly, under highly oxidizing conditions (high E H ) water is oxidized into oxygen gas according to: [ 3 ]
and,
Using the Nernst equation as above, but with E 0 = −ΔG 0 H 2 O /2 F = 1.229 V for water oxidation, gives an upper stability limit of water as a function of the pH value:
at standard temperature and pressure. Above this line, water is oxidized to form oxygen gas, and it will usually not be possible to pass beyond this line as long as there is still water present in the system to be oxidized.
The two upper and lower stability lines having the same negative slope (−59 mV/pH unit), they are parallel in a Pourbaix diagram and the reduction potential decreases with pH.
Pourbaix diagrams have many applications in different fields dealing with e.g. , corrosion problems, geochemistry , and environmental sciences . Using the Pourbaix diagram correctly will help shedding light not only on the nature of the species present in aqueous solution , or in the solid phases , but may also help to understand the reaction mechanism . [ 8 ]
Pourbaix diagrams are widely used to describe the behaviour of chemical species in the hydrosphere . In this context, reduction potential pe is often used instead of E H . [ 3 ] The main advantage is to directly work with a logarithm scale. pe is a dimensionless number and can easily be related to E H by the equation:
Where, V T = R T F {\displaystyle V_{T}={\frac {RT}{F}}} is the thermal voltage , with R , the gas constant ( 8.314 J⋅K −1 ⋅mol −1 ), T , the absolute temperature in Kelvin (298.15 K = 25 °C = 77 °F), and F , the Faraday constant (96 485 coulomb/mol of e − ). Lambda, λ = ln(10) ≈ 2.3026.
Moreover,
pe values in environmental chemistry ranges from −12 to +25, since at low or high potentials water will be respectively reduced or oxidized. In environmental applications, the concentration of dissolved species is usually set to a value between 10 −2 M and 10 −5 M for the determination of the equilibrium lines. | https://en.wikipedia.org/wiki/Pourbaix_diagram |
The Pournelle chart , developed by Jerry Pournelle in his 1963 political science Ph.D. dissertation, is a two-dimensional coordinate system which can be used to distinguish political ideologies . It is similar to the political compass and the Nolan Chart in that it is a two-dimensional chart, but the axes of the Pournelle chart are different from those of other systems. The two axes are as follows:
Pournelle arranged American liberalism , socialism , and communism , in the upper right-hand quadrant of high state control and high rationalism. Conservatism , fascism , and Nazism are placed in the lower right-hand quadrant of high state control and low rationalism. Classical anarchists are in the lower left-hand corner of low state control and low rationalism. Libertarians (including anarcho-capitalists ) and Objectivists are placed in the upper left-hand corner of low state control and high rationalism. Each diagonal axis contains natural political allies. | https://en.wikipedia.org/wiki/Pournelle_chart |
In number theory , a branch of mathematics , the Poussin proof is the proof of an identity related to the fractional part of a ratio .
In 1838, Peter Gustav Lejeune Dirichlet proved an approximate formula for the average number of divisors of all the numbers from 1 to n:
where d represents the divisor function , and γ represents the Euler-Mascheroni constant .
In 1898, Charles Jean de la Vallée-Poussin proved that if a large number n is divided by all the primes up to n, then the average fraction by which the quotient falls short of the next whole number is γ:
where { x } represents the fractional part of x , and π represents the prime-counting function .
For example, if we divide 29 by 2, we get 14.5, which falls short of 15 by 0.5.
This number theory -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Poussin_proof |
The Povarov reaction is an organic reaction described as a formal cycloaddition between an aromatic imine and an alkene . The imine in this organic reaction is a condensation reaction product from an aniline type compound and a benzaldehyde type compound. [ 1 ] [ 2 ] [ 3 ] The alkene must be electron rich which means that functional groups attached to the alkene must be able to donate electrons. Such alkenes are enol ethers and enamines . The reaction product in the original Povarov reaction is a quinoline . Because the reactions can be carried out with the three components premixed in one reactor it is an example of a multi-component reaction .
The reaction mechanism for the Povarov reaction to the quinoline is outlined in Scheme 1. In step one aniline and benzaldehyde react to the Schiff base in a condensation reaction . The Povarov reaction requires a Lewis acid such as boron trifluoride to activate the imine for an electrophilic addition of the activated alkene . This reaction step forms an oxonium ion which then reacts with the aromatic ring in a classical electrophilic aromatic substitution . Two additional elimination reactions create the quinoline ring structure.
The reaction is also classified as a subset of aza Diels-Alder reactions ; [ 4 ] however, it occurs by a step-wise rather than concerted mechanism.
The reaction depicted in Scheme 2 illustrates the Povarov reaction with an imine and an enamine in the presence of yttrium triflate as the Lewis acid . [ 5 ] This reaction is regioselective because the iminium ion preferentially attacks the nitro ortho position and not the para position. The nitro group is a meta directing substituent but since this position is blocked, the most electron rich ring position is now ortho and not para. The reaction is also stereoselective because the enamine addition occurs with a diastereomeric preference for trans addition without formation of the cis isomer. This is in contrast to traditional Diels–Alder reactions, which are stereospecific based on the alkene geometry.
In 2013, Doyle and coworkers reported a Povarov-type, formal [4+2]-cycloaddition reaction between donor-acceptor cyclopropenes and imines (Scheme 3). In the first step, a dirhodium catalyst effects diazo decomposition from silyl enol ether diazo compound to yield a donor/acceptor cyclopropene. The donor/acceptor cyclopropene is then reacted with an aryl imine under scandium(III) triflate catalyzed conditions to yield cyclopropane-fused tetrahydroquinolines in good yields and diastereoselectivities. Treatment of these compounds with TBAF invokes a ring-expansion that provides the corresponding benzazepines. [ 6 ]
One variation of the Povarov reaction is a four component reaction. [ 7 ] Whereas in the traditional Povarov reaction the intermediate carbocation gives an intramolecular reaction with the aryl group, this intermediate can also be terminated by an additional nucleophile such as an alcohol . Scheme 4 depicts this 4 component reaction with the ethyl ester of glyoxylic acid , 3,4-dihydro-2H-pyran, aniline and ethanol with lewis acid scandium(III) triflate and molecular sieves . | https://en.wikipedia.org/wiki/Povarov_reaction |
Powa Technologies was a UK-based technology company, known for its commerce, mobile commerce and e-commerce services.
The company’s flagship product was the mobile application PowaTag . [ 1 ] In February 2016, investment company Wellington Management appointed professional services firm Deloitte as administrators of Powa Technologies. [ 2 ]
Powa was founded in 2007 by British entrepreneur Dan Wagner . The company received the largest Series A funding round for a technology start-up at the time, collecting $76 million in August 2013. [ 3 ] The investment attracted the attention of David Cameron . [ 4 ]
In June 2014, Powa Technologies acquired Hong Kong business MPayMe and its ZNAP technology. Following the acquisition, Wagner suggested that Powa had an enterprise value of $2.6 billion. [ 5 ] [ 6 ]
In 2015, they announced that their planned LSE £1.6 billion float would be put on hold until the following year. [ 7 ] By early 2016, the company had run into financial difficulties, missing payments to staff and third parties. [ 8 ] Its Hong Kong office had failed to pay its employees wages on time and to its ex-employees within 7 days, with some employees having to seek help from the Labor Department. On 28 January 2016, Alessandro Gadotti became CEO of PowaTag in the effort of restructuring the business. During the administration, he also served as interim CEO for the Group, supporting the process and the sale of the companies in the group. On 19 February 2016, Powa Technologies was placed into administration, [ 9 ] and on 23 February 2016, Powa Technologies made 74 of its London-based staff redundant. [ 10 ] On 24 February 2016, Powa Technologies filed for bankruptcy and laid off most of their employees. [ 11 ] The investment company Wellington Management appointed professional services firm Deloitte as administrators of PowaTag. [ 12 ]
Business Insider revealed that most of Powa's 'contracts' had in fact only been non-binding letters of intent ; [ 13 ] and on 2 March 2016, Sky News revealed that two of Powa's core businesses, PowaWeb and PowaTag, had been sold. Under separate deals, PowaTag was sold to a private consortium led by former Powa Technologies director Ben White, [ 14 ] while PowaWeb was sold in a buyout backed by Greenlight Digital, a UK-based digital group whose interests include Greenlight Commerce Platform and OneHydra for SEO. [ 15 ]
After the collapse of the business, a series of articles by the Financial Times called into question several of the claims that had previously been made. Powa's self-proclaimed 2014 valuation of $2.6 billion was investigated, and it was concluded that $106 million (£75 million) was a more accurate figure. [ 16 ] The claimed "10-year strategic alliance with ‘limitless’ potential” deal with China UnionPay that Dan Wagner personally described in a quote to the BBC as “Why did China UnionPay decide to partner with a little British technology company? We’ve trumped ApplePay and the rest of the world here...” was found to be unknown to China UnionPay who had their lawyers request that Powa stop making the false claims [ 17 ] and the majority of the partners upon which the investment and consequent valuation had been based, were found to be just Letters of Intent at best. [ 18 ]
ZNAP was a mobile business platform developed by Hong Kong–based company MPayMe, a business technology company founded in 2010. [ 19 ] ZNAP supported Internet (online shopping), mobile shopping (via mobile handsets), print (magazines, newspapers), outdoor ads (posters, bus shelters), television, and app-to-app. Basic features included electronic vouchers/coupons, real-time loyalty programme management, alongside secure/efficient mobile payments . [ 20 ] The ZNAP mobile app was available for Apple iOS , Google Android , and BlackBerry OS supported devices.
In May 2014, ZNAP was acquired by Powa for US$75 million in an all share deal. [ 21 ] ZNAP product and customers merged with Powa Technologies PowaTag division. [ 22 ]
PowaTag was a mobile payment enabling technology and mobile application by Powa Technologies. [ 23 ] [ 24 ] PowaTag was launched at a March 2014 event in New York by Powa CEO Dan Wagner . [ 25 ] At the time of launch, more than 240 retailers were reported to have signed to use the service, [ 26 ] but later reports revealed that most of the companies had only written non-binding letters of intent. [ 27 ]
With the app, users could make purchases using a smartphone, with payment and delivery details tied to a specific device. [ 28 ] The app incorporated elements of QR code detection, audio recognition, and beacon technology. Audio watermarks in the form of inaudible tones embedded within radio, commercials, or live broadcast events were detectable by the app, taking users to a mobile commerce store where a purchase could be made. [ 29 ] | https://en.wikipedia.org/wiki/Powa_Technologies |
Powder coating on glass is a specialized procedure related to traditional powder coating , which is the technique of applying electrostatically charged, dry powdered particles of pigment and resin to a solid item's surface. It requires its own unique process, however, because glass is a poor electrical conductor in comparison to metal, the traditional powder coating substrate . [ 1 ]
Powder coating on glass is used in industries such as cosmetics, fragrances, wine and spirits, where the contents inside of the glass containers require protection from ultraviolet (UV) rays, particularly UVA electromagnetic radiation, which is capable of penetrating glass. [ 2 ] When applied with a dual-coat method, powder coating techniques on glass provide an opaque shield against the light's effects.
Powder coating on glass requires specialized equipment. The biggest challenge is getting the powder to adhere to the glass surface since there is no natural electrostatic attraction like there is with different metals.
A clean glass subsurface that will not interfere with the process is essential before beginning the powder coating procedure. [ 3 ] Washing to remove oil, dirt and grease can be accomplished with solvents, wipes or a traditional wash system. Proper temperature control is critical from the very beginning, including during the preparation stage. Certain temperature ranges are recommended, but they are proprietary at the moment to companies who have pioneered the technique.
After cleaning, an opaque base coat of powder is applied to the glass substrate as the initial, most important layer of UV protection. Once the powder attracts, the product is heated to activate the process of gelling, which secures the adhesive bond. It is crucial to control the amount of powder that goes on to the surface. With too little, the coating becomes transparent and the protection is diminished. Too much can create a dripping effect or disperse uneven amounts, leading to one side of the glass container being heavier than the other. In the case of powder coating nail polish and other cosmetics bottles, experienced powder coaters typically use a highly chemical-resistant form of powder, which makes it impervious to the aggressive chemicals inherent with polish and primer.
As more heat is applied, the powder coater adds the top coat, which flows together with the base coat. Oven curing follows, and the two coats become one, locking themselves together and encapsulating the bottle or container as a singular protective casing. Not only should this process effectively block out UV rays, but the molecular structure of the powder should provide added chip resistance and scratch resistance to the bottle.
Generally speaking, the transfer of powdered paint to a glass substrate can be broken into four specific phases. Assuming the object is properly cleaned, this includes: 1) Attraction – achieving the electrostatic charge; 2) Gelling – transforming the powder from dry to wet; 3) Flowing – melding or cross-linking the coat applications together for a strong, hardened protective casing; and 4) Curing – heat drying the powder coated product to arrive at its finished form.
It is possible to powder coat a wide variety of glass forms and dimensions, including cylindrical, oval and square shapes, to name just a few. Care must be given toward achieving even coverage, [ tone ] which is accomplished through proper heat control and powder application.
Glass will accept an almost limitless number of powder coated colors. [ 4 ] Different textures and even metallics can also be applied. Professionals in this field have been able to achieve satisfactory silk screen printing and pad printing on the powder coated glass substrate, including in the case of difficult cylindrical shapes. Glass items compatible with powder coating include bottles and containers, decorative pieces, dinnerware, picture frames and more.
Powder coating is considered to be an environmentally-friendly application. Unlike solvent-based wet paint systems, the process uses no volatile organic compounds (VOCs). In addition, there is no release of chemicals into the air through evaporation, and over-sprayed powder is recoverable and easily and safely disposable. [ 5 ] | https://en.wikipedia.org/wiki/Powder_coating_on_glass |
Powder Deaerators (also powder compactor or powder densifier ) are working apparatuses for deaerating and compacting of dry, fine-grained powders. The machine removes excess air and open spaces in the powder, leaving it a more solid, compact, material.
Powder Deaerators consist of two parallel drums – a filter drum and a pressure drum – which rotate in opposite directions. The drums are driven via drive motor and spur gear . The filter drum is coated with a porous sinter metal layer. It is connected to a vacuum line via a hollow shaft creating a negative pressure within the filter drum. An adjusting device serves for the setting of the gap width between the rollers. On the adjusting device there are spring assemblies to generate the necessary pressure.
The material is aspirated (sucked in) and held on the filter drum by a vacuum, where it is drawn in the space between the filter and pressure drums. The combination of vacuum and pressure causes a deaerating and densification of the product. At the end of the densification process, the densified product is stripped off the filter drum by knives so it can leave the machine.
Deaerators can be used for the deaerating and densification of all powders and other fine-piece bulk materials. The aim of the application is to raise the bulk density and/or improve the handling properties of a product. Deaerators are also used for the dosing and precompaction in granulation processes. Typical products which can be handled are silicic acid, carbon black , pigments, aluminium oxide , magnesium oxide , etc. The product temperatures can reach up to 100 °C.
Deaerators achieve savings in package, transport and storage capacity by significantly reducing the powder volume. [ 1 ] Explosive products can also be compacted as well. | https://en.wikipedia.org/wiki/Powder_deaerator |
Powder metallurgy ( PM ) is a term covering a wide range of ways in which materials or components are made from metal powders . PM processes are sometimes used to reduce or eliminate the need for subtractive processes in manufacturing, lowering material losses and reducing the cost of the final product. [ 1 ] This occurs especially often with small metal parts, like gears for small machines. [ 1 ] Some porous products, allowing liquid or gas to permeate them, are produced in this way. [ 1 ] They are also used when melting a material is impractical, due to it having a high melting point, or an alloy of two mutually insoluble materials, such as a mixture of copper and graphite. [ 1 ]
In this way, powder metallurgy can be used to make unique materials impossible to get from melting or forming in other ways. [ 1 ] A very important product of this type is tungsten carbide . [ 1 ] Tungsten carbide is used to cut and form other metals and is made from tungsten carbide particles bonded with cobalt. [ 2 ] Tungsten carbide is the largest and most important use of tungsten , [ 3 ] consuming about 50% of the world supply. [ 4 ] Other products include sintered filters, porous oil-impregnated bearings, electrical contacts and diamond tools.
Powder metallurgy techniques usually consist of the compression of a powder, and heating ( sintering ) it at a temperature below the melting point of the metal, to bind the particles together. [ 1 ] Powder for the processes can be produced in a number of ways, including reducing metal compounds, [ 1 ] electrolyzing metal-containing solutions, [ 1 ] and mechanical crushing, [ 1 ] as well as more complicated methods, including a variety of ways to fragment liquid metal into droplets, and condensation from metal vapor. Compaction is usually done with a die press, but can also be done with explosive shocks or placing a flexible container in a high-pressure gas or liquid. Sintering is usually done in a dedicated furnace, but can also be done in tandem with compression (hot isostatic compression), or with the use of electric currents.
Since the advent of industrial production-scale metal powder-based additive manufacturing in the 2010s, selective laser sintering and other metal additive manufacturing processes are a new category of commercially important powder metallurgy applications.
The powder metallurgy "press and sinter" process generally consists of three basic steps: powder blending (or pulverisation ), die compaction, and sintering . Compaction of the powder in the die is generally performed at room temperature. Sintering is the process of binding a material together with heat without liquefying it. It is usually conducted at atmospheric pressure and under carefully controlled atmosphere composition. To obtain special properties or enhanced precision, secondary processing like coining or heat treatment often follows. [ 5 ]
One of the older such methods is the process of blending fine (<180 microns) metal powders with additives, pressing them into a die of the desired shape, and then sintering the compressed material together, under a controlled atmosphere. The metal powder is usually iron , and additives include a lubricant wax, carbon , copper , and/or nickel . This produces precise parts, normally very close to the die dimensions, but with 5–15% porosity, and thus sub-wrought steel properties. This method is still used to make around 1 Mt/y of structural components of iron-based alloys. [ citation needed ]
There are several other PM processes that have been developed over the last fifty years. These include:
The history of powder metallurgy and the art of metal and ceramic sintering are intimately related to each other. Sintering involves the production of a hard solid metal or ceramic piece from a starting powder. The ancient Incas made jewelry and other artifacts from precious metal powders, though mass manufacturing of PM products did not begin until the mid or late 19th century. In these early manufacturing operations, iron was extracted by hand from a metal sponge following reduction and was then reintroduced as a powder for final melting or sintering. [ 12 ]
A much wider range of products can be obtained from powder processes than from direct alloying of fused materials. In melting operations, the " phase rule " applies to all pure and combined elements and strictly dictates the distribution of liquid and solid phases which can exist for specific compositions. In addition, whole body melting of starting materials is required for alloying, thus imposing unwelcome chemical, thermal, and containment constraints on manufacturing. Unfortunately, the handling of aluminium /iron powders poses major problems. [ 12 ] [ 13 ] Other substances that are especially reactive with atmospheric oxygen, such as tin , are sinterable in special atmospheres or with temporary coatings. [ 12 ] [ 14 ]
In powder metallurgy or ceramics it is possible to fabricate components which otherwise would decompose or disintegrate. All considerations of solid-liquid phase changes can be ignored, so powder processes are more flexible than casting , extrusion , or forging techniques. [ 12 ] Controllable characteristics of products prepared using various powder technologies include mechanical, magnetic, [ 12 ] [ 15 ] and other unconventional properties of such materials as porous solids, aggregates, and intermetallic compounds. [ 12 ] Competitive characteristics of manufacturing processing (e.g. tool wear, complexity, or vendor options) also may be closely controlled. [ 12 ]
Many special products are possible with powder metallurgy technology. A non-exhaustive list includes Al 2 O 3 whiskers coated with very thin oxide layers for improved refraction; iron compacts with Al 2 O 3 coatings for improved high-temperature creep strength; light bulb filaments made with powder technology; linings for friction brakes; metal glasses for high-strength films and ribbons; heat shields for spacecraft reentry into Earth's atmosphere; electrical contacts for handling large current flows; magnets ; microwave ferrites ; filters for gases; and bearings which can be infiltrated with lubricants . [ 12 ]
Extremely thin films and tiny spheres exhibit high strength. One application of this observation is to coat brittle materials in whisker form with a submicrometre film of much softer metal (e.g. cobalt -coated tungsten). The surface strain of the thin layer places the harder metal under compression, so that when the entire composite is sintered the rupture strength increases markedly. With this method, strengths on the order of 2.8 GPa versus 550 MPa have been observed for, respectively, coated (25% cobalt) and uncoated tungsten carbides . [ 12 ]
Any fusible material can be atomized. [ 12 ] Several techniques have been developed that permit large production rates of powdered particles, often with considerable control over the size ranges of the final grain population. [ 12 ] Powders may be prepared by crushing, grinding, chemical reactions, or electrolytic deposition. [ 12 ] The most commonly used powders are copper-base and iron-base materials. [ 16 ]
Powders of the elements titanium , vanadium , thorium , niobium , tantalum , calcium , and uranium have been produced by high-temperature reduction of the corresponding nitrides and carbides . Iron, nickel, uranium, and beryllium submicrometre powders are obtained by reducing metallic oxalates and formates . Exceedingly fine particles also have been prepared by directing a stream of molten metal through a high-temperature plasma jet or flame , atomizing the material. Various chemical and flame-associated powdering processes are adopted in part to prevent serious degradation of particle surfaces by atmospheric oxygen. [ 12 ]
Powder can be obtained through gas or water atomization, [ 17 ] centrifugal atomization, [ 12 ] chemically reducing particulate compounds, [ 17 ] electrolytic deposition in appropriate conditions, [ 17 ] simple pulverization and grinding, [ 17 ] thermal decomposition of particulate hydrides or carbonyls, [ 17 ] precipitation out of solution, [ 17 ] and also condensation from vaporized metal. [ 17 ]
Atomization is accomplished by forcing a molten metal stream through an orifice at moderate pressures. [ 12 ] A gas is introduced into the metal stream just before it leaves the nozzle, serving to create turbulence as the entrained gas expands (due to heating) and exits into a large collection volume exterior to the orifice. [ 12 ] The collection volume is filled with gas to promote further turbulence of the molten metal jet. [ 12 ] Air and powder streams are segregated using gravity or cyclonic separation . [ 12 ]
Simple atomization techniques are available in which liquid metal is forced through an orifice at a sufficiently high velocity to ensure turbulent flow. The usual performance index used is the Reynolds number . At low Re the liquid jet oscillates, but at higher velocities the stream becomes turbulent and breaks into droplets. Pumping energy is applied to droplet formation with very low efficiency (on the order of 1% ) and control over the size distribution of the metal particles produced is rather poor. Other techniques such as nozzle vibration, nozzle asymmetry, multiple impinging streams, or molten-metal injection into ambient gas are all available to increase atomization efficiency, produce finer grains, and to narrow the particle size distribution. Unfortunately, it is difficult to eject metals through orifices smaller than a few millimeters in diameter, which in practice limits the minimum size of powder grains to approximately 10 μm . Atomization also produces a wide spectrum of particle sizes, necessitating downstream classification by screening and remelting a significant fraction of the grain boundary. [ 12 ]
Centrifugal disintegration of molten particles offers one way around these problems. Extensive experience is available with iron, steel, and aluminium. Metal to be powdered is formed into a rod which is introduced into a chamber through a rapidly rotating spindle. Opposite the spindle tip is an electrode from which an arc is established which heats the metal rod. As the tip material fuses, the rapid rod rotation throws off tiny melt droplets which solidify before hitting the chamber walls. A circulating gas sweeps particles from the chamber. Similar techniques could be employed in space or on the Moon. The chamber wall could be rotated to force new powders into remote collection vessels, and the electrode could be replaced by a solar mirror focused at the end of the rod. [ 12 ]
An alternative approach capable of producing a very narrow distribution of grain sizes but with low throughput consists of a rapidly spinning bowl heated to well above the melting point of the material to be powdered. Liquid metal, introduced onto the surface of the basin near the center at flow rates adjusted to permit a thin metal film to skim evenly up the walls and over the edge, breaks into droplets, each approximately the thickness of the film. [ 12 ]
Another powder-production technique involves a thin jet of liquid metal intersected by high-speed streams of atomized water which break the jet into drops and cool the powder before it reaches the bottom of the bin. In subsequent operations the powder is dried. [ 12 ] This is called water atomization. [ 17 ] Water atomization cools and solidifies the metal particles more rapidly than gas atomization. [ 17 ] Since the solidification rate is inversely proportional to the particle size, smaller particles can be made using water atomization. [ citation needed ] [ 18 ] The smaller the particles, the more homogeneous the microstructure will be. [ citation needed ] Particles produced this way will also have a more irregular shape [ 17 ] and the particle size distribution will be wider. [ citation needed ] In addition, some surface contamination can occur by oxidation skin formation. [ citation needed ] Powder can be reduced by some kind of pre-consolidation treatment, such as annealing used for the manufacture of ceramic tools. [ citation needed ]
Powder compaction, one of the most critical steps in powder metallurgy processes, is the process of compacting metal powder through the application of high pressures. [ 19 ] Most powder compaction is done with mechanical presses and rigid tools, but hydraulic and pneumatic techniques can also be used, as well as methods that combine compaction with sintering, like hot isostatic compaction. [ 19 ] Traditional metalforming processes, including rolling, forging, extrusion, and swaging, are also used. [ 19 ]
The density of the compacted powder increases with the amount of pressure applied. Typical pressures range from 80 to 1,000 psi (0.55 to 6.89 MPa), pressures from 1,000 to 1,000,000 psi (6.9 to 6,894.8 MPa) have been obtained. Pressure of 10 t/in 2 to 50 t/in 2 (150 MPa to 700 MPa) are commonly used for metal powder compaction. To attain the same compression ratio across a component with more than one level or height, it is necessary to work with multiple lower punches. A cylindrical workpiece is made by single-level tooling. A more complex shape can be made by the common multiple-level tooling. [ citation needed ]
The dominant technology for the forming of products from powder materials, in terms of both tonnage quantities and numbers of parts produced, is die pressing. There are mechanical, servo-electrical and hydraulic presses available in the market, whereby the biggest powder throughput is processed by hydraulic presses. This forming technology involves the production cycle below, which offers a readily automated and high production rate process: [ citation needed ]
Typically the tools are held in the vertical orientation with the punch tool forming the bottom of the cavity. [ 20 ] Probably the most basic consideration is being able to remove the part from the die after it is pressed, along with avoiding sharp corners in the design. Keeping the maximum surface area below 20 square inches (0.013 m 2 ) and the height-to-diameter ratio below 7-to-1 is recommended. Along with having walls thicker than 0.08 inches (2.0 mm) and keeping the adjacent wall thickness ratios below 2.5-to-1. [ 20 ]
One of the major advantages of this process is its ability to produce complex geometries. Parts with undercuts and threads require a secondary machining operation. Typical part sizes range from 0.1 square inches (0.65 cm 2 ) to 20 square inches (130 cm 2 ). in area and from 0.1 to 4 inches (0.25 to 10.16 cm) in length. However, it is possible to produce parts that are less than 0.1 square inches (0.65 cm 2 ) and larger than 25 square inches (160 cm 2 ). in area and from a fraction of an inch (2.54 cm) to approximately 8 inches (20 cm) in length. [ 20 ] Small mechanical presses can generally compact about 100 pieces per minute. [ 19 ]
In die compaction, there are four major classes of tool styles: single-action compaction, used for thin, flat components; opposed double-action with two punch motions, which accommodates thicker components; double-action with floating die; and double-action withdrawal die. Double action classes give much better density distribution than single action. Tooling must be designed so that it will withstand the extreme pressure without deforming or bending. Tools must be made from materials that are polished and wear-resistant. [ 20 ]
Shock consolidation, or dynamic consolidation, is an experimental technique of consolidating powders using high pressure shock waves. [ 21 ] [ 22 ] This technique is useful for very large products, including those over 3000 tons and larger than 100 square inches. [ 19 ] These are commonly produced by impacting the workpiece with an explosively accelerated plate. [ citation needed ] Despite being researched for a long time, the technique still has some problems in controllability and uniformity. [ citation needed ] However, it offers some valuable potential advantages. As an example, consolidation occurs so rapidly that metastable microstructures may be retained. [ 23 ]
Isostatic powder compacting is an alternate method of powder compaction. [ 19 ] In cold isostatic compaction, fine metal particles are placed into a flexible mould, which is then immersed in a high-pressure gas or liquid from all directions (isostatic). [ 19 ] After sintering, this manufacturing process produces very little scrap metal and can be used to make many different shapes. The tolerances that this process can achieve in combination with sintering are very precise, ranging from +/- 0.008 inches (0.2 mm) for axial dimensions and +/- 0.020 inches (0.5 mm) for radial dimensions. This is the most efficient type of powder compacting (the following subcategories are also from this reference). [ 20 ] This operation is generally only applicable on small production quantities, and although the cost of a mold is much lower than that of pressing dies, it is generally not reusable and the production time is much longer. [ 24 ] Production rates are usually very low, but parts weighing up to 100 pounds can be effectively compacted. [ 19 ] Because pressure is applied from all directions, lower compaction pressures are required to produce higher densities of powder in the end product. [ 19 ]
Compacting pressures range from 15,000 psi (100,000 kPa ) to 40,000 psi (280,000 kPa) for most metals and approximately 2,000 psi (14,000 kPa) to 10,000 psi (69,000 kPa) for non-metals. [ 20 ] The density of isostatic compacted parts is 5% to 10% higher than with other powder metallurgy processes. [ 20 ] Typical workpiece sizes range from 0.25 in (6.35 mm) to 0.75 in (19.05 mm) thick and 0.5 in (12.70 mm) to 10 in (254 mm) long. It is possible to compact workpieces that are between 0.0625 in (1.59 mm) and 5 in (127 mm) thick and 0.0625 in (1.59 mm) to 40 in (1,016 mm) long. [ 20 ]
Advantages over standard powder compaction are the possibility of thinner walls and larger workpieces. The height-to-diameter ratio has no limitation. No specific limitations exist in wall thickness variations, undercuts , reliefs, threads, and cross holes. No lubricants are needed for isostatic powder compaction. The minimum wall thickness is 0.05 inches (1.27 mm) and the product can have a weight between 40 and 300 pounds (18 and 136 kg). There is 25 to 45% shrinkage of the powder after compacting. [ 20 ]
Isostatic tools are available in three styles, free mold (wet-bag), coarse mold (damp-bag), and fixed mold (dry-bag). The free mold style is the traditional style of isostatic compaction and is not generally used for high production work. In free mold tooling the mold is removed and filled outside the canister. Damp bag is where the mold is located in the canister, yet filled outside. In fixed mold tooling, the mold is contained within the canister, which facilitates automation of the process. [ 20 ]
After compaction, powdered materials are heated in a controlled atmosphere in a process known as sintering. During this process, the surfaces of the particles are bonded and desirable properties are achieved. [ 6 ]
Sintering of powder metals is a process in which particles under pressure chemically bond to themselves in order to form a coherent shape when exposed to a high temperature. The temperature in which the particles are sintered is most commonly below the melting point of the main component in the powder. [ 25 ] If the temperature is above the melting point of a component in the powder metal part, the liquid of the melted particles fills the pores. This type of sintering is known as liquid-state sintering. [ 6 ] A major challenge with sintering in general is knowing the effect of the process on the dimensions of the compact particles. This is especially difficult for tooling purposes in which specific dimensions may be needed. It is most common for the sintered part to shrink and become denser, but it can also expand or experience no net change. [ 25 ]
The main driving force for solid-state sintering is an excess of surface-free energy. The process of solid-state sintering is complex and dependent on the material and furnace (temperature and gas) conditions. There are six main stages that sintering processes can be grouped in which may overlap with one another: 1 initial bonding among particles, 2) neck growth, 3) pore channel closure, 4) pore rounding, 5) densification or pore shrinkage, and 6) pore coarsening. The main mechanisms present in these stages are evaporation , condensation , grain boundaries , volume diffusion , and plastic deformation . [ 25 ]
During this process, a number of characteristics are increased including the strength , ductility , toughness , and electrical and thermal conductivity of the material. If different elemental powders are compact and sintered, the material would form into alloys and intermetallic phases. [ 6 ] As the pore sizes decrease, the density of the material will increase. As stated above, this shrinkage is a huge problem in making parts or tooling in which particular dimensions are required. The shrinkage of test materials is monitored and used to manipulate the furnace conditions or to oversize the compact materials in order to achieve the desired dimensions. Although, sintering does not deplete the compact part of porosity . In general, powder metal parts contain five to twenty-five percent porosity after sintering. [ 6 ]
Most sintering furnaces contain three zones with three different properties that help to carry out the six steps above. The first zone, commonly coined the burn-off or purge stage, is designed to combust air, burn any contaminants such as lubricant or binders, and slowly raise the temperature of the compact materials. If the temperature of the compact parts is raised too quickly, the air in the pores will be at a very high internal pressure which could lead to expansion or fracture of the part. The second zone, known as the high-temperature stage, is used to produce solid-state diffusion and particle bonding. The material is seeking to lower its surface energy and does so by moving toward the points of contact between particles. The contact points become larger and eventually a solid mass with small pores is created. The third zone, also called the cooling period, is used to cool down the parts while still in a controlled atmosphere. This is an important zone as it prevents oxidation from immediate contact with the air or a phenomenon known as rapid cooling. All of the three stages must be carried out in a controlled atmosphere containing no oxygen. Hydrogen, nitrogen, dissociated ammonia, and cracked hydrocarbons are common gases pumped into the furnace zones providing a reducing atmosphere, preventing oxide formation. [ 6 ]
Hot isostatic pressing (HIP) compresses and sinters the part simultaneously [ 12 ] by applying heat on the order of 2300 °F (1250 °C), in the case of iron, or 2750 °F (1500 °C) in the case of nickel alloys. [ 19 ] This procedure, together with explosion-driven compressive techniques is used extensively in the production of high-temperature and high-strength parts such as turbine disks for jet engines. [ 12 ] In most applications of powder metallurgy the compact is hot-pressed, heated to a temperature above which the materials cannot remain work-hardened. [ 12 ] Hot pressing lowers the pressures required to reduce porosity and speeds welding and grain deformation processes. [ 12 ] It also permits better dimensional control of the product, lessens sensitivity to physical characteristics of starting materials, and allows powder to be compressed to higher densities than with cold pressing, resulting in higher strength. [ 12 ] Negative aspects of hot pressing include shorter die life, slower throughput because of powder heating, and the frequent necessity for protective atmospheres or simple vacuum during forming and cooling stages. [ 12 ] [ 19 ]
HIP produces products often of higher quality than other processes. [ 19 ] However, HIP is expensive, and generally unnattractive for high-volume production, due to the high cost of placing the powder in a flexible isolating medium that can withstand the temperatures and pressures ( canning ) and then removing it from that medium ( decanning ), as well as the long time periods involve, which can range from 6 to 8 hours. [ 19 ]
These techniques employ electric currents to drive or enhance sintering. [ 26 ] A combination of mechanical pressure and electrical current, passed through either the powder or the container, significantly reduces the sintering time compared to conventional solutions. [ 26 ] There are many classifications of these techniques, but they can be divided into two main categories: resistance sintering techniques, which apply lower voltages and currents and take on the from around ten seconds to ten minutes; and electric discharge sintering, which use capacitor banks to achieve higher currents and voltages, and take from tens of microseconds to tens of milliseconds. [ 26 ] Resistance sintering techniques include spark plasma sintering (SPS), plasma-activated sintering (PAS), and pulse electric current sintering (PECS). [ 27 ] electric discharge sintering techniques include capacitor discharge sintering . [ 27 ] Currently, spark plasma sintering is currently the most commonly used method of electric pulse consolidation in general. [ 27 ]
Resistance sintering currents usually reach about 1 kA per square centimer, while electric discharge sintering voltages of up to several kilovolts also require very high currents, over 10 kA per square centimer. [ 27 ] Resistance sintering techniques are consolidation methods based on temperature, where heating of the mold and of the powders is accomplished through electric currents, usually with a characteristic processing time of 15 to 30 minutes. On the other hand, electric discharge sintering methods rely on high-density currents (from 0.1 to 1 kA/mm^2) to directly sinter electrically conductive powders, with a characteristic time between tens of microseconds to hundreds of milliseconds. [ citation needed ]
Strictly, the phrase "continuous process" should be used only to describe modes of manufacturing which could be extended indefinitely in time. Normally, however, the term refers to processes whose products are much longer in one physical dimension than in the other two. Compression, rolling, and extrusion are the most common examples. [ 12 ]
In a simple compression process, powder flows from a bin onto a two-walled channel and is repeatedly compressed vertically by a horizontally stationary punch. After stripping the compress from the conveyor, the compacted mass is introduced into a sintering furnace. An even easier approach is to spray powder onto a moving belt and sinter it without compression. However, good methods for stripping cold-pressed materials from moving belts are hard to find. One alternative that avoids the belt-stripping difficulty altogether is the manufacture of metal sheets using opposed hydraulic rams , although weakness lines across the sheet may arise during successive press operations. [ 12 ] [ further explanation needed ]
Powders can also be rolled to produce sheets. The powdered metal is fed into a two-high rolling mill, [ a ] and is compacted into strip form at up to 100 feet per minute (0.5 m/s). The strip is then sintered and subjected to another rolling and further sintering. Rolling is commonly used to produce sheet metal for electrical and electronic components, as well as coins . Considerable work also has been done on rolling multiple layers of different materials simultaneously into sheets. [ 12 ]
Extrusion processes are of two general types. In one type, the powder is mixed with a binder or plasticizer at room temperature; in the other, the powder is extruded at elevated temperatures without fortification. [ further explanation needed ] Extrusions with binders are used extensively in the preparation of tungsten-carbide composites. Tubes, complex sections, and spiral drill shapes are manufactured in extended lengths and diameters varying in the range 0.5–300 mm (0.020–11.811 in). Hard metal wires of 0.1 mm (0.0039 in) diameter have been drawn from powder stock. At the opposite extreme, large extrusions on a tonnage basis may be feasible. [ 12 ]
For softer, easier-to-form metals such as aluminium and copper alloys continuous extrusion may also be performed using processes such as conform or continuous rotary extrusion. These processes use a rotating wheel with a groove around its circumference to drive the loose powder through a forming die. Through a combination of high pressure and a complex strain path the powder particles deform, generate a large amount of frictional heat and bond together to form a bulk solid. Theoretically, fully continuous operation is possible as long as the powder can be fed into the process. [ 28 ]
There appears to be no limitation to the variety of metals and alloys that can be extruded, provided the temperatures and pressures involved are within the capabilities of die materials. [ 12 ] Extrusion lengths may range from 3 to 30 m [ 29 ] and diameters from 0.2 to 1 m. Modern presses are largely automatic and operate at high speeds (on the order of m/s). [ 12 ]
The special materials and processes used in powder metallurgy can pose hazards to life and property. The high surface-area-to-volume ratio of the powders can increase their chemical reactivity in biological exposures (for example, inhalation or ingestion), and increases the risk of dust explosions . Materials considered relatively benign in bulk can pose special toxicological risks when in a finely divided form. Inhalation of heavy metals can result in many health issues. Lead and cadmium are generally toxic, and cobalt can cause asthma and fibrosis in sensitive individuals. [ 30 ] | https://en.wikipedia.org/wiki/Powder_metallurgy |
A powder is an assembly of dry particles dispersed in air. If two different powders are mixed perfectly, theoretically, three types of powder mixtures can be obtained: the random mixture, the ordered mixture or the interactive mixture.
