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fluid dynamics | Why is pressure gradient assumed to be constant with respect to radius in the derivation of Poiseuille's Law? | https://physics.stackexchange.com/questions/67398/why-is-pressure-gradient-assumed-to-be-constant-with-respect-to-radius-in-the-de | <p>Poiseuille's Law relies on the fact that velocity is not constant throughout a cross-section of the pipe (it is zero at the boundary due to the no-slip condition and maximum in the center). By Bernoulli's Law, this means that pressure is maximum at the boundary and minimum at the center. But in the book I have it ... | <p>First of all, Bernoulli's law is applicable only to inviscid flow, while Poiseuille's flow is for the viscous fluid. The fact that pressure is constant along the orthogonal cross section of the pipe could be derived from the assumption that the flow is parallel, that is everywhere inside the pipe the velocity field ... | 800 |
fluid dynamics | Boundary layer equation | https://physics.stackexchange.com/questions/74853/boundary-layer-equation | <p>I was trying to understand the derivation of the boundary layer equations at p.145 of <a href="http://www.unimasr.net/ums/upload/files/2012/Sep/UniMasr.com_919e27ecea47b46d74dd7e268097b653.pdf" rel="nofollow">http://www.unimasr.net/ums/upload/files/2012/Sep/UniMasr.com_919e27ecea47b46d74dd7e268097b653.pdf</a>. : the... | <p>Let's remove this from the list of unanswered questions.</p>
<p>The derivation in the book is a bit odd. I favor the derivation in Schlichting's book "Boundary-Layer Theory", because it's cleaner.</p>
<p>Usually the derivatives of $\sigma_{xx}$, $\sigma_{yy}$, $\tau_{xy}$ and $\tau_{yx}$ in equations (12-5) and (1... | 801 |
fluid dynamics | Blasius boundary layer solutions | https://physics.stackexchange.com/questions/74906/blasius-boundary-layer-solutions | <p>I'm trying to understand the Blasius boundary layer solution, but I'm having some difficulties. Using wikipedia, I wonder how they get the first formula: <a href="http://en.wikipedia.org/wiki/Blasius_boundary_layer" rel="nofollow">http://en.wikipedia.org/wiki/Blasius_boundary_layer</a>. $$\frac{U^2}{L}\approx\nu \fr... | <p>The first formula (scaling argument)</p>
<p>$$ \frac{U^2}{L} \sim \nu \frac{U}{\delta^2}, \tag{*} $$</p>
<p>comes directly from equations for boundary layer equations (and not specifically for Blasius boundary layer). We have continuity equation:
$$\dfrac{\partial u}{\partial x}+\dfrac{\partial v}{\partial y}=0 $... | 802 |
fluid dynamics | Non-uniform field pressure on fluid | https://physics.stackexchange.com/questions/76127/non-uniform-field-pressure-on-fluid | <p>I have been studying fluid mechanics and currently I was trying to understand Euler's equation for fluid flow. For that purpose, I was following <a href="http://www.av8n.com/physics/euler-flow.htm" rel="nofollow">this</a> webpage.</p>
<p>My problem is in understanding Eq.(12). The author states that that is the con... | <p>In general, any external body force would give a contribution $\int \mathbf{f} \ dV$, where $\mathbf{f}$ is the force per unit volume resulting from the external force. For those who didn't read the link, the integral is over a small volume at the point in consideration. Here external means that the source of the fo... | 803 |
fluid dynamics | What does the Froude number represent? | https://physics.stackexchange.com/questions/75585/what-does-the-froude-number-represent | <p>While reading on <a href="http://en.wikipedia.org/wiki/Froude_number" rel="noreferrer">Wikipedia</a>, I read the following</p>
<blockquote>
<p><em>The Froude number is defined as:</em></p>
<p>$$\mathrm{Fr} = \frac{v}{c}$$</p>
<p><em>where $v$ is a characteristic velocity, and $c$ is a characteristic wat... | <p><strong>To answer the question in the title:</strong> <em>What does the Froude number represent?</em></p>
<p>The Froude (<span class="math-container">$Fr$</span>) number is a non-dimensional value that (typically) is used to quantify the degree of linearity/nonlinearity of a gravity wave through the ratio of a chara... | 804 |
fluid dynamics | how to reduce pressure drop in a 5/16 ss tube | https://physics.stackexchange.com/questions/76019/how-to-reduce-pressure-drop-in-a-5-16-ss-tube | <p>I have a fluid line which passes high density fluid at $60 \text{psi}$. At the end there is a valve. I have a $30 \text{psi}$ dynamic pressure drop in the line valve itself creates a back pressure of $10 \text{psi}$. How do I reduce my pressure drop without changing tube parameters?</p>
| <p>I couldn’t get any answer for this question and so ended up in performing experiments in the lab to find answer by myself. To reduce my dynamic pressure drops in the SS tube.</p>
<p>The factors externally (Without changing tube parameters) which I can vary to reduce dynamic pressure drop in the line is maintaining ... | 805 |
fluid dynamics | Aerofoil Theory Project | https://physics.stackexchange.com/questions/76765/aerofoil-theory-project | <p>I'm doing a project (dissertation) on the mathematics of Aerofoil Theory. I wonder if I could get some advice on a possible structure. I'm new to fluid dynamics, so it's quite hard to know where to start. </p>
<p>So far I've looked at different types of flows; streamlines and velocity potentials. I've also covered ... | <p>To use the Joukowski concept of an airfoil I have learnt from the professors Claes Johnson and his student professor Johan Hoffman is the "old" and wrong theory of flight because it is totally based on 2D calculation. It is a beautiful theory in complex variables but completely unphysical it is by no means based on ... | 806 |
fluid dynamics | (Why) is a solid easier to suspend in a thick slurry than in a liquid? | https://physics.stackexchange.com/questions/80023/why-is-a-solid-easier-to-suspend-in-a-thick-slurry-than-in-a-liquid | <p>When making cacao (the non-instant type), one usually mixes the powder with a small amount of milk or water before mixing this slurry into the rest of the milk/water. Some manufacturers of slurry feeding systems for biogas plants claim the same principle for their product: One mixes the solid feedstock into a small ... | <p>If you're trying to mix anything with starch grains (cornflour is the classic example) a problem you'll run into is that concentrated suspensions are <a href="http://en.wikipedia.org/wiki/Dilatant" rel="nofollow">dilatant</a>. If you add the powder slowly this may not be a problem, but if you throw it in as a lump y... | 807 |
fluid dynamics | Energy of liquid and gas at same pressure is different? | https://physics.stackexchange.com/questions/81156/energy-of-liquid-and-gas-at-same-pressure-is-different | <p>Air compresses (change in volume) and it creates pressure. It's the internal energy (momentum of each molecules) creates that pressure. But in liquids as it can't be compressed (may be by .3% if I am sure about water) it can't be pressurised, right? This is only possible by an external force on water itself. Does it... | <p><em>All</em> molecular forms of matter can be compressed and consequently pressurized. Generally speaking you can pressurize fluids by adding energy to them. This includes heat transfer as well as external forces performing work. The energy needed to achieve a given pressure change in a liquid will in general be ... | 808 |
fluid dynamics | Pressure difference in water tanks at different heights | https://physics.stackexchange.com/questions/82132/pressure-difference-in-water-tanks-at-different-heights | <p>Suppose there are two tanks(airtight) fully filled with water.one is kept on top of a ten storey building and one on top of a twenty storeyed one.They are NOT interconnected.Will there be a pressure difference?</p>
| <p>Forget the airtight part. That just confuses the issue by making you deal with the air pressure (or lack of it) at the top and bottom.</p>
<p>The pressure depends on how far below the surface of the water you measure it.</p>
<p>The pressure on a unit of area is nothing but the weight of the water in a slender colu... | 809 |
fluid dynamics | What is the motivation behind $\tau=\mu \frac{\mathrm{d}u}{\mathrm{d}y}$ for Newtonian fluid? | https://physics.stackexchange.com/questions/88897/what-is-the-motivation-behind-tau-mu-frac-mathrmdu-mathrmdy-for-new | <p>Where does the motivation come from? $\tau$ is the shear stress, $u$ is the velocity and $\mu$ is the shear viscosity. </p>
<p>EDIT: Since I wrote the question on phone I wasn't clear enough about what I was actually wondering about (see comments below); thus let me clarify. </p>
<p>I was simply wondering where di... | <p>The motivation comes from applying the <a href="http://en.wikipedia.org/wiki/No-slip_condition" rel="noreferrer">no-slip boundary condition</a> on a fluid flow. This is probably easier to understand pictorially,</p>
<p><img src="https://i.sstatic.net/F20QX.png" alt="enter image description here"></p>
<p>The fluid ... | 810 |
fluid dynamics | Streamlines in Boundary Layer | https://physics.stackexchange.com/questions/90456/streamlines-in-boundary-layer | <p>Suppose that a fluid is flowing parallel to and over a flat plate. Obviously, a boundary layer develops in which the velocity ranges from 0 to 99% of the upstream velocity U. Could somebody please show me how the streamlines would look in this boundary layer? What do they typically look like in boundary layers?</... | 811 | |
fluid dynamics | Festive physics: gold flake vodka | https://physics.stackexchange.com/questions/91243/festive-physics-gold-flake-vodka | <p>I have a bottle of vodka that has a load of gold flakes suspended in it. It has been sat still for over 24 hours and the flakes are all still suspended within the liquid: they have not risen to the surface or sunk to the bottom. Any ideas as to the physics behind this? </p>
| <p>The viscosity of water ethanol mixtures isn't especially high, though the wetting properties of vodka may make it seem oily. Actually water ethanol mixtures are highly non-ideal: both water and ethanol have a viscosity of about 1 mPa.s at room temperature, but a mixture can achieve a viscosity of over 3 mPa.s. See <... | 812 |
fluid dynamics | Approximating density from pressure and flow | https://physics.stackexchange.com/questions/92554/approximating-density-from-pressure-and-flow | <p>I want to get the density of a fluid going through a pipe. I can measure the flow and pressure with a flowmeter and the temperature using a thermometer. With this information, I want to calculate (or approximate) the instantaneous density of the fluid passing through my instruments.</p>
<p>How would I go about do... | 813 | |
fluid dynamics | Efflux speed of ideal fluid dependent on diameter? | https://physics.stackexchange.com/questions/94217/efflux-speed-of-ideal-fluid-dependent-on-diameter | <p>I have a cylinder full of water with diameter $D$ with a round opening on the bottom with diameter $d$. The water is friction-free and incompressible. Now I need a relationship for the efflux speed $v$ with which water exits the cylinder and I shouldn't use the approximation $d \ll D$, but formulate a general relati... | <p>While calculating velocity of efflux you use bernoulli's theorem as follows : </p>
<p>At the top of container :$ P + \frac{\rho {v_1}^2}{2} + \rho gh_1 = k$<br>
At the efflux : $P_a + \frac{\rho {v_2}^2}{2} + \rho g h_2 = k$ </p>
<p>$P - P_a + \rho g (h_1 - h_2) = \frac{\rho ({v_2}^2 -{v_1}^2)}{2} $</p>
<p>Now, ... | 814 |
fluid dynamics | Can ship/boat propellers be placed, with adequate protection, alongside the fuselage instead of at the back? | https://physics.stackexchange.com/questions/32532/can-ship-boat-propellers-be-placed-with-adequate-protection-alongside-the-fuse | <p>On small private aircraft the engine is placed at the front of the fuselage, or on the wings
E.g. Stationair, Otter </p>
<p>On combat aircraft the engine/s is placed at the end of the fuselage
E.g. Raptor, Typhoon </p>
<p>On larger aircraft constructed to carry cargo/passengers the engines are placed on the wings... | <p>The main reason is mechanical: the size of the the engine, shaft and propeller require them to be aligned. However many modern ships do have auxiliary engines located in 360° oriantable pod and located at different places under the boat hull. They are used to rotate the boat.</p>
<p><a href="https://www.google.com/... | 815 |
fluid dynamics | If there is significant temperature difference between indoor air and outdoor air, will that significantly increase the rate of air exchange? | https://physics.stackexchange.com/questions/43236/if-there-is-significant-temperature-difference-between-indoor-air-and-outdoor-ai | <p>There would be heat diffusion, of course, but heat diffusion occurs even without the exchange of fluid parcels between each environment.</p>
<p>We do know that cold air tends to be denser than warm air, and that pressure differences drive the exchange of fluid parcels. But let's assume that there is no pressure dif... | <p>I would like you to precise some point : you want to know the rate of air exchange without any air displacement due to pressure difference?