A powder is called free-flowing if the particles do not stick together. If particles are cohesive , they cling to one another to form aggregates . The significance of cohesion increases with decreasing size of the powder particles; particles smaller than 100 μm are generally cohesive. [ 1 ] [ 2 ]
A random mixture can be obtained if two different free-flowing powders of approximately the same particle size, density and shape are mixed (see figure A). [ 3 ] Only primary particles are present in this type of mixture, i.e., the particles are not cohesive and do not cling to one another. The mixing time will determine the quality of the random mixture. However, if powders with particles of different size, density or shape are mixed, segregation can occur. [ 4 ] Segregation will cause separation of the powders as, for example, lighter particles will be prone to travel to the top of the mixture whereas heavier particles are kept at the bottom.
The term ordered mixture was first introduced to describe a completely homogeneous mixture where the two components adhere to each other to form ordered units. [ 5 ] However, a completely homogeneous mixture is only achievable in theory and other denotations were introduced later such as adhesive mixture or interactive mixture.
If a free-flowing powder is mixed with a cohesive powder an interactive mixture can be obtained. The cohesive particles adhere to the free-flowing particles (now called carrier particles) to form interactive units as shown in figure B. [ 3 ] An interactive mixture may not contain free aggregates of the cohesive powder, which means that all small particles must be adhered to the larger ones. The difference from an ordered mixture is instead that all carrier particles do not need to be of the same size and a different number of small particles attached to each one. A narrow size range of the carrier particles is preferred to avoid segregation of the interactive units. [ 6 ] In practice a combination of a random mixture and an interactive mixture may be obtained which consists of carrier particles, aggregates of the small particles and interactive units. [ 7 ]
The formation of interactive mixtures cannot automatically be assumed, especially if smaller carrier particles [ 8 ] or a greater proportion of fine particles [ 9 ] [ 10 ] are used. If an interactive mixture is to be formed, it is necessary that enough force is exerted by the carrier particles during dry mixing to break up the aggregates formed by the fine particles. Adhesion can then be achieved if the adhesive forces exceed the gravitational forces that otherwise lead to separation of the constituents. [ 3 ]
Interactive mixtures for example can be used in the manufacturing of tablets [ 11 ] enhancing the dissolution of poorly soluble drugs [ 12 ] or for nasal administration . [ 3 ] One common application is for inhalation therapy, where the concept has been used in the development of alternatives to pressurised metered dose inhalers. [ 13 ]
The quality by design initiative (QbD) of the U.S. Food and Drug Administration requires a process to be controllable and predictable. Theories and methods to characterize powder mixture have facilitated the implementation of QbD approaches to predict flow properties of powder mixture. For example, QbD approach is shown to be useful for predicting flow performance and finding design space during formulation development. [ 14 ] | https://en.wikipedia.org/wiki/Powder_mixture |
Powder of sympathy was a form of early pseudoscientific navigation and alchemy , in the 17th century in Europe , whereby a remedy was applied to the weapon that had caused a wound with the aim of healing the injury it had made. Weapon salve was a preparation, again applied to the weapon, but based on material from the wounded patient rather than on any remedy for the wound.
The powder is said to have consisted of green vitriol , first dissolved in water and afterward recrystallized or calcined in the sun. The Duke of Buckingham testified that Kenelm Digby had healed his secretary of a gangrenous wound by simply soaking the bloody bandage in a solution of the powder (possibly due to the oligodynamic effect ). Digby claimed to have got the secret remedy from a Carmelite friar in Florence, and attributed its potency to the fact that the sun's rays extracted the spirits of the blood and the vitriol, while, at the same time, the heat of the wound caused the healing principle thus produced to be attracted to it by means of a current of air — a sort of wireless therapy. [ 1 ]
The powder was also applied to solve the longitude problem in the suggestion of an anonymous pamphlet of 1687 entitled Curious Enquiries . The pamphlet theorised that a wounded dog could be put aboard a ship, with the knife used to injure the dog left in the trust of a timekeeper on shore, who would then dip said knife into the powder at a predetermined time and cause the creature to yelp, thus giving the captain of the ship an accurate knowledge of the time. [ 2 ]
This history of medicine article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Powder_of_sympathy |
Powel Crosley Jr. (September 18, 1886 – March 28, 1961) was an American inventor , industrialist , and entrepreneur . He was also a pioneer in radio broadcasting and owner of the Cincinnati Reds major league baseball team. In addition, Crosley's companies manufactured Crosley automobiles and radios, and operated WLW radio station. Crosley, once dubbed "The Henry Ford of Radio," was inducted into the Automotive Hall of Fame in 2010 and the National Radio Hall of Fame in 2013.
He and his brother, Lewis M. Crosley , were responsible for many firsts in consumer products and broadcasting. During World War II , Crosley's facilities produced more proximity fuzes than any other U.S. manufacturer and made several production design innovations. Crosley Field , a stadium in Cincinnati , Ohio, was renamed for him, and the street-level main entrance to Great American Ball Park in Cincinnati is named Crosley Terrace in his honor. Crosley's Pinecroft estate home in Cincinnati , and Seagate , his former winter retreat in Sarasota, Florida , are listed in the National Register of Historic Places .
Powel Crosley Jr. was born on September 18, 1886, in Cincinnati , Ohio, to Charlotte Wooley (Utz) (1864–1949) and Powel Crosley Sr. (1849–1932), a lawyer. Powel Jr. was the oldest of the family's four children. Crosley became interested in the mechanics of automobiles at a young age and wanted to become an automaker. While living with his family in College Hill, a suburb of Cincinnati, 12-year-old Crosley made his first attempt at building a vehicle. [ 1 ]
Crosley began high school in College Hill and transferred to the Ohio Military Institute . In 1904, Crosley enrolled at the University of Cincinnati , where he began studies in engineering but switched to law, primarily to satisfy his father. He dropped out of college in 1906 after two years of study. [ 1 ]
Crosley married Gwendolyn Bakewell Aiken (1889–1939) in Hamilton County, Ohio, on October 17, 1910. They had two children. After his marriage, Crosley continued to work in automobile sales in Muncie to earn money to buy a house, while his wife returned to Cincinnati to live with her parents. The young couple saw each other on the weekends until Crosley returned to Cincinnati in 1911 to live and work after the birth of his first child. [ 2 ] Gwendolyn Crosley, who suffered from tuberculosis , died at the Crosleys' winter home in Sarasota, Florida , on February 26, 1939. [ 3 ]
Crosley married Eva Emily Brokaw (1912–1955) in 1952. She died in Cincinnati, Ohio.
Crosley's primary residence was Pinecroft , an estate home built in 1929 in the Mount Airy section of Cincinnati, Ohio. He also had Seagate , a winter retreat in Manatee County, Florida , built for his first wife, Gwendolyn. In addition, Crosley owned several vacation properties.
Pinecroft, Crosley's two-story, 13,334-square-foot (1,238.8 m 2 ), Tudor Revival -style mansion and other buildings on his estate in Mount Airy was designed by New York -based architect Dwight James Baum and built in 1928–29. Crosley's daughter, Marth Page (Crosley) Kess, sold the property after her father's death in 1961, and the Franciscan Sisters of the Poor acquired the property in 1963. Saint Francis Hospital bought a portion of the property north of the Crosley mansion in 1971 and built a hospital, which was renamed Mercy Hospitals West in 2001. The land surrounding the home has been subdivided into parcels, but the Franciscan Sisters have used the mansion as a retreat since the early 1970s. Pinecroft was added to the National Register of Historic Places in 2008. [ 4 ]
Seagate, also known as the Bay Club, along Sarasota Bay in the southwest corner of Manatee County, Florida , was a Mediterranean Revival-style home designed for Crosley by New York City and Sarasota architect George Albree Freeman Jr. , with Ivo A. de Minicis , a Tampa, Florida , architect, drafting the plans. Sarasota contractor Paul W. Bergman built the 11,000-square-foot (1,000 m 2 ) winter retreat in 1929–30 on a 63-acre (25-hectare) parcel of land. The two-and-a-half-story house include ten bedrooms and ten bathrooms, as well as auxiliary garages and living quarters for staff. The house contains and is reportedly the first residence built in Florida using steel -frame construction to provide protection against fires and hurricanes . After Crosley's wife, Gwendolyn, died of tuberculosis at the retreat in 1939, he rarely used the house. [ 5 ] [ 6 ] During World War II , Crosley allowed the U.S. Army Air Corps to use the retreat for its airmen training at the nearby Sarasota Army Air Base. Crosley sold his estate property in 1947 to the D and D Corporation. [ 4 ]
Mabel and Freeman Horton purchased the property in 1948 and owned Seagate for nearly forty years. The house and 45 acres (18 hectares) was added to the National Register of Historic Places on January 21, 1983, by a subsequent owner who intended to build an exclusive condominium project on the site using the historic house as a clubhouse, but the project failed when the economy faltered shortly thereafter. Kafi Benz , the Friends of Seagate Inc. , a nonprofit corporation, and local residents saved Seagate from commercial development, and initiated a campaign for its preservation and public acquisition. [ 7 ] In 1991 the state of Florida purchased the property and 16.5 acres (6.7 hectares) of the bay-front estate that included the structures that Crosley had built in 1929–30. A larger portion of the original property was developed into a satellite campus for the University of South Florida . The University of South Florida Sarasota-Manatee campus opened its new facilities in August 2006. The present-day mansion, called the Powel Crosley Estate, is used as a meeting, conference, and event venue. [ 4 ] [ 8 ] [ 9 ]
Crosley, an avid sportsman, also owned several sports, hunting, and fishing camps, including an island retreat called Nikassi on McGregor Bay , Lake Huron , Canada; Bull Island, South Carolina ; Pimlico Plantation, along the Cooper River north of Charleston, South Carolina ; Sleepy Hollow Farm, a retreat in Jennings County, Indiana and a house at Cat Cays , Bahamas . [ 3 ] [ 4 ]
Crosley began work selling bonds for an investment banker ; however, at the age of twenty-one he decided to pursue a career in automobile manufacturing. [ 1 ] The mass-production techniques employed by Henry Ford also caught his attention and would be implemented by his brother, Lewis, when the two began manufacturing radios in 1921. [ citation needed ]
In 1907 Crosley formed a company to build the Marathon Six, a six-cylinder model priced at $1,700, which was at the low end of the luxury car market. With $10,000 in capital that he raised from investors, Crosley established Marathon Six Automotive inexpensive automobile, in Connersville, Indiana , and built a prototype of his car, but a nationwide financial panic caused investment capital to dwindle and he failed to fund its production. [ 10 ]
Still determined to establish himself as an automaker, Crosley moved to Indianapolis , Indiana , where he worked for Carl G. Fisher as a shop hand at the Fisher Automobile Company . Crosley stayed for about a year, but left after he broke his arm starting a car at the auto dealership. After recovering from his injury at home in College Hill, Crosley returned to Indianapolis in 1909 to briefly work for several auto manufacturers, including jobs as an assistant sales manager for the Parry Auto Company and a salesman for the National Motor Vehicle Company . He also volunteered to help promote National's auto racing team. His next job was selling advertising for Motor Vehicle , an automotive trade journal, but left in 1910 to move to Muncie, Indiana , where he worked in sales for the Inter-State Automobile Company and promoted its racing team. [ 2 ]
After returning to Cincinnati, Ohio, in 1911, Crosley sold and wrote advertisements for local businesses, but continued to pursue his interests in the automobile industry. He
failed in early efforts to manufacture cars for the Hermes Automobile Company and cyclecars for the De Cross Cyclecar Company and the L. Porter Smith and Brothers Company before finding financial success in manufacturing and distributing automobile accessories. [ 11 ]
In 1916 he co-founded the American Automobile Accessory Company with Ira J. Cooper. The company's bestseller was a tire liner of Crosley's invention. [ 4 ] Another popular product was a flag holder that held five American flags and clamped to auto radiator caps. [ citation needed ] By 1919 Crosley had sales of more than $1 million in parts. He also diversified into other consumer products such as phonograph cabinets, radios, and home appliances. Crosley's greatest strength was his ability to invent new products, while his brother, Lewis M. Crosley , excelled in business. Lewis also became head of Crosley's manufacturing operations. [ 12 ] [ 13 ]
In 1920, Crosley first selected independent local dealers as the best way to take his products to market. He insisted that all sellers of his products must give the consumer the best in parts, service, and satisfaction. Always sensitive to consumers, his products were often less expensive than other name brands, but were guaranteed. Crosley's " money back guarantee " set a precedent for some of today's most outstanding sales policies.
In 1921 Crosley's young son asked for a radio , a new item at that time, but Crosley was surprised that toy radios cost more than $100 at a local department store. With the help of a booklet called "The ABC of Radio," he and his son decided to assemble the components and build their own crystal radio set. Crosley immediately recognized the appeal of an inexpensive radio and hired two University of Cincinnati students to help design a low-cost set that could be mass-produced. Crosley named the radio the "Harko" and introduced it to the market in 1921. The inexpensive radio set sold for $7, making it affordable to the masses. Soon, the Crosley Radio Corporation was manufacturing radio components for the rapidly growing industry and making its own line of radios. [ 14 ] [ 15 ]
By 1924 Crosley had moved his company to a larger plant and later made subsequent expansions. The Crosley Radio Corporation became the largest radio manufacturer in the world in 1925; its slogan, "You’re There With A Crosley," was used in all its advertising. [ 12 ]
In 1925 Crosley introduced another low-cost radio set. The small, one-tube, regenerative radio was called the " Crosley Pup " and sold for $9.75. [ citation needed ] While Victor had the rights to " His Master's Voice ", its famous trademark showing Nipper listening to a phonograph , Crosley adopted a mascot in the form of a dog with headphones listening to a Crosley Pup radio [ 16 ]
In 1928 Crosley's firm arranged for the construction of the Crosley Building at Camp Washington , a Cincinnati neighborhood, and used the facility for radio manufacturing, radio broadcasting, and for manufacturing other devices. [ 17 ]
In 1930 Crosley was marketing the "Roamio," with "screen grid neutrodyne power speaker" [ 18 ] for automotive use. Priced at $75, before accessories and installation, it was claimed to be able to receive thirty stations with no signal strength change. [ 18 ]
Once Crosley established himself as a radio manufacturer, he decided to expand into broadcasting as a way to encourage consumers to purchase more radios. In 1921, soon after he built his first radios, Crosley began experimental broadcasts from his home with a 20-watt transmitter using the call sign 8CR. [ 14 ] On March 22, 1922, the Crosley Broadcasting Corporation received a commercial license to operate as WLW at 50 watts. Dorman D. Israel, a young radio engineer from the University of Cincinnati, designed and built the station's first two radio transmitters (at 100 and 1,000 watts). [ 19 ] [ 20 ] The Crosley Corporation claimed that, in 1928, WLW became the first 50- kilowatt commercial station in the United States with a regular broadcasting schedule. In 1934, Crosley put a 500-kilowatt transmitter on the air, making WLW the station with the world's most powerful radio transmitter for the next five years. [ 12 ] [ 19 ] (On occasion, the station's power was boosted as high as 700,000 watts.) [ citation needed ]
Throughout the 1930s, Cincinnati's WLW was considered "the Nation's Station," producing many hours of network programming each week. [ 21 ] Among the entertainers who performed live from WLW's studios were Red Skelton , Doris Day , Jane Froman , Fats Waller , Rosemary Clooney , and the Mills Brothers . [ 4 ] In 1939, the Federal Communications Commission (FCC) ruled that WLW had to reduce its power to 50 kilowatts, partly because it interfered with the broadcasts of other stations, but largely due to its smaller competitors, who complained about the station's technical and commercial advantages with its 500-kilowatt broadcasts. [ 4 ]
During World War II , WLW resumed its powerful, 500-kilowatt transmissions in cooperation with the U.S. government. [ 4 ] The 500-kilowatt transmitter was crated for shipment to Asia, but the war ended before it was shipped. [ citation needed ] WLW's engineers also built high-power shortwave transmitters on a site about 25 miles (40 km) north of Cincinnati. Crosley Broadcasting, under contract to the U.S. government, began operating the Bethany Relay Station , which was dedicated on September 23, 1944, to broadcast " Voice of America " programming. The relay station's broadcasts continued until 1994. [ 4 ]
Crosley's broadcasting company eventually expanded into additional markets. The company was experimenting with television broadcasting as early as 1929, when it received an experimental television license from the Federal Radio Commission (FRC), which later became the FCC. Crosley Broadcasting did not go on-air with regular television programming as WLWT until after Crosley sold the company to Aviation Corporation ( Avco ) and he had become a member of Avco's board of directors.. [ citation needed ]
In the 1930s Crosley added refrigerators and other household appliances and consumer goods to his company's product line. [ citation needed ]
Crosley's " Icyball " was an early non-electrical refrigeration device. The unit used an evaporative cycle to create cold, and had no moving parts. The dumbbell shaped unit was "charged" by heating one end with a small kerosene heater. Crosley's company sold several hundred thousand Icyball units before discontinuing its manufacture in the late 1930s. [ citation needed ]
In 1932 Crosley had the idea of putting shelves in the doors of refrigerators. He patented the "Shelvador" refrigerator and launched the new appliance in 1933. At that time it was the only model with shelves in the door. [ 15 ] In addition to refrigerators, Crosley's company sold other consumer products that included the "XERVAC," a device purported to "revitalize inactive hair cells" and "stimulate hair growth". [ 22 ] Crosley also introduced the "Autogym," a motor-driven weight-loss device with a vibrating belt, and the "Go-Bi-Bi," a "rideable baby walker," among other products. [ 23 ]
In February 1934, Crosley purchased the Cincinnati Reds professional baseball team from Sidney Weil , who had lost much of his wealth after the Wall Street Crash of 1929 . Crosley kept the team from going bankrupt and leaving Cincinnati. He was also owner of the Reds when the team won two National League titles (in 1939 and 1940) and the World Series in 1940. [ 14 ] [ 24 ]
Crosley was also a pioneer in broadcasting baseball games on the radio. On May 24, 1935, the first nighttime game in Major League baseball history was held at Cincinnati's Crosley Field , which was renamed in Crosley's honor after he acquired the team (before this, the ballpark was named Redland Field), between the Cincinnati Reds and Philadelphia Phillies under newly installed electric lighting. With attendance at its evening games more than four times greater that its daytime events, the team's financial position was greatly improved. [ 13 ] Crosley also approved baseball's first regularly-scheduled play-by-play broadcasts of all scheduled games on his local station, WSAI , whose call letters stood for "sports and information," and later on WLW. The coverage increased attendance so much that within five years all 16 major league teams had radio broadcasts of every scheduled game. [ citation needed ]
On a personal level, Crosley was an avid sportsman. Although he never had a pilot's license, Crosley owned several seaplanes , such as the Douglas Dolphin , and airplanes , including building five Crosley "Moonbeam" airplanes. In addition, Crosley claimed that at one time he was slotted to be a driver in the Indianapolis 500 , but that claim was not entirely accurate. He was entered but broke his arm working for Carl Fisher (see above). Crosley was also the owner of luxury yachts with powerful engines, and an active fisherman who participated in celebrated tournaments in Sarasota, Florida. He served as president of the Sarasota area's Anglers Club and was a founder of the American Wildlife Institute. [ 24 ] [ 23 ] Crosley owned several sports, hunting, and fishing camps: Nikassi, an island retreat in Ontario, Canada; Bull Island off the coast of South Carolina; a hunting retreat he called Sleepy Hollow Farm in Jennings County, Indiana, and a Caribbean vacation home at Cat Cays, Bahamas. [ 4 ] [ 25 ]
The Crosley "Moonbeam" was built in Sharonville, Ohio and was first flown on December 8, 1929. It was designed by Harold D. Hoekstra, an employee of Crosley's when Crosley was president of the Crosley Aircraft Company. (Hoeskstra later became Chief of Engineering and Design for the Federal Aviation Administration .) Unique features of this aircraft are the square tube longerons used in the fuselage construction, use of torque tubes instead of control cable, and the corrugated aluminum ailerons. Original power was supplied by a four-cylinder inverted inline 90 hp Crosley engine. At one time it was also tested with a 110 Warner Scarab engine. N147N reportedly was the first airplane on which the spoilers were tested (in May 1930) as a lateral control device. Five Moonbeams airplanes were produced. The first was a three-place parasol; next, a four-place, high wing cabin model; third and fourth were one place high wings. Due to the Great Depression, planned production did not take place. N147N is the last of these planes in existence. It is housed at the Aviation Museum of Kentucky in Lexington Kentucky . [ citation needed ]
In 1933 Frenchman Henri Mignet designed the HM.14 "Pou du Ciel" ("Flying Flea"). He envisioned a simple aircraft that amateurs could build, and even teach themselves to fly. In an attempt to render the aircraft stall proof and safe for amateur pilots to fly, Mignet staggered the two main wings. The Mignet-Crosley "Pou du Ciel" is the first HM.14 made and flown in the United States. Edward Nirmaier, a Crosley employee, and two other men built the airplane in November 1935 for Crosley, who believed that the affordable "Flea" could become a popular aircraft in the United States. After several flights, a crash at the Miami Air Races in December 1935 finally grounded the Crosley HM.14. Although the airplane enjoyed a period of intense popularity in France and England, a series of accidents in 1935-36 permanently ruined the airplane's reputation. [ citation needed ]
Of all Crosley's dreams, success at building an affordable automobile for Americans was possibly the only major one eventually to elude him. In the years leading up to World War II , Crosley developed new products that included reviving one of his earliest endeavors at automobile design and manufacturing. In 1939, when Crosley introduced the low-priced Crosley automobiles, he broke with tradition and sold his cars through independent appliance, hardware, and department stores instead of automobile dealerships. [ 13 ] [ 26 ]
The first Crosley Motors, Inc. automobile made its debut at the Indianapolis Motor Speedway on April 28, 1939, to mixed reviews. [ 23 ] The compact car had an 80-inch (200 cm) wheelbase and a 38.87-cubic-inch (637.0 cm 3 ), two-cylinder , air cooled Waukesha engine . Crosley estimated that his cloth-top car, which weighed less than 1,000 pounds (450 kg), could get fifty miles per gallon at speeds of up to fifty miles per hour. [ 24 ] [ 25 ] The sedan model sold for $325, while the coupe sold for $350. Panel truck and pickup truck models were added to the product line in 1940. [ 26 ] During the pre-war period, the company had manufacturing plants in Camp Washington, Ohio ; Richmond, Indiana ; and Marion, Indiana . When the onset of war ended all automobile production in the United States in 1942, Crosley had produced 5,757 cars. [ 4 ]
After World War II ended, Crosley resumed building its small cars for civilian use. His company's first post-war automobile rolled off the assembly line on May 9, 1946. [ 27 ] The new Crosley "CC" model automobile continued the company's pre-war tradition of offering small, lightweight, and low-priced cars. It sold for $850 and got thirty to fifty miles per U.S. gallon. In 1949 Crosley became the first American carmaker to put disc brakes on all of its models. [ 1 ]
Unfortunately for Crosley, fuel economy ceased to be an inducement after gas rationing ended, and American consumers also began to prefer bigger cars. [ 23 ] Crosley's best year was 1948, when it sold 24,871 cars, but sales began to fall in 1949. Adding the Crosley "Hotshot" sports model and an all-purpose vehicle called the "Farm-O-Road" model in 1950 did not stop the decline. Only 1,522 Crosley vehicles were sold in 1952. Crosley sold about 84,000 cars before closing down the operation on July 3, 1952. The Crosley plant in Marion, Indiana, was sold to the General Tire and Rubber Company . [ 27 ] [ 28 ]
Crosley's company was involved in war production planning before December 1941, and like the rest of American industry, it focused on manufacturing war-related products during World War II. The company made a variety of products, including proximity fuzes , experimental military vehicles, radio transceivers , and gun turrets , among other items. [ 29 ] [ 30 ]
The most significant Crosley's wartime production was the proximity fuze , which was manufactured by several companies for the military. Crosley's facilities produced more fuzes than any other manufacturer and made several production design innovations. The fuze is widely considered the third most important product development of the war years, ranking behind the atomic bomb and radar . [ 31 ]
Ironically, Crosley himself did not have U.S. government security clearance and was not involved with the project. Without government security clearance, Crosley was prohibited from entering the area of his plant that manufactured the fuzes and did not know what top-secret products it produced until the war's end. Production was directed and supervised by Lewis M. Clement, the Crosley company's vice-president of engineering. [ 32 ] [ 33 ]
James V. Forrestal , U.S. Secretary of the Navy said: "The proximity fuze has helped blaze the trail to Japan. Without the protection this ingenious device has given the surface ships of the Fleet, our westward push could not have been so swift and the cost in men and ships would have been immeasurably greater." [ 34 ] George S. Patton , Commanding General of the Third Army, remarked: "The funny fuze won the Battle of the Bulge for us. I think that when all armies get this shell we will have to devise some new method of warfare." [ citation needed ]
Also of significance were the many radio transceivers that Crosley's company manufactured during the war, including 150,000 BC-654s , a receiver and transmitter that was the main component of the SCR-284 radio set. The Crosley Corporation also made components for Walkie-talkie transceivers and IFR radio guidance equipment, among other products. In addition, Crosley's also manufactured field kitchens, air supply units for Sperry S-1 bombsites (used in B-24 bombers ), air conditioning units, Martin PBM Mariner bow- gun turrets , and quarter-ton trailers. Gun turrets for PT boats and B-24 and B-29 bombers were the company's largest military contract. [ 30 ]
During the war, Crosley's auto manufacturing division, CRAD (for Crosley Radio Auto Division), in Richmond, Indiana, produced experimental motorcycles , tricycles , four-wheel-drive vehicles, and continuous track vehicles, including some amphibious models. [ 35 ] All of these military prototypes were powered by the two-cylinder boxer engine that had powered the original Crosley automobile. [ 36 ] Crosley had nearly 5,000 of these engines on hand when civilian automobile production ceased in 1942, and hoped to put them to use in his miniature war machines. [ citation needed ]
One vehicle prototype was the 1942/1943 Crosley CT-3 "Pup," a lightweight, single-passenger, four-wheel-drive vehicle that was transportable and air-droppable from a C-47 Skytrain . Six of the 1,125-pound (510 kg) Pups were deployed overseas after undergoing tests at Fort Benning , Georgia , but the Pup project was discontinued due to several weak components. Seven of the thirty-seven Pups that were built are known to survive. [ 30 ] [ 36 ]
Although Crosley retained ownership of the Cincinnati Reds baseball team and Crosley Motors, he sold his other business interests, including WLW radio and the Crosley Corporation, to the Aviation Corporation (Avco) in 1945. [ 29 ] Crosley remained on the Avco board for several years afterward. Avco put Ohio's second television station, WLWT-TV , on the air in 1948, the same year it began manufacturing television sets. Avco manufactured some of the first portable television sets under the Crosley brand name. Crosley ceased to exist as a brand in 1956, when Avco closed the unprofitable product line; however, the Crosley name was so well established that Avco's broadcasting division, owner of WLWT-TV, retained the Crosley name until 1968, seven years after Crosley's death. [ citation needed ]
Crosley sold Pimlico Plantation, now demolished, in 1942, and Seagate, his winter retreat in Florida in 1947. In 1954 Crosley sold his vacation home at Cat Keys, Bahamas. In 1956 he sold Sleepy Hollow Farm in Jennings County, Indiana, to the state of Indiana for use as a wildlife preserve . Bull Island, South Carolina, became part of a national wildlife refuge . It is not known when Crosley sold his vacation retreat in Ontario, Canada. [ 4 ] [ 27 ]
Crosley died on March 28, 1961, of a heart attack at the age of 74. [ 29 ] He is buried at Spring Grove Cemetery in Cincinnati.
Crosley liked to label himself "the man with 50 jobs in 50 years," a catchy sobriquet that was far from true, although he did have more than a dozen jobs before he got into automobile accessories. Crosley helped quite a few inventors up the ladder of success by buying the rights to their inventions and sharing in the profits. His work provided employment and products for millions of people. [ citation needed ]
A few of Crosley's company's more noteworthy accomplishments:
Part of Crosley's Pinecroft estate, his former Cincinnati, Ohio, home, is the site of Mercy Hospitals West; however, the Franciscan Sisters of the Poor have used his mansion as a retreat since the early 1970s. Seagate, Crosley's former winter retreat on Sarasota Bay in Florida, is operated as an event rental facility. Pinecroft and Seagate have been restored and are listed in the National Register of Historic Places. [ 3 ] [ 4 ] [ 38 ] Crosley's farm in Jennings County, Indiana, is the site of the present-day Crosley Fish and Wildlife Area; [ 39 ] Bull Island, South Carolina, is part of the Cape Romain National Wildlife Refuge . [ 4 ]
WLW radio continues to operate as an AM station. Crosley's manufacturing plants in Richmond and Marion, Indiana, are still standing, but they no longer produce automobiles. [ 39 ] In 1973 a group of Avco executives purchased the Evendale, Ohio, operation of AVCO Electronics Division, a successor to one of Crosley's business ventures, and renamed it the Cincinnati Electronics Corporation. The company manufactured a broad range of sophisticated electronic equipment for communications and space, infrared and radar, and electronic warfare, among others. Since its creation in 1973, Cincinnati Electronics has been acquired by a handful of companies, including GEC Marconi (1981), BAE Systems (1999), CMC Electronics (2001), L-3 Communications (2004–2019), and L3Harris (2019-present). [ citation needed ]
The present-day Crosley Corporation is not connected to the original Crosley. An independent appliance distributor formed the current company after purchasing the rights to the name from Avco in 1976. Its appliances are manufactured mostly in North America by Electrolux and Whirlpool Corporation . Crosley-branded, top-loading washing machines are made by the Whirlpool at its plant in Clyde, Ohio . [ 40 ] In 1984, Modern Marketing Concepts, one of the leading U.S. manufacturers of vintage-styled turntables, radios, and other audio electronics, reintroduced Crosley brand name for its Crosley Radio . [ citation needed ]
Crosley's automobiles and experimental military vehicles are in the collections of several museums. Crosleys are also sought-after vehicles by vintage auto collectors. [ 23 ] The Crosley company's Bonzo promotional items and Crosley Pup radios have become valuable as collectibles . A papier mâché Crosley Bonzo is on display at the Smithsonian Institution in Washington, D.C. [ 41 ]
The University of Cincinnati , where Crosley was a student, has named their building Crosley Tower after him. [ 42 ] | https://en.wikipedia.org/wiki/Powel_Crosley_Jr. |
A power quantity is a power or a quantity directly proportional to power , e.g., energy density , acoustic intensity , and luminous intensity . [ 1 ] Energy quantities may also be labelled as power quantities in this context. [ 2 ]
A root-power quantity is a quantity such as voltage , current , sound pressure , electric field strength , speed , or charge density , the square of which, in linear systems, is proportional to power. [ 3 ] The term root-power quantity refers to the square root that relates these quantities to power. The term was introduced in ISO 80000-1 § Annex C ; it replaces and deprecates the term field quantity .
It is essential to know which category a measurement belongs to when using decibels (dB) for comparing the levels of such quantities. A change of one bel in the level corresponds to a 10× change in power , so when comparing power quantities x and y , the difference is defined to be 10×log 10 ( y / x ) decibel. With root-power quantities, however the difference is defined as 20×log 10 ( y / x ) dB. [ 3 ]
In the analysis of signals and systems using sinusoids, field quantities and root-power quantities may be complex -valued, [ 4 ] [ 5 ] [ 6 ] [ disputed – discuss ] as in the propagation constant .
In justifying the deprecation of the term "field quantity" and instead using "root-power quantity" in the context of levels, ISO 80000 draws attention to the conflicting use of the former term to mean a quantity that depends on the position, [ 7 ] which in physics is called a field . Such a field is often called a field quantity in the literature, [ citation needed ] but is called a field here for clarity. Several types of field (such as the electromagnetic field ) meet the definition of a root-power quantity, whereas others (such as the Poynting vector and temperature ) do not. Conversely, not every root-power quantity is a field (such as the voltage on a loudspeaker ). [ citation needed ] | https://en.wikipedia.org/wiki/Power,_root-power,_and_field_quantities |
Power-system automation is the act of automatically controlling the power system via instrumentation and control devices. Substation automation refers to using data from Intelligent electronic devices (IED), control and automation capabilities within the substation, and control commands from remote users to control power-system devices.
Since full substation automation relies on substation integration, the terms are often used interchangeably. Power-system automation includes processes associated with generation and delivery of power. Monitoring and control of power delivery systems in the substation and on the pole reduce the occurrence of outages and shorten the duration of outages that do occur. The IEDs , communications protocols, and communications methods, work together as a system to perform power-system automation.
The term “power system” describes the collection of devices that make up the physical systems that generate, transmit, and distribute power. The term “instrumentation and control (I&C) system” refers to the collection of devices that monitor, control, and protect the power system. Many power-system automation are monitored by SCADA.
Power-system automation is composed of several tasks.
In addition, another task is power-system integration, which is the act of communicating data to, from, or among IEDs in the I&C system and remote users. Substation integration refers to combining data from the IED's local to a substation so that there is a single point of contact in the substation for all of the I&C data.
Power-system automation processes rely on data acquisition; power-system supervision and power-system control all working together in a coordinated automatic fashion. The commands are generated automatically and then transmitted in the same fashion as operator initiated commands.
The instrument transformers with protective relays are used to sense the power-system voltage and current. They are physically connected to power-system apparatus and convert the actual power-system signals. The transducers convert the analog output of an instrument transformer from one magnitude to another or from one value type to another, such as from an ac current to dc voltage. Also the input data is taken from the auxiliary contacts of switch gears and power-system control equipment.
The I&C devices built using microprocessors are commonly referred to as intelligent electronic devices (IEDs). Microprocessors are single chip computers that allow the devices into which they are built to process data, accept commands, and communicate information like a computer. Automatic processes can be run in the IEDs. Some IEDs used in power-system automation are:
All lines and all electrical equipment must be protected against prolonged overcurrent . If the cause of the overcurrent is nearby then automatically that current is interrupted immediately. But if the cause of the overcurrent is outside the local area then a backup provision automatically disconnects all affected circuits after a suitable time delay.
Note that disconnection can, unfortunately, have a cascade effect, leading to overcurrent in other circuits that then also must therefore disconnect automatically.
Also note that generators that suddenly have lost their load because of such a protection operation will have to shut down automatically immediately, and it may take many hours to restore a proper balance between demand and supply in the system, partly because there must be proper synchronization before any two parts of the system can be reconnected.
Reclosing operations of circuit breakers usually are attempted automatically, and often are successful during thunderstorms, for example.
A supervisory control and data acquisition system ( SCADA ) transmits and receives commands or data from process instruments and equipment. Power system elements ranging from pole-mounted switches to entire power plants can be controlled remotely over long distance communication links. Remote switching, telemetering of grids (showing voltage, current, power, direction, consumption in kWh , etc.), even automatic synchronization is used in some power systems.
Power utility companies protect high voltage lines by monitoring them constantly. This supervision requires the transmission of information between the power substations in order to ensure correct operation while controlling every alarm and failure. Legacy telecom networks were interconnected with metallic wires, but the substation environment is characterized by a high level of electromagnetic fields that may disturb copper wires.
Authorities use a tele-protection scheme to enable substations to communicate with one another to selectively isolate faults on high voltage lines , transformers , reactors and other important elements of the electrical plants. This functionality requires the continuous exchange of critical data in order to assure correct operation. In order to warranty the operation the telecom network should always be in perfect conditions in terms of availability, performance, quality and delays.
Initially these networks were made of metallic conductive media, however the vulnerability of the 56–64 kbit/s channels to electromagnetic interference , signal ground loops , and ground potential rise made them too unreliable for the power industry. Strong electromagnetic fields caused by the high voltages and currents in power lines occur regularly in electric substations.
Moreover, during fault conditions electromagnetic perturbations may rise significantly and disturb those communications channels based on copper wires. The reliability of the communications link interconnecting the protection relays is critical and therefore must be resistant to effects encountered in high voltage areas, such as high frequency induction and ground potential rise.
Consequently, the power industry moved to optical fibers to interconnect the different items installed in substations. Fiber optics need not be grounded and are immune to the interferences caused by electrical noise, eliminating many of the errors commonly seen with electrical connections. The use of fully optical links from power relays to multiplexers as described by IEEE C37.94 became standard.
A more sophisticated architecture for the protection scheme emphasizes the notion of fault tolerant networks. Instead of using a direct relay connection and dedicated fibers, redundant connections make the protection process more reliable by increasing the availability of critical data interchanges.
IEEE C37.94 , full title IEEE Standard for N Times 64 Kilobit Per Second Optical Fiber Interfaces Between Teleprotection and Multiplexer Equipment , is an IEEE standard, published in 2002, that defines the rules to interconnect tele-protection and multiplexer devices of power utility companies. The standard defines a data frame format for optical interconnection, and references standards for the physical connector for multi-mode optical fiber . Furthermore, it defines behavior of connected equipment on failure of the link, and the timing and optical signal characteristics.
Teleprotection systems must isolate faults very quickly to prevent damage to the network and power outages. The IEEE committee defined C37.94 as a programmable n x 64 kbit/s (n=1...12) multimode optical fiber interface to provide transparent communications between teleprotection relays and multiplexers for distances of up to 2 km. To reach longer distances, the power industry later adopted a single mode optical fiber interface as well.
The standard defines the protection and communications equipment inside a substation using optical fibers, the method for clock recovery, the jitter tolerances allowed in the signals, the physical connection method, and the actions the protection equipment must follow when any kind of network anomalies and faults occur. C37.94 was already implemented by many protection relay manufacturers such as ABB, SEL, RFL, and RAD; and tester manufacturers such as Net Research (NetProbe 2000), ALBEDO and VEEX. Teleprotection equipment once offered a choice of transmission interfaces, such as the IEEE C37.94 compliant optical fiber interface for transmission over fiber pairs, and G.703 , 64 kbit/s co-directional and E1 interfaces. | https://en.wikipedia.org/wiki/Power-system_automation |
Power-to-weight ratio ( PWR , also called specific power , or power-to-mass ratio ) is a calculation commonly applied to engines and mobile power sources to enable the comparison of one unit or design to another. Power-to-weight ratio is a measurement of actual performance of any engine or power source. It is also used as a measurement of performance of a vehicle as a whole, with the engine's power output being divided by the weight (or mass ) of the vehicle, to give a metric that is independent of the vehicle's size. Power-to-weight is often quoted by manufacturers at the peak value, but the actual value may vary in use and variations will affect performance.
The inverse of power-to-weight, weight-to-power ratio (power loading) is a calculation commonly applied to aircraft, cars, and vehicles in general, to enable the comparison of one vehicle's performance to another. Power-to-weight ratio is equal to thrust per unit mass multiplied by the velocity of any vehicle.
The power-to-weight ratio (specific power) is defined as the power generated by the engine(s) divided by the mass. In this context, the term "weight" can be considered a misnomer, as it colloquially refers to mass. In a zero-gravity (weightless) environment, the power-to-weight ratio would not be considered infinite.
A typical turbocharged V8 diesel engine might have an engine power of 250 kW (340 hp) and a mass of 380 kg (840 lb), [ 1 ] giving it a power-to-weight ratio of 0.65 kW/kg (0.40 hp/lb).
Examples of high power-to-weight ratios can often be found in turbines. This is because of their ability to operate at very high speeds. For example, the Space Shuttle 's main engines used turbopumps (machines consisting of a pump driven by a turbine engine) to feed the propellants (liquid oxygen and liquid hydrogen ) into the engine's combustion chamber. The original liquid hydrogen turbopump is similar in size to an automobile engine (weighing approximately 352 kilograms (775 lb)) and produces 72,000 hp (54 MW) [ 2 ] for a power-to-weight ratio of 153 kW/kg (93 hp/lb).
In classical mechanics , instantaneous power is the limiting value of the average work done per unit time as the time interval Δ t approaches zero (i.e. the derivative with respect to time of the work done).
The typically used metric unit of the power-to-weight ratio is W kg {\displaystyle {\tfrac {\text{W}}{\text{kg}}}\;} which equals m 2 s 3 {\displaystyle {\tfrac {{\text{m}}^{2}}{{\text{s}}^{3}}}\;} . This fact allows one to express the power-to-weight ratio purely by SI base units . A vehicle's power-to-weight ratio equals its acceleration times its velocity; so at twice the velocity, it experiences half the acceleration, all else being equal.
If the work to be done is rectilinear motion of a body with constant mass m {\displaystyle m\;} , whose center of mass is to be accelerated along a (possibly non-straight) line to a speed | v ( t ) | {\displaystyle |\mathbf {v} (t)|\;} and angle ϕ {\displaystyle \phi \;} with respect to the centre and radial of a gravitational field by an onboard powerplant , then the associated kinetic energy is
where:
The work–energy principle states that the work done to the object over a period of time is equal to the difference in its total energy over that period of time, so the rate at which work is done is equal to the rate of change of the kinetic energy (in the absence of potential energy changes).
The work done from time t to time t + Δ t along the path C is defined as the line integral ∫ C F ⋅ d x = ∫ t t + Δ t F ⋅ v ( t ) d t {\displaystyle \int _{C}\mathbf {F} \cdot d\mathbf {x} =\int _{t}^{t+\Delta t}\mathbf {F} \cdot \mathbf {v} (t)dt} , so the fundamental theorem of calculus has that power is given by F ( t ) ⋅ v ( t ) = m a ( t ) ⋅ v ( t ) = τ ( t ) ⋅ ω ( t ) {\displaystyle \mathbf {F} (t)\cdot \mathbf {v} (t)=m\mathbf {a} (t)\cdot \mathbf {v} (t)=\mathbf {\tau } (t)\cdot \mathbf {\omega } (t)} .
where:
In propulsion , power is only delivered if the powerplant is in motion, and is transmitted to cause the body to be in motion. It is typically assumed here that mechanical transmission allows the powerplant to operate at peak output power. This assumption allows engine tuning to trade power band width and engine mass for transmission complexity and mass. Electric motors do not suffer from this tradeoff, instead trading their high torque for traction at low speed. The power advantage or power-to-weight ratio is then
where:
The useful power of an engine with shaft power output can be calculated using a dynamometer to measure torque and rotational speed , with maximum power reached when torque multiplied by rotational speed is a maximum. For jet engines the useful power is equal to the flight speed of the aircraft multiplied by the force, known as net thrust, required to make it go at that speed. It is used when calculating propulsive efficiency .
Thermal energy is made up from molecular kinetic energy and latent phase energy. Heat engines are able to convert thermal energy in the form of a temperature gradient between a hot source and a cold sink into other desirable mechanical work . Heat pumps take mechanical work to regenerate thermal energy in a temperature gradient. Standard definitions should be used when interpreting how the propulsive power of a jet or rocket engine is transferred to its vehicle.
An electric motor uses electrical energy to provide mechanical work , usually through the interaction of a magnetic field and current-carrying conductors . By the interaction of mechanical work on an electrical conductor in a magnetic field, electrical energy can be generated .
Fluids (liquid and gas) can be used to transmit and/or store energy using pressure and other fluid properties. Hydraulic (liquid) and pneumatic (gas) engines convert fluid pressure into other desirable mechanical or electrical work . Fluid pumps convert mechanical or electrical work into movement or pressure changes of a fluid, or storage in a pressure vessel .
A variety of effects can be harnessed to produce thermoelectricity , thermionic emission , pyroelectricity and piezoelectricity . Electrical resistance and ferromagnetism of materials can be harnessed to generate thermoacoustic energy from an electric current.
All electrochemical cell batteries deliver a changing voltage as their chemistry changes from "charged" to "discharged". A nominal output voltage and a cutoff voltage are typically specified for a battery by its manufacturer. The output voltage falls to the cutoff voltage when the battery becomes "discharged". The nominal output voltage is always less than the open-circuit voltage produced when the battery is "charged". The temperature of a battery can affect the power it can deliver, where lower temperatures reduce power. Total energy delivered from a single charge cycle is affected by both the battery temperature and the power it delivers. If the temperature lowers or the power demand increases, the total energy delivered at the point of "discharge" is also reduced.
Battery discharge profiles are often described in terms of a factor of battery capacity . For example, a battery with a nominal capacity quoted in ampere-hours (Ah) at a C/10 rated discharge current (derived in amperes) may safely provide a higher discharge current – and therefore higher power-to-weight ratio – but only with a lower energy capacity. Power-to-weight ratio for batteries is therefore less meaningful without reference to corresponding energy-to-weight ratio and cell temperature. This relationship is known as Peukert's law . [ 54 ]
Capacitors store electric charge onto two electrodes separated by an electric field semi-insulating ( dielectric ) medium. Electrostatic capacitors feature planar electrodes onto which electric charge accumulates. Electrolytic capacitors use a liquid electrolyte as one of the electrodes and the electric double layer effect upon the surface of the dielectric-electrolyte boundary to increase the amount of charge stored per unit volume. Electric double-layer capacitors extend both electrodes with a nanoporous material such as activated carbon to significantly increase the surface area upon which electric charge can accumulate, reducing the dielectric medium to nanopores and a very thin high permittivity separator.
While capacitors tend not to be as temperature sensitive as batteries, they are significantly capacity constrained and without the strength of chemical bonds suffer from self-discharge. Power-to-weight ratio of capacitors is usually higher than batteries because charge transport units within the cell are smaller (electrons rather than ions), however energy-to-weight ratio is conversely usually lower.
Fuel cells and flow cells , although perhaps using similar chemistry to batteries, do not contain the energy storage medium or fuel . With a continuous flow of fuel and oxidant, available fuel cells and flow cells continue to convert the energy storage medium into electric energy and waste products. Fuel cells distinctly contain a fixed electrolyte whereas flow cells also require a continuous flow of electrolyte. Flow cells typically have the fuel dissolved in the electrolyte.
Power-to-weight ratios for vehicles are usually calculated using curb weight (for cars) or wet weight (for motorcycles), that is, excluding weight of the driver and any cargo. This could be slightly misleading, especially with regard to motorcycles, where the driver might weigh 1/3 to 1/2 as much as the vehicle itself. In the sport of competitive cycling athlete's performance is increasingly being expressed in VAMs and thus as a power-to-weight ratio in W/kg. This can be measured through the use of a bicycle powermeter or calculated from measuring incline of a road climb and the rider's time to ascend it. [ 104 ]
A locomotive generally must be heavy in order to develop enough adhesion on the rails to start a train. As the coefficient of friction between steel wheels and rails seldom exceeds 0.25 in most cases, improving a locomotive's power-to-weight ratio is often counterproductive. However, the choice of power transmission system, such as variable-frequency drive versus direct-current drive , may support a higher power-to-weight ratio by better managing propulsion power.
Most vehicles are designed to meet passenger comfort and cargo carrying requirements. Vehicle designs trade off power-to-weight ratio to increase comfort, cargo space, fuel economy , emissions control , energy security and endurance. Reduced drag and lower rolling resistance in a vehicle design can facilitate increased cargo space without increase in the (zero cargo) power-to-weight ratio. This increases the role flexibility of the vehicle. Energy security considerations can trade off power (typically decreased) and weight (typically increased), and therefore power-to-weight ratio, for fuel flexibility or drive-train hybridisation . Some utility and practical vehicle variants such as hot hatches and sports-utility vehicles reconfigure power (typically increased) and weight to provide the perception of sports car like performance or for other psychological benefit .
Increased engine performance is a consideration, but also other features associated with luxury vehicles . Longitudinal engines are common. Bodies vary from hot hatches , sedans (saloons) , coupés , convertibles and roadsters . Mid-range dual-sport and cruiser motorcycles tend to have similar power-to-weight ratios.
Power-to-weight ratio is an important vehicle characteristic that affects the acceleration of sports vehicles.
[ 386 ]
Propeller aircraft depend on high power-to-weight ratios to generate sufficient thrust to achieve sustained flight, and then for speed.
Jet aircraft produce thrust directly .
Power-to-weight ratio is important in cycling, since it determines acceleration and the speed during hill climbs . Since a cyclist's power-to-weight output decreases with fatigue, it is normally discussed with relation to the length of time that he or she maintains that power. A professional cyclist can produce over 20 W/kg (0.012 hp/lb) as a five-second maximum. [ 648 ] | https://en.wikipedia.org/wiki/Power-to-weight_ratio |
Power-voltage curve (also P-V curve ) describes the relationship between the active power delivered to the electrical load and the voltage at the load terminals in an electric power system under a constant power factor . [ 1 ] When plotted with power as a horizontal axis, the curve resembles a human nose, thus it is sometimes called a nose curve . [ 2 ] The overall shape of the curve (similar to a parabola placed on its side) is defined by the basic electrical equations and does not change much when the characteristics of the system vary: leading power factor lead stretches the "nose" further to the right and upwards, while the lagging one shrinks the curve. [ 3 ] The curve is important for voltage stability analysis , as the coordinate of the tip of the nose defines the maximum power that can be delivered by the system.
As the load increases from zero, the power-voltage point travels from the top left part of the curve to the tip of the "nose" (power increases, but the voltage drops). The tip corresponds to the maximum power that can be delivered to the load (as long as sufficient reactive power reserves are available). Past this "collapse" point additional loads cause drop in both voltage and power, as the power-voltage point travels to the bottom left corner of the plot. [ 2 ] Intuitively this result can be explained when a load that consists entirely of resistors is considered: as the load increases (its resistance thus lowers), more and more of the generator power dissipates inside the generator itself (that has it own fixed resistance connected sequentially with the load). [ 4 ] Operation on the bottom part of the curve (where the same power is delivered with lower voltage – and thus higher current and losses) is not practical, as it corresponds to the "uncontrollability" region. [ 2 ]
If sufficient reactive power is not available, the limit of the load power will be reached prior to the power-voltage point getting to the tip of the "nose". The operator shall maintain a sufficient margin between the operating point on the P-V curve and this maximum loading condition , otherwise, a voltage collapse can occur. [ 5 ]
A similar curve for the reactive power is called Q-V curve . [ 1 ]
This electricity-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Power-voltage_curve |
PowerCLI is a PowerShell -based command-line interface for managing VMware vSphere .
VMware describes PowerCLI as "a powerful command-line tool that lets you automate all aspects of vSphere management, including network, storage, VM , guest OS and more. PowerCLI is distributed as PowerShell modules, and includes over 500 PowerShell cmdlets for managing and automating vSphere and vCloud , along with documentation and samples." [ 1 ]
PowerCLI runs in PowerShell on Windows, macOS , and Ubuntu operating systems. [ 2 ]
This software article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/PowerCLI |
Powerfleet, Inc. (formerly I.D. Systems, Inc. ) is an American company headquartered in Woodcliff Lake, New Jersey , with offices located around the globe and a technology innovation center in Israel. The company is a global provider of wireless IoT and M2M solutions [ buzzword ] for securing, controlling, tracking, and managing high-value enterprise assets such as industrial trucks, tractor trailers, intermodal shipping containers, cargo, and vehicle and truck fleets.
Powerfleet was formed on October 3, 2019 when I.D. Systems acquired Pointer Telocation Ltd. and their subsidiary brand Cellocator, and subsequently rebranded the new company as Powerfleet Inc. [ 1 ]
Powerfleet provides a technology suite that delivers telematics , asset tracking, freight visibility, and driver behavior reporting and modification. [ 2 ]
I.D. Systems was founded in 1993 by Kenneth S. Ehrman. The company introduced the use of radio frequency identification (RFID) technology for industrial asset tracking and management. In 1995, I.D. Systems was awarded a $6.6 million [ 3 ] contract from U.S. Postal Service (USPS) to develop and implement a tracking system for test letters and packages. [ 4 ] I.D. Systems went public on the NASDAQ in 1999. [ 3 ]
In 2005, I.D. Systems received a three-year contract from the U.S. Postal Service to implement its Wireless Asset Net, a wireless industrial vehicle management system, at 460 USPS facilities nationwide. In 2009, I.D. Systems acquired didBOX Ltd., a privately held, United Kingdom-based manufacturer and marketer of driver identification systems for forklift fleets. The acquisition made didBOX a wholly owned subsidiary of I.D. Systems, broadened I.D. Systems' product line, and expanded sales of the company's vehicle management solutions [ buzzword ] in the European market. [ 5 ]
In 2010, I.D. Systems acquired GE Asset Intelligence, LLC, a business unit of the General Electric Company. The acquisition expanded the scope of I.D. Systems' product line and complemented its portfolio of wireless asset management patents. [ 6 ]
In 2011, I.D. Systems and Avis Budget Group signed an exclusive agreement to deploy I.D. Systems' wireless vehicle management technology on more than 25,000 Avis Budget vehicles, [ 7 ] enabling Avis customers to self-manage their rentals by computer or smartphone. The technology can also automate and expedite the rental and return process, track vehicle mileage, measure fuel consumption, and remotely control a vehicle's door locks. [ 8 ] In February 2013, the company was awarded its second patent (patent number 8370268) for an automated wireless rental car management system. [ 9 ]
In 2012, the company launched I.D. Systems Analytics, a set of web-based data reporting software tools. [ 10 ] [ 11 ]
In 2017, the company acquired Keytroller LLC for 9 million U.S. dollars. Keytroller sold electronic products for managing forklifts, construction vehicles, and other industrial equipment. [ 12 ] [ independent source needed ]
Finally, in 2019 the company acquired Pointer Telocation LTD and renamed itself as Powerfleet Inc. As part of this change, the company retired its NASDAQ ticker symbol of IDSY and adopted PWFL. [ 13 ] [ independent source needed ] | https://en.wikipedia.org/wiki/PowerFleet |
PowerLab (before 1998 was referred to as MacLab) is a data acquisition system developed by ADInstruments comprising hardware and software and designed for use in life science research [ 1 ] and teaching applications. It is commonly used in physiology, pharmacology, biomedical engineering, sports/exercise studies and psychophysiology laboratories to record and analyse physiological signals from human or animal subjects or from isolated organs. The system consists of an input device connected to a Microsoft Windows or Mac OS computer using a USB cable and LabChart software which is supplied with the PowerLab and provides the recording, display and analysis functions. The use of PowerLab and supplementary ADInstruments products have been demonstrated on the Journal of Visualised Experiments. [ 2 ]
The original MacLab unit was developed in the late 1980s to run with only Macintosh computers to perform computer-based data acquisition and analysis. The MacLab product range was renamed "PowerLab" in 1997 to reflect the cross-platform nature of the system. [ citation needed ]
The PowerLab system is essentially a peripheral device designed to perform various functions needed for data acquisition , signal conditioning and pre-processing. [ 3 ] Versatile display options and analysis functions are complemented by the ability to export data to other software (such as Microsoft Excel).
Source: [ 4 ]
Formerly known as Chart. The software functions like a traditional multi-channel chart recorder , XY plotter , polygraph and digital voltmeter . It is compatible with both Windows and Macintosh operating systems. The software has hardware settings control, performs analysis in real-time and offline without the loss of raw data, procedure automation via editable macros, and multiple block samplings for the recording and settings of different signals within one file. [ 5 ] Large specialised add-ons called Modules provide data acquisition and analysis features for specific applications such as ECG, blood pressure, cardiac output, HRV etc. Smaller software plugins provide additional and specialized functionality to LabChart. Extensions perform functions such as file translations into other formats (including PVAN and Igor Pro ) and specialist analysis functions (for specific research areas such as spirometry and ventricular pressure). The last version of LabChart6 (version 6.1.3) was released in January 2009. [ citation needed ]
In April 2009, LabChart 7 was released and incorporates the features of a multi-channel digital oscilloscope that allows recording and averaging of up to sixteen signals in real time. Latest version of LabChart7 is version 7.0.
LabChart 8 is also now available.
Software provides a range of hands-on laboratory background for students that includes experimental background & protocols, data acquisition & analysis, and report generation within one interface. [ 6 ] [ 7 ] The software and accompanying PowerLab hardware is configured for immediate use with step by step instructions designed to maximize student productivity by applying independent learning techniques to a suite of human and animal physiological experiments. [ 6 ] Recently, LabAuthor software was released to provide educators the ability to design or edit existing LabTutor experiments and tailor the experiments to suit their practical classes without the need of programming or HTML skills.
Records and analyzes high frequency signals that are time-locked to a stimulus. The display allows computer screen to act as an oscilloscope and XY plotter
The PowerLab messaging protocol is not publicly available and there is no public API for traditional programming languages such as C. | https://en.wikipedia.org/wiki/PowerLab |
PowerPlant is an object-oriented GUI toolkit , application framework and set of class libraries for the Classic Mac OS , created by Metrowerks . The framework was fairly popular during the late (OS versions 8 and 9) Classic Mac OS era, and was primarily used with CodeWarrior . It was designed to work with a GUI editor called Constructor, which was primarily a resource editor specializing in UI elements. Constructor used several custom resource types, 'PPob' ("PowerPlant object"—a general view description), 'CTYP' (custom widgets), and Mcmd (used for dispatching menu-related events). Later it was ported to also support MacOS X development with a single code base. [ 1 ]
After Metrowerks was acquired by Motorola , then spun out as part of Freescale Semiconductor , PowerPlant and the rest of the CodeWarrior desktop development tools were discontinued. [ 2 ]
During its heyday from the mid-1990s until the early 2000s, PowerPlant was the most popular framework available for Mac programmers, [ 1 ] [ 3 ] [ 4 ] replacing both the THINK Class Library and MacApp as the premier object-oriented toolkit for the MacOS; however, the transition to MacOS X was rather difficult for many PowerPlant programmers. [ citation needed ] In 1997, there was no plan to port PowerPlant to the Yellow Box API found on Rhapsody, a radically different API that would become Cocoa , the official MacOS X API. [ 5 ] Instead Metrowerks plan was to port PowerPlant using Codewarior Latitude, a Mac to UNIX porting library they acquired recently. [ 6 ] In 2000, as Apple revised its transition plans, PowerPlant was ported to Carbon , with the Aqua user interface on MacOS X , offering a solution for developers wanting to support the new operating system. [ 4 ] [ 7 ]
A new version, PowerPlant X , was introduced in 2004 as a native Carbon framework, using Carbon Events but never became as popular on Mac OS X as PowerPlant had been on Classic Mac OS. [ 8 ]
In February 2006, the PowerPlant class libraries were released as open source under the BSD license hosted on SourceForge . [ 9 ] Although it could theoretically be recompiled for x86-64 Macs, it is Carbon-dependent and therefore can only be used in 32-bit mode, which preclude its use for software to run on macOS Catalina or later as 32-bit application support was dropped by the system. [ 10 ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/PowerPlant |
Power is the amount of energy transferred or converted per unit time. In the International System of Units , the unit of power is the watt , equal to one joule per second. Power is a scalar quantity.
Specifying power in particular systems may require attention to other quantities; for example, the power involved in moving a ground vehicle is the product of the aerodynamic drag plus traction force on the wheels, and the velocity of the vehicle. The output power of a motor is the product of the torque that the motor generates and the angular velocity of its output shaft. Likewise, the power dissipated in an electrical element of a circuit is the product of the current flowing through the element and of the voltage across the element. [ 1 ] [ 2 ]
Power is the rate with respect to time at which work is done or, more generally, the rate of change of total mechanical energy. It is given by: P = d E d t , {\displaystyle P={\frac {dE}{dt}},} where P is power, E is the total mechanical energy (sum of kinetic and potential energy), and t is time.
For cases where only work is considered, power is also expressed as: P = d W d t , {\displaystyle P={\frac {dW}{dt}},} where W is the work done on the system. However, in systems where potential energy changes without explicit work being done (e.g., changing fields or conservative forces), the total energy definition is more general.