If you want to know what happens during a cold winter and the diffusion of heat through walls (which block any air flow), the heat flux will be proportional to the temperature g... | 816 |
fluid dynamics | Why does central jet velocity of a flute air stream not include aperture size? | https://physics.stackexchange.com/questions/43355/why-does-central-jet-velocity-of-a-flute-air-stream-not-include-aperture-size | <p>Some fellow flutists and I are pretending to be experts at fluid dynamics and reading <a href="https://ccrma.stanford.edu/~pdelac/research/MyPublishedPapers/Thesis.pdf" rel="nofollow">Patricio Cuadra's thesis</a> on the topic:</p>
<p>On page 17, it says:</p>
<blockquote>
<p>The central speed of the jet $U_j$ at ... | <p><a href="http://en.wikipedia.org/wiki/Bernoulli%27s_principle" rel="nofollow">Bernoulli's principle</a> states that</p>
<p>$$ \frac{1}{2}U^2+gz+\frac{P}{\rho} = \text{constant} $$</p>
<p>A very important remark here, is that the quantity is only constant a long a streamline. That means that the constant is differe... | 817 |
fluid dynamics | When playing the flute, does lip-hole aperture size affect air pressure in the mouth? | https://physics.stackexchange.com/questions/43364/when-playing-the-flute-does-lip-hole-aperture-size-affect-air-pressure-in-the-m | <p>I apologize if this is too basic of a question for this forum, but when having arm-chair discussions about the fluid dynamics of flute playing, a friend has said:</p>
<blockquote>
<p>The lip-hole area together with the lung pressure is the cause of the pressure built in the mouth.</p>
<p>When measuring the m... | <p>Unless the air moving through the lips goes sonic, the downstream does influence the pressure in the chamber. </p>
<p>So long as the fluid, any fluid, is moving less than the speed of sound, the downstream influences the upstream because pressure waves can move against the flow direction. </p>
<p>The smaller the o... | 818 |
fluid dynamics | How can these fluid dynamical smoke-ring phenomena be explained? | https://physics.stackexchange.com/questions/46506/how-can-these-fluid-dynamical-smoke-ring-phenomena-be-explained | <p>The Navier-Stokes fluid dynamics equations, said that, as Sir William Thomson (or Lord Kelvin) predicted:</p>
<ol>
<li><p>When two smoke-rings are moving in the same direction, with the same speed, one behind the other, the 'leading' ring will slow down and enlarge, while the 'following' one will get smaller and sp... | <p>I currently don't have access to the paper, but this should meet your needs:</p>
<p><strong>Vortex Ring Interactions</strong> (by Wakelin-Riley)<br />
<a href="https://doi.org/10.1093/qjmam/49.2.287" rel="nofollow noreferrer">https://doi.org/10.1093/qjmam/49.2.287</a></p>
<p>Here is my interpretation: Consider two ... | 819 |
fluid dynamics | Could the Bernoulli effect be causing my ceiling to come down? | https://physics.stackexchange.com/questions/47925/could-the-bernoulli-effect-be-causing-my-ceiling-to-come-down | <p>Very 'applied' question, but I have nowhere else to turn, so I'm asking the physics experts here: I have a carport whose ceiling is made of very lightweight paneling. I've had several times now that those panels have fallen down, without an evident reason. So I'm wondering: the wind (because of the placement of othe... | <p>If a downward force was applied to the panels to 'pull' them down it would be the result of a pressure difference on either side of the panel. Consider a flat plate in a wind tunnel. On each side of the plate the freestream velocity is equal, thus the static pressures are equal (assuming the flow is homogeneous and ... | 820 |
fluid dynamics | How to calculate the Darcy-Weissbach friction factor for shear thinning laminar flow in a pipe? | https://physics.stackexchange.com/questions/48587/how-to-calculate-the-darcy-weissbach-friction-factor-for-shear-thinning-laminar | <p>The <a href="http://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation" rel="nofollow">Darcy-Weissbach</a> friction factor for laminar flow would be $\frac{64}{Re}$</p>
<p>Now, having a shear thinning (non-newtonian) fluid where the viscosity is not constant how do I arrive at $Re$?<br>
To know an apparaent visc... | <p>In my view, the objective of knowing the friction factor, is for one to be able to calculate what is the pressure drop needed to push a given flow $Q$ through a given pipe diameter. This kind of relations exists for several models of non Newtonian fluid, take for example the power law model:</p>
<p>$\tau=K\gamma^n$... | 821 |
fluid dynamics | Swimming and forces | https://physics.stackexchange.com/questions/52187/swimming-and-forces | <p>I was told that the total integral of the stress over the surface of a swimmer (i.e. the total force exerted by the swimmer on the fluid) always vanishes, because there are no external forces applied on it. That seems fair by Newton’s third Law.</p>
<p>But, how does it take into account the effects of the Newton's ... | <p>Let's imagine a swimmer in a swimming pool and approximate the Earth as an inertial frame. The swimmer can certainly accelerate relative to the Earth frame (in the direction parallel to the Earth's surface); we see this happen all the time in real life. It follows from Newton's second Law, as you point out, that t... | 822 |
fluid dynamics | How does a hinge affect the amount of a submerged material? | https://physics.stackexchange.com/questions/51275/how-does-a-hinge-affect-the-amount-of-a-submerged-material | <p>Suppose I have a rod that has a density of $X <1$. If I were to submerge that rod in water (density 1), I would expect $X$ of the rod to be below water and $1-X$ of it to be above water (simple buoyancy).</p>
<p>But here's the catch. Suppose I attach one corner of the rod to a frictionless hinge, suspended close... | <p>Here's a solution assuming a "thin rod"; i.e. assuming that the free end of the rod is fully submerged and "the stretch where the rod begins to dive and is only partially submerged" is negligibly small compared to the stretch (from the end attached to the hinge) that is lifted completely above the water as well as c... | 823 |
fluid dynamics | Query about Bernoulli's principle | https://physics.stackexchange.com/questions/55820/query-about-bernoullis-principle | <p>We know that the lower atmosphere has high pressure and as we go up, the pressure decreases, if it's so then why doesn't all gases fly up into the upper atmosphere from the lower following <a href="http://en.wikipedia.org/wiki/Bernoulli%27s_principle" rel="nofollow">Bernoulli's theorem</a>? I do expect that gravitat... | <p>If you have ever swum to the bottom of a swimming pool you'll know that in water the pressure increases as you go deeper. At a depth of about 10 metres the pressure is twice what it is at the surface, but the water 10 metres down doesn't burst up to the surface because it is held down by the weight of water above it... | 824 |
fluid dynamics | Water, how do you make ripples | https://physics.stackexchange.com/questions/56032/water-how-do-you-make-ripples | <p>How do I make a ripple effect in a bowl of water. I have tried throwing small pebble sin but it just splashes and sinks. I have read that I need to make the water a thicker liquid ie add glycerine, will this work and why? </p>
| <p>Making water ripples in the bowel of water by throwing a pebble in it would be difficult an it will also be little bit bigger and faster to see it in a water bowel. Rather you can try vibrating the bowel at it's centre at the bottom of the bowel with something like electronic raser or a massage machine or you can ju... | 825 |