We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product: P = d W d t = F ⋅ v {\displaystyle P={\frac {dW}{dt}}=\mathbf {F} \cdot \mathbf {v} }
If a constant force F is applied throughout a distance x , the work done is defined as W = F ⋅ x {\displaystyle W=\mathbf {F} \cdot \mathbf {x} } . In this case, power can be written as: P = d W d t = d d t ( F ⋅ x ) = F ⋅ d x d t = F ⋅ v . {\displaystyle P={\frac {dW}{dt}}={\frac {d}{dt}}\left(\mathbf {F} \cdot \mathbf {x} \right)=\mathbf {F} \cdot {\frac {d\mathbf {x} }{dt}}=\mathbf {F} \cdot \mathbf {v} .}
If instead the force is variable over a three-dimensional curve C , then the work is expressed in terms of the line integral: W = ∫ C F ⋅ d r = ∫ Δ t F ⋅ d r d t d t = ∫ Δ t F ⋅ v d t . {\displaystyle W=\int _{C}\mathbf {F} \cdot d\mathbf {r} =\int _{\Delta t}\mathbf {F} \cdot {\frac {d\mathbf {r} }{dt}}\ dt=\int _{\Delta t}\mathbf {F} \cdot \mathbf {v} \,dt.}
From the fundamental theorem of calculus , we know that P = d W d t = d d t ∫ Δ t F ⋅ v d t = F ⋅ v . {\displaystyle P={\frac {dW}{dt}}={\frac {d}{dt}}\int _{\Delta t}\mathbf {F} \cdot \mathbf {v} \,dt=\mathbf {F} \cdot \mathbf {v} .} Hence the formula is valid for any general situation.
In older works, power is sometimes called activity . [ 3 ] [ 4 ] [ 5 ]
The dimension of power is energy divided by time. In the International System of Units (SI), the unit of power is the watt (W), which is equal to one joule per second. Other common and traditional measures are horsepower (hp), comparing to the power of a horse; one mechanical horsepower equals about 745.7 watts. Other units of power include ergs per second (erg/s), foot-pounds per minute, dBm , a logarithmic measure relative to a reference of 1 milliwatt, calories per hour, BTU per hour (BTU/h), and tons of refrigeration .
As a simple example, burning one kilogram of coal releases more energy than detonating a kilogram of TNT , [ 6 ] but because the TNT reaction releases energy more quickly, it delivers more power than the coal.
If Δ W is the amount of work performed during a period of time of duration Δ t , the average power P avg over that period is given by the formula P a v g = Δ W Δ t . {\displaystyle P_{\mathrm {avg} }={\frac {\Delta W}{\Delta t}}.} It is the average amount of work done or energy converted per unit of time. Average power is often called "power" when the context makes it clear.
Instantaneous power is the limiting value of the average power as the time interval Δ t approaches zero. P = lim Δ t → 0 P a v g = lim Δ t → 0 Δ W Δ t = d W d t . {\displaystyle P=\lim _{\Delta t\to 0}P_{\mathrm {avg} }=\lim _{\Delta t\to 0}{\frac {\Delta W}{\Delta t}}={\frac {dW}{dt}}.}
When power P is constant, the amount of work performed in time period t can be calculated as W = P t . {\displaystyle W=Pt.}
In the context of energy conversion, it is more customary to use the symbol E rather than W .
Power in mechanical systems is the combination of forces and movement. In particular, power is the product of a force on an object and the object's velocity, or the product of a torque on a shaft and the shaft's angular velocity.
Mechanical power is also described as the time derivative of work. In mechanics , the work done by a force F on an object that travels along a curve C is given by the line integral : W C = ∫ C F ⋅ v d t = ∫ C F ⋅ d x , {\displaystyle W_{C}=\int _{C}\mathbf {F} \cdot \mathbf {v} \,dt=\int _{C}\mathbf {F} \cdot d\mathbf {x} ,} where x defines the path C and v is the velocity along this path.
If the force F is derivable from a potential ( conservative ), then applying the gradient theorem (and remembering that force is the negative of the gradient of the potential energy) yields: W C = U ( A ) − U ( B ) , {\displaystyle W_{C}=U(A)-U(B),} where A and B are the beginning and end of the path along which the work was done.
The power at any point along the curve C is the time derivative: P ( t ) = d W d t = F ⋅ v = − d U d t . {\displaystyle P(t)={\frac {dW}{dt}}=\mathbf {F} \cdot \mathbf {v} =-{\frac {dU}{dt}}.}
In one dimension, this can be simplified to: P ( t ) = F ⋅ v . {\displaystyle P(t)=F\cdot v.}
In rotational systems, power is the product of the torque τ and angular velocity ω , P ( t ) = τ ⋅ ω , {\displaystyle P(t)={\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }},} where ω is angular frequency , measured in radians per second . The ⋅ {\displaystyle \cdot } represents scalar product .
In fluid power systems such as hydraulic actuators, power is given by P ( t ) = p Q , {\displaystyle P(t)=pQ,} where p is pressure in pascals or N/m 2 , and Q is volumetric flow rate in m 3 /s in SI units.
If a mechanical system has no losses, then the input power must equal the output power. This provides a simple formula for the mechanical advantage of the system.
Let the input power to a device be a force F A acting on a point that moves with velocity v A and the output power be a force F B acts on a point that moves with velocity v B . If there are no losses in the system, then P = F B v B = F A v A , {\displaystyle P=F_{\text{B}}v_{\text{B}}=F_{\text{A}}v_{\text{A}},} and the mechanical advantage of the system (output force per input force) is given by M A = F B F A = v A v B . {\displaystyle \mathrm {MA} ={\frac {F_{\text{B}}}{F_{\text{A}}}}={\frac {v_{\text{A}}}{v_{\text{B}}}}.}
The similar relationship is obtained for rotating systems, where T A and ω A are the torque and angular velocity of the input and T B and ω B are the torque and angular velocity of the output. If there are no losses in the system, then P = T A ω A = T B ω B , {\displaystyle P=T_{\text{A}}\omega _{\text{A}}=T_{\text{B}}\omega _{\text{B}},} which yields the mechanical advantage M A = T B T A = ω A ω B . {\displaystyle \mathrm {MA} ={\frac {T_{\text{B}}}{T_{\text{A}}}}={\frac {\omega _{\text{A}}}{\omega _{\text{B}}}}.}
These relations are important because they define the maximum performance of a device in terms of velocity ratios determined by its physical dimensions. See for example gear ratios .
The instantaneous electrical power P delivered to a component is given by P ( t ) = I ( t ) ⋅ V ( t ) , {\displaystyle P(t)=I(t)\cdot V(t),} where
If the component is a resistor with time-invariant voltage to current ratio, then: P = I ⋅ V = I 2 ⋅ R = V 2 R , {\displaystyle P=I\cdot V=I^{2}\cdot R={\frac {V^{2}}{R}},} where R = V I {\displaystyle R={\frac {V}{I}}} is the electrical resistance , measured in ohms .
In the case of a periodic signal s ( t ) {\displaystyle s(t)} of period T {\displaystyle T} , like a train of identical pulses, the instantaneous power p ( t ) = | s ( t ) | 2 {\textstyle p(t)=|s(t)|^{2}} is also a periodic function of period T {\displaystyle T} . The peak power is simply defined by: P 0 = max [ p ( t ) ] . {\displaystyle P_{0}=\max[p(t)].}
The peak power is not always readily measurable, however, and the measurement of the average power P a v g {\displaystyle P_{\mathrm {avg} }} is more commonly performed by an instrument. If one defines the energy per pulse as ε p u l s e = ∫ 0 T p ( t ) d t {\displaystyle \varepsilon _{\mathrm {pulse} }=\int _{0}^{T}p(t)\,dt} then the average power is P a v g = 1 T ∫ 0 T p ( t ) d t = ε p u l s e T . {\displaystyle P_{\mathrm {avg} }={\frac {1}{T}}\int _{0}^{T}p(t)\,dt={\frac {\varepsilon _{\mathrm {pulse} }}{T}}.}
One may define the pulse length τ {\displaystyle \tau } such that P 0 τ = ε p u l s e {\displaystyle P_{0}\tau =\varepsilon _{\mathrm {pulse} }} so that the ratios P a v g P 0 = τ T {\displaystyle {\frac {P_{\mathrm {avg} }}{P_{0}}}={\frac {\tau }{T}}} are equal. These ratios are called the duty cycle of the pulse train.
Power is related to intensity at a radius r {\displaystyle r} ; the power emitted by a source can be written as: [ citation needed ] P ( r ) = I ( 4 π r 2 ) . {\displaystyle P(r)=I(4\pi r^{2}).} | https://en.wikipedia.org/wiki/Power_(physics) |
Microsoft PowerToys is a set of freeware (later open source ) system utilities designed for power users developed by Microsoft for use on the Windows operating system. These programs add or change features to maximize productivity or add more customization. PowerToys are available for Windows 95 , Windows XP , Windows 10 , and Windows 11 (and explicitly not compatible with Windows Vista , 7 , 8 , or 8.1 ). [ 3 ] The PowerToys for Windows 10 and Windows 11 are free and open-source software licensed under the MIT License and hosted on GitHub .
PowerToys for Windows 95 was the first version of Microsoft PowerToys and included 15 tools for power users. It included Tweak UI , a system utility for tweaking the more obscure settings in Windows. In most cases, Tweak UI exposed settings that were otherwise only accessible by directly modifying Windows Registry . [ 4 ]
The following PowerToys for Windows 95 were available: [ 5 ]
PowerToys for Windows 95 were developed by the Windows Shell Development Team. Some of the tools work on later versions of Windows up to Windows XP , but others may interfere with newer built-in features on Windows 98 , ME , and XP . [ 6 ]
After the success of the Windows 95 PowerToys, the Windows Kernel Development Team released another set of tools for power users called Windows 95 Kernel Toys . [ 7 ]
Six tools were included in this package: [ 8 ]
According to Raymond Chen , he wrote all of the Kernel Toys except for the Time Zone Editor, which came from the Windows NT Resource Kit . [ 9 ]
PowerToys for Windows XP was the second version of the PowerToys set and brought major changes from the Windows 95 version. The tools in this set were available as separate downloads rather than in a single package.
As of November 2009 [update] , the following PowerToys for Windows XP were available: [ 10 ]
The following PowerToys for Windows XP were discontinued: [ 10 ]
Windows 10 received PowerToys four years after its release. On May 8, 2019, Microsoft relaunched PowerToys and made them open-source on GitHub . [ 20 ] The first preview release was available in September 2019, which included FancyZones and the Windows key shortcut guide. [ 21 ]
PowerToys for Windows 10 comes with the following utilities: [ 22 ]
PowerToys did not receive any releases supporting Windows Vista . Making equivalent calls to various Windows APIs were still possible though and enabling third-party applications to be implemented with the same, or a subset, of the original functionality. Additionally, among Windows 7 , [ 37 ] Windows 8 and Windows 8.1 , [ 38 ] none received official support. [ citation needed ] Not accounting for time spent developing Windows Vista , PowerToys was not updated for over 12 years, before being re-released as open source software for Windows 10 .
Microsoft also released PowerToys for Windows XP Tablet PC Edition [ 39 ] and Windows XP Media Center Edition . [ 40 ]
A set of PowerToys for Windows Media Player was released as part of the Windows Media Player Bonus Pack (for Windows XP), consisting of five tools to "provide a variety of enhancements to Windows Media Player." [ 41 ] [ 42 ]
Finally, Microsoft has also released PowerToys for Windows Mobile , Visual Studio [ 43 ] [ 44 ] [ 45 ] and OneNote . [ 46 ] [ 47 ] | https://en.wikipedia.org/wiki/Power_Calculator |
The Power Distribution Equipment Identification (PDEID) ( Persian : کد شناسایی یکپارچه توزیع ) is a unique identification label used for exclusively identifying equipment and customers of the power distribution network of Iran , which has been in use since 1997. PDEID is used to simplify identifying equipment, their approximate address, updating the electrical network information and to transfer information to computers.
The first unique identification code for equipment was introduced in the Iran's Power Distribution Network Standard in 1969. Only three equipment which were medium and low voltage poles, medium and low voltage branching nodes and distribution substations suggested to have equipment identification label. In 1996, at the 6th Conference on Electrical Power Distribution Networks, [ 1 ] an article entitled "Application of the Integrated Equipment Identification Label for Distribution Networks in the Iran" [ 2 ] [ 3 ] by Gholamreza Saffarpour ( Persian : غلامرضا صفارپور ) and Ali Mamdoohi ( Persian : علی ممدوحی ) was presented in which a method for uniquely identifying all equipment and subscribers of distribution networks introduced. This method was selected in 1997 with minor modifications by Tavanir to integrate the identification of equipment and subscribers of distribution networks.
Every code in the Power Distribution Equipment Identification label consists of 12 numbers and letters. The labels are grouped into two categories: network equipment and customers.
The equipment label contains 12 numbers and characters. The first 5 identifies the zip code of the area where the equipment is located. The 5-digit postcode contains the location information provided by Iran Post for the whole country. The next two are letters which identify the equipment type-ID. The last five digits are an assigned sequence (or serial) number for the equipment in the postcode area.
The sequence or serial number used in the integrated PDEID is an arbitrary number that is unique within the area of postcode. For example, the first distribution substation in the 13457 postcode should have the serial number 00001 and the second substation in the same postcode area (13457) should have serial number 00002, and so on. In this system, determining which equipment (substation in the above example) is first and which one is second is absolutely arbitrary.
Type ID
For customers the Power Distribution Equipment Identification label is composed of 12 digits, and similar to the equipment, the 5 leftmost digits are the 5-digit postcode of the area where the electricity mete r of the customer is located. The right 7 digits of the PDEID are the customer-id which is used in the billing system of power distribution utilities. In some parts of the Iran where the customer-id is more than 7 digits, the PDEID has 14 digits, and the 9 rightmost digits contain the customer-id number.
In the Power Distribution Equipment Identification label, identification is not considered for all equipment. However, by identifying and labeling 23 equipment, all equipment which is important in regard to engineering calculations or information statistics can be uniquely identified. Equipment type-ID does not include the letters I (i), O (o), and Q (q) to avoid confusion with numerals 1 and 0.
In assigning PDEID to the distribution equipment, a single-line diagram is used, so when the three-phase system is used, insulators , cable terminations , and cable joints of all three phases take just one PDEID each.
There are three differences between the final implemented PDEID and what was proposed in the article entitled "Application of the Integrated Equipment Identification Label for Distribution Networks in the Iran” [ 2 ] [ 3 ] as following:
Also to improve the readability of the labels, the type id is placed between the postcode (zip code) and sequence number (or customer id number for customers). | https://en.wikipedia.org/wiki/Power_Distribution_Equipment_Identification |
Power Shift is an annual youth summit which has been held in New Zealand , Australia , Canada , the United Kingdom and the United States . [ 1 ] [ 2 ] Other Power Shift Conferences are also being organised by members of the International Youth Climate Movement including Africa , Japan and India . [ 3 ] The focus of the events is on climate change policy .
The first Power Shift conference was held from November 2 to 5, 2007 in Washington, D.C. , and was organised by the Energy Action Coalition . [ 1 ] The second American conference occurred two years later on February 27 to March 2, 2009.
Following on from the success of the American format, the Australian Youth Climate Coalition organised a Power Shift event in Sydney , Australia , on July 11 to July 13, 2009. Similarly, the UK Youth Climate Coalition has scheduled the first British version of the event to run from October 9 to October 12, 2009. The first New Zealand Power Shift will be run between the 7th and 9 December 2012 in Auckland .
The aim of the Power Shift Conferences is to build the youth climate movement in their respective nations, which is achieved through workshops, expert panel discussions, keynote speakers, and a lobby day or a "Day of Action" as it is alternatively known. [ 4 ]
The first Power Shift Conference took place from November 2 to 5 in 2007 with between 5,000 and 6,000 students and young people in attendance. [ 1 ] It is claimed that due to the number of young people who attended the conference, it became the largest activist youth event on climate change in history. [ 5 ] At the University of Maryland, College Park , a rally of between 2,000 and 3,000 people on the steps of the Capitol building and a Lobby Day. The event was also attended by a number of keynote speakers which included Al Gore . The main aim of the first conference was to urge elected officials to pass legislation which would include three planks taken from the platform of the climate advocacy coalition 1Sky : [ 4 ]
On February 27 to March 2, 2009, the second American Power Shift Conference took place. Similarly to the first summit, it included workshops, panel discussions, and speakers focusing on addressing climate change and environmental justice . Casper ter Kuile the co-director of the UK Youth Climate Coalition states that it is more than a youth movement, it is " social movement " . [ 6 ] This time, keynote speakers included Van Jones , Bill McKibben of 350.org , Ralph Nader , and Speaker of the House Nancy Pelosi . [ 7 ]
The third American Power Shift took place April 15 to 18, 2011, in Washington, D.C., at the Walter E. Washington Convention Center . The conference had over 10,000 attenders. People came to support various environmental movements , many in protest of President Barack Obama 's alleged weakness on environmental issues. [ citation needed ] Guest speakers included former U.S. vice-president Al Gore, Greenpeace Executive Director Phil Radford , and environmental advocate Van Jones .
The fourth Power Shift conference in the US was also the first outside of Washington. It was instead held in Pittsburgh, Pennsylvania , at the David L. Lawrence Convention Center on October 19–21, 2013. Keynote speakers included Gasland director Josh Fox , Sierra Club director Michael Brune , and Kandi Mossett of the Indigenous Environmental Network . The program included a rally against coal production and the organization of protests against the Keystone XL Pipeline .
In 2006, a series of student conferences on energy security were organized under the name PowerShift by the 20/20 Vision Education Fund, a 501(c)(3) organization based out of Maryland . (They were not affiliated with the 2007 and later Power Shift conferences organized by the Energy Action Coalition .) Over 250 people participated in the first conference which took place in Kalamazoo , MI on April 1, 2006, and featured former Central Intelligence Agency director Jim Woolsey giving a keynote speech on U.S. oil dependence and national security . The conferences also featured a simulated energy wargame called Oil Shockwave , developed by non-profit groups Securing America's Future Energy (SAFE) and the National Commission on Energy Policy [ who? ] . The website for the conference series has been taken down, but is viewable using the Internet Wayback Machine .
Two years later in 2009, the Australian Youth Climate Coalition , in partnership with the University of Western Sydney , GetUp and Greenpeace , organised the Australian Power Shift Conference on July 11 to 13, 2009. [ 8 ] Approximately 1,500 young people attended the summit. Guests included former Vice President of the United States Al Gore , the swimmer Ian Thorpe and the actress Brooke Satchwell . [ 9 ] The event concluded with a flashmob action outside the Sydney Opera House . [ 10 ] In 2010, the AYCC held three regional Power Shift Conferences in Adelaide , Canberra and Geelong . [ 11 ]
In 2011, the AYCC organised Power Shift Conferences in Perth and Brisbane with over 1,000 young people. Speakers included Bill McKibben , Kumi Naidoo , Anna Rose , Dick Smith and Dr. Karl Kruszelnicki .
In 2013, the AYCC will hold Australia's largest ever Power Shift, in Melbourne from July 13–15.
In 2022, Power Shift is set to be held in the city of Brisbane from September 23–25.
The first Canadian Power Shift event was held from October 23 to October 26, 2009, in Ottawa, Ontario , by the Canadian Youth Climate Coalition. [ 12 ] Subsequent summits were held in Ottawa, ON in 2012; Victoria, BC in 2013; Halifax, NS in 2014; and Edmonton, AB in 2016.
A collaboration between 350.org Aotearoa and Generation Zero , a student environmental movement, and other individuals, will bring "Power Shift NZ-Pacific" to New Zealand for the first time, December 7–9, 2012, at the University of Auckland . [ 13 ]
Confirmed speakers so far include; American Environmentalist Bill McKibben , Mayor of Auckland Len Brown and Xena: Warrior Princess actress Lucy Lawless . [ 14 ]
On October 9–12, 2009, the UK version of Power Shift was held at the Institute of Education in London . Modelled on a similar event to one organised by the Australian Youth Climate Coalition and carrying the same name as the Energy Action Coalition event in the US, the event intended to develop the youth climate movement and provide young people with training on public speaking. [ 15 ] The training was based on the techniques developed by Marshall Ganz , a civil rights activist who is credited with devising the successful grassroots organizing model and public narrative training for 2008 Barack Obama presidential campaign . [ 16 ] [ 17 ] The Power Shift event intended to serve as a feeder to the International Day of Action organised by 350.org on October 24.
A PowerShift UK event scheduled in 2011 was cancelled, but large-scale youth climate movement events have been taking place annually under the name Shared Planet since 1999, organised by the UK's largest student-led climate campaigning network People & Planet .
On May 3–4, 2014, a Power Shift UK event was held in London, titled 'Breaking Down the Barriers and Diversifying the Climate Movement'. Open to people from all walks of society who want to contribute to action on climate change, the event brought people across the UK together for a weekend of discussions and workshops, to share stories and ideas for action, and to challenge assumptions about diversifying the climate movement. [ 18 ] | https://en.wikipedia.org/wiki/Power_Shift_(conference) |
Power alley is a term used in audio engineering to denote the line between subwoofers where output from each subwoofer is in phase and is noticeably louder.
Subwoofers placed at each side of the stage will typically cancel unpredictably everywhere in the listening area except along the center line between the speakers . Because of this, placing subwoofer cabinets together tends to give a smoother response to each member of the audience. [ 1 ]
Centering the subwoofers between the high-end cabinets tends to minimize the timing error throughout the listening area. [ 2 ] The effects of separated subwoofers are more predictable outdoors; however, subwoofers are often placed together as a starting point for indoor venues as well. | https://en.wikipedia.org/wiki/Power_alley |
In linear algebra , a power cone is a kind of a convex cone that is particularly important in modeling convex optimization problems. [ 1 ] [ 2 ] It is a generalization of the quadratic cone : the quadratic cone is defined using a quadratic equation (with the power 2), whereas a power cone can be defined using any power, not necessarily 2.
The n -dimensional power cone is parameterized by a real number 0 < r < 1 {\displaystyle 0<r<1} . It is defined as: [ 1 ]
P n , r , 1 − r := { x ∈ R n : x 1 ≥ 0 , x 2 ≥ 0 , x 1 r ⋅ x 2 1 − r ≥ x 3 2 + ⋯ + x n 2 } {\displaystyle P_{n,r,1-r}:=\left\{\mathbf {x} \in \mathbb {R} ^{n}:~~x_{1}\geq 0,~~x_{2}\geq 0,~~x_{1}^{r}\cdot x_{2}^{1-r}\geq {\sqrt {x_{3}^{2}+\cdots +x_{n}^{2}}}\right\}}
An alternative definition is
P r , 1 − r := { x 1 , x 2 , x 3 : x 1 ≥ 0 , x 2 ≥ 0 , x 1 r ⋅ x 2 1 − r ≥ | x 3 | } {\displaystyle P_{r,1-r}:=\left\{\mathbf {x_{1},x_{2},x_{3}} :~~x_{1}\geq 0,~~x_{2}\geq 0,~~x_{1}^{r}\cdot x_{2}^{1-r}\geq |x_{3}|\right\}}
The main application of the power cone is in constraints of convex optimization programs. There are many problems that can be described as minimizing a convex function over a power cone. [ 1 ]
This geometry-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Power_cone |
Power engineering , also called power systems engineering , is a subfield of electrical engineering that deals with the generation, transmission, distribution, and utilization of electric power , and the electrical apparatus connected to such systems. Although much of the field is concerned with the problems of three-phase AC power – the standard for large-scale power transmission and distribution across the modern world – a significant fraction of the field is concerned with the conversion between AC and DC power and the development of specialized power systems such as those used in aircraft or for electric railway networks. Power engineering draws the majority of its theoretical base from electrical engineering and mechanical engineering .
Electricity became a subject of scientific interest in the late 17th century. Over the next two centuries a number of important discoveries were made including the incandescent light bulb and the voltaic pile . [ 1 ] [ 2 ] Probably the greatest discovery with respect to power engineering came from Michael Faraday who in 1831 discovered that a change in magnetic flux induces an electromotive force in a loop of wire—a principle known as electromagnetic induction that helps explain how generators and transformers work. [ 3 ]
In 1881 two electricians built the world's first power station at Godalming in England. The station employed two waterwheels to produce an alternating current that was used to supply seven Siemens arc lamps at 250 volts and thirty-four incandescent lamps at 40 volts. [ 4 ] However supply was intermittent and in 1882 Thomas Edison and his company, The Edison Electric Light Company, developed the first steam-powered electric power station on Pearl Street in New York City. The Pearl Street Station consisted of several generators and initially powered around 3,000 lamps for 59 customers. [ 5 ] [ 6 ] The power station used direct current and operated at a single voltage. Since the direct current power could not be easily transformed to the higher voltages necessary to minimise power loss during transmission, the possible distance between the generators and load was limited to around half-a-mile (800 m). [ 7 ]
That same year in London Lucien Gaulard and John Dixon Gibbs demonstrated the first transformer suitable for use in a real power system. The practical value of Gaulard and Gibbs' transformer was demonstrated in 1884 at Turin where the transformer was used to light up forty kilometres (25 miles) of railway from a single alternating current generator. [ 8 ] Despite the success of the system, the pair made some fundamental mistakes. Perhaps the most serious was connecting the primaries of the transformers in series so that switching one lamp on or off would affect other lamps further down the line. Following the demonstration George Westinghouse , an American entrepreneur, imported a number of the transformers along with a Siemens generator and set his engineers to experimenting with them in the hopes of improving them for use in a commercial power system.
One of Westinghouse's engineers, William Stanley , recognised the problem with connecting transformers in series as opposed to parallel and also realised that making the iron core of a transformer a fully enclosed loop would improve the voltage regulation of the secondary winding. Using this knowledge he built the world's first practical transformer based alternating current power system at Great Barrington, Massachusetts in 1886. [ 9 ] [ 10 ] In 1885 the Italian physicist and electrical engineer Galileo Ferraris demonstrated an induction motor and in 1887 and 1888 the Serbian-American engineer Nikola Tesla filed a range of patents related to power systems including one for a practical two-phase induction motor [ 11 ] [ 12 ] which Westinghouse licensed for his AC system.
By 1890 the power industry had flourished and power companies had built thousands of power systems (both direct and alternating current) in the United States and Europe – these networks were effectively dedicated to providing electric lighting. During this time a fierce rivalry in the US known as the " war of the currents " emerged between Edison and Westinghouse over which form of transmission (direct or alternating current) was superior. In 1891, Westinghouse installed the first major power system that was designed to drive an electric motor and not just provide electric lighting. The installation powered a 100 horsepower (75 kW) synchronous motor at Telluride, Colorado with the motor being started by a Tesla induction motor. [ 13 ] On the other side of the Atlantic, Oskar von Miller built a 20 kV 176 km three-phase transmission line from Lauffen am Neckar to Frankfurt am Main for the Electrical Engineering Exhibition in Frankfurt. [ 14 ] In 1895, after a protracted decision-making process, the Adams No. 1 generating station at Niagara Falls began transmitting three-phase alternating current power to Buffalo at 11 kV. Following completion of the Niagara Falls project, new power systems increasingly chose alternating current as opposed to direct current for electrical transmission. [ 15 ]
The generation of electricity was regarded as particularly important following the Bolshevik seizure of power . Lenin stated "Communism is Soviet power plus the electrification of the whole country." [ 16 ] He was subsequently featured on many Soviet posters, stamps etc. presenting this view. The GOELRO plan was initiated in 1920 as the first Bolshevik experiment in industrial planning and in which Lenin became personally involved. Gleb Krzhizhanovsky was another key figure involved, having been involved in the construction of a power station in Moscow in 1910. He had also known Lenin since 1897 when they were both in the St. Petersburg chapter of the Union of Struggle for the Liberation of the Working Class .
In 1936 the first commercial high-voltage direct current (HVDC) line using mercury-arc valves was built between Schenectady and Mechanicville, New York . HVDC had previously been achieved by installing direct current generators in series (a system known as the Thury system ) although this suffered from serious reliability issues. [ 17 ] In 1957 Siemens demonstrated the first solid-state rectifier (solid-state rectifiers are now the standard for HVDC systems) however it was not until the early 1970s that this technology was used in commercial power systems. [ 18 ] In 1959 Westinghouse demonstrated the first circuit breaker that used SF 6 as the interrupting medium. [ 19 ] SF 6 is a far superior dielectric to air and, in recent times, its use has been extended to produce far more compact switching equipment (known as switchgear ) and transformers . [ 20 ] [ 21 ] Many important developments also came from extending innovations in the ICT field to the power engineering field. For example, the development of computers meant load flow studies could be run more efficiently allowing for much better planning of power systems. Advances in information technology and telecommunication also allowed for much better remote control of the power system's switchgear and generators.
Power Engineering deals with the generation , transmission , distribution and utilization of electricity as well as the design of a range of related devices. These include transformers , electric generators , electric motors and power electronics .
Power engineers may also work on systems that do not connect to the grid. These systems are called off-grid power systems and may be used in preference to on-grid systems for a variety of reasons. For example, in remote locations it may be cheaper for a mine to generate its own power rather than pay for connection to the grid and in most mobile applications connection to the grid is simply not practical.
Electricity generation covers the selection, design and construction of facilities that convert energy from primary forms to electric power.
Electric power transmission requires the engineering of high voltage transmission lines and substation facilities to interface to generation and distribution systems. High voltage direct current systems are one of the elements of an electric power grid.
Electric power distribution engineering covers those elements of a power system from a substation to the end customer.
Power system protection is the study of the ways an electrical power system can fail, and the methods to detect and mitigate for such failures.
In most projects, a power engineer must coordinate with many other disciplines such as civil and mechanical engineers, environmental experts, and legal and financial personnel. Major power system projects such as a large generating station may require scores of design professionals in addition to the power system engineers. At most levels of professional power system engineering practice, the engineer will require as much in the way of administrative and organizational skills as electrical engineering knowledge.
In both the UK and the US, professional societies had long existed for civil and mechanical engineers. The Institution of Electrical Engineers (IEE) was founded in the UK in 1871, and the AIEE in the United States in 1884. These societies contributed to the exchange of electrical knowledge and the development of electrical engineering education.
On an international level, the International Electrotechnical Commission (IEC), which was founded in 1906, prepares standards for power engineering, with 20,000 electrotechnical experts from 172 countries developing global specifications based on consensus. | https://en.wikipedia.org/wiki/Power_engineering |
In electrical engineering , the power factor of an AC power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit. Real power is the average of the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of root mean square (RMS) current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power, so more current flows in the circuit than would be required to transfer real power alone. A power factor magnitude of less than one indicates the voltage and current are not in phase, reducing the average product of the two. A negative power factor occurs when the device (normally the load) generates real power, which then flows back towards the source.
In an electric power system, a load with a low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The larger currents increase the energy lost in the distribution system and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers with a low power factor.
Power-factor correction increases the power factor of a load, improving efficiency for the distribution system to which it is attached. Linear loads with a low power factor (such as induction motors ) can be corrected with a passive network of capacitors or inductors . Non-linear loads, such as rectifiers , distort the current drawn from the system. In such cases, active or passive power factor correction may be used to counteract the distortion and raise the power factor. The devices for correction of the power factor may be at a central substation , spread out over a distribution system, or built into power-consuming equipment.
The general expression for power factor is given by
where P {\displaystyle P} is the real power measured by an ideal wattmeter , I r m s {\displaystyle I_{rms}} is the rms current measured by an ideal ammeter , and V r m s {\displaystyle V_{rms}} is the rms voltage measured by an ideal voltmeter . Apparent power, P a {\displaystyle P_{a}} , is the product of the rms current and the rms voltage.
If the load is sourcing power back toward the generator, then P {\displaystyle P} and power factor {\displaystyle {\mbox{power factor}}} will be negative.
If the waveforms are periodic with the same fundamental period, then the power factor can be computed as follows: P = 1 T ∫ t ′ t ′ + T i ( t ) v ( t ) d t , I r m s = 1 T ∫ t ′ t ′ + T i ( t ) 2 d t , V r m s = 1 T ∫ t ′ t ′ + T v ( t ) 2 d t , power factor = P I r m s V r m s , {\displaystyle {\begin{aligned}P&={\frac {1}{T}}\int _{t'}^{t'+T}i(t)v(t)dt,\\I_{rms}&={\sqrt {{\frac {1}{T}}\int _{t'}^{t'+T}{i(t)}^{2}dt}},\\V_{rms}&={\sqrt {{\frac {1}{T}}\int _{t'}^{t'+T}{v(t)}^{2}dt}},\\{\mbox{power factor}}&={\frac {P}{I_{rms}V_{rms}}},\end{aligned}}} where i ( t ) {\displaystyle i(t)} is the instantaneous current, v ( t ) {\displaystyle v(t)} is the instantaneous voltage, t ′ {\displaystyle t'} is an arbitrary starting time, and T {\displaystyle T} is the period of the waveforms.
If the waveforms are not periodic and the physical meters have the same averaging time, then the equations for the periodic case can be used with the exception that T {\displaystyle T} is the averaging time of the meters instead of the waveform period.
In a linear circuit , consisting of combinations of resistors, inductors, and capacitors, current flow has a sinusoidal response to the sinusoidal line voltage. [ 1 ] A linear load does not change the shape of the input waveform but may change the relative timing (phase) between voltage and current, due to its inductance or capacitance.
In a purely resistive AC circuit, voltage and current waveforms are in step (or in phase ), changing polarity at the same instant in each cycle. All the power entering the load is consumed (or dissipated).
Where reactive loads are present, such as with capacitors or inductors , energy storage in the loads results in a phase difference between the current and voltage waveforms. During each cycle of the AC voltage, extra energy, in addition to any energy consumed in the load, is temporarily stored in the load in electric or magnetic fields then returned to the power grid a fraction of the period later.
Electrical circuits containing predominantly resistive loads ( incandescent lamps , devices using heating elements like electric toasters and ovens ) have a power factor of almost 1, but circuits containing inductive or capacitive loads (electric motors, solenoid valves, transformers, fluorescent lamp ballasts , and others) can have a power factor well below 1.
A circuit with a low power factor will use a greater amount of current to transfer a given quantity of real power than a circuit with a high power factor thus causing increased losses due to resistive heating in power lines, and requiring the use of higher-rated conductors and transformers.
AC power has two components:
Together, they form the complex power ( S {\displaystyle S} ) expressed as volt-amperes (VA). The magnitude of the complex power is the apparent power ( | S | {\displaystyle |S|} ), also expressed in volt-amperes (VA).
The VA and var are non-SI units dimensionally similar to the watt but are used in engineering practice instead of the watt to state what quantity is being expressed. The SI explicitly disallows using units for this purpose or as the only source of information about a physical quantity as used. [ 4 ]
The power factor is defined as the ratio of real power to apparent power. As power is transferred along a transmission line, it does not consist purely of real power that can do work once transferred to the load, but rather consists of a combination of real and reactive power, called apparent power. The power factor describes the amount of real power transmitted along a transmission line relative to the total apparent power flowing in the line. [ 5 ] [ 6 ]
The power factor can also be computed as the cosine of the angle θ by which the current waveform lags or leads the voltage waveform. [ 7 ]
One can relate the various components of AC power by using the power triangle in vector space. Real power extends horizontally in the real axis and reactive power extends in the direction of the imaginary axis. Complex power (and its magnitude, apparent power) represents a combination of both real and reactive power, and therefore can be calculated by using the vector sum of these two components. We can conclude that the mathematical relationship between these components is:
As the angle θ increases with fixed total apparent power, current and voltage are further out of phase with each other. Real power decreases, and reactive power increases.
Power factor is described as leading if the current waveform is advanced in phase concerning voltage, or lagging when the current waveform is behind the voltage waveform. A lagging power factor signifies that the load is inductive, as the load will consume reactive power. The reactive component Q {\displaystyle Q} is positive as reactive power travels through the circuit and is consumed by the inductive load. A leading power factor signifies that the load is capacitive, as the load supplies reactive power, and therefore the reactive component Q {\displaystyle Q} is negative as reactive power is being supplied to the circuit.
If θ is the phase angle between the current and voltage, then the power factor is equal to the cosine of the angle, cos θ {\displaystyle \cos \theta } :
Since the units are consistent, the power factor is by definition a dimensionless number between -1 and 1. When the power factor is equal to 0, the energy flow is entirely reactive, and stored energy in the load returns to the source on each cycle. When the power factor is 1, referred to as the unity power factor, all the energy supplied by the source is consumed by the load. Power factors are usually stated as leading or lagging to show the sign of the phase angle. Capacitive loads are leading (current leads voltage), and inductive loads are lagging (current lags voltage).
If a purely resistive load is connected to a power supply, current and voltage will change polarity in step, the power factor will be 1, and the electrical energy flows in a single direction across the network in each cycle. Inductive loads such as induction motors (any type of wound coil) consume reactive power with the current waveform lagging the voltage. Capacitive loads such as capacitor banks or buried cables generate reactive power with the current phase leading the voltage. Both types of loads will absorb energy during part of the AC cycle, which is stored in the device's magnetic or electric field, only to return this energy back to the source during the rest of the cycle.
For example, to get 1 kW of real power, if the power factor is unity, 1 kVA of apparent power needs to be transferred (1 kW ÷ 1 = 1 kVA). At low values of power factor, more apparent power needs to be transferred to get the same real power. To get 1 kW of real power at 0.2 power factor, 5 kVA of apparent power needs to be transferred (1 kW ÷ 0.2 = 5 kVA). This apparent power must be produced and transmitted to the load and is subject to losses in the production and transmission processes.
Electrical loads consuming alternating current power consume both real power and reactive power. The vector sum of real and reactive power is the complex power, and its magnitude is the apparent power. The presence of reactive power causes the real power to be less than the apparent power, and so, the electric load has a power factor of less than 1.
A negative power factor (0 to −1) can result from returning active power to the source, such as in the case of a building fitted with solar panels when surplus power is fed back into the supply. [ 8 ] [ 9 ] [ 10 ]
A high power factor is generally desirable in a power delivery system to reduce losses and improve voltage regulation at the load. Compensating elements near an electrical load will reduce the apparent power demand on the supply system. Power factor correction may be applied by an electric power transmission utility to improve the stability and efficiency of the network. Individual electrical customers who are charged by their utility for low power factor may install correction equipment to increase their power factor to reduce costs.
Power factor correction brings the power factor of an AC power circuit closer to 1 by supplying or absorbing reactive power, adding capacitors or inductors that act to cancel the inductive or capacitive effects of the load, respectively. In the case of offsetting the inductive effect of motor loads, capacitors can be locally connected. These capacitors help to generate reactive power to meet the demand of the inductive loads. This will keep that reactive power from having to flow from the utility generator to the load. In the electricity industry, inductors are said to consume reactive power, and capacitors are said to supply it, even though reactive power is just energy moving back and forth on each AC cycle.
The reactive elements in power factor correction devices can create voltage fluctuations and harmonic noise when switched on or off. They will supply or sink reactive power regardless of whether there is a corresponding load operating nearby, increasing the system's no-load losses. In the worst case, reactive elements can interact with the system and with each other to create resonant conditions, resulting in system instability and severe overvoltage fluctuations. As such, reactive elements cannot simply be applied without engineering analysis.
An automatic power factor correction unit consists of some capacitors that are switched by means of contactors . These contactors are controlled by a regulator that measures power factor in an electrical network. Depending on the load and power factor of the network, the power factor controller will switch the necessary blocks of capacitors in steps to make sure the power factor stays above a selected value.
In place of a set of switched capacitors , an unloaded synchronous motor can supply reactive power. The reactive power drawn by the synchronous motor is a function of its field excitation. It is referred to as a synchronous condenser . It is started and connected to the electrical network . It operates at a leading power factor and puts vars onto the network as required to support a system's voltage or to maintain the system power factor at a specified level.
The synchronous condenser's installation and operation are identical to those of large electric motors . Its principal advantage is the ease with which the amount of correction can be adjusted; it behaves like a variable capacitor. Unlike with capacitors, the amount of reactive power furnished is proportional to voltage, not the square of voltage; this improves voltage stability on large networks. Synchronous condensers are often used in connection with high-voltage direct-current transmission projects or in large industrial plants such as steel mills .
For power factor correction of high-voltage power systems or large, fluctuating industrial loads, power electronic devices such as the static VAR compensator or STATCOM are increasingly used. These systems are able to compensate sudden changes of power factor much more rapidly than contactor-switched capacitor banks and, being solid-state, require less maintenance than synchronous condensers.
Examples of non-linear loads on a power system are rectifiers (such as used in a power supply), and arc discharge devices such as fluorescent lamps , electric welding machines, or arc furnaces . Because current in these systems is interrupted by a switching action, the current contains frequency components that are multiples of the power system frequency. Distortion power factor is a measure of how much the harmonic distortion of a load current decreases the average power transferred to the load.
In linear circuits having only sinusoidal currents and voltages of one frequency, the power factor arises only from the difference in phase between the current and voltage. This is displacement power factor . [ 11 ]
Non-linear loads change the shape of the current waveform from a sine wave to some other form. Non-linear loads create harmonic currents in addition to the original (fundamental frequency) AC current. This is of importance in practical power systems that contain non-linear loads such as rectifiers , some forms of electric lighting, electric arc furnaces , welding equipment, switched-mode power supplies , variable speed drives and other devices. Filters consisting of linear capacitors and inductors can prevent harmonic currents from entering the supplying system.
To measure the real power or reactive power, a wattmeter designed to work properly with non-sinusoidal currents must be used.
The distortion power factor is the distortion component associated with the harmonic voltages and currents present in the system.
THD i {\displaystyle {\mbox{THD}}_{i}} is the total harmonic distortion of the load current.
I 1 {\displaystyle I_{1}} is the fundamental component of the current, I r m s {\displaystyle I_{rms}} is the total current, and I h {\displaystyle I_{h}} is the current on the h th harmonic; all are root mean square values (distortion power factor can also be used to describe individual order harmonics, using the corresponding current in place of total current). This definition with respect to total harmonic distortion assumes that the voltage stays undistorted (sinusoidal, without harmonics). This simplification is often a good approximation for stiff voltage sources (not being affected by changes in load downstream in the distribution network). Total harmonic distortion of typical generators from current distortion in the network is on the order of 1–2%, which can have larger scale implications but can be ignored in common practice. [ 12 ]
The result when multiplied with the displacement power factor is the overall, true power factor or just power factor (PF):
In practice, the local effects of distortion current on devices in a three-phase distribution network rely on the magnitude of certain order harmonics rather than the total harmonic distortion.
For example, the triplen , or zero-sequence, harmonics (3rd, 9th, 15th, etc.) have the property of being in-phase when compared line-to-line. In a delta-wye transformer , these harmonics can result in circulating currents in the delta windings and result in greater resistive heating . In a wye-configuration of a transformer, triplen harmonics will not create these currents, but they will result in a non-zero current in the neutral wire . This could overload the neutral wire in some cases
and create error in kilowatt-hour metering systems and billing revenue. [ 13 ] [ 14 ] The presence of current harmonics in a transformer also result in larger eddy currents in the magnetic core of the transformer. Eddy current losses generally increase as the square of the frequency, lowering the transformer's efficiency, dissipating additional heat, and reducing its service life. [ 15 ]
Negative-sequence harmonics (5th, 11th, 17th, etc.) combine 120 degrees out of phase, similarly to the fundamental harmonic but in a reversed sequence. In generators and motors, these currents produce magnetic fields which oppose the rotation of the shaft and sometimes result in damaging mechanical vibrations. [ 16 ]
The simplest way to control the harmonic current is to use a filter that passes current only at line frequency (50 or 60 Hz). The filter consists of capacitors or inductors and makes a non-linear device look more like a linear load. An example of passive PFC is a valley-fill circuit .
A disadvantage of passive PFC is that it requires larger inductors or capacitors than an equivalent power active PFC circuit. [ 17 ] [ 18 ] [ 19 ] Also, in practice, passive PFC is often less effective at improving the power factor. [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ]
Active PFC is the use of power electronics to change the waveform of current drawn by a load to improve the power factor. [ 25 ] Some types of the active PFC are buck , boost , buck-boost and synchronous condenser . Active power factor correction can be single-stage or multi-stage.
In the case of a switched-mode power supply, a boost converter is inserted between the bridge rectifier and the main input capacitors. The boost converter attempts to maintain a constant voltage at its output while drawing a current that is always in phase with and at the same frequency as the line voltage. Another switched-mode converter inside the power supply produces the desired output voltage from the DC bus. This approach requires additional semiconductor switches and control electronics but permits cheaper and smaller passive components. It is frequently used in practice.
For a three-phase SMPS, the Vienna rectifier configuration may be used to substantially improve the power factor.
SMPSs with passive PFC can achieve power factor of about 0.7–0.75, SMPSs with active PFC, up to 0.99 power factor, while a SMPS without any power factor correction have a power factor of only about 0.55–0.65. [ 26 ]
Due to their very wide input voltage range, many power supplies with active PFC can automatically adjust to operate on AC power from about 100 V (Japan) to 240 V (Europe). That feature is particularly welcome in power supplies for laptops.
Dynamic power factor correction (DPFC), sometimes referred to as real-time power factor correction, is used for electrical stabilization in cases of rapid load changes (e.g. at large manufacturing sites). DPFC is useful when standard power factor correction would cause over or under correction. [ 27 ] DPFC uses semiconductor switches, typically thyristors , to quickly connect and disconnect capacitors or inductors to improve power factor.
Power factors below 1.0 require a utility to generate more than the minimum volt-amperes necessary to supply the real power (watts). This increases generation and transmission costs. For example, if the load power factor were as low as 0.7, the apparent power would be 1.4 times the real power used by the load. Line current in the circuit would also be 1.4 times the current required at 1.0 power factor, so the losses in the circuit would be doubled (since they are proportional to the square of the current). Alternatively, all components of the system such as generators, conductors, transformers, and switchgear would be increased in size (and cost) to carry the extra current. When the power factor is close to unity, for the same kVA rating of the transformer more load current can be supplied. [ 28 ]
Utilities typically charge additional costs to commercial customers who have a power factor below some limit, which is typically 0.9 to 0.95. Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission.
With the rising cost of energy and concerns over the efficient delivery of power, active PFC has become more common in consumer electronics. [ 29 ] Current Energy Star guidelines for computers [ 30 ] call for a power factor of ≥ 0.9 at 100% of rated output in the PC's power supply . According to a white paper authored by Intel and the U.S. Environmental Protection Agency , PCs with internal power supplies will require the use of active power factor correction to meet the ENERGY STAR 5.0 Program Requirements for Computers. [ 31 ]
In Europe, EN 61000-3-2 requires power factor correction be incorporated into consumer products.
Small customers, such as households, are not usually charged for reactive power and so power factor metering equipment for such customers will not be installed.
The power factor in a single-phase circuit (or balanced three-phase circuit) can be measured with the wattmeter-ammeter-voltmeter method, where the power in watts is divided by the product of measured voltage and current. The power factor of a balanced polyphase circuit is the same as that of any phase. The power factor of an unbalanced polyphase circuit is not uniquely defined.
A direct reading power factor meter can be made with a moving coil meter of the electrodynamic type, carrying two perpendicular coils on the moving part of the instrument. The field of the instrument is energized by the circuit current flow. The two moving coils, A and B, are connected in parallel with the circuit load. One coil, A, will be connected through a resistor and the second coil, B, through an inductor, so that the current in coil B is delayed with respect to current in A. At unity power factor, the current in A is in phase with the circuit current, and coil A provides maximum torque, driving the instrument pointer toward the 1.0 mark on the scale. At zero power factor, the current in coil B is in phase with circuit current, and coil B provides torque to drive the pointer towards 0. At intermediate values of power factor, the torques provided by the two coils add and the pointer takes up intermediate positions. [ 32 ]
Another electromechanical instrument is the polarized-vane type. [ 33 ] In this instrument a stationary field coil produces a rotating magnetic field, just like a polyphase motor. The field coils are connected either directly to polyphase voltage sources or to a phase-shifting reactor if a single-phase application. A second stationary field coil, perpendicular to the voltage coils, carries a current proportional to current in one phase of the circuit. The moving system of the instrument consists of two vanes that are magnetized by the current coil. In operation, the moving vanes take up a physical angle equivalent to the electrical angle between the voltage source and the current source. This type of instrument can be made to register for currents in both directions, giving a four-quadrant display of power factor or phase angle.
Digital instruments exist that directly measure the time lag between voltage and current waveforms. Low-cost instruments of this type measure the peak of the waveforms. More sophisticated versions measure the peak of the fundamental harmonic only, thus giving a more accurate reading for phase angle on distorted waveforms. Calculating power factor from voltage and current phases is only accurate if both waveforms are sinusoidal. [ 34 ]
Power Quality Analyzers, often referred to as Power Analyzers, make a digital recording of the voltage and current waveform (typically either one phase or three phase) and accurately calculate true power (watts), apparent power (VA) power factor, AC voltage, AC current, DC voltage, DC current, frequency, IEC61000-3-2/3-12 Harmonic measurement, IEC61000-3-3/3-11 flicker measurement, individual phase voltages in delta applications where there is no neutral line, total harmonic distortion, phase and amplitude of individual voltage or current harmonics, etc. [ 35 ] [ 36 ]
Anglophone power engineering students are advised to remember: ELI the ICE man or ELI on ICE – the voltage E, leads the current I, in an inductor L. The current I leads the voltage E in a capacitor C.
Another common mnemonic is CIVIL – in a capacitor (C) the current (I) leads voltage (V), voltage (V) leads current (I) in an inductor (L). | https://en.wikipedia.org/wiki/Power_factor |
In computational biology , power graph analysis is a method for the analysis and
representation of complex networks . Power graph analysis is the computation, analysis and visual representation of a power graph from a graph ( networks ).
Power graph analysis can be thought of as a lossless compression algorithm for graphs. [ 1 ] It extends graph syntax with representations of cliques , bicliques and stars . Compression levels of up to 95% have been obtained for complex biological networks .
Hypergraphs are a generalization of graphs in which edges are not just couples of nodes but arbitrary n-tuples . Power graphs are not another generalization of graphs, but instead a novel representation of graphs that proposes a shift from the "node and edge" language to one using cliques, bicliques and stars as primitives.
Graphs are drawn with circles or points that represent nodes and lines connecting pairs of nodes that represent edges . Power graphs extend the syntax of graphs with power nodes , which are drawn as a circle enclosing nodes or other power nodes , and power edges , which are lines between power nodes.
Bicliques are two sets of nodes with an edge between every member of one set and every member of the other set. In a power graph, a biclique is represented as an edge between two power nodes.
Cliques are a set of nodes with an edge between every pair of nodes. In a power graph, a clique is represented by a power node with a loop .
Stars are a set of nodes with an edge between every member of that set and a single node outside the set. In a power graph, a star is represented by a power edge between a regular node and a power node.
Given a graph G = ( V , E ) {\displaystyle G={\bigl (}{V,E}{\bigr )}} where V = { v 0 , … , v n } {\displaystyle V={\bigl \{}v_{0},\dots ,v_{n}{\bigr \}}} is the set of nodes and E ⊆ V × V {\displaystyle E\subseteq V\times V} is the set of edges, a power graph G ′ = ( V ′ , E ′ ) {\displaystyle G'={\bigl (}{V',E'}{\bigr )}} is a graph defined on the power set V ′ ⊆ P ( V ) {\displaystyle V'\subseteq {\mathcal {P}}{\bigl (}V{\bigr )}} of power nodes connected to each other by power edges : E ′ ⊆ V ′ × V ′ {\displaystyle E'\subseteq V'\times V'} . Hence power graphs are defined on the power set of nodes as well as on the power set of edges of the graph G {\displaystyle G} .
The semantics of power graphs are as follows: if two power nodes are connected by a power edge, this means that all nodes of the first power node are connected to all nodes of the second power node. Similarly, if a power node is connected to itself by a power edge, this signifies that all nodes in the power node are connected to each other by edges.
The following two conditions are required:
The Fourier analysis of a function
can be seen as a rewriting of the function in terms of harmonic functions instead of t ↦ x {\displaystyle t\mapsto x} pairs. This transformation changes the point of view from time domain to frequency domain and enables many interesting applications in signal analysis , data compression ,
and filtering.
Similarly, Power graph analysis is a rewriting or decomposition of a network using bicliques, cliques and stars
as primitive elements (just as harmonic functions for Fourier analysis).
It can be used to analyze, compress and filter networks.
There are, however, several key differences. First, in Fourier analysis the two spaces (time and frequency domains)
are the same function space - but stricto sensu, power graphs are not graphs.
Second, there is not a unique power graph representing a given graph. Yet a very interesting class of power graphs
are minimal power graphs which have the fewest power edges and power nodes necessary to represent a given graph.
In general, there is no unique minimal power graph for a given graph.
In this example (right) a graph of four nodes and five edges admits two minimal power graphs of two power edges each.
The main difference between these two minimal power graphs is the higher nesting level of the second power graph as well as a loss of symmetry with respect to the underlying graph.
Loss of symmetry is only a problem in small toy examples since complex networks rarely exhibit such symmetries in the first place.
Additionally, one can minimize the nesting level but even then, there is in general not a unique minimal power graph of minimal nesting level.
The power graph greedy algorithm relies on two simple steps to perform the decomposition:
The first step identifies candidate power nodes through a hierarchical clustering of the nodes in the network
based on the similarity of their neighboring nodes. The similarity of two sets of neighbors is taken as the Jaccard index of the two sets.
The second step performs a greedy search for possible power edges between candidate power nodes.
Power edges abstracting the most edges in the original network are added first to the power graph.
Thus bicliques, cliques and stars are incrementally replaced with power edges, until all remaining single edges are also added.
Candidate power nodes that are not the end point of any power edge are ignored.
Modular decomposition can be used to compute a power graph by using
the strong modules of the modular decomposition.
Modules in modular decomposition are groups of nodes in a graph that
have identical neighbors. A Strong Module is a module that does not overlap
with another module.
However, in complex networks strong modules are more the exception than the
rule. Therefore, the power graphs obtained through modular decomposition are far
from minimality.
The main difference between modular decomposition and power graph analysis is the
emphasis of power graph analysis in decomposing graphs not only using modules of nodes
but also modules of edges (cliques, bicliques). Indeed, power graph analysis can be seen as a loss-less
simultaneous clustering of both nodes and edges.
Power graph analysis has been shown to be useful for the analysis of several types of biological networks such as protein-protein interaction networks, [ 2 ] domain-peptide binding motifs, gene regulatory networks [ 3 ] and homology/paralogy networks.
Also a network of significant disease-trait pairs [ 4 ] have been recently visualized and analyzed with power graphs.
Network compression, a new measure derived from power graphs, has been proposed as a quality measure for protein interaction networks. [ 5 ]
Power graphs have been also applied to the analysis of drug-target-disease networks [ 6 ] for drug repositioning .
Power graphs have been applied to large-scale data in social networks, for community mining [ 7 ] or for modeling author types. [ 8 ] | https://en.wikipedia.org/wiki/Power_graph_analysis |
A power loom is a mechanized loom .
The main components of the loom are the warp beam, heddles, harnesses, shuttle, reed, and takeup roll. In the loom, yarn processing includes shedding, picking, battening and taking-up operations.
With each weaving operation, the newly constructed fabric must be wound on a cloth beam. This process is called taking up. At the same time, the warp yarns must be let off or released from the warp beams. To become fully automatic, a loom needs a filling stop motion which will brake the loom, if the weft thread breaks.
Operation of weaving in a textile mill is undertaken by a specially trained operator known as a weaver. Weavers are expected to uphold high industry standards and are tasked with monitoring anywhere from ten to as many as thirty separate looms at any one time. During their operating shift, weavers will first utilize a wax pencil or crayon to sign their initials onto the cloth to mark a shift change, and then walk along the cloth side (front) of the looms they tend, gently touching the fabric as it comes from the reed. This is done to feel for any broken "picks" or filler thread. Should broken picks be detected, the weaver will disable the machine and undertake to correct the error, typically by replacing the bobbin of filler thread in as little time as possible. They are trained that, ideally, no machine should stop working for more than one minute, with faster turnaround times being preferred.
Operation of this needs more than 2 people because of the way it works.
The first ideas for an automatic loom were developed in 1784 by M. de Gennes in Paris and by Vaucanson in 1745, but these designs were never developed and were forgotten. In 1785 Edmund Cartwright patented a power loom which used water power to speed up the weaving process, the predecessor to the modern power loom. His ideas were licensed first by Grimshaw of Manchester who built a small steam-powered weaving factory in Manchester in 1790, but the factory burnt down. Cartwright's was not a commercially successful machine; his looms had to be stopped to dress the warp. Over the next decades, Cartwright's ideas were modified into a reliable automatic loom. These designs followed John Kay 's invention of the flying shuttle, and they passed the shuttle through the shed using levers. With the increased speed of weaving, weavers were able to use more thread than spinners could produce. [ 1 ]
A series of inventors incrementally improved all aspects of the three principal processes and the ancillary processes.
There now appear a series of useful improvements that are contained in patents for useless devices
At this point the loom has become automatic except for refilling weft pirns. The Cartwight loom weaver could work one loom at 120-130 picks per minute- with a Kenworthy and Bullough's Lancashire Loom , a weaver can run four or more looms working at 220-260 picks per minute- thus giving eight (or more) times more throughput.
The development of the power loom in and around Manchester was not a coincidence. Manchester had been a centre for Fustians by 1620 and acted as a hub for other Lancashire towns, so developing a communication network with them. It was an established point of export using the meandering River Mersey , and by 1800 it had a thriving canal network, with links to the Ashton Canal , Rochdale Canal the Peak Forest Canal and Manchester Bolton & Bury Canal . The fustian trade gave the towns a skilled workforce that was used to the complicated Dutch looms, and was perhaps accustomed to industrial discipline. While Manchester became a spinning town, the towns around were weaving towns producing cloth by the putting out system. The business was dominated by a few families, who had the capital needed to invest in new mills and to buy hundreds of looms. Mills were built along the new canals, so immediately had access to their markets. Spinning developed first and, until 1830, the handloom was still more important economically than the power loom when the roles reversed. [ 4 ] Because of the economic growth of Manchester, a new industry of precision machine tool engineering was born and here were the skills needed to build the precision mechanisms of a loom.
Draper' strategy was to standardize on a couple of Northrop Loom models which it mass-produced. The lighter E-model of 1909 was joined in the 1930 by the heavier X-model. Continuous fibre machines, say for rayon, which was more break-prone, needed a specialist loom. This was provided by the purchase of the Stafford Loom Co. in 1932, and using their patents a third loom the XD, was added to the range. Because of their mass production techniques they were reluctant and slow to retool for new technologies such as shuttleless looms. [ 6 ]
Originally, power looms used a shuttle to throw the weft across, but in 1927 the faster and more efficient shuttleless loom came into use. Sulzer Brothers , a Swiss company had the exclusive rights to shuttleless looms in 1942, and licensed the American production to Warner & Swasey. Draper licensed the slower rapier loom. Today, advances in technology have produced a variety of looms designed to maximise production for specific types of material. The most common of these are Sulzer shuttleless weaving machines , rapier looms , air-jet looms and water-jet looms. [ 7 ]
Power looms reduced demand for skilled handweavers, initially causing reduced wages and unemployment. Protests followed their introduction. For example, in 1816 two thousand rioting Calton weavers tried to destroy power loom mills and stoned the workers. [ 8 ] In the longer term, by making cloth more affordable the power loom increased demand and stimulated exports, causing a growth in industrial employment, albeit low-paid. [ 9 ] The power loom also opened up opportunities for women mill workers. [ 10 ] A darker side of the power loom's impact was the growth of employment of children in power loom mills. [ 11 ]
There are a number of inherent dangers in the machines, to which inattentive or poorly trained weavers can fall victim. The most obvious is the moving reed, the frames which hold the heddles and the "pinch" or "sand" roll utilized to keep the cloth tight as it passes over the front of the machine and onto the doff roll. The most common injury in weaving is pinched fingers from distracted or bored workers, though this is not the only such injury found. There are numerous accounts of weavers with long hair getting it tangled in the warp itself and having their scalp pulled away from the skull, or large chunks of hair pulled off. [ 12 ] As a result of this, it has become industry standard for companies to require weavers to either keep hair up and tied, or to keep their hair short so as not to allow it to become tangled. Also, due to possible pinch points on the front of machines, loose, baggy clothing is prohibited. In addition, there is a risk of the shuttle flying out of the loom at a high-speed (200+ mph/322 kmh) and striking a worker if the moving reed encounters a thread/yarn or other mechanical jam/error. One complication for weavers, in the terms of safety, is the loud nature in which weave mills operate (115 dB +). Because of this, it is nearly impossible to hear a person calling for help when entangled. This has led OSHA to outline specific guidelines [ 13 ] for companies to mitigate the chances of such accidents occurring. However, even with such guidelines in place, injuries in textile production due to the machines themselves, are still commonplace.
Media related to Power looms at Wikimedia Commons | https://en.wikipedia.org/wiki/Power_loom |
In telecommunications , the power margin is the difference between available signal power and the minimum signal power needed to overcome system losses and still satisfy the minimum input requirements of the receiver for a given performance level.
System power margin reflects the excess signal level , present at the input of the receiver, that is available to compensate for (a) the effects of component aging in the transmitter, receiver, or physical transmission medium , and (b) a deterioration in propagation conditions. Synonym system power margin.
This article incorporates public domain material from Federal Standard 1037C . General Services Administration . Archived from the original on 2022-01-22.
This article related to telecommunications is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Power_margin |
The power number N p (also known as Newton number ) is a commonly used dimensionless number relating the resistance force to the inertia force .
The power-number has different specifications according to the field of application. E.g., for stirrers the power number is defined as: [ 1 ]
with
This fluid dynamics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Power_number |
A power of two is a number of the form 2 n where n is an integer , that is, the result of exponentiation with number two as the base and integer n as the exponent . In the fast-growing hierarchy , 2 n is exactly equal to f 1 n ( 1 ) {\displaystyle f_{1}^{n}(1)} . In the Hardy hierarchy , 2 n is exactly equal to H ω n ( 1 ) {\displaystyle H_{\omega {n}}(1)} .
Powers of two with non-negative exponents are integers: 2 0 = 1 , 2 1 = 2 , and 2 n is two multiplied by itself n times. [ 1 ] [ 2 ] The first ten powers of 2 for non-negative values of n are:
By comparison, powers of two with negative exponents are fractions : for positive integer n , 2 − n is one half multiplied by itself n times. Thus the first few negative powers of 2 are 1 / 2 , 1 / 4 , 1 / 8 , 1 / 16 , etc. Sometimes these are called inverse powers of two because each is the multiplicative inverse of a positive power of two.
Because two is the base of the binary numeral system , powers of two are common in computer science . Written in binary, a power of two always has the form 100...000 or 0.00...001, just like a power of 10 in the decimal system.
Two to the power of n , written as 2 n , is the number of values in which the bits in a binary word of length n can be set, where each bit is either of two values. A word, interpreted as representing an integer in a range starting at zero, referred to as an "unsigned integer", can represent values from 0 ( 000...000 2 ) to 2 n − 1 ( 111...111 2 ) inclusively. An alternative representation, referred to as a signed integer, allows values that can be positive, negative and zero; see Signed number representations . Either way, one less than a power of two is often the upper bound of an integer in binary computers. As a consequence, numbers of this form show up frequently in computer software. As an example, a video game running on an 8-bit system might limit the score or the number of items the player can hold to 255—the result of using a byte , which is 8 bits long , to store the number, allowing the representation of 256 distinct values from 0 to 2 8 − 1 = 255 . For example, in the original Legend of Zelda the main character was limited to carrying 255 rupees (the currency of the game) at any given time, and the video game Pac-Man famously has a kill screen at level 256.
Powers of two are often used to define units in which to quantify computer memory sizes. A "byte" now typically refers to eight bits (an octet ), resulting in the possibility of 256 values (2 8 ). (The term byte once meant (and in some cases, still means) a collection of bits that was defined by the hardware context, typically of 5 to 32 bits, rather than only an 8-bit unit.) The prefix kilo , in conjunction with byte , has been used by computer scientists to mean 1024 (2 10 ). However, in general, the term kilo has been used in the International System of Units to mean 1000 (10 3 ). Binary prefixes have been standardized, such as kibi (Ki) meaning 1024 . Nearly all processor registers have sizes that are a power of two bits, 8, 16, 32 or 64 bits being very common, with the last two being most common except for very small processors.
Powers of two occur in a range of other places as well. For many disk drives , at least one of the sector size, number of sectors per track, and number of tracks per surface is a power of two. [ citation needed ] The logical block size is almost always a power of two.
Numbers that are closely related to powers of two occur in a number of computer hardware designs, such as with the number of pixels in the width and height of video screens, where the number of pixels in each direction is often the product of a power of two and a small number. For example, 640 = 128 × 5 , and 480 = 32 × 15 .
A prime number that is one less than a power of two is called a Mersenne prime . For example, the prime number 31 is a Mersenne prime because it is 1 less than 32 (2 5 ). Similarly, a prime number (like 257 ) that is one more than a positive power of two is called a Fermat prime —the exponent itself is a power of two. A fraction that has a power of two as its denominator is called a dyadic rational . The numbers that can be represented as sums of consecutive positive integers are called polite numbers ; they are exactly the numbers that are not powers of two.
The geometric progression 1, 2, 4, 8, 16, 32, ... (or, in the binary numeral system , 1, 10, 100, 1000, 10000, 100000, ... ) is important in number theory . Book IX, Proposition 36 of Elements proves that if the sum of the first n terms of this progression is a prime number (and thus is a Mersenne prime as mentioned above), then this sum times the n th term is a perfect number . For example, the sum of the first 5 terms of the series 1 + 2 + 4 + 8 + 16 = 31 , which is a prime number. The sum 31 multiplied by 16 (the 5th term in the series) equals 496, which is a perfect number.
Book IX, Proposition 35, proves that in a geometric series if the first term is subtracted from the second and last term in the sequence, then as the excess of the second is to the first—so is the excess of the last to all those before it. (This is a restatement of our formula for geometric series from above.) Applying this to the geometric progression 31, 62, 124, 248, 496 (which results from 1, 2, 4, 8, 16 by multiplying all terms by 31), we see that 62 minus 31 is to 31 as 496 minus 31 is to the sum of 31, 62, 124, 248. Therefore, the numbers 1, 2, 4, 8, 16, 31, 62, 124 and 248 add up to 496 and further these are all the numbers that divide 496. For suppose that p divides 496 and it is not amongst these numbers. Assume pq is equal to 16 × 31 , or 31 is to q as p is to 16. Now p cannot divide 16 or it would be amongst the numbers 1, 2, 4, 8 or 16.
Therefore, 31 cannot divide q . And since 31 does not divide q and q measures 496, the fundamental theorem of arithmetic implies that q must divide 16 and be among the numbers 1, 2, 4, 8 or 16. Let q be 4, then p must be 124, which is impossible since by hypothesis p is not amongst the numbers 1, 2, 4, 8, 16, 31, 62, 124 or 248.