fluid dynamics | Membrane that allows liquid to pass only when forced under pressure | https://physics.stackexchange.com/questions/56046/membrane-that-allows-liquid-to-pass-only-when-forced-under-pressure | <p>Is it possible to have a membrane that will not let a liquid through it at normal pressures due to gravity, but pass that liquid when substantially pressurised?</p>
<p>For instance, a few inches of water (say 0.1psi) would be blocked, but 100psi would pass through. </p>
| <p>Such membranes do exist, like in <a href="http://en.wikipedia.org/wiki/Reverse_osmosis" rel="nofollow">reversed osmosis</a> plants creating fresh water from sea water. Such plants use huge pressure to press fresh water through the membrane, and without pressure very little water will come through. If there are air o... | 826 |
fluid dynamics | Flow in parallel paths after pressure regulator | https://physics.stackexchange.com/questions/55954/flow-in-parallel-paths-after-pressure-regulator | <p>Consider the following:</p>
<pre><code> /‾‾ Valve --- Watering hose
Pump --- Pressure regulator ------ Valve --- Watering hose
\__ Valve --- Watering hose
</code></pre>
<p>A pump generating an arbitrary pressure and a pressure regulator
to curb it at 1.5... | <blockquote>
<p>I hope that the pressure regulator would compensate closing/opening valves by keeping the pressure constant but I'm not sure. </p>
</blockquote>
<p>In the absence of confounding factors, this is the correct viewpoint.</p>
<p>In order for the pressure regulator to be "perfect", you would ideally have... | 827 |
fluid dynamics | What does Euler equation mean? | https://physics.stackexchange.com/questions/56116/what-does-euler-equation-mean | <p>In order to prove the Bernoulli’s principle ($\frac{p}{\rho} + \frac{1}{2}u^2+\phi = constant$ ), I have to use the <a href="http://en.wikipedia.org/wiki/Euler_equations_%28fluid_dynamics%29" rel="nofollow">Euler equation</a>: $\frac{Du}{Dt} = -\frac{1}{\rho}\nabla p + g$.</p>
<p>I know how to prove it, but I didn'... | <p>Euler equation is the special case of the Navier-Stokes equation that describes fluid motion. Euler equation stands for inviscid flow, i.e. flow with zero viscosity.</p>
<p>To get it a bit more explicit please visit
<a href="http://en.wikipedia.org/wiki/Euler_equations_%28fluid_dynamics%29" rel="nofollow">wikipedia... | 828 |
fluid dynamics | Bernoulli's theorem: $\frac{p}{\rho}+\frac{1}{2}u^2+\phi$ is constant along a streamline | https://physics.stackexchange.com/questions/56323/bernoullis-theorem-fracp-rho-frac12u2-phi-is-constant-along-a-st | <p>I am trying to understand <strong>the Bernoulli's theorem:</strong></p>
<ul>
<li><strong>$\frac{p}{\rho}+\frac{1}{2}u^2+\phi$ is a constant along a streamline</strong></li>
</ul>
<p>I got that:</p>
<p>$\frac{\partial u}{\partial t}$ + ($\nabla \times u)\times u$ = $-\nabla(\frac{p}{\rho}+\frac{1}{2}u^2+\phi)$</p>... | <p>Let $\mathbf u(t, \mathbf x)$ represent the velocity vector field of the fluid. Let $\mathbf x(t)$ denote the position of a particle moving with the fluid, then the velocity $\dot{\mathbf x}(t)$ of the particle at a time $t$ will be equal to the velocity of the fluid flow at the point $(t, \mathbf x(t))$, namely
$$... | 829 |
fluid dynamics | Wall pressure of a fluid flow in a pipe of variable radius | https://physics.stackexchange.com/questions/57254/wall-pressure-of-a-fluid-flow-in-a-pipe-of-variable-radius | <p>Using all cylindrical coordinates, pipe with z-axis vertically upward and radius of $r = G(z)$, flow is incompressible, inviscid and steady, Using appropriate boundary conditions I want to find the wall pressure.Flow is axis symmetric and irrotational, and of the form $(a(r,z), 0, c(r,z))$ in cylindrical coordinates... | 830 | |
fluid dynamics | blood fluidics - can you determine the force exerted on a bound red blood cell under shear stress? | https://physics.stackexchange.com/questions/59304/blood-fluidics-can-you-determine-the-force-exerted-on-a-bound-red-blood-cell-u | <p>Is it possible to calculate the force exerted on a bound, infected red blood cell under various shear stresses? The strength of an adhesive interaction is normally measured by SPR or AFM, however using microfluidics, you can increase the shear stress until the cell dislodges, therefore, can you use this data to calc... | 831 | |
fluid dynamics | Spinning liquid to create a centrifuge effect | https://physics.stackexchange.com/questions/59629/spinning-liquid-to-create-a-centrifuge-effect | <p>I'm in the business of purifying used cooking oil. Normally, I heat the oil up and let it settle for a couple of days. Water and solids settle to the bottom and cleaner oil remains on top. I'm trying to accelerate this process. </p>
<p>So, the idea is to take a vertical tank 5ft diameter, about 10ft tall and put a ... | <p>This approach will not work; since it will result in mixing of the oil and particles, not a settling/separation. This is called a "stir-tank reactor" in chemical-engineering jargon. If you look into this properly, you will realize that this configuration will REDUCE THE MIXING TIME, and in fact, deter separation. Re... | 832 |
fluid dynamics | how to explain the upright force for the plane? | https://physics.stackexchange.com/questions/59977/how-to-explain-the-upright-force-for-the-plane | <p>I remember in the high school physics, my teacher told us that the design of the plane wing is because we want the air above the wing flowing faster than the air flowing below so the pressure above and below will be different so the net force is pointing upright. I am thinking if it is possible to explain this by be... | 833 | |
fluid dynamics | What is a good reynolds number for this process? | https://physics.stackexchange.com/questions/62786/what-is-a-good-reynolds-number-for-this-process | <p>I’m trying to convince my boss that the mixers we are using are too much. I’m trying to prove that we are over-mixing our product. Our product is ink…just your basic ink found in your printer at home. We mix in a 23 inch diameter 50 gallon vessel using a 2.75 inch diameter axial flow impeller going at 1050 rpm with ... | <p>At least in the industry I work in, sizing mixers is more an art than a science. If you are convinced the process works at too high a Reynolds Number, try if you can make an experiment:</p>
<ul>
<li>find out why it is done the way it is done and how the mixer was sized</li>
<li>when you still think the Re is too hi... | 834 |
fluid dynamics | Water ripples and nonzero divergence | https://physics.stackexchange.com/questions/64038/water-ripples-and-nonzero-divergence | <p>In 2-d, one ripple would mean the velocity of water particles move out radially forming a circular wavefront. The Navier Stokes equations say the divergence of velocity has to be zero, but this circular radiation pattern has nonzero divergence. What am I missing here, since water ripples clearly exist?</p>
| <p>Waves in fluids carry momentum not mass. When we see ripples diverging from a point, there is no radial (horizontal) movement of mass. Rather the mass moves in the vertical direction, some what sinusoidally.</p>
<p>If you have observed birds floating on water surface, you see them moving up and down but not along t... | 835 |
fluid dynamics | What keeps the sugar suspended in the tea? | https://physics.stackexchange.com/questions/5562/what-keeps-the-sugar-suspended-in-the-tea | <p>At room temperature....</p>
<p>How long will the sugar stay suspended once dissolved ?</p>
<p>What governs the rate of settling ? </p>
<p>What part does Brownian motion play ?</p>
<p><em>Sugar might be a bad example...please substitute as needed.</em></p>
| <p>Anything dissolved is kept "suspended" by brownian motion.