(sequence A000079 in the OEIS )
Starting with 2 the last digit is periodic with period 4, with the cycle 2–4–8–6–, and starting with 4 the last two digits are periodic with period 20. These patterns are generally true of any power, with respect to any base . The pattern continues where each pattern has starting point 2 k , and the period is the multiplicative order of 2 modulo 5 k , which is φ (5 k ) = 4 × 5 k −1 (see Multiplicative group of integers modulo n ). [ citation needed ]
(sequence A140300 in the OEIS )
The first few powers of 2 10 are slightly larger than those same powers of 1000 (10 3 ). The first 11 powers of 2 10 values are listed below:
It takes approximately 17 powers of 1024 to reach 50% deviation and approximately 29 powers of 1024 to reach 100% deviation of the same powers of 1000. [ 3 ] Also see Binary prefixes and IEEE 1541-2002 .
Because data (specifically integers) and the addresses of data are stored using the same hardware, and the data is stored in one or more octets ( 2 3 ), double exponentials of two are common in computing. The first 21 of them are:
Also see Fermat number , Tetration and Hyperoperation § Lower hyperoperations .
All of these numbers over 4 end with the digit 6. Starting with 16 the last two digits are periodic with period 4, with the cycle 16–56–36–96–, and starting with 16 the last three digits are periodic with period 20. These patterns are generally true of any power, with respect to any base . The pattern continues where each pattern has starting point 2 k , and the period is the multiplicative order of 2 modulo 5 k , which is φ (5 k ) = 4 × 5 k −1 (see Multiplicative group of integers modulo n ). [ citation needed ]
In a connection with nimbers , these numbers are often called Fermat 2-powers .
The numbers 2 2 n {\displaystyle 2^{2^{n}}} form an irrationality sequence : for every sequence x i {\displaystyle x_{i}} of positive integers , the series
converges to an irrational number . Despite the rapid growth of this sequence, it is the slowest-growing irrationality sequence known. [ 4 ]
Since it is common for computer data types to have a size which is a power of two, these numbers count the number of representable values of that type. For example, a 32-bit word consisting of 4 bytes can represent 2 32 distinct values, which can either be regarded as mere bit-patterns, or are more commonly interpreted as the unsigned numbers from 0 to 2 32 − 1 , or as the range of signed numbers between −2 31 and 2 31 − 1 . For more about representing signed numbers see Two's complement .
In musical notation , all unmodified note values have a duration equal to a whole note divided by a power of two; for example a half note (1/2), a quarter note (1/4), an eighth note (1/8) and a sixteenth note (1/16). Dotted or otherwise modified notes have other durations. In time signatures the lower numeral, the beat unit , which can be seen as the denominator of a fraction, is almost always a power of two.
If the ratio of frequencies of two pitches is a power of two, then the interval between those pitches is full octaves . In this case, the corresponding notes have the same name.
The mathematical coincidence 2 7 ≈ ( 3 2 ) 12 {\displaystyle 2^{7}\approx ({\tfrac {3}{2}})^{12}} , from log 3 log 2 = 1.5849 … ≈ 19 12 {\displaystyle {\frac {\log 3}{\log 2}}=1.5849\ldots \approx {\frac {19}{12}}} , closely relates the interval of 7 semitones in equal temperament to a perfect fifth of just intonation : 2 7 / 12 ≈ 3 / 2 {\displaystyle 2^{7/12}\approx 3/2} , correct to about 0.1%. The just fifth is the basis of Pythagorean tuning ; the difference between twelve just fifths and seven octaves is the Pythagorean comma . [ 10 ]
The sum of all n -choose binomial coefficients is equal to 2 n . Consider the set of all n -digit binary integers. Its cardinality is 2 n . It is also the sums of the cardinalities of certain subsets: the subset of integers with no 1s (consisting of a single number, written as n 0s), the subset with a single 1, the subset with two 1s, and so on up to the subset with n 1s (consisting of the number written as n 1s). Each of these is in turn equal to the binomial coefficient indexed by n and the number of 1s being considered (for example, there are 10-choose-3 binary numbers with ten digits that include exactly three 1s).
Currently, powers of two are the only known almost perfect numbers .
The cardinality of the power set of a set a is always 2 | a | , where | a | is the cardinality of a .
The number of vertices of an n -dimensional hypercube is 2 n . Similarly, the number of ( n − 1) -faces of an n -dimensional cross-polytope is also 2 n and the formula for the number of x -faces an n -dimensional cross-polytope has is 2 x ( n x ) . {\displaystyle 2^{x}{\tbinom {n}{x}}.}
The sum of the first n {\displaystyle n} powers of two (starting from 1 = 2 0 {\displaystyle 1=2^{0}} ) is given by
for n {\displaystyle n} being any positive integer.
Thus, the sum of the powers
can be computed simply by evaluating: 2 64 − 1 {\displaystyle 2^{64}-1} (which is the "chess number").
The sum of the reciprocals of the powers of two is 1 . The sum of the reciprocals of the squared powers of two (powers of four) is 1/3.
The smallest natural power of two whose decimal representation begins with 7 is [ 11 ]
Every power of 2 (excluding 1) can be written as the sum of four square numbers in 24 ways . The powers of 2 are the natural numbers greater than 1 that can be written as the sum of four square numbers in the fewest ways.
As a real polynomial , a n + b n is irreducible , if and only if n is a power of two. (If n is odd, then a n + b n is divisible by a + b , and if n is even but not a power of 2, then n can be written as n = mp , where m is odd, and thus a n + b n = ( a p ) m + ( b p ) m {\displaystyle a^{n}+b^{n}=(a^{p})^{m}+(b^{p})^{m}} , which is divisible by a p + b p .)
But in the domain of complex numbers , the polynomial a 2 n + b 2 n {\displaystyle a^{2n}+b^{2n}} (where n ≥ 1) can always be factorized as a 2 n + b 2 n = ( a n + b n i ) ⋅ ( a n − b n i ) {\displaystyle a^{2n}+b^{2n}=(a^{n}+b^{n}i)\cdot (a^{n}-b^{n}i)} ,
even if n is a power of two.
The only known powers of 2 with all digits even are 2 1 = 2, 2 2 = 4, 2 3 = 8, 2 6 = 64 and 2 11 = 2048 . [ 12 ] The first 3 powers of 2 with all but last digit odd is 2 4 = 16, 2 5 = 32 and 2 9 = 512. The next such power of 2 of form 2 n should have n of at least 6 digits. The only powers of 2 with all digits distinct are 2 0 = 1 to 2 15 = 32 768 , 2 20 = 1 048 576 and 2 29 = 536 870 912 .
Huffman codes deliver optimal lossless data compression when probabilities of the source symbols are all negative powers of two. [ 13 ] | https://en.wikipedia.org/wiki/Power_of_two |
The efficiency of a plant is the percentage of the total energy content of a power plant 's fuel that is converted into electricity . The remaining energy is usually lost to the environment as heat unless it is used for district heating .
Rating efficiency is complicated by the fact that there are two different ways to measure the fuel energy input : [ 1 ]
Depending on which convention is used, a differences of 10% in the apparent efficiency of a gas fired plant can arise, so it is very important to know which convention, HCV or LCV (NCV or GCV) is being used.
Heat rate is a term commonly used in power stations to indicate the power plant efficiency.
The heat rate is the inverse of the efficiency: a lower heat rate is better.
Heat Rate = Thermal Energy In Electrical Energy Out {\displaystyle {\text{Heat Rate}}={\frac {\text{Thermal Energy In}}{\text{Electrical Energy Out}}}} [ 2 ]
The term efficiency is a dimensionless measure (sometimes quoted in percent), and strictly heat rate is dimensionless as well, but often written as energy per energy in relevant units. In SI-units it is joule per joule, but often also expressed as joule / kilowatt hour or British thermal units /kWh. [ 3 ] This is because kilowatt hour is often used when referring to electrical energy and joule or Btu is commonly used when referring to thermal energy .
Heat rate in the context of power plants can be thought of as the input needed to produce one unit of output. It generally indicates the amount of fuel required to generate one unit of electricity. Performance parameters tracked for any thermal power plant like efficiency, fuel costs, plant load factor, emissions level, etc. are a function of the station heat rate and can be linked directly. [ 4 ]
Given that heat rate and efficiency are inversely related to each other, it is easy to convert from one to the other.
Most power plants have a target or design heat rate. If the actual heat rate does not match the target, the difference between the actual and target heat rate is the heat rate deviation. | https://en.wikipedia.org/wiki/Power_plant_efficiency |
Power plant engineering , abbreviated as TPTL , is a branch of the field of energy engineering , and is defined as the engineering and technology required for the production of an electric power station. [ 1 ] Technique is focused on power generation for industry and community, not just for household electricity production. This field is a discipline field using the theoretical basis of mechanical engineering and electrical . The engineering aspects of power generation have developed with technology and are becoming more and more complicated. The introduction of nuclear technology and other existing technology advances have made it possible for power to be created in more ways and on a larger scale than was previously possible. Assignment of different types of engineers for the design, construction, and operation of new power plants depending on the type of system being built, such as whether it is fueled by fossil fuels , nuclear, hydropower, or solar power.
Power plant engineering got its start in the 1800s when small systems were used by individual factories to provide electrical power . Originally the only source of power came from DC, or direct current , systems. [ 2 ] While this was suitable for business, electricity was not accessible for most of the public body. During these times, the coal-powered steam engine was costly to run and there was no way for the power to be transmitted over distances. Hydroelectricity was one of the most utilized forms of power generation as water mills could be used to create power to transmit to small towns. [ 2 ]
It wasn't until the introduction of AC, or alternating current , power systems that allowed for the creation of power plants as we know them today. AC systems allowed power to be transmitted over larger distances than DC systems allowed and thus, large power stations were able to be created. One of the progenitors of long-distance power-transmission was the Lauffen to Frankfurt power plant which spanned 109 miles. [ 3 ] The Lauffen-Frankfurt demonstrated how three-phase power could be effectively applied to transmit power over long distances. [ 3 ] [ 4 ] Three-phase power had been the progeny of years of research in power distribution and the Lauffen-Frankfurt was the first exhibition to show its future potential.
The engineering knowledge needed to perform these tasks enlists the help of several fields of engineering including mechanical, electrical, nuclear and civil engineers . When power plants were up and coming, engineering tasks needed to create these facilities mainly consisted of mechanical, civil, and electrical engineers. [ 2 ] These disciplines allowed for the planning and construction of power plants. But when nuclear power plants were created it introduced nuclear engineers to perform the calculations necessary to maintain safety standards. [ 5 ]
In simple terms, the first law of thermodynamics states that energy cannot be created nor destroyed; however, power can be converted from one form of energy to another form of energy. This is especially important in power generation because power production in nearly all types of power plants relies upon the use of a generator . [ 4 ] Generators are used to convert mechanical energy into electrical energy; for example, wind turbines utilize a large blade connected to a shaft which turns the generator when rotated. The generator then creates electricity due to the interaction of a conductor within a magnetic field. In this case, the mechanical energy generated by the wind is converted, through the generator, into electric energy. Most power plants rely on these conversions to create usable electric power. [ 6 ]
The second law of thermodynamics conceptualizes that the entropy of a closed system can never decrease. As the law relates to power plants, it dictates that heat is to flow from a body at high temperature to a body at low temperature (the device in which electricity is being generated). [ 4 ] This law is particularly pertinent to thermal power plants which derive their energy from the combustion of a fuel source. [ 1 ]
All power plants are created with the same goal: to produce electric power as efficiently as possible. However, as technology has evolved, the sources of energy used in power plants has evolved as well. [ 1 ] The introduction of more renewable/sustainable forms of energy has caused an increase in the improvement and creation of certain power plants. [ 1 ]
Hydroelectric power plants generate power using the force of water to turn generators. They can be categorized into three different types; impoundment, diversion and pumped storage. [ 7 ] Impoundment and diversion hydroelectric power plants operate similarly in that each involves creating a barrier to keep water from flowing at an uncontrollable rate, and then controlling the flow rate of water to pass through turbines to create electricity at an ideal level. Hydraulic civil engineers are in charge of calculating flow rates and other volumetric calculations necessary to turn the generators to the electrical engineers specifications. [ 8 ] Pumped storage hydroelectric power plants operate in a similar manner but only function at peak hours of power demand. At calm hours the water is pumped uphill, then is released at peak hours to flow from a high to low elevation to turn turbines. [ 9 ] The engineering knowledge required to assess the performance of pumped-storage hydroelectric power plants is very similar to that of the impoundment and diversion power plants.
Thermal power plants are split into two different categories; those that create electricity by burning fuel and those that create electricity via prime mover. A common example of a thermal power plant that produces electricity by the consumption of fuel is the nuclear power plant. Nuclear power plants use a nuclear reactor's heat to turn water into steam. [ 1 ] This steam is sent through a turbine which is connected to an electric generator to generate electricity. Nuclear power plants account for 20% of America's electricity generation . [ 10 ] Another example of a fuel burning power plant is coal power plant . Coal power plants generate 50% of the United States' electricity supply. [ 10 ] Coal power plants operate in a manner similar to nuclear power plants in that the heat from the burning coal powers a steam turbine and electric generator. [ 1 ] There are several types of engineers that work in a Thermal Power Plant. Mechanical engineers maintain performance of the thermal power plants while keeping the plants in operation. [ 11 ] Nuclear engineers generally handle fuel efficiency and disposal of nuclear waste; however, in Nuclear Power Plants they work directly with nuclear equipment. [ 12 ] Electrical Engineers deals with the power generating equipment as well as the calculations. [ 13 ]
Solar power plants derive their energy from sunlight, which is made accessible via photovoltaics (PV's). Photovoltaic panels, or solar panels , are constructed using photovoltaic cells which are made of silica materials that release electrons when they are warmed by the thermal energy of the sun. The new flow of electrons generates electricity within the cell. [ 14 ] While PV's are an efficient method of producing electricity, they do burn out after a decade and thus, must be replaced; however, their efficiency, cost of operation, and lack of noise / physical pollutants make them one of the cleanest and least expensive forms of energy. [ 1 ] Solar power plants require the work of many facets of engineering; electrical engineers are especially crucial in constructing the solar panels and connecting them into a grid, and computer engineers code the cells themselves so that electricity can be effectively and efficiently produced, and civil engineers play the very important role of identifying areas where solar plants are able to collect the most energy. [ 11 ]
Wind power plants , also known as wind turbines, derive their energy from the wind by connecting a generator to the fan blades and using the rotational motion caused by wind to power the generator. [ 15 ] Then the generated power is fed back into the power grid. Wind power plants can be implemented on large, open expanses of land or on large bodies of water such as the oceans; they rely on being in areas that experience significant amounts of wind. [ 1 ] Technically, wind turbines are a form of solar power in that they rely on pressure differentials caused by uneven heating of the Earth's atmosphere. [ 15 ] Wind turbines solicit knowledge from mechanical, electrical, and civil engineers. Knowledge of fluid dynamics from the help of mechanical engineers is crucial in determining the viability of locations for wind turbines. [ 16 ] Electrical engineers ensure that power generation and transmission is possible. [ 13 ] Civil engineers are important in the construction and utilization of wind turbines. [ 17 ]
Power plant engineering covers a broad spectrum of engineering disciplines. The field can solicit information from mechanical, chemical, electrical, nuclear, and civil engineers.
Mechanical engineers work to maintain and control machinery that is used to power the plant. [ 12 ] To work in this field, mechanical engineers require a bachelor's degree in Engineering and license passing both the Professional Engineering Exam (PE) and Fundamental Engineering Exam (FE). Mechanical engineers have additional roles that are needed to be considered based on their careers. When working in thermal power plants, mechanical engineers make sure heavy machinery like boilers and turbines, are working in optimal condition and power is continually generated. [ 12 ] Mechanical engineers also work with the operations of the plant. In nuclear and hydraulic power plants the engineers work to make sure that heavy machinery is maintained and preventive maintenance is performed.
Electrical engineers work with electrical appliances while making sure electronic instruments and appliances are working in company and state level satisfaction. [ 13 ] They require licenses passing both the Professional Engineering Exam (PE) and Fundamental Engineering Exam (FE). It is also preferred that they have a bachelor's degree approved by the Accreditation Board of Engineering and Technology, Inc. (ABET) and field experience before getting an entry-level position.
Nuclear engineers develop and research methods, machinery and systems concerning radiation and energy in subatomic levels. [ 12 ] They require on-site experience and a bachelor's degree in engineering. These engineers work in Nuclear Power plants and require licenses for practice while working in the power plant. They require work experience, passing the Professional Engineering Exam(PE), Fundamental Engineering Exam (FE), and a degree from an Accreditation Board for Engineering and Technology, Inc (ABET) approved school. [ 12 ] Nuclear engineers work with the handling of nuclear material and operations of a nuclear power plant. These operations can range from handling of nuclear wastes, nuclear material experiments, and design of nuclear equipment. [ 18 ]
Civil engineers focuses on the power plant's construction, expenses, and building. [ 19 ] Civil Engineers require passing the Professional Engineering Exam (PE), Fundamental Engineering Exam (FE), and a degree from an Accreditation Board of Engineering and Technology, Inc. (ABET) approved school. [ 19 ] They work with making sure the structure of the power plant, the location, and the design and safety of the power plant.
While there are many disparities between the aforementioned engineering disciplines, they all cover material related to heat or electricity transmission. Obtaining a degree from an ABET accredited school in any one of these disciplines is essential to becoming a power plant engineer. [ 20 ] There are also many associations which qualified engineers can join, including the American Society of Mechanical Engineers (ASME), the Institute of Electric and Electronic Engineers (IEEE), and the American Society of Power Engineers (ASOPE).
Power plant operation and maintenance consists of optimizing the efficiency and power output of power plants and ensuring long term operation. [ 21 ] These power plants are large scale, and used to supply power for communities and industry. Individual household electric power generators are not included. [ 1 ]
Power station design consists of the design of new power plant systems. [ 4 ] There are many types of power plants, and each type requires specific expertise, as well as interdisciplinary teamwork, to build a modern system. [ 1 ]
Brighthub Engineering. Retrieved 2018-04-18. | https://en.wikipedia.org/wiki/Power_plant_engineering |
A power processing unit ( PPU ) is a circuit device that convert an electricity input from a utility line into the appropriate voltage and current to be used for the device in question. They serve the same purpose as linear amplifiers , but they are much more efficient, since the use of linear amplifiers results in much power loss due to the use of a resistor to change the voltage and current. Instead of using a resistor, PPUs use switches to turn a signal on and off quite rapidly in order to change the average current and voltage. In this way, they could be conflated with DC-AC converters , but the frequency at which they switch the signal on and off is a few orders of magnitude higher than that of AC signals. They are used to convert the current and voltage of both direct current (DC) and alternating current (AC) signals. [ 1 ]
In the context of spacecraft , the power processing unit (PPU) is a module containing the electrical subsystem responsible for providing electrical power to other parts of the spacecraft. The PPU needs to be able to cope with varying demands for power output and provide that power in the most efficient manner possible.
There are two main constraints placed on PPUs:
Major considerations in building PPUs are weight , size and efficiency . [ 2 ] [ 3 ]
Most PPUs process and supply direct current because that is what is generated by a solar array.
The PPU is also responsible for voltage conversion and supplying the required voltage to other subsystems of the spacecraft. | https://en.wikipedia.org/wiki/Power_processing_unit |
In telecommunications, power ramp is the way in which the signal increases ("power-on ramp") or falls off ("power-down ramp"), which may result in spectral splatter .
For example, many GSM front-ends make use of a calibration table specifying the ramp shape for the power amplifier.
This article related to telecommunications is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Power_ramp |
In calculus , the power rule is used to differentiate functions of the form f ( x ) = x r {\displaystyle f(x)=x^{r}} , whenever r {\displaystyle r} is a real number . Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule. The power rule underlies the Taylor series as it relates a power series with a function's derivatives .
Let f {\displaystyle f} be a function satisfying f ( x ) = x r {\displaystyle f(x)=x^{r}} for all x {\displaystyle x} , where r ∈ R {\displaystyle r\in \mathbb {R} } . [ a ] Then,
The power rule for integration states that
for any real number r ≠ − 1 {\displaystyle r\neq -1} . It can be derived by inverting the power rule for differentiation. In this equation C is any constant .
Let f ( x ) = x r {\displaystyle f(x)=x^{r}} , where r {\displaystyle r} is any real number.
If f ( x ) = e x {\displaystyle f(x)=e^{x}} , then ln ( f ( x ) ) = x {\displaystyle \ln(f(x))=x} , where ln {\displaystyle \ln } is the natural logarithm function,
or f ′ ( x ) = f ( x ) = e x {\displaystyle f'(x)=f(x)=e^{x}} , as was required.
Therefore, applying the chain rule to f ( x ) = e r ln x {\displaystyle f(x)=e^{r\ln x}} , we see that f ′ ( x ) = r x e r ln x = r x x r {\displaystyle f'(x)={\frac {r}{x}}e^{r\ln x}={\frac {r}{x}}x^{r}} which simplifies to r x r − 1 {\displaystyle rx^{r-1}} .
When x < 0 {\displaystyle x<0} , we may use the same definition with x r = ( ( − 1 ) ( − x ) ) r = ( − 1 ) r ( − x ) r {\displaystyle x^{r}=((-1)(-x))^{r}=(-1)^{r}(-x)^{r}} , where we now have − x > 0 {\displaystyle -x>0} . This necessarily leads to the same result. Note that because ( − 1 ) r {\displaystyle (-1)^{r}} does not have a conventional definition when r {\displaystyle r} is not a rational number, irrational power functions are not well defined for negative bases. In addition, as rational powers of −1 with even denominators (in lowest terms) are not real numbers, these expressions are only real valued for rational powers with odd denominators (in lowest terms).
Finally, whenever the function is differentiable at x = 0 {\displaystyle x=0} , the defining limit for the derivative is: lim h → 0 h r − 0 r h {\displaystyle \lim _{h\to 0}{\frac {h^{r}-0^{r}}{h}}} which yields 0 only when r {\displaystyle r} is a rational number with odd denominator (in lowest terms) and r > 1 {\displaystyle r>1} , and 1 when r = 1 {\displaystyle r=1} . For all other values of r {\displaystyle r} , the expression h r {\displaystyle h^{r}} is not well-defined for h < 0 {\displaystyle h<0} , as was covered above, or is not a real number, so the limit does not exist as a real-valued derivative. For the two cases that do exist, the values agree with the value of the existing power rule at 0, so no exception need be made.
The exclusion of the expression 0 0 {\displaystyle 0^{0}} (the case x = 0 {\displaystyle x=0} ) from our scheme of exponentiation is due to the fact that the function f ( x , y ) = x y {\displaystyle f(x,y)=x^{y}} has no limit at (0,0), since x 0 {\displaystyle x^{0}} approaches 1 as x approaches 0, while 0 y {\displaystyle 0^{y}} approaches 0 as y approaches 0. Thus, it would be problematic to ascribe any particular value to it, as the value would contradict one of the two cases, dependent on the application. It is traditionally left undefined.
Let n ∈ N {\displaystyle n\in \mathbb {N} } . It is required to prove that d d x x n = n x n − 1 . {\displaystyle {\frac {d}{dx}}x^{n}=nx^{n-1}.} The base case may be when n = 0 {\displaystyle n=0} or 1 {\displaystyle 1} , depending on how the set of natural numbers is defined.
When n = 0 {\displaystyle n=0} , d d x x 0 = d d x ( 1 ) = lim h → 0 1 − 1 h = lim h → 0 0 h = 0 = 0 x 0 − 1 . {\displaystyle {\frac {d}{dx}}x^{0}={\frac {d}{dx}}(1)=\lim _{h\to 0}{\frac {1-1}{h}}=\lim _{h\to 0}{\frac {0}{h}}=0=0x^{0-1}.}
When n = 1 {\displaystyle n=1} , d d x x 1 = lim h → 0 ( x + h ) − x h = lim h → 0 h h = 1 = 1 x 1 − 1 . {\displaystyle {\frac {d}{dx}}x^{1}=\lim _{h\to 0}{\frac {(x+h)-x}{h}}=\lim _{h\to 0}{\frac {h}{h}}=1=1x^{1-1}.}
Therefore, the base case holds either way.
Suppose the statement holds for some natural number k , i.e. d d x x k = k x k − 1 . {\displaystyle {\frac {d}{dx}}x^{k}=kx^{k-1}.}
When n = k + 1 {\displaystyle n=k+1} , d d x x k + 1 = d d x ( x k ⋅ x ) = x k ⋅ d d x x + x ⋅ d d x x k = x k + x ⋅ k x k − 1 = x k + k x k = ( k + 1 ) x k = ( k + 1 ) x ( k + 1 ) − 1 {\displaystyle {\frac {d}{dx}}x^{k+1}={\frac {d}{dx}}(x^{k}\cdot x)=x^{k}\cdot {\frac {d}{dx}}x+x\cdot {\frac {d}{dx}}x^{k}=x^{k}+x\cdot kx^{k-1}=x^{k}+kx^{k}=(k+1)x^{k}=(k+1)x^{(k+1)-1}} By the principle of mathematical induction, the statement is true for all natural numbers n .
Let y = x n {\displaystyle y=x^{n}} , where n ∈ N {\displaystyle n\in \mathbb {N} } .
Then, d y d x = lim h → 0 ( x + h ) n − x n h = lim h → 0 1 h [ x n + ( n 1 ) x n − 1 h + ( n 2 ) x n − 2 h 2 + ⋯ + ( n n ) h n − x n ] = lim h → 0 [ ( n 1 ) x n − 1 + ( n 2 ) x n − 2 h + ⋯ + ( n n ) h n − 1 ] = n x n − 1 {\displaystyle {\begin{aligned}{\frac {dy}{dx}}&=\lim _{h\to 0}{\frac {(x+h)^{n}-x^{n}}{h}}\\[4pt]&=\lim _{h\to 0}{\frac {1}{h}}\left[x^{n}+{\binom {n}{1}}x^{n-1}h+{\binom {n}{2}}x^{n-2}h^{2}+\dots +{\binom {n}{n}}h^{n}-x^{n}\right]\\[4pt]&=\lim _{h\to 0}\left[{\binom {n}{1}}x^{n-1}+{\binom {n}{2}}x^{n-2}h+\dots +{\binom {n}{n}}h^{n-1}\right]\\[4pt]&=nx^{n-1}\end{aligned}}}
Since n choose 1 is equal to n, and the rest of the terms all contain h, which is 0, the rest of the terms cancel. This proof only works for natural numbers as the binomial theorem only works for natural numbers.
For a negative integer n , let n = − m {\displaystyle n=-m} so that m is a positive integer.
Using the reciprocal rule , d d x x n = d d x ( 1 x m ) = − d d x x m ( x m ) 2 = − m x m − 1 x 2 m = − m x − m − 1 = n x n − 1 . {\displaystyle {\frac {d}{dx}}x^{n}={\frac {d}{dx}}\left({\frac {1}{x^{m}}}\right)={\frac {-{\frac {d}{dx}}x^{m}}{(x^{m})^{2}}}=-{\frac {mx^{m-1}}{x^{2m}}}=-mx^{-m-1}=nx^{n-1}.} In conclusion, for any integer n {\displaystyle n} , d d x x n = n x n − 1 . {\displaystyle {\frac {d}{dx}}x^{n}=nx^{n-1}.}
Upon proving that the power rule holds for integer exponents, the rule can be extended to rational exponents.
This proof is composed of two steps that involve the use of the chain rule for differentiation.
From the above results, we can conclude that when r {\displaystyle r} is a rational number , d d x x r = r x r − 1 . {\displaystyle {\frac {d}{dx}}x^{r}=rx^{r-1}.}
A more straightforward generalization of the power rule to rational exponents makes use of implicit differentiation.
Let y = x r = x p / q {\displaystyle y=x^{r}=x^{p/q}} , where p , q ∈ Z {\displaystyle p,q\in \mathbb {Z} } so that r ∈ Q {\displaystyle r\in \mathbb {Q} } .
Then, y q = x p {\displaystyle y^{q}=x^{p}} Differentiating both sides of the equation with respect to x {\displaystyle x} , q y q − 1 ⋅ d y d x = p x p − 1 {\displaystyle qy^{q-1}\cdot {\frac {dy}{dx}}=px^{p-1}} Solving for d y d x {\displaystyle {\frac {dy}{dx}}} , d y d x = p x p − 1 q y q − 1 . {\displaystyle {\frac {dy}{dx}}={\frac {px^{p-1}}{qy^{q-1}}}.} Since y = x p / q {\displaystyle y=x^{p/q}} , d d x x p / q = p x p − 1 q x p − p / q . {\displaystyle {\frac {d}{dx}}x^{p/q}={\frac {px^{p-1}}{qx^{p-p/q}}}.} Applying laws of exponents, d d x x p / q = p q x p − 1 x − p + p / q = p q x p / q − 1 . {\displaystyle {\frac {d}{dx}}x^{p/q}={\frac {p}{q}}x^{p-1}x^{-p+p/q}={\frac {p}{q}}x^{p/q-1}.} Thus, letting r = p q {\displaystyle r={\frac {p}{q}}} , we can conclude that d d x x r = r x r − 1 {\displaystyle {\frac {d}{dx}}x^{r}=rx^{r-1}} when r {\displaystyle r} is a rational number.
The power rule for integrals was first demonstrated in a geometric form by Italian mathematician Bonaventura Cavalieri in the early 17th century for all positive integer values of n {\displaystyle {\displaystyle n}} , and during the mid 17th century for all rational powers by the mathematicians Pierre de Fermat , Evangelista Torricelli , Gilles de Roberval , John Wallis , and Blaise Pascal , each working independently. At the time, they were treatises on determining the area between the graph of a rational power function and the horizontal axis. With hindsight, however, it is considered the first general theorem of calculus to be discovered. [ 1 ] The power rule for differentiation was derived by Isaac Newton and Gottfried Wilhelm Leibniz , each independently, for rational power functions in the mid 17th century, who both then used it to derive the power rule for integrals as the inverse operation. This mirrors the conventional way the related theorems are presented in modern basic calculus textbooks, where differentiation rules usually precede integration rules. [ 2 ]
Although both men stated that their rules, demonstrated only for rational quantities, worked for all real powers, neither sought a proof of such, as at the time the applications of the theory were not concerned with such exotic power functions, and questions of convergence of infinite series were still ambiguous.
The unique case of r = − 1 {\displaystyle r=-1} was resolved by Flemish Jesuit and mathematician Grégoire de Saint-Vincent and his student Alphonse Antonio de Sarasa in the mid 17th century, who demonstrated that the associated definite integral,
representing the area between the rectangular hyperbola x y = 1 {\displaystyle xy=1} and the x-axis, was a logarithmic function, whose base was eventually discovered to be the transcendental number e . The modern notation for the value of this definite integral is ln ( x ) {\displaystyle \ln(x)} , the natural logarithm.
If we consider functions of the form f ( z ) = z c {\displaystyle f(z)=z^{c}} where c {\displaystyle c} is any complex number and z {\displaystyle z} is a complex number in a slit complex plane that excludes the branch point of 0 and any branch cut connected to it, and we use the conventional multivalued definition z c := exp ( c ln z ) {\displaystyle z^{c}:=\exp(c\ln z)} , then it is straightforward to show that, on each branch of the complex logarithm, the same argument used above yields a similar result: f ′ ( z ) = c z exp ( c ln z ) {\displaystyle f'(z)={\frac {c}{z}}\exp(c\ln z)} . [ 3 ]
In addition, if c {\displaystyle c} is a positive integer, then there is no need for a branch cut: one may define f ( 0 ) = 0 {\displaystyle f(0)=0} , or define positive integral complex powers through complex multiplication, and show that f ′ ( z ) = c z c − 1 {\displaystyle f'(z)=cz^{c-1}} for all complex z {\displaystyle z} , from the definition of the derivative and the binomial theorem.
However, due to the multivalued nature of complex power functions for non-integer exponents, one must be careful to specify the branch of the complex logarithm being used. In addition, no matter which branch is used, if c {\displaystyle c} is not a positive integer, then the function is not differentiable at 0. | https://en.wikipedia.org/wiki/Power_rule |
In mathematics , a power series (in one variable ) is an infinite series of the form ∑ n = 0 ∞ a n ( x − c ) n = a 0 + a 1 ( x − c ) + a 2 ( x − c ) 2 + … {\displaystyle \sum _{n=0}^{\infty }a_{n}\left(x-c\right)^{n}=a_{0}+a_{1}(x-c)+a_{2}(x-c)^{2}+\dots } where a n {\displaystyle a_{n}} represents the coefficient of the n th term and c is a constant called the center of the series. Power series are useful in mathematical analysis , where they arise as Taylor series of infinitely differentiable functions . In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function.
In many situations, the center c is equal to zero, for instance for Maclaurin series . In such cases, the power series takes the simpler form ∑ n = 0 ∞ a n x n = a 0 + a 1 x + a 2 x 2 + … . {\displaystyle \sum _{n=0}^{\infty }a_{n}x^{n}=a_{0}+a_{1}x+a_{2}x^{2}+\dots .}
The partial sums of a power series are polynomials , the partial sums of the Taylor series of an analytic function are a sequence of converging polynomial approximations to the function at the center, and a converging power series can be seen as a kind of generalized polynomial with infinitely many terms. Conversely, every polynomial is a power series with only finitely many non-zero terms.
Beyond their role in mathematical analysis, power series also occur in combinatorics as generating functions (a kind of formal power series ) and in electronic engineering (under the name of the Z-transform ). The familiar decimal notation for real numbers can also be viewed as an example of a power series, with integer coefficients, but with the argument x fixed at 1 ⁄ 10 . In number theory , the concept of p -adic numbers is also closely related to that of a power series.
Every polynomial of degree d can be expressed as a power series around any center c , where all terms of degree higher than d have a coefficient of zero. [ 1 ] For instance, the polynomial f ( x ) = x 2 + 2 x + 3 {\textstyle f(x)=x^{2}+2x+3} can be written as a power series around the center c = 0 {\textstyle c=0} as f ( x ) = 3 + 2 x + 1 x 2 + 0 x 3 + 0 x 4 + ⋯ {\displaystyle f(x)=3+2x+1x^{2}+0x^{3}+0x^{4}+\cdots } or around the center c = 1 {\textstyle c=1} as f ( x ) = 6 + 4 ( x − 1 ) + 1 ( x − 1 ) 2 + 0 ( x − 1 ) 3 + 0 ( x − 1 ) 4 + ⋯ . {\displaystyle f(x)=6+4(x-1)+1(x-1)^{2}+0(x-1)^{3}+0(x-1)^{4}+\cdots .}
One can view power series as being like "polynomials of infinite degree", although power series are not polynomials in the strict sense.
The geometric series formula 1 1 − x = ∑ n = 0 ∞ x n = 1 + x + x 2 + x 3 + ⋯ , {\displaystyle {\frac {1}{1-x}}=\sum _{n=0}^{\infty }x^{n}=1+x+x^{2}+x^{3}+\cdots ,} which is valid for | x | < 1 {\textstyle |x|<1} , is one of the most important examples of a power series, as are the exponential function formula e x = ∑ n = 0 ∞ x n n ! = 1 + x + x 2 2 ! + x 3 3 ! + ⋯ {\displaystyle e^{x}=\sum _{n=0}^{\infty }{\frac {x^{n}}{n!}}=1+x+{\frac {x^{2}}{2!}}+{\frac {x^{3}}{3!}}+\cdots } and the sine formula sin ( x ) = ∑ n = 0 ∞ ( − 1 ) n x 2 n + 1 ( 2 n + 1 ) ! = x − x 3 3 ! + x 5 5 ! − x 7 7 ! + ⋯ , {\displaystyle \sin(x)=\sum _{n=0}^{\infty }{\frac {(-1)^{n}x^{2n+1}}{(2n+1)!}}=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots ,} valid for all real x . These power series are examples of Taylor series (or, more specifically, of Maclaurin series ).
Negative powers are not permitted in an ordinary power series; for instance, x − 1 + 1 + x 1 + x 2 + ⋯ {\textstyle x^{-1}+1+x^{1}+x^{2}+\cdots } is not considered a power series (although it is a Laurent series ). Similarly, fractional powers such as x 1 2 {\textstyle x^{\frac {1}{2}}} are not permitted; fractional powers arise in Puiseux series . The coefficients a n {\textstyle a_{n}} must not depend on x {\textstyle x} , thus for instance sin ( x ) x + sin ( 2 x ) x 2 + sin ( 3 x ) x 3 + ⋯ {\textstyle \sin(x)x+\sin(2x)x^{2}+\sin(3x)x^{3}+\cdots } is not a power series.
A power series ∑ n = 0 ∞ a n ( x − c ) n {\textstyle \sum _{n=0}^{\infty }a_{n}(x-c)^{n}} is convergent for some values of the variable x , which will always include x = c since ( x − c ) 0 = 1 {\displaystyle (x-c)^{0}=1} and the sum of the series is thus a 0 {\displaystyle a_{0}} for x = c . The series may diverge for other values of x , possibly all of them. If c is not the only point of convergence, then there is always a number r with 0 < r ≤ ∞ such that the series converges whenever | x – c | < r and diverges whenever | x – c | > r . The number r is called the radius of convergence of the power series; in general it is given as r = lim inf n → ∞ | a n | − 1 n {\displaystyle r=\liminf _{n\to \infty }\left|a_{n}\right|^{-{\frac {1}{n}}}} or, equivalently, r − 1 = lim sup n → ∞ | a n | 1 n . {\displaystyle r^{-1}=\limsup _{n\to \infty }\left|a_{n}\right|^{\frac {1}{n}}.} This is the Cauchy–Hadamard theorem ; see limit superior and limit inferior for an explanation of the notation. The relation r − 1 = lim n → ∞ | a n + 1 a n | {\displaystyle r^{-1}=\lim _{n\to \infty }\left|{a_{n+1} \over a_{n}}\right|} is also satisfied, if this limit exists.
The set of the complex numbers such that | x – c | < r is called the disc of convergence of the series. The series converges absolutely inside its disc of convergence and it converges uniformly on every compact subset of the disc of convergence.
For | x – c | = r , there is no general statement on the convergence of the series. However, Abel's theorem states that if the series is convergent for some value z such that | z – c | = r , then the sum of the series for x = z is the limit of the sum of the series for x = c + t ( z – c ) where t is a real variable less than 1 that tends to 1 .
When two functions f and g are decomposed into power series around the same center c , the power series of the sum or difference of the functions can be obtained by termwise addition and subtraction. That is, if f ( x ) = ∑ n = 0 ∞ a n ( x − c ) n {\displaystyle f(x)=\sum _{n=0}^{\infty }a_{n}(x-c)^{n}} and g ( x ) = ∑ n = 0 ∞ b n ( x − c ) n {\displaystyle g(x)=\sum _{n=0}^{\infty }b_{n}(x-c)^{n}} then f ( x ) ± g ( x ) = ∑ n = 0 ∞ ( a n ± b n ) ( x − c ) n . {\displaystyle f(x)\pm g(x)=\sum _{n=0}^{\infty }(a_{n}\pm b_{n})(x-c)^{n}.}
The sum of two power series will have a radius of convergence of at least the smaller of the two radii of convergence of the two series, [ 2 ] but possibly larger than either of the two. For instance it is not true that if two power series ∑ n = 0 ∞ a n x n {\textstyle \sum _{n=0}^{\infty }a_{n}x^{n}} and ∑ n = 0 ∞ b n x n {\textstyle \sum _{n=0}^{\infty }b_{n}x^{n}} have the same radius of convergence, then ∑ n = 0 ∞ ( a n + b n ) x n {\textstyle \sum _{n=0}^{\infty }\left(a_{n}+b_{n}\right)x^{n}} also has this radius of convergence: if a n = ( − 1 ) n {\textstyle a_{n}=(-1)^{n}} and b n = ( − 1 ) n + 1 ( 1 − 1 3 n ) {\textstyle b_{n}=(-1)^{n+1}\left(1-{\frac {1}{3^{n}}}\right)} , for instance, then both series have the same radius of convergence of 1, but the series ∑ n = 0 ∞ ( a n + b n ) x n = ∑ n = 0 ∞ ( − 1 ) n 3 n x n {\textstyle \sum _{n=0}^{\infty }\left(a_{n}+b_{n}\right)x^{n}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{3^{n}}}x^{n}} has a radius of convergence of 3.
With the same definitions for f ( x ) {\displaystyle f(x)} and g ( x ) {\displaystyle g(x)} , the power series of the product and quotient of the functions can be obtained as follows: f ( x ) g ( x ) = ( ∑ n = 0 ∞ a n ( x − c ) n ) ( ∑ n = 0 ∞ b n ( x − c ) n ) = ∑ i = 0 ∞ ∑ j = 0 ∞ a i b j ( x − c ) i + j = ∑ n = 0 ∞ ( ∑ i = 0 n a i b n − i ) ( x − c ) n . {\displaystyle {\begin{aligned}f(x)g(x)&={\biggl (}\sum _{n=0}^{\infty }a_{n}(x-c)^{n}{\biggr )}{\biggl (}\sum _{n=0}^{\infty }b_{n}(x-c)^{n}{\biggr )}\\&=\sum _{i=0}^{\infty }\sum _{j=0}^{\infty }a_{i}b_{j}(x-c)^{i+j}\\&=\sum _{n=0}^{\infty }{\biggl (}\sum _{i=0}^{n}a_{i}b_{n-i}{\biggr )}(x-c)^{n}.\end{aligned}}}
The sequence m n = ∑ i = 0 n a i b n − i {\textstyle m_{n}=\sum _{i=0}^{n}a_{i}b_{n-i}} is known as the Cauchy product of the sequences a n {\displaystyle a_{n}} and b n {\displaystyle b_{n}} .
For division, if one defines the sequence d n {\displaystyle d_{n}} by f ( x ) g ( x ) = ∑ n = 0 ∞ a n ( x − c ) n ∑ n = 0 ∞ b n ( x − c ) n = ∑ n = 0 ∞ d n ( x − c ) n {\displaystyle {\frac {f(x)}{g(x)}}={\frac {\sum _{n=0}^{\infty }a_{n}(x-c)^{n}}{\sum _{n=0}^{\infty }b_{n}(x-c)^{n}}}=\sum _{n=0}^{\infty }d_{n}(x-c)^{n}} then f ( x ) = ( ∑ n = 0 ∞ b n ( x − c ) n ) ( ∑ n = 0 ∞ d n ( x − c ) n ) {\displaystyle f(x)={\biggl (}\sum _{n=0}^{\infty }b_{n}(x-c)^{n}{\biggr )}{\biggl (}\sum _{n=0}^{\infty }d_{n}(x-c)^{n}{\biggr )}} and one can solve recursively for the terms d n {\displaystyle d_{n}} by comparing coefficients.
Solving the corresponding equations yields the formulae based on determinants of certain matrices of the coefficients of f ( x ) {\displaystyle f(x)} and g ( x ) {\displaystyle g(x)} d 0 = a 0 b 0 {\displaystyle d_{0}={\frac {a_{0}}{b_{0}}}} d n = 1 b 0 n + 1 | a n b 1 b 2 ⋯ b n a n − 1 b 0 b 1 ⋯ b n − 1 a n − 2 0 b 0 ⋯ b n − 2 ⋮ ⋮ ⋮ ⋱ ⋮ a 0 0 0 ⋯ b 0 | {\displaystyle d_{n}={\frac {1}{b_{0}^{n+1}}}{\begin{vmatrix}a_{n}&b_{1}&b_{2}&\cdots &b_{n}\\a_{n-1}&b_{0}&b_{1}&\cdots &b_{n-1}\\a_{n-2}&0&b_{0}&\cdots &b_{n-2}\\\vdots &\vdots &\vdots &\ddots &\vdots \\a_{0}&0&0&\cdots &b_{0}\end{vmatrix}}}
Once a function f ( x ) {\displaystyle f(x)} is given as a power series as above, it is differentiable on the interior of the domain of convergence. It can be differentiated and integrated by treating every term separately since both differentiation and integration are linear transformations of functions: f ′ ( x ) = ∑ n = 1 ∞ a n n ( x − c ) n − 1 = ∑ n = 0 ∞ a n + 1 ( n + 1 ) ( x − c ) n , ∫ f ( x ) d x = ∑ n = 0 ∞ a n ( x − c ) n + 1 n + 1 + k = ∑ n = 1 ∞ a n − 1 ( x − c ) n n + k . {\displaystyle {\begin{aligned}f'(x)&=\sum _{n=1}^{\infty }a_{n}n(x-c)^{n-1}=\sum _{n=0}^{\infty }a_{n+1}(n+1)(x-c)^{n},\\\int f(x)\,dx&=\sum _{n=0}^{\infty }{\frac {a_{n}(x-c)^{n+1}}{n+1}}+k=\sum _{n=1}^{\infty }{\frac {a_{n-1}(x-c)^{n}}{n}}+k.\end{aligned}}}
Both of these series have the same radius of convergence as the original series.
A function f defined on some open subset U of R or C is called analytic if it is locally given by a convergent power series. This means that every a ∈ U has an open neighborhood V ⊆ U , such that there exists a power series with center a that converges to f ( x ) for every x ∈ V .
Every power series with a positive radius of convergence is analytic on the interior of its region of convergence. All holomorphic functions are complex-analytic. Sums and products of analytic functions are analytic, as are quotients as long as the denominator is non-zero.
If a function is analytic, then it is infinitely differentiable, but in the real case the converse is not generally true. For an analytic function, the coefficients a n can be computed as a n = f ( n ) ( c ) n ! {\displaystyle a_{n}={\frac {f^{\left(n\right)}\left(c\right)}{n!}}}
where f ( n ) ( c ) {\displaystyle f^{(n)}(c)} denotes the n th derivative of f at c , and f ( 0 ) ( c ) = f ( c ) {\displaystyle f^{(0)}(c)=f(c)} . This means that every analytic function is locally represented by its Taylor series .
The global form of an analytic function is completely determined by its local behavior in the following sense: if f and g are two analytic functions defined on the same connected open set U , and if there exists an element c ∈ U such that f ( n ) ( c ) = g ( n ) ( c ) for all n ≥ 0 , then f ( x ) = g ( x ) for all x ∈ U .
If a power series with radius of convergence r is given, one can consider analytic continuations of the series, that is, analytic functions f which are defined on larger sets than { x | | x − c | < r } and agree with the given power series on this set. The number r is maximal in the following sense: there always exists a complex number x with | x − c | = r such that no analytic continuation of the series can be defined at x .
The power series expansion of the inverse function of an analytic function can be determined using the Lagrange inversion theorem .
The sum of a power series with a positive radius of convergence is an analytic function at every point in the interior of the disc of convergence. However, different behavior can occur at points on the boundary of that disc. For example:
In abstract algebra , one attempts to capture the essence of power series without being restricted to the fields of real and complex numbers, and without the need to talk about convergence. This leads to the concept of formal power series , a concept of great utility in algebraic combinatorics .
An extension of the theory is necessary for the purposes of multivariable calculus . A power series is here defined to be an infinite series of the form f ( x 1 , … , x n ) = ∑ j 1 , … , j n = 0 ∞ a j 1 , … , j n ∏ k = 1 n ( x k − c k ) j k , {\displaystyle f(x_{1},\dots ,x_{n})=\sum _{j_{1},\dots ,j_{n}=0}^{\infty }a_{j_{1},\dots ,j_{n}}\prod _{k=1}^{n}(x_{k}-c_{k})^{j_{k}},} where j = ( j 1 , …, j n ) is a vector of natural numbers, the coefficients a ( j 1 , …, j n ) are usually real or complex numbers, and the center c = ( c 1 , …, c n ) and argument x = ( x 1 , …, x n ) are usually real or complex vectors. The symbol Π {\displaystyle \Pi } is the product symbol , denoting multiplication. In the more convenient multi-index notation this can be written f ( x ) = ∑ α ∈ N n a α ( x − c ) α . {\displaystyle f(x)=\sum _{\alpha \in \mathbb {N} ^{n}}a_{\alpha }(x-c)^{\alpha }.} where N {\displaystyle \mathbb {N} } is the set of natural numbers , and so N n {\displaystyle \mathbb {N} ^{n}} is the set of ordered n - tuples of natural numbers.
The theory of such series is trickier than for single-variable series, with more complicated regions of convergence. For instance, the power series ∑ n = 0 ∞ x 1 n x 2 n {\textstyle \sum _{n=0}^{\infty }x_{1}^{n}x_{2}^{n}} is absolutely convergent in the set { ( x 1 , x 2 ) : | x 1 x 2 | < 1 } {\displaystyle \{(x_{1},x_{2}):|x_{1}x_{2}|<1\}} between two hyperbolas. (This is an example of a log-convex set , in the sense that the set of points ( log | x 1 | , log | x 2 | ) {\displaystyle (\log |x_{1}|,\log |x_{2}|)} , where ( x 1 , x 2 ) {\displaystyle (x_{1},x_{2})} lies in the above region, is a convex set. More generally, one can show that when c=0, the interior of the region of absolute convergence is always a log-convex set in this sense.) On the other hand, in the interior of this region of convergence one may differentiate and integrate under the series sign, just as one may with ordinary power series. [ 4 ]
Let α be a multi-index for a power series f ( x 1 , x 2 , …, x n ) . The order of the power series f is defined to be the least value r {\displaystyle r} such that there is a α ≠ 0 with r = | α | = α 1 + α 2 + ⋯ + α n {\displaystyle r=|\alpha |=\alpha _{1}+\alpha _{2}+\cdots +\alpha _{n}} , or ∞ {\displaystyle \infty } if f ≡ 0. In particular, for a power series f ( x ) in a single variable x , the order of f is the smallest power of x with a nonzero coefficient. This definition readily extends to Laurent series . | https://en.wikipedia.org/wiki/Power_series |
A power shovel , also known as a motor shovel , stripping shovel , front shovel , mining shovel or rope shovel , [ 2 ] is a bucket-equipped machine usually powered by steam , diesel fuel , gasoline or electricity and used for digging and loading earth or fragmented rock and for mineral extraction . [ 3 ] Power shovels are a type of rope/cable excavator, where the digging arm is controlled and powered by winches and steel ropes, rather than hydraulics like in the modern hydraulic excavators .
Basic parts of a power shovel include the track system, cabin, cables, rack, stick, boom foot-pin, saddle block, boom, boom point sheaves and bucket.
The size of bucket varies from 0.73 to 53 cubic meters.
Power shovels normally consist of a revolving deck with a power plant, drive and control mechanisms, usually a counterweight , and a front attachment, such as a crane ("boom") which supports a handle ("dipper" or "dipper stick") with a digger (" bucket ") at the end. The term "dipper" is also sometimes used to refer to the handle and digger combined. The machinery is mounted on a base platform with tracks or wheels. [ 4 ] Modern bucket capacities range from 8m 3 to nearly 80m 3 .
Power shovels are used principally for excavation and removal of overburden in open-cut mining operations; they may also be used for the loading of minerals, such as coal . They are the classic equivalent of excavators, and operate in a similar fashion.
Other uses of the power shovel include:
The shovel operates using several main motions including:
A shovel's work cycle, or digging cycle, consists of four phases:
The digging phase consists of crowding the dipper into the bank, hoisting the dipper to fill it, then retracting the full dipper from the bank. The swinging phase occurs once the dipper is clear of the bank both vertically and horizontally. The operator controls the dipper through a planned swing path and dump height until it is suitably positioned over the haul unit (e.g. truck). Dumping involves opening the dipper door to dump the load, while maintaining the correct dump height. Returning is when the dipper swings back to the bank, and involves lowering the dipper into the track position to close the dipper door.
In the 1950s with the demand for coal at a peak high and more coal companies turning to the cheaper method of strip mining , excavator manufacturers started offering a new super class of power shovels, commonly called giant stripping shovels . Most were built between the 1950s and the 1970s. The world's first giant stripping shovel for the coal fields was the Marion 5760. Unofficially known to its crew and eastern Ohio residents alike as The Mountaineer , [ 5 ] it was erected in 1955/56 near Cadiz, Ohio off of Interstate I-70. Larger models followed the successful 5760, culminating in the mid 60s with the gigantic 12,700 ton Marion 6360 , nicknamed The Captain . One stripping shovel, The 4,220 ton Bucyrus-Erie 1850-B known as " Big Brutus " has been preserved as a national landmark and a museum with tours and camping. Another stripping shovel, The Bucyrus-Erie 3850-B known as "Big Hog" was eventually cut down in 1985 and buried on the Peabody Sinclair Surface Mining site near the Paradise Mining Plant where it was operated. It remains there on non-public, government-owned land.
Ranked by bucket capacity.
Extreme Mining Machines - Stripping shovels and walking draglines, by Keith Haddock, pub by MBI, ISBN 0-7603-0918-3 | https://en.wikipedia.org/wiki/Power_shovel |
A power station , also referred to as a power plant and sometimes generating station or generating plant , is an industrial facility for the generation of electric power . Power stations are generally connected to an electrical grid .
Many power stations contain one or more generators , rotating machine that converts mechanical power into three-phase electric power . The relative motion between a magnetic field and a conductor creates an electric current .
The energy source harnessed to turn the generator varies widely. Most power stations in the world burn fossil fuels such as coal , oil , and natural gas to generate electricity. Low-carbon power sources include nuclear power , and use of renewables such as solar , wind , geothermal , and hydroelectric .
In early 1871 Belgian inventor Zénobe Gramme invented a generator powerful enough to produce power on a commercial scale for industry. [ 1 ]
In 1878, a hydroelectric power station was designed and built by William, Lord Armstrong at Cragside , England . It used water from lakes on his estate to power Siemens dynamos . The electricity supplied power to lights, heating, produced hot water, ran an elevator as well as labor-saving devices and farm buildings. [ 2 ]
In January 1882 the world's first public coal-fired power station , the Edison Electric Light Station , was built in London, a project of Thomas Edison organized by Edward Johnson . A Babcock & Wilcox boiler powered a 93 kW (125 horsepower) steam engine that drove a 27-tonne (27-long-ton) generator. This supplied electricity to premises in the area that could be reached through the culverts of the viaduct without digging up the road, which was the monopoly of the gas companies. The customers included the City Temple and the Old Bailey . Another important customer was the Telegraph Office of the General Post Office , but this could not be reached through the culverts. Johnson arranged for the supply cable to be run overhead, via Holborn Tavern and Newgate . [ 3 ]
In September 1882 in New York, the Pearl Street Station was established by Edison to provide electric lighting in the lower Manhattan Island area. The station ran until destroyed by fire in 1890. The station used reciprocating steam engines to turn direct-current generators. Because of the DC distribution, the service area was small, limited by voltage drop in the feeders. In 1886 George Westinghouse began building an alternating current system that used a transformer to step up voltage for long-distance transmission and then stepped it back down for indoor lighting, a more efficient and less expensive system which is similar to modern systems. The war of the currents eventually resolved in favor of AC distribution and utilization, although some DC systems persisted to the end of the 20th century. DC systems with a service radius of a mile (kilometer) or so were necessarily smaller, less efficient of fuel consumption, and more labor-intensive to operate than much larger central AC generating stations.
AC systems used a wide range of frequencies depending on the type of load; lighting load using higher frequencies, and traction systems and heavy motor load systems preferring lower frequencies. The economics of central station generation improved greatly when unified light and power systems, operating at a common frequency, were developed. The same generating plant that fed large industrial loads during the day, could feed commuter railway systems during rush hour and then serve lighting load in the evening, thus improving the system load factor and reducing the cost of electrical energy overall. Many exceptions existed, generating stations were dedicated to power or light by the choice of frequency, and rotating frequency changers and rotating converters were particularly common to feed electric railway systems from the general lighting and power network.
Throughout the first few decades of the 20th century central stations became larger, using higher steam pressures to provide greater efficiency, and relying on interconnections of multiple generating stations to improve reliability and cost. High-voltage AC transmission allowed hydroelectric power to be conveniently moved from distant waterfalls to city markets. The advent of the steam turbine in central station service, around 1906, allowed great expansion of generating capacity. Generators were no longer limited by the power transmission of belts or the relatively slow speed of reciprocating engines, and could grow to enormous sizes. For example, Sebastian Ziani de Ferranti planned what would have reciprocating steam engine ever built for a proposed new central station, but scrapped the plans when turbines became available in the necessary size. Building power systems out of central stations required combinations of engineering skill and financial acumen in equal measure. Pioneers of central station generation include George Westinghouse and Samuel Insull in the United States, Ferranti and Charles Hesterman Merz in UK, and many others [ 5 ] . [ citation needed ]
In thermal power stations, mechanical power is produced by a heat engine that transforms thermal energy , often from combustion of a fuel , into rotational energy. Most thermal power stations produce steam, so they are sometimes called steam power stations. Not all thermal energy can be transformed into mechanical power, according to the second law of thermodynamics ; therefore, there is always heat lost to the environment. If this loss is employed as useful heat, for industrial processes or district heating , the power plant is referred to as a cogeneration power plant or CHP (combined heat-and-power) plant. In countries where district heating is common, there are dedicated heat plants called heat-only boiler stations . An important class of power stations in the Middle East uses by-product heat for the desalination of water.
The efficiency of a thermal power cycle is limited by the maximum working fluid temperature produced. The efficiency is not directly a function of the fuel used. For the same steam conditions, coal-, nuclear- and gas power plants all have the same theoretical efficiency. Overall, if a system is on constantly (base load) it will be more efficient than one that is used intermittently (peak load). Steam turbines generally operate at higher efficiency when operated at full capacity.
Besides use of reject heat for process or district heating, one way to improve overall efficiency of a power plant is to combine two different thermodynamic cycles in a combined cycle plant. Most commonly, exhaust gases from a gas turbine are used to generate steam for a boiler and a steam turbine. The combination of a "top" cycle and a "bottom" cycle produces higher overall efficiency than either cycle can attain alone.
In 2018, Inter RAO UES and State Grid Archived 21 December 2021 at the Wayback Machine planned to build an 8-GW thermal power plant, [ 7 ] which's the largest coal-fired power plant construction project in Russia . [ 8 ]
A prime mover is a machine that converts energy of various forms into energy of motion.
Power plants that can be dispatched (scheduled) to provide energy to a system include:
Non-dispatchable plants include such sources as wind and solar energy; while their long-term contribution to system energy supply is predictable, on a short-term (daily or hourly) base their energy must be used as available since generation cannot be deferred. Contractual arrangements ("take or pay") with independent power producers or system interconnections to other networks may be effectively non-dispatchable. [ citation needed ]
All thermal power plants produce waste heat energy as a byproduct of the useful electrical energy produced. The amount of waste heat energy equals or exceeds the amount of energy converted into useful electricity [ clarification needed ] . Gas-fired power plants can achieve as much as 65% conversion efficiency, while coal and oil plants achieve around 30–49%. The waste heat produces a temperature rise in the atmosphere, which is small compared to that produced by greenhouse-gas emissions from the same power plant. Natural draft wet cooling towers at many nuclear power plants and large fossil-fuel-fired power plants use large hyperboloid chimney -like structures (as seen in the image at the right) that release the waste heat to the ambient atmosphere by the evaporation of water.
However, the mechanical induced-draft or forced-draft wet cooling towers in many large thermal power plants, nuclear power plants, fossil-fired power plants, petroleum refineries , petrochemical plants , geothermal , biomass and waste-to-energy plants use fans to provide air movement upward through down coming water and are not hyperboloid chimney-like structures. The induced or forced-draft cooling towers are typically rectangular, box-like structures filled with a material that enhances the mixing of the upflowing air and the down-flowing water. [ 14 ] [ 15 ]
In areas with restricted water use, a dry cooling tower or directly air-cooled radiators may be necessary, since the cost or environmental consequences of obtaining make-up water for evaporative cooling would be prohibitive. These coolers have lower efficiency and higher energy consumption to drive fans, compared to a typical wet, evaporative cooling tower. [ citation needed ]
Power plants can use an air-cooled condenser, traditionally in areas with a limited or expensive water supply. Air-cooled condensers serve the same purpose as a cooling tower (heat dissipation) without using water. They consume additional auxiliary power and thus may have a higher carbon footprint compared to a traditional cooling tower. [ citation needed ]
Electric companies often prefer to use cooling water from the ocean or a lake, river, or cooling pond instead of a cooling tower. This single pass or once-through cooling system can save the cost of a cooling tower and may have lower energy costs for pumping cooling water through the plant's heat exchangers . However, the waste heat can cause thermal pollution as the water is discharged. Power plants using natural bodies of water for cooling are designed with mechanisms such as fish screens , to limit intake of organisms into the cooling machinery. These screens are only partially effective and as a result billions of fish and other aquatic organisms are killed by power plants each year. [ 16 ] [ 17 ] For example, the cooling system at the Indian Point Energy Center in New York kills over a billion fish eggs and larvae annually. [ 18 ] A further environmental impact is that aquatic organisms which adapt to the warmer discharge water may be injured if the plant shuts down in cold weather [ citation needed ] .
Water consumption by power stations is a developing issue. [ 19 ]
In recent years, recycled wastewater, or grey water , has been used in cooling towers. The Calpine Riverside and the Calpine Fox power stations in Wisconsin as well as the Calpine Mankato power station in Minnesota are among these facilities. [ citation needed ]
Power stations can generate electrical energy from renewable energy sources.
In a hydroelectric power station water flows through turbines using hydropower to generate hydroelectricity . Power is captured from the gravitational force of water falling through penstocks to water turbines connected to generators . The amount of power available is a combination of height and water flow. A wide range of Dams may be built to raise the water level, and create a lake for storing water .
Hydropower is produced in 150 countries, with the Asia-Pacific region generating 32 percent of global hydropower in 2010. China is the largest hydroelectricity producer, with 721 terawatt-hours of production in 2010, representing around 17 percent of domestic electricity use. [ citation needed ]
Solar energy can be turned into electricity either directly in solar cells , or in a concentrating solar power plant by focusing the light to run a heat engine. [ 20 ]
A solar photovoltaic power plant converts sunlight into direct current electricity using the photoelectric effect . Inverters change the direct current into alternating current for connection to the electrical grid. This type of plant does not use rotating machines for energy conversion. [ 21 ]
Solar thermal power plants use either parabolic troughs or heliostats to direct sunlight onto a pipe containing a heat transfer fluid, such as oil. The heated oil is then used to boil water into steam, which turns a turbine that drives an electrical generator. The central tower type of solar thermal power plant uses hundreds or thousands of mirrors, depending on size, to direct sunlight onto a receiver on top of a tower. The heat is used to produce steam to turn turbines that drive electrical generators. [ citation needed ]
Wind turbines can be used to generate electricity in areas with strong, steady winds, sometimes offshore . Many different designs have been used in the past, but almost all modern turbines being produced today use a three-bladed, upwind design. [ 22 ] Grid-connected wind turbines now being built are much larger than the units installed during the 1970s. They thus produce power more cheaply and reliably than earlier models. [ 23 ] With larger turbines (on the order of one megawatt), the blades move more slowly than older, smaller, units, which makes them less visually distracting and safer for birds. [ 24 ]
Marine energy or marine power (also sometimes referred to as ocean energy or ocean power ) refers to the energy carried by ocean waves , tides , salinity , and ocean temperature differences . The movement of water in the world's oceans creates a vast store of kinetic energy , or energy in motion. This energy can be harnessed to generate electricity to power homes, transport and industries.
The term marine energy encompasses both wave power —power from surface waves, and tidal power —obtained from the kinetic energy of large bodies of moving water. Offshore wind power is not a form of marine energy, as wind power is derived from the wind , even if the wind turbines are placed over water.
The oceans have a tremendous amount of energy and are close to many if not most concentrated populations. Ocean energy has the potential of providing a substantial amount of new renewable energy around the world. [ 25 ]
Salinity gradient energy is called pressure-retarded osmosis. In this method, seawater is pumped into a pressure chamber that is at a pressure lower than the difference between the pressures of saline water and fresh water. Freshwater is also pumped into the pressure chamber through a membrane, which increases both the volume and pressure of the chamber. As the pressure differences are compensated, a turbine is spun creating energy. This method is being specifically studied by the Norwegian utility Statkraft, which has calculated that up to 25 TWh/yr would be available from this process in Norway. Statkraft has built the world's first prototype osmotic power plant on the Oslo fjord which was opened on 24 November 2009. In January 2014, however, Statkraft announced not to continue this pilot. [ 26 ]
Biomass energy can be produced from combustion of waste green material to heat water into steam and drive a steam turbine. Bioenergy can also be processed through a range of temperatures and pressures in gasification , pyrolysis or torrefaction reactions. Depending on the desired end product, these reactions create more energy-dense products ( syngas , wood pellets , biocoal ) that can then be fed into an accompanying engine to produce electricity at a much lower emission rate when compared with open burning. [ citation needed ]
It is possible to store energy and produce electrical power at a later time as in pumped-storage hydroelectricity , thermal energy storage , flywheel energy storage , battery storage power station and so on.
The world's largest form of storage for excess electricity, pumped-storage is a reversible hydroelectric plant. They are a net consumer of energy but provide storage for any source of electricity, effectively smoothing peaks and troughs in electricity supply and demand. Pumped storage plants typically use "spare" electricity during off peak periods to pump water from a lower reservoir to an upper reservoir. Because the pumping takes place "off peak", electricity is less valuable than at peak times. This less valuable "spare" electricity comes from uncontrolled wind power and base load power plants such as coal, nuclear and geothermal, which still produce power at night even though demand is very low. During daytime peak demand, when electricity prices are high, the storage is used for peaking power , where water in the upper reservoir is allowed to flow back to a lower reservoir through a turbine and generator. Unlike coal power stations, which can take more than 12 hours to start up from cold, a hydroelectric generator can be brought into service in a few minutes, ideal to meet a peak load demand. Two substantial pumped storage schemes are in South Africa, Palmiet Pumped Storage Scheme and another in the Drakensberg, Ingula Pumped Storage Scheme .
The power generated by a power station is measured in multiples of the watt , typically megawatts (10 6 watts) or gigawatts (10 9 watts). Power stations vary greatly in capacity depending on the type of power plant and on historical, geographical and economic factors. The following examples offer a sense of the scale.