Theoreticly there will be a small gradient of concentration
due to gravity, but this is unmeasurable for sugar.
(Barometric formula). For much bigger particles (ãbout µm) , this
gradient can be determined. </p>
<p>The sugar will stay dissolved until the... | 836 |
fluid dynamics | Pressure vs wind speed, on a rectangular surface | https://physics.stackexchange.com/questions/5850/pressure-vs-wind-speed-on-a-rectangular-surface | <p>How do I go about finding the pressure exerted on a rectangular surface in a free flowing air stream?</p>
<p>I wouldn't imagine that this is directly related to the airspeed / surface area, but have no idea where to start. Is there even an equation, or does one need to do some kind of FEA?</p>
<p>For instance a 1.... | <p><a href="http://www.reasonablepower.com/nice_to_know/an_introduction_to_wind_loads.htm" rel="nofollow">Wind Load Formula:</a></p>
<p>$F_d = \frac{1}{2} \rho v^2 A C_d$</p>
<p>where<br>
$F_d$ is the force of drag (or in this case Force Against the flat plate)<br>
$\rho$ is the density of the air<br>
$v$ is the spee... | 837 |
fluid dynamics | Reynolds number, turbulence regime, and drag force | https://physics.stackexchange.com/questions/6098/reynolds-number-turbulence-regime-and-drag-force | <p>I am trying to model a system in which cubes of about 2 cm in size are floating in a circular water thank of about 30 cm in diameter. The cubes move around under the influence of the fluid flow induced by four inlets that point toward the center of the tank, and are located at the positions $0$, $\pi/2$, $\pi$, and ... | <p>I'd say that you have several regimes that are well defined:</p>
<ul>
<li>The behavior of the fluid as it exits in inlet jets and enters the bulk without interference from the cubes. [Length scale set by the exit aperture?]</li>
<li>Flow of the fluid around isolated cubes when far from the edges of the tank (far be... | 838 |
fluid dynamics | Sutherland's constant of argon | https://physics.stackexchange.com/questions/9995/sutherlands-constant-of-argon | <p>I want to compute the viscosity of argon at different temperatures. What is <a href="http://en.wikipedia.org/wiki/Viscosity#Gases" rel="nofollow">Sutherland's constant</a> of argon?</p>
| <p>I meanwhile found the constant by intensive googling (for example in <a href="http://www.cse.scitech.ac.uk/ceg/papers/Gu_et_al_Nanoscale_Microscale_Thermophysical_Eng.pdf" rel="nofollow">this article</a>). It is (depending on the source) around 144 K.</p>
| 839 |
fluid dynamics | Entropy decrease using Stoke's flow? | https://physics.stackexchange.com/questions/11065/entropy-decrease-using-stokes-flow | <p>There is a <a href="http://io9.com/5811236/this-is-the-coolest-science-experiment-youll-see-all-week" rel="noreferrer">video</a> of an experiment from University of Mexico using corn syrup (highly viscous) and water. They are "mixed together" in a container by turning a crank but when the crank is turned in the oppo... | <p>Entropy never increases during this "mixing process" as it normally would, because it is <em>not</em> really a mixing process. The only thing that happens is a huge distortion of the distribution of the colors, but no information about it is lost. Compare it to performing a Fourier transform on some function: this a... | 840 |
fluid dynamics | communicating vessels formula | https://physics.stackexchange.com/questions/10778/communicating-vessels-formula | <p>I having trouble with this formula (asked first in math.Se, I didn't know the existence of physics.se)</p>
<p><span class="math-container">$$
Z_1(t) = Z_e+(\sqrt{Z_1-Z_e}-\frac{2S_0}{S_1}\sqrt{2g\left(1+\frac{S_1}{S_2}\right)}.t^2
$$</span></p>
<p>where <span class="math-container">$Z_1(t)$</span> and <span class=... | <p>like the comment aheadd said , i was doing it wrong , using perimeter instead of area ($2\pi R$ instead of $\pi R^2$).</p>
<p>if you wan to watch the result look <a href="http://www.wolframalpha.com/input/?i=plot%2025%2b%28Sqrt%5B45-25%5D-%282Pi0.3%C2%B2%29/%28Pi10%C2%B2%29Sqrt%5B2%2a980%281%2b%28Pi10%C2%B2%29/%28P... | 841 |
fluid dynamics | Pressing a fluid through leaks | https://physics.stackexchange.com/questions/13242/pressing-a-fluid-through-leaks | <p>Say I have a cylindrical container of some volume $V$, that I fill with water or some other fluid with dynamic viscosity $\mu$. Here, the bottom of the container is milled such that some fraction, $p$, of its surface area, $A$, is removed to allow passage of fluid. One could, for example, drill pores until this cr... | <p>Your answer will depend greatly upon the size of the holes you drill. If I remember correctly, fluid flow through an orifice is proportional to the fourth power of the orifice diameter. So, for a given force, you would get twice as much fluid out of a single hole of diameter 1 mm as you would out of eight holes, e... | 842 |
fluid dynamics | Can I measure the Reynolds number or the heat transfer coefficient | https://physics.stackexchange.com/questions/13321/can-i-measure-the-reynolds-number-or-the-heat-transfer-coefficient | <p>Suppose I have a flow of hot air around a cold and unevenly shaped object with holes and tunnels (think about it as a bed packed with some objects). I would like to know the Reynolds number of this flow and its convective heat transfer coefficient. The definition of the Reynolds number contains a "characteristic len... | <p>From what you describe there are two different length scales associated with this problem. The one ascociated with flow through the porous medium (the 'bed packed with some objects'), and the second ascociated with the flow around the 'bed'. I will assume you are talking about the flow through the porous 'bed'. </p>... | 843 |
fluid dynamics | Behaviour of liquid in vaccume | https://physics.stackexchange.com/questions/14722/behaviour-of-liquid-in-vaccume | <p>Is it possible for a liquid to exist in a high quality vacuume? For example, a few Torr.</p>
<p>If so what are the methods for doing this?</p>
| <p>It's absolutely possible to have stable liquids at low pressures. It all depends on the equilibrium phase diagram of the liquid in question.</p>
<p>Looking at the <a href="http://en.wikipedia.org/wiki/Triple_point" rel="nofollow">triple points</a> (a good estimate of the lowest pressure at which the liquid is stabl... | 844 |