Many of the largest operational onshore wind farms are located in China. As of 2022, the Roscoe Wind Farm is the largest onshore wind farm in the world, producing 8000 MW of power, followed by the Zhang Jiakou (3000 MW). As of January 2022, the Hornsea Wind Farm in United Kingdom is the largest offshore wind farm in the world at 1218 MW, followed by Walney Wind Farm in United Kingdom at 1026 MW.
In 2021, the worldwide installed capacity of power plants increased by 347 GW. Solar and wind power plant capacities rose by 80% in one year. [ 27 ] As of 2022 [update] , the largest photovoltaic (PV) power plants in the world are led by Bhadla Solar Park in India, rated at 2245 MW.
Solar thermal power stations in the U.S. have the following output:
Large coal-fired, nuclear, and hydroelectric power stations can generate hundreds of megawatts to multiple gigawatts. Some examples:
Gas turbine power plants can generate tens to hundreds of megawatts. Some examples:
The rated capacity of a power station is nearly the maximum electrical power that the power station can produce.
Some power plants are run at almost exactly their rated capacity all the time, as a non-load-following base load power plant , except at times of scheduled or unscheduled maintenance.
However, many power plants usually produce much less power than their rated capacity.
In some cases a power plant produces much less power than its rated capacity because it uses an intermittent energy source .
Operators try to pull maximum available power from such power plants, because their marginal cost is practically zero, but the available power varies widely—in particular, it may be zero during heavy storms at night.
In some cases operators deliberately produce less power for economic reasons.
The cost of fuel to run a load following power plant may be relatively high, and the cost of fuel to run a peaking power plant is even higher—they have relatively high marginal costs.
Operators keep power plants turned off ("operational reserve") or running at minimum fuel consumption [ citation needed ] ("spinning reserve") most of the time.
Operators feed more fuel into load following power plants only when the demand rises above what lower-cost plants (i.e., intermittent and base load plants) can produce, and then feed more fuel into peaking power plants only when the demand rises faster than the load following power plants can follow.
Not all of the generated power of a plant is necessarily delivered into a distribution system. Power plants typically also use some of the power themselves, in which case the generation output is classified into gross generation , and net generation .
Gross generation or gross electric output is the total amount of electricity generated by a power plant over a specific period of time. [ 29 ] It is measured at the generating terminal and is measured in kilowatt-hours (kW·h), megawatt-hours (MW·h), [ 30 ] gigawatt-hours (GW·h) or for the largest power plants terawatt-hours (TW·h). It includes the electricity used in the plant auxiliaries and in the transformers. [ 31 ]
Net generation is the amount of electricity generated by a power plant that is transmitted and distributed for consumer use. Net generation is less than the total gross power generation as some power produced is consumed within the plant itself to power auxiliary equipment such as pumps , motors and pollution control devices. [ 32 ] Thus
Operating staff at a power station have several duties. Operators are responsible for the safety of the work crews that frequently do repairs on the mechanical and electrical equipment. They maintain the equipment with periodic inspections and log temperatures, pressures and other important information at regular intervals. Operators are responsible for starting and stopping the generators depending on need. They are able to synchronize and adjust the voltage output of the added generation with the running electrical system, without upsetting the system. They must know the electrical and mechanical systems to troubleshoot problems in the facility and add to the reliability of the facility. Operators must be able to respond to an emergency and know the procedures in place to deal with it. | https://en.wikipedia.org/wiki/Power_station |
In mathematics , specifically in commutative algebra , the power sum symmetric polynomials are a type of basic building block for symmetric polynomials , in the sense that every symmetric polynomial with rational coefficients can be expressed as a sum and difference of products of power sum symmetric polynomials with rational coefficients. However, not every symmetric polynomial with integral coefficients is generated by integral combinations of products of power-sum polynomials: they are a generating set over the rationals, but not over the integers.
The power sum symmetric polynomial of degree k in n {\displaystyle n} variables x 1 , ..., x n , written p k for k = 0, 1, 2, ..., is the sum of all k th powers of the variables. Formally,
The first few of these polynomials are
Thus, for each nonnegative integer k {\displaystyle k} , there exists exactly one power sum symmetric polynomial of degree k {\displaystyle k} in n {\displaystyle n} variables.
The polynomial ring formed by taking all integral linear combinations of products of the power sum symmetric polynomials is a commutative ring .
The following lists the n {\displaystyle n} power sum symmetric polynomials of positive degrees up to n for the first three positive values of n . {\displaystyle n.} In every case, p 0 = n {\displaystyle p_{0}=n} is one of the polynomials. The list goes up to degree n because the power sum symmetric polynomials of degrees 1 to n are basic in the sense of the theorem stated below.
For n = 1:
For n = 2:
For n = 3:
The set of power sum symmetric polynomials of degrees 1, 2, ..., n in n variables generates the ring of symmetric polynomials in n variables. More specifically:
However, this is not true if the coefficients must be integers. For example, for n = 2, the symmetric polynomial
has the expression
which involves fractions. According to the theorem this is the only way to represent P ( x 1 , x 2 ) {\displaystyle P(x_{1},x_{2})} in terms of p 1 and p 2 . Therefore, P does not belong to the integral polynomial ring Z [ p 1 , … , p n ] . {\displaystyle \mathbb {Z} [p_{1},\ldots ,p_{n}].} For another example, the elementary symmetric polynomials e k , expressed as polynomials in the power sum polynomials, do not all have integral coefficients. For instance,
The theorem is also untrue if the field has characteristic different from 0. For example, if the field F has characteristic 2, then p 2 = p 1 2 {\displaystyle p_{2}=p_{1}^{2}} , so p 1 and p 2 cannot generate e 2 = x 1 x 2 .
Sketch of a partial proof of the theorem : By Newton's identities the power sums are functions of the elementary symmetric polynomials; this is implied by the following recurrence relation , though the explicit function that gives the power sums in terms of the e j is complicated:
Rewriting the same recurrence, one has the elementary symmetric polynomials in terms of the power sums (also implicitly, the explicit formula being complicated):
This implies that the elementary polynomials are rational, though not integral, linear combinations of the power sum polynomials of degrees 1, ..., n .
Since the elementary symmetric polynomials are an algebraic basis for all symmetric polynomials with coefficients in a field, it follows that every symmetric polynomial in n variables is a polynomial function f ( p 1 , … , p n ) {\displaystyle f(p_{1},\ldots ,p_{n})} of the power sum symmetric polynomials p 1 , ..., p n . That is, the ring of symmetric polynomials is contained in the ring generated by the power sums, Q [ p 1 , … , p n ] . {\displaystyle \mathbb {Q} [p_{1},\ldots ,p_{n}].} Because every power sum polynomial is symmetric, the two rings are equal.
(This does not show how to prove the polynomial f is unique.)
For another system of symmetric polynomials with similar properties see complete homogeneous symmetric polynomials . | https://en.wikipedia.org/wiki/Power_sum_symmetric_polynomial |
In electronic systems, power supply rejection ratio ( PSRR ), also supply-voltage rejection ratio [ 1 ] ( k SVR ; SVR ), is a term widely used to describe the capability of an electronic circuit to suppress any power supply variations to its output signal.
In the specifications of operational amplifiers , the PSRR is defined as the ratio of the change in supply voltage to the equivalent (differential) output voltage it produces, [ 2 ] often expressed in decibels . [ 3 ] [ 4 ] [ 5 ] An ideal op-amp would have infinite PSRR, as the device should have no change to the output voltage with any changes to the power supply voltage. The output voltage will depend on the feedback circuit, as is the case of regular input offset voltages. But testing is not confined to DC (zero frequency); often an operational amplifier will also have its PSRR given at various frequencies (in which case the ratio is one of RMS amplitudes of sinewaves present at a power supply compared with the output, with gain taken into account). Unwanted oscillation , including motorboating , can occur when an amplifying stage is too sensitive to signals fed via the power supply from a later power amplifier stage.
Some manufacturers specify PSRR in terms of the offset voltage it causes at the amplifiers inputs; others specify it in terms of the output; there is no industry standard for this issue. [ 6 ] The following formula assumes it is specified in terms of input:
where A v {\textstyle A_{v}} is the voltage gain.
For example: an amplifier with a PSRR of 100 dB in a circuit to give 40 dB closed-loop gain would allow about 1 millivolt of power supply ripple to be superimposed on the output for every 1 volt of ripple in the supply. This is because
And since that's 60 dB of rejection, the sign is negative so:
Note: | https://en.wikipedia.org/wiki/Power_supply_rejection_ratio |
In aviation, a power transfer unit ( PTU ) is a device that transfers hydraulic power from one of an aircraft's hydraulic systems to another in the event that the other system has failed or been turned off.
The PTU is used when, for example, there is right hydraulic system pressure but no left hydraulic system pressure. In this example, the PTU transfers hydraulic power from the right hydraulic system to the left hydraulic system. A PTU consists of a hydraulic motor paired with a hydraulic pump via a shaft. [ 1 ]
As the connection is purely mechanical, there is no intermixing of hydraulic fluid between the left and right hydraulic systems during PTU operation.
Large transport category aircraft with hydraulically powered flight controls and utilities typically have multiple, independent hydraulic systems powered by a combination of engine-driven and electrically driven hydraulic pumps. Multiple hydraulic systems are typically needed for redundancy, where for instance if one system fails or loses hydraulic fluid, a surviving system may still provide sufficient power for critical systems to continue safe flight and landing.
On airliners or business jets with powered flight controls, it is typical to have at least two hydraulic power control units (actuators) for each critical flight control surface — these are the elevators, rudder and ailerons. Only two sources might be used if some form of mechanical reversion is present (i.e. the pilot can still fly the aeroplane manually, but with some difficulty, via mechanical linkages and cables if hydraulic power is lost).
On fly-by-wire aircraft, at least three independent power sources are needed. Spoilers and flaps meanwhile are considered secondary flight controls, and may only have a single hydraulic power source, providing the flight control can be deployed symmetrically.
Likewise, landing gear, brakes and nosewheel steering are systems which are not considered critical for flight, and are subsequently typically only powered by a single hydraulic system on an airliner or business jet.
Where an aircraft utility is powered by a single hydraulic system, PTUs become beneficial in allowing a single source of power, e.g. a pump powered by one surviving engine, to power more than one hydraulic system if the source of power in that system has failed. PTUs only work on the proviso that the system has not punctured and lost its fluid, because they do not permit fluid transfer, only the transfer of mechanical work.
For example, on the original design of the Airbus A320, the landing gear hydraulics (extension/retraction, brakes and steering) were solely powered from the green (left hand) system, powered by the left-hand engine driven pump. In the event of a port engine failure during take-off, the landing gear would not be able to retract as there is no auxiliary motorpump in the green hydraulic system on an A320. (Modern A320s have the nosewheel steering powered by the yellow system.)
The PTU solves this problem by allowing a rotary mechanical coupling between both systems, so the engine driven pump for the yellow (right hand) system on the starboard engine, which is oversized for normal hydraulic demand, can dump the excess power into the green system via the PTU, and allow powered landing gear retraction to continue, while maintaining hydraulic pressure to the green system flight controls as well.
Assuring landing gear retraction in a failure case is one potential assurance provided by a PTU. Alternatively, the designer may elect to have a second electric motorpump perform this role if a PTU is not desired. An additional motorpump may be heavier than a PTU however, and complex trade studies may favor one option or the other, depending on which failure cases are considered and how important weight is in the trade-off.
On the Airbus A320, the yellow system may power the green system, but because it is also bi-directional, if the starboard engine fails, the green system can help to power the yellow system by dumping excess power into it via the same mechanism. This is also known as a 'reversible' PTU.
On some other aircraft, the direction of rotation of the PTU, and thereby the fluid flow through it, may be designed to work in only one direction. The Citation X business jet is one such aircraft with a uni-directional PTU, protected by check-valves and a back-pressure stall line, designed to allow the right hand hydraulic system to assist the left hand hydraulic system and the left hand auxiliary motorpump to retract the landing gear during a port engine failure only.
On yet other aircraft, the function of a bi-directional reversible PTU can be accomplished with two uni-directional PTUs installed side-by-side arranged in opposite orientations to each other. The hydraulic system of the CH-47 Chinook helicopter uses twin uni-directional PTUs in this fashion.
Hydraulic power transfer units are essentially nothing more than a hydraulic motor coupled to a hydraulic pump via a shaft; as such, they can be any kind of motor or pump such as a vane , gear , impeller or an in-line piston, or a variable displacement in-line piston pump.
Commonly though, PTUs are paired in-line piston motors/pumps, in either bent or straight axis arrangements.
A straight-axis in-line piston pump/motor relies on a canted internal swashplate to drive the piston shoes up and down around the internal piston slipway of the pump, lubricated by the fluid itself — this kind of PTU may appear to resemble two cylinders bolted together, with an inlet and outlet port at either end. An example of a straight axis in-line PTU can be found in the Cessna Citation X hydraulic system.
A bent-axis in-line piston pump works the same way, but forgoes the canted swashplate; instead the whole rotating group is tilted to achieve the piston displacement. An example of a bent-axis in-line PTU can be found on the Hawker 4000 hydraulic system.
In yet further representations, a bent-axis fixed-displacement motor/pump can be mated with a straight-axis variable displacement motorpump, as in the case of the Airbus A320 PTU.
The mechanism by which a PTU works is by surging, PTUs self-start by pure mechanical influence alone resulting from the delta-pressure between the two hydraulic systems it is connected to. Consequently, a PTU accelerates very rapidly under the delta-P induced load, and then stops just as suddenly once the pressure equalizes. Each pressure surge may only be a second long, causing a stop-start mode of operation.
In practice, this results in a 'whoosh-whoosh' sudden spool up and spool down, which produces a loud noise that can be likened to a barking dog. Passengers who have flown on the Airbus A320 will frequently hear the PTU 'barking dog', generally when only one engine is running, or when the yellow system electric motorpump is the only active hydraulic power source; the PTU is mechanically activated in these cases. Consequently, the PTU is normally only heard on start-up or shut down. Very rarely is it heard in flight unless a momentary power deficit is present when retracting the gear, or a hydraulic fault has occurred.
In Airbus literature, it is stated that the PTU 'self-tests', on startup, however the PTU does not contain any electronic motor assistance and cannot be commanded to start; it starts by itself only when hydraulic pressure is present. However, solenoid energized shut-off valves can isolate the PTU via a push-button switch (pb/sw) in the cockpit, but this feature is rarely used. | https://en.wikipedia.org/wiki/Power_transfer_unit |
A power trowel (also known as a "power float" and "troweling machine") is a piece of light construction equipment used by construction companies and contractors to apply a smooth finish to concrete slabs. [ 1 ]
Power trowels differ in the way they are controlled:
A power trowel performs the tasks of several hand tools, hand trowel, hand float, darby and concrete float . [ 5 ] | https://en.wikipedia.org/wiki/Power_trowel |
Powered speakers , also known as self-powered speakers and active speakers , are loudspeakers that have built-in amplifiers . Powered speakers are used in a range of settings, including in sound reinforcement systems (used at live music concerts), both for the main speakers facing the audience and the monitor speakers facing the performers; by DJs performing at dance events and raves ; in private homes as part of hi-fi or home cinema audio systems and as computer speakers . They can be connected directly to a mixing console or other low-level audio signal source without the need for an external amplifier. Some active speakers designed for sound reinforcement system use have an onboard mixing console and microphone preamplifier , which enables microphones to be connected directly to the speaker.
Active speakers have several advantages, the most obvious being their compactness and simplicity. Additionally the amplifier(s) can be designed to closely match the optimal requirements of the speaker it will power; and the speaker designer is not required to include a passive crossover, decreasing production cost and possibly sound quality. Some also claim that the shorter distances between components can decrease external interference and increase fidelity; although this is highly dubious, and the reciprocal argument can also be made. Disadvantages include heavier loudspeaker enclosures ; reduced reliability due to active electronic components within; and the need to supply both the audio signal and power to every unit separately, typically requiring two cables to be run to each speaker (as opposed to the single cable required with passive speakers and an external amplifier).
Powered speakers are available with passive or active crossovers built into them. Since the early 2000s, powered speakers with active crossovers and other DSP have become common in sound reinforcement applications and in studio monitors . [ 1 ] Home theater and add-on domestic/automotive subwoofers have used active powered speaker technology since the late 1980s.
The terms "powered" and "active" have been used interchangeably in loudspeaker designs, however, a differentiation may be made between the terms: [ 2 ]
Hybrid active designs exist such as having three drivers powered by two internal amplifiers. In this case, an active two-way crossover splits the audio signal, usually into low frequencies and mid-high frequencies. The low-frequency driver is driven by its own amplifier channel while the mid- and high-frequency drivers share an amplifier channel, the output of which is split by a passive two-way crossover.
The term "active speakers" can also refer to an integrated "active system" [ 5 ] in which passive loudspeakers are mated to an external system of multiple amplifiers fed by an active crossover. These active loudspeaker systems may be built for professional concert touring such as the pioneering JM-3 system designed in 1971 by Harry McCune Sound Service , [ 6 ] or they may be built for high-end home use such as various systems from Naim Audio and Linn Products . [ 7 ]
Some of the first powered loudspeakers were JBL monitor speakers. With the addition of the SE401 Stereo Energizer, introduced in 1964, any pair of monitor speakers could be converted to self-powered operation with the second speaker powered by the first. [ 8 ] The first studio monitor with an active crossover was the OY invented 1967 by Klein-Hummel. It was a hybrid three-way design with two internal amplifier channels. [ 9 ] An early example of a bi-amplified powered studio monitor is the Altec 9846B, introduced in 1971, which combined the passive 9846-8A speaker with the new 771B Bi-amplifier with 60 watts for the woofer and 30 watts for the high frequency compression driver . [ 10 ] In the late 1970s, Paramount Pictures contracted with AB Systems to design a powered speaker system. [ 1 ]
In 1980, Meyer Sound Laboratories produced an integrated active 2-way system, the passive UPA-1, which incorporated lessons John Meyer learned on the McCune JM-3. [ 11 ] It used active electronics mounted outside of the loudspeaker enclosure, including Meyer's integrated active crossover with feedback comparator circuits determining the level of limiting, often connected to third-party customer-specified amplifiers. In 1990, Meyer produced its first powered speaker: the HD-1, a 2-way studio monitor with all internal electronics. [ 1 ] In the early '90s, after years of dealing with the disadvantages of passive systems, especially varying gain settings on third-party amplifiers, John Meyer decided to stop making passive speakers and devote his company to active designs. Meyer said he "hired an ad agency to research how people felt about powered speakers for sound reinforcement, and they came back after a survey and said that nobody wanted them." [ 12 ] Sound reinforcement system operators said they did not want loudspeakers in which they could not see the amplifier meters to determine whether the loudspeakers were working properly during a concert. Nevertheless, Meyer kept to his decision and produced the MSL-4 in 1994, the first powered loudspeaker intended for concert touring. [ 12 ] The UPA-1 was converted to a self-powered configuration in 1996 and the rest of Meyer's product line followed suit.
The main benefit of active versus passive speakers is in the higher fidelity associated with active crossovers and multiple amplifiers, including less IMD, higher dynamic range and greater output power. [ 13 ] The amplifiers within the loudspeaker enclosure may be ideally matched to the individual drivers, eliminating the need for each amplifier channel to operate in the entire audio bandpass. Driver characteristics such as power handling and impedance may be matched to amplifier capabilities. [ 1 ] More specifically, active speakers have very short speaker cables inside the enclosure, so very little voltage and control is lost in long speaker cables with higher resistance.
An active speaker often incorporates equalization tailored to each driver's response in the enclosure. [ 14 ] This yields a flatter, more neutral sound. Limiting circuits (high-ratio audio compression circuits) can be incorporated to increase the likelihood of the driver surviving high-SPL use. Such limiters may be carefully matched to driver characteristics, resulting in a more dependable loudspeaker requiring less service. Distortion detection may be designed into the electronics to help determine the onset of protective limiting, reducing output distortion and eliminating clipping . [ 15 ]
Passive speakers need only one speaker cable but active speakers need two cables: an audio signal cable and an AC power cable. For multiple-enclosure high-power concert systems, the AC cabling is often smaller in diameter than the equivalent speaker cable bundles, so less copper is used. Some powered speaker manufacturers are now incorporating UHF or more frequently Wi-Fi wireless receivers so the speaker requires only an AC power cable.
A powered speaker usually weighs more than an equivalent passive speaker because the internal amplifier circuitry usually outweighs a speaker-level passive crossover. A loudspeaker associated with an integrated active system is even lighter because it has no internal crossover. A lightweight loudspeaker can be more easily carried and it is less of a load in rigging (flying). However, active speakers using lightweight Class-D amplifiers have narrowed the difference. Trucking for a sound system involves transporting all of the various components including amplifier racks, speaker cabling and loudspeaker enclosures. Overall shipping weight for an active loudspeaker system may be less than for a passive system because heavy passive speaker cable bundles are replaced by lighter AC cables and small diameter signal cables. Truck space and weight is reduced by eliminating amplifier racks. [ 1 ]
The expense of a large concert active speaker system is less than the expense of an equivalent passive system. [ 1 ] The passive system, or integrated active system with external electronics, requires separate components such as crossovers, equalizers, limiters and amplifiers, all mounted in rolling racks. Cabling for passive concert systems is heavy, large-diameter speaker cable, more expensive than smaller diameter AC power cables and much smaller audio signal cables. For high-end home use, active speakers usually cost more than passive speakers because of the additional amplifier channels required. [ 13 ]
In professional audio and some home cinema and hi-fi applications, the active speaker may be easier to use because it eliminates the complexity of properly setting crossover frequencies, equalizer curves and limiter thresholds. Cabling is not as simple, however, because active speakers require two cables instead of one (an AC power cable and a cable with the signal, typically an XLR cable). In home audio, some audio engineers argue that a passive speaker, in which an unpowered speaker is connected to an amplifier, is the easiest to install and operate.
The amplifiers are adapted to the single loudspeakers employed, which avoids damage to the amplifier or loudspeaker due to mismatched or overloaded components. In certain cases, with passive speakers, tweeters may be destroyed due to strong distortions resulting from amplifier clipping due to overload resulting in overheating. [ 16 ] [ 17 ] This particularly occurs when the loudness button on a conventional amplifier is activated and the bass tone control is also turned up while the listening volume is high, a typical situation when hi-fi speakers are used at private parties.
By including a negative feedback loop in the amplifier-speaker system, distortion can be substantially reduced. If mounted at the speaker cone, the sensor is usually an accelerometer. It is possible to monitor the back emf generated by the driver voice coil as it moves within the magnetic gap. In either case, specialist amplifier designs are needed and so servo speakers are inherently powered speakers.
Some bass amplifier manufacturers sell powered speakers designed for adding to the stage power of a combo bass amp. The user plugs a patch cord or XLR cable from the combo amp into the powered speaker. | https://en.wikipedia.org/wiki/Powered_speakers |
Crosman Corporation is an American designer, manufacturer and supplier of shooting sport products, with a long-standing presence in airgun design and a tradition of producing pellet and BB guns . Crosman is also a producer of many varieties of airgun and airsoft ammunition and CO 2 Powerlet cartridges. In addition, Crosman sells branded, licensed products as well as a variety of airsoft guns .
Crosman was incorporated in 1924 as Crosman Rifle Company , after the sale of "Crosman Brothers" to Frank Hahn. The firm was based in Fairport, New York , a suburb of Rochester (from the print on the bottom of free vintage targets available as a pdf on the company's website). In 1960 it was acquired by Bangor Punta Corp. [ 1 ] In 1970, the company moved to a small town in the finger lakes region, East Bloomfield .
Crosman's first models were the traditional American multi-pump pneumatic design, where 3 to 10 pumps would pressurize a reservoir for each shot. Descendants of these original models are still made, in rifle , pistol and carbine form, and they remain quite popular. In 1992, Crosman acquired the Benjamin Sheridan company's assets.
From 1971 through 1989, Coleman of Wichita, Kansas owned Crosman. In 1989, MacAndrews & Forbes Holdings of New York acquired Coleman and sold Crosman to Worldwide Sports and Recreation. In 1997, an investment group headed by Leonard Pickett purchased the company. Pickett was named CEO and held that position until his death in 2000. Ken D'Arcy served as CEO from 1997 to 2012.
In 2011, Wellspring Capital Management purchased Crosman and in August 2012 Phil Dolci was named CEO and served until May 2015. Brad Johnson was named as Executive Chairman and Interim CEO while remaining Chairman & CEO of United Sporting Companies, a separate company that is also part of the Wellspring portfolio.
In June 2017, Wellspring sold Crosman to Compass Diversified Holdings, INC (NYSE: CODI). Upon the sale of the company, Robert Beckwith was appointed the new CEO. Robert had previously been the CFO under Brad Johnson.
In May 2024, Crosman was sold to Daisy , which is a portfolio company of BRS & Co . [ 2 ]
In 1882, Walter R. Benjamin of St. Louis , Missouri , introduced the first Benjamin air rifle. These Benjamin Pump guns were manufactured by the Wissler Instrument Co. of St. Louis under a U.S. patent that had been issued to Benjamin. Unlike many air guns of this period, the Benjamin was intended not as a toy, but as a high-power compressed air gun in which pressure was built up by pumping a built-in piston located beneath the barrel.
The Benjamin Air Rifle Company was formed in 1902 when Walter R. Benjamin purchased the patent rights from the defunct St. Louis Air Rifle Company. Production from 1902 to 1904 and from 1906 to 1986 was in St. Louis. In 1977, the Benjamin Air Rifle Company purchased Sheridan Products in Racine, Wisconsin . Benjamin and Sheridan were acquired by Crosman in 1992. By 2015, Benjamin was positioned as Crosman Corporation's adult hunting and high performance line and Sheridan had its name on one model: the Cowboy, a youth-oriented lever action .
In the 1930s, Crosman began to experiment with CO 2 power. Like other CO 2 guns of the day, they were bulk fill , which meant that liquid CO 2 was loaded into a pressurized reservoir on the gun. Other manufacturers started to use 8 gram CO 2 bulbs used in soda dispensers. Crosman capitalized on this in 1954 by introducing a new 12 gram CO 2 bulb, called a Powerlet . The new Powerlet gave more shots per bulb than the soda bulb, and with the addition of a simple spacer, a Powerlet gun could use the shorter 8 gram bulb.
A Powerlet cartridge, commonly referred to as a CO 2 charger, is a small disposable metal gas cylinder holding 8–12 grams (0.28–0.42 oz) of liquid CO 2 and often a small quantity of lubricating oil , used as a pneumatic power source for certain air guns , airsoft guns , paintball guns , carbonation , and for quick inflation of various devices such as a personal flotation device . [ 3 ] Originally developed and the trademark owned by Crosman Corporation [ citation needed ] and introduced to the market in 1954, the Powerlet CO 2 cartridge has become the dominant source of power for inexpensive, rapid fire air guns from many manufacturers.
Typically manufactured from the same steel alloys and using the same metal spinning fabrication processes as much larger refillable gas cylinders , a Powerlet cartridge typically provides 20 to 40 shots in an airgun, depending on the gun and environmental conditions. The first 10 shots from a new bottle are consistent, with subsequent shots losing power. For paintball markers, fewer shots are produced due to the greater weight of the paintball compared to an airgun projectile .
For modern paintball guns, this technology is considered outdated, as they cannot fire as many shots as a modern large-capacity CO 2 tank can provide, though some still use Powerlet cartridges for stock paintball . They are also still favored for paintball pistols, for players wishing to run "light" with considerably less weight. Because liquid CO 2 needs to vaporize to gaseous form to be usable, latent heat is absorbed every time a shot is discharged, cooling the canister. When discharging repeatedly, the temperature within the Powerlet canister can drop low enough to affect the vapor-liquid equilibrium and reduce the vapor pressure significantly. The drop in output pressure (known as the " working pressure") not only can affect the ballistic performance, but also can cause the gun to "freeze up" and cease operating completely due to insufficient pneumatic force, until the canister warms back up again. This causes a problem due to the rapid-fire nature of many competitive paintball skirmishes, so the high-pressure air (HPA, or "N 2 ") systems are more commonly used.
In 2004, Crosman introduced a new disposable CO 2 power source, the 88 gram AirSource.
- 766 American Classic 1-3
Includes Variants*
Crosman has manufactured and sold the Benjamin-Sheridan and Sheridan model airguns for many years. These models are still made to the higher quality standards of the originals, with wood stocks and primarily brass and steel components. The Sheridan line is strictly 5 mm (.20 caliber), while the Benjamin-Sheridan models are available in .177 (4.5 mm, .22 (5.56 mm), .25 (6.4 mm) and .357 (9.0 mm) calibers, depending on model.
• NRA Museums: Benjamin history
• Blue Book of Airgun Values – BENJAMIN AIR RIFLE COMPANY (BENJAMIN) BENJAMIN AIR RIFLE COMPANY BACKGROUND Benjamin History | https://en.wikipedia.org/wiki/Powerlet |
Powtoon Ltd. is a British company which sells cloud-based animation software (SaaS) for creating animated presentations and animated explainer videos. [ 1 ] The name "Powtoon" is a portmanteau of the words " PowerPoint " (trademarked by Microsoft) and " cartoon ". [ citation needed ] VR
Powtoon was founded in January 2012. [ citation needed ] The company released a beta version in August 2012. [ 2 ] In December 2012, Powtoon secured $600,000 investment from Los Angeles–based venture capital firm Startup Minds. [ 3 ]
Powtoon is a web-based animation software that allows users to create animated presentations by manipulating pre-created objects, imported images, provided music and user-created voice-overs. [ 4 ] Powtoon uses an Apache Flex engine to generate an XML file that can be played in the Powtoon online viewer, exported to YouTube or downloaded as an MP4 file. [ 2 ]
Powtoon provides several styles of animated video creation including whiteboard doodles and animated content. A user can apply pre-built backgrounds, scenes, objects, and characters to their work, or a user can choose to customize their content by creating their own diverse characters (diverse here refers to the age, race, ethnicity, and body size of the desired character) and uploading their own images, videos, or audio files.
Powtoon is a software that requires a subscription for use.
This animation -related article is a stub . You can help Wikipedia by expanding it .
This software article is a stub . You can help Wikipedia by expanding it .
This article about a company of the UK is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Powtoon |
Poxytrins or dihydroxy- E , Z , E -polyunsaturated fatty acids (dihydroxy- E , Z , E -PUFAs) are PUFA metabolites that possess two hydroxyl residues and three in-series conjugated double bonds in an E , Z , E cis–trans configuration. Poxytrins have platelet -inhibiting properties that are not found in isomers with three conjugated double bonds presenting in a different geometry. The unique E , Z , E configuration in poxytrins may prove to be relevant in treating human conditions and diseases that involve pathological platelet activation.
Poxytrins are metabolites of docosahexaenoic acid (DHA), arachidonic acid (AA), and α-linolenic acid (ALA). Poxytrins derived from AA are termed linotrins. [ 1 ]
Protectin DX (PDX) is perhaps the most prominent poxytrin. It is not to be confused with its isomer protectin D1 (PD1). PD1 is structurally identical to PDX except that its three conjugated double bonds 11 E ,13 E ,15 Z have the E , E , Z configuration. PDX and PD1 both possess potent specialized pro-resolving mediator (SPM) anti-inflammatory activity, but only PDX inhibits human platelet aggregation responses. [ 2 ] PDX's anti-platelet activity is shared with various other dihydroxy- E , Z , E -PUFAs, but not with dihydroxy-PUFAs that have an E , E , E or E , E , Z configuration. [ 1 ] [ 3 ]
Cells make PDX by metabolizing DHA by double oxygenation with a 15-lipoxygenase to form the 10 R ,17 S -hydroxperoxy intermediate which is reduced to its 10 R ,17 S -hydroxyl product, PDX, probably by cytosolic glutathione peroxidase 1 (GPX1). [ 2 ] Serial metabolism by two different lipoxygenases or by a lipoxygenase and a cytochrome P45 on a 1 Z ,4 Z ,7 Z -PUFA may also make a 1,7-dihydroxy 2 E ,4 Z ,6 E product.
Linotrin-1 and linotrin-2 are among the four isomeric metabolites produced by incubating ALA with ALOX15B . [ 6 ] The extent to which the linotrins form in cells or in vitro is not clear.
Stimulating agents such as collagen depend on platelets to make and release thromboxane A 2 (TXA 2 ) to mediate and/or enhance their aggregating activity. 10 R ,17 S -diHDHA, and PDX to a slightly lesser degree, inhibit the human platelet aggregation response to collagen at ≥ 100–200 nanomolar concentrations. This appears to reflect the ability of poxytrins to inhibit the activities of COX-1 and COX-2 , thereby blocking the production of TXA 2 and thus interfering with the activation of the thromboxane receptor by TXA 2 . [ 1 ] [ 3 ] The linotrins appear to use a similar mechanism, and to have similar or slightly lower potencies. [ 1 ] [ 6 ] However, the linotrins are 20- to 100-fold stronger in inhibiting human platelet aggregation compared to 5-HETE and 12-HETE, two mono-hydroxyl-containing eicosanoids that contain an E,Z conjugated double bond configuration. [ 7 ] Other biologically-active poxytrins have yet to be tested for, but are projected to possess anti-platelet activity. | https://en.wikipedia.org/wiki/Poxytrin |
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