fluid dynamics | Clarification of equilibrium expression for upside down can in water | https://physics.stackexchange.com/questions/16147/clarification-of-equilibrium-expression-for-upside-down-can-in-water | <p>Let's say I initially have an open, empty, soda can. I then turn it over and lower it into a bowl of water, and then release it. Obviously water rises to some level in the cup and then there is air at the top of the can, which was initially the bottom.</p>
<p>Are there only three forces on the can once it reaches e... | <p>Maybe you can be a bit more clear in your formulation. Unless the soda can changes into something else, do not use the word 'initially'. Are cup and bowl the same in your experiment?</p>
<p>In small scale experiments like this(unlike the earths atmosphere) air does not really fall anywhere, and the pressure will be... | 845 |
fluid dynamics | What formulae for calculating fluid pressure change involves these parameters? | https://physics.stackexchange.com/questions/16403/what-formulae-for-calculating-fluid-pressure-change-involves-these-parameters | <p>Okay... this is a bit desperate...</p>
<p>I am reverse engineering an excel program that is used for calculating outputs for a pressure vessel used for industrial process fluid heating.</p>
<p>There is a part in the excel sheet where a pressure drop is being calculated. But there are too many unit conversions and ... | 846 | |
fluid dynamics | Timber floating in the river | https://physics.stackexchange.com/questions/16696/timber-floating-in-the-river | <p>There's an old puzzle (but the physical it is):</p>
<p>Lumberjack chop wood and float it down the river. He noticed an interesting feature: in the spring, when the water is comming, timber is nailed to the shore. In the hot summer, when the water lowers, timber, by contrast, floats exactly in the middle of the rive... | <p>I believe the answer has to do with currents perpendicular to the main flow of the river. In temperate climates, lakes freeze over winter; in the spring, the lake "turns" because the melting ice water is colder than the insulated under layers. In a river, you might not get such a dramatic movement all at once, but... | 847 |
fluid dynamics | Rotating fluid under gravity, fluid dynamics question | https://physics.stackexchange.com/questions/19880/rotating-fluid-under-gravity-fluid-dynamics-question | <p>An incompressible inviscid fluid is rotating under gravity g with constant angular
velocity $\Omega$ about the z-axis, which is vertical, so that $u = (−\Omega y, \Omega x, 0)$ relative
to fixed Cartesian axes. We wish to find the surfaces of constant pressure, and
hence surface of a uniformly rotating bucket of water ... | <p>In the Physics Forums you should find the answer to your exact problem <a href="http://www.physicsforums.com/showthread.php?t=476134" rel="nofollow">'Fluid dynamics - finding pressure for a rotating fluid'</a>. Another answer is <a href="http://www.physicsforums.com/showthread.php?t=38112" rel="nofollow">here</a> (t... | 848 |
fluid dynamics | Speed of a dynamic hydraulic system | https://physics.stackexchange.com/questions/21184/speed-of-a-dynamic-hydraulic-system | <p>We all have noticed that changing the temperature of the water in the shower is not instantaneous, rather the result is felt when the water that was in the tap works its way up to the showerhead. However, changing the pressure does feel instantaneous. I wonder at what speed the change in pressure propagates in the d... | <p>The pressure wave does indeed travel with the speed of sound of the media. This is much higher for water then for air with a speed of $\approx$ 1500 m/s. </p>
<p>This effect is well known and feared under the name <a href="http://en.wikipedia.org/wiki/Water_hammer" rel="nofollow">water hammer</a>. Basically by rapi... | 849 |
fluid dynamics | Why tea dust in a cup of tea seems to concentrate in the bottom center? | https://physics.stackexchange.com/questions/21041/why-tea-dust-in-a-cup-of-tea-seems-to-concentrate-in-the-bottom-center | <blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="https://physics.stackexchange.com/questions/3244/vortex-in-liquid-collects-particles-in-center">Vortex in liquid collects particles in center</a> </p>
</blockquote>
<p>Sorry for my bad English. :-) Hello !</p>
<p>Here is my question :
If you enj... | 850 | |
fluid dynamics | Is it possible to calcualte the yield-stress of a fluid by measuring the smalles bubble that rises through it? | https://physics.stackexchange.com/questions/29153/is-it-possible-to-calcualte-the-yield-stress-of-a-fluid-by-measuring-the-smalles | <p>Consider a yield-stress liquid in gravity. I assume that the buyouncy of a small gas-bubble will not be enough to overcome the yield stress (so the liquid doesn't behave liquid), thus leaving the bubble trapped. Is this so in theory, or is there a flaw in my thinking?</p>
<p>Sme argue that there are no yield-stress... | <p>Yes, your method is a perfectly good way of measuring viscosities. It's a bit limited because it's hard to measure the bubble diameter exactly, but assuming you can do this you can calculate the viscosity of the fluid using <a href="http://en.wikipedia.org/wiki/Stokes%27_law" rel="nofollow">Stokes' law</a>.</p>
<p>... | 851 |
fluid dynamics | How do Kolmogorov scales work in shear thinning fluis? | https://physics.stackexchange.com/questions/30125/how-do-kolmogorov-scales-work-in-shear-thinning-fluis | <p>My understanding of Kolmogorov scales doesn't really go beyond this poem:</p>
<blockquote>
<p>Big whirls have little whirls that feed on their velocity,<br>
and little whirls have lesser whirls and so on to viscosity.</p>
</blockquote>
<p>The smallest scale according to wikipedia* would be
$\eta = (\frac{\nu^3... | <p>Yes it is not clear why you are mentionning shear. Hence it is not clear whether your are interested by very exotic cases or on the contrary by the classical Kolmogorov turbulence theory.</p>
<p>I will give an answer assuming the latter.
The Kolmogorov theory starts by analogy with statistical mechanics by assuming... | 852 |
fluid dynamics | Concentration of fluid pumped through a tube? | https://physics.stackexchange.com/questions/30907/concentration-of-fluid-pumped-through-a-tube | <p>I have a bottle filled with a fluid A, and a tube of volume $V_0$ filled with a fluid B leading away from it.
When I now start pumping fluid A out of the bottle, I am interested in the concentration $c(V)$ of fluid A in fluid B at the end of the tube after the volume $V$ exited the tube.</p>
<p>In my second situati... | 853 | |
fluid dynamics | Behaviour of fluids in thin spaces | https://physics.stackexchange.com/questions/427610/behaviour-of-fluids-in-thin-spaces | <p>Suppose you have a simple setting: a thin (scale of hundreds of nanometer to single digit micrometer) but in relation to that very wide (up to millimeters) box with an input and an output hole in it.</p>
<p>Given how thin the space is, would a fluid even go in there and fill out the box? How long would it take? </... | <p>Your setup is known as a Hele Shaw cell, in which the bulk of the flow is a balance between pressure and viscosity, and around the edge of a region if fluid the balance is between pressure and surface tension.</p>
<p>Also look at the <a href="https://en.m.wikipedia.org/wiki/Hele-Shaw_flow" rel="nofollow noreferrer"... | 854 |
fluid dynamics | Blood as Newtonian fluid | https://physics.stackexchange.com/questions/428813/blood-as-newtonian-fluid | <p>In some of the literature I read that blood can be considered as Newtonian fluid when a larger vesses with high shear stress is considered... How is the shear stress calculated for aorta and how do they claim that shear stress is more for larger vessel when compared to the smaller ones . What is the relationship bet... | <p>welcome. As a general rule, when you read something provide a reference.</p>
<p>Laminar blood flow in cylindrical blood vessels is <a href="https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation" rel="nofollow noreferrer">Poiseuille</a> flow. In Poiseuille flow the velocity profile is parabolic
$$
u_z = \... | 855 |
fluid dynamics | Justification of an assumption in fluid mechanics (free surface) | https://physics.stackexchange.com/questions/445776/justification-of-an-assumption-in-fluid-mechanics-free-surface | <p>What justifies this assumption on the free surface of the sea, taken from Faltinson's book (page 15), for a potential flow?</p>
<blockquote>
<p>A fluid particle on the free-surface is assumed to stay on the free-surface</p>
</blockquote>
| 856 | |
fluid dynamics | Is gas flow always compressible? | https://physics.stackexchange.com/questions/449903/is-gas-flow-always-compressible | <p>From Franz Durst's <em>Fluid Mechanics: An Introduction to the Theory of Fluid Flows:</em></p>
<blockquote>
<p>When a fluid element reacts to pressure changes by adjusting its volume and consequently its density, the fluid is called compressible. When no volume or
density changes occur with pressure or temperat... | <p>At the steady state, the density of a flow will be constant. That's tautological.</p>
<p>Fluids like water can be treated as incompressible because its response to a pressure change is negligible for most practical calculations.</p>
<p>For more information see <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/pe... | 857 |
fluid dynamics | Does pressure decreases in accelerating fluids? | https://physics.stackexchange.com/questions/461861/does-pressure-decreases-in-accelerating-fluids | <p>Bernuolli says that in a pipe when speed <strong>increases</strong> pressure also <strong>decreases</strong> and that happen when pipe become <strong>narrower</strong>. </p>
<ol>
<li>So,if a fluid <strong>accelerate</strong> (increases speed) due to pressure difference in a pipe that <strong>... | <p>Assuming the area doesn't change and do not become narrower, and that the pipe is oriented horizontally, the Bernoulli equation becomes: <span class="math-container">$P_2 - P_1 = \frac{\rho}{2}(v_1^2 - v_2^2)$</span>. If a fluid accelerates, then <span class="math-container">$v_1^2 - v_2^2$</span> will be lowered, s... | 858 |
fluid dynamics | Diver's air torus rising from 10m underwater (edited) | https://physics.stackexchange.com/questions/490190/divers-air-torus-rising-from-10m-underwater-edited | <p>[Edit: earlier version was even more messy]
I just watched a video of a jellyfish caught in a diver's 'air ring' - a torus blown for the sake of watching it rise. The jellyfish gets drawn into the torus and spun like a top as the bubble rises.
I want to know how fast, in rpm, the jellyfish is spinning at a given dis... | <p>Bernoulli's Principle provides a sufficient explanation. In the toroidal flow, water moves faster near the long circular axis. Water is not flowing <em>toward</em> the axis; but flows faster <em>around</em> the axis as you get closer. Bernoulli's Principle indicates that the pressure, then, decreases as the dista... | 859 |
fluid dynamics | Can you create a pressure differential with a material that only allows flow in one direction? | https://physics.stackexchange.com/questions/498348/can-you-create-a-pressure-differential-with-a-material-that-only-allows-flow-in | <p>(Theoretically) suppose you had a material that only allowed water through one way but not the other.</p>
<p>Then you have a box of water and then put this material at the halfway point dividing the box in two. Eventually one side of the box would have less water than the other?</p>
| 860 | |
fluid dynamics | What is a boundary layer, exactly? | https://physics.stackexchange.com/questions/504467/what-is-a-boundary-layer-exactly | <p>I've been struggling with this concept for a very long time. I know about boundary layers in a very informal sense, such as in boundary layer separations at the trailing edge of airfoils and other objects immersed in flowing fluid. I also know about the boundary layer development in a pipe, as a plug flow develops i... | <p>The boundary layer is the region of a flow close to a surface, where there is a gradient of velocity between zero at the wall and the free-stream velocity (<span class="math-container">$v_\infty$</span>), which is caused by viscosity and the no-slip condition. It is also possible to have boundary layers for other fl... | 861 |
fluid dynamics | Can pitot tubes be used for unsteady flows? | https://physics.stackexchange.com/questions/512675/can-pitot-tubes-be-used-for-unsteady-flows | <p>The classical derivation of the Pitot tube equation assumes that the fluid is in a steady flow to use the Bernoulli equation version for steady flows. But in practice, does Pitot tube can be used also for unsteady flows? </p>
| <p>Certainly. Unsteady flows (i.e., where the flow velocity changes with time, sometimes quickly) happens all the time in aviation, and pitot tubes are used almost universally to monitor airspeed in planes. </p>
| 862 |
fluid dynamics | What does the Laplacian of a fluid velocity potential mean? | https://physics.stackexchange.com/questions/523906/what-does-the-laplacian-of-a-fluid-velocity-potential-mean | <p>I was studying something related to fluid mechanics and then I found that <span class="math-container">$\nabla^2 \Phi = 0$</span> where <span class="math-container">$\Phi$</span> is the fluid velocity potential (<span class="math-container">$\vec{V}=\nabla \Phi$</span>). So I was wondering what does it mean that the... | <p>One of the consequences of <span class="math-container">$\nabla\cdot V = 0$</span> is the incompressibility of the fluid. It is perfectly possible for air, for example, that some portions of space are temporary being depleted <span class="math-container">$\nabla\cdot V > 0$</span> or filled <span class="math-cont... | 863 |
fluid dynamics | Molecular explanation of floating and sinking | https://physics.stackexchange.com/questions/595362/molecular-explanation-of-floating-and-sinking | <p>If we have an object submerged in water with a density greater than it then it will sink while objects with less density will float. This is found in many scientific articles and videos.. but why?</p>
<p>Particularly speaking, How do we understand this in a molecular picture? If we think of it using a free body diag... | <p>At a macroscopic level, <a href="https://en.wikipedia.org/wiki/Buoyancy" rel="nofollow noreferrer">buoyancy</a> is the result of the increase of pressure with depth. This creates a net force on a submerged object which is equal and opposite to the weight of the volume of liquid that it displaces. Hence if a fully su... | 864 |
fluid dynamics | Does the bottom of a rotating cylinder influence the shape of the fluid surface? | https://physics.stackexchange.com/questions/604116/does-the-bottom-of-a-rotating-cylinder-influence-the-shape-of-the-fluid-surface | <p>Given a cylinder of fluid that is rotating the surface is of a parabolic shape. From what I can tell when deriving this the shape of the bottom of the cylinder should not influence the shape of the surface (as long as it is bellow the fluid surface). Is this true in practice?
Consider a parabolic bottom very close t... | 865 | |
fluid dynamics | Derive the Momentum Equation from a Lagrangian (Fluid Dynamics) | https://physics.stackexchange.com/questions/616297/derive-the-momentum-equation-from-a-lagrangian-fluid-dynamics | <p>I'm trying to derive the fully compressible Euler-Momentum equation for the given Lagrangian.</p>
<p>We wish to derive <span class="math-container">$$\rho\frac{D\boldsymbol{u}}{Dt} + \nabla P + \rho\nabla\phi = 0 $$</span> from the Lagrangian <span class="math-container">$$ \mathcal{L} = \rho \left( \frac{|\boldsym... | <p>It works out just fine</p>
<p>Starting from your equation:
<span class="math-container">$$\frac{\partial}{\partial t}(\rho\boldsymbol{u})+\nabla\cdot(\rho\boldsymbol{u}\boldsymbol{u})+\rho\nabla\frac{|\boldsymbol{u}|^{2}}{2}-\rho\nabla\left(\frac{|\boldsymbol{u}|^{2}}{2}-e-\frac{P}{\rho}-\phi\right)-\rho T\nabla s=0... | 866 |
fluid dynamics | Mokka pot coffee homogeneity | https://physics.stackexchange.com/questions/620048/mokka-pot-coffee-homogeneity | <p>I've noticed some people pouring coffee from a mokka pot alternates between two cups instead of directly filling one after the other. The reason argued is related to the beverage homogeneity, as the initial vapor will go through totally fresh coffee, in opposition to the very last drops. Neglecting the possible soli... | <p>I think the explanation about the stages of the percolation process is incorrect, for the reasons that the OP describes. What seems more plausible is that more dense coffee layers (regardless of when they originate) descend while the pot is boiling, so the coffee at the top is more diluted (another possibility is th... | 867 |
fluid dynamics | Why liquid in a duct flows when there is a pressure difference? | https://physics.stackexchange.com/questions/650028/why-liquid-in-a-duct-flows-when-there-is-a-pressure-difference | <p>Liquid flows in a pipe when a pressure difference is applied on the ends. But can a liquid flow even if there is no pressure difference?
Like in case the liquid (ideal) is flowing with uniform velocity through a horizontal pipe, the pressure along the horizontal direction remains same.</p>
<p>Please explain this in... | <p>No. When a pressure difference exists between two points, the fluid will start to move from the higher pressure point to the low pressure point. This happens to minimize the pressure difference.</p>
<p>Without such a pressure differential, the fluid is stationary, and the system is absent of any flow.</p>
<p>But if ... | 868 |
fluid dynamics | Euler equation of fluid dynamics | https://physics.stackexchange.com/questions/45648/euler-equation-of-fluid-dynamics | <p>I'm trying to obtain <a href="http://en.wikipedia.org/wiki/Euler_equations_%28fluid_dynamics%29" rel="nofollow">Euler equation</a> for a perfect fluid in laminar or stationary flow. A particle fluid is submitted at volume forces and surface force. The fist, in my case, is giving only by gravity and the second by pre... | <p>This confusion is caused by vector calculus. You should treat each component separately, and then it is obvious. For example, for the x component:</p>
<p>$$ \int_V \partial_x p dx dy dz = \int_{\partial V} p(x) dy dz = \int_{\partial V} p dS_x $$</p>
<p>by the fundamental theorem of calculus (do the x integral fir... | 869 |
fluid dynamics | Water coming out of dam gates | https://physics.stackexchange.com/questions/343249/water-coming-out-of-dam-gates | <p>I recently went to a dam and when I saw the water coming out of its gates with huge pressure. The water instantly got converted to cloudy fog and there was fog all around. Why and how this water gets converted to fog? Does pressure has to do something with this?</p>
| <p>Sudden decrease in pressure causes some part of water to vaporise or split into small droplets
But if the dam is high on the ground it can also happen as water falling hits air and spreads as seen in waterfalls</p>
| 870 |
fluid dynamics | Centripetal forces acting on fluid flow in a bent pipe? | https://physics.stackexchange.com/questions/208430/centripetal-forces-acting-on-fluid-flow-in-a-bent-pipe | <p>Yesterday I answered <a href="https://physics.stackexchange.com/questions/208353/force-applied-to-a-90-degree-elbow-by-hydraulic-flow/208362#208362">this question</a>, using analysis of forces <a href="http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/cvanalysis/node49.html" rel="nofo... | <p>I got the same answer using momentum considerations.</p>
<p>In time $dt$ the amount of mass hitting the side of the pipe is: </p>
<p>$$dm=\rho A v dt$$</p>
<p>Now, we know that the force must satisfy:</p>
<p>$$F_{x}dt=dp=0-vdm=-\rho A v^2 dt $$</p>
<p>Dividing both sides by $dt$ gives:</p>
<p>$$F_{x}=-\rho A v... | 871 |
fluid dynamics | Angular velocity of a fluid element | https://physics.stackexchange.com/questions/210072/angular-velocity-of-a-fluid-element | <p>If we have a fluid element that is subjected to:</p>
<ul>
<li>Translation</li>
<li>Rotation</li>
<li>Extensional strain (dilatation)</li>
<li>Shear strain</li>
</ul>
<p>As in this picture starting from time <span class="math-container">$t$</span>
<a href="https://i.sstatic.net/eIXgz.png" rel="nofollow noreferrer"><i... | <p>It's important to note that these displacements are all infinitesimal, so while one may be thousands of times the other, during an infinitesimal time slice the displacement is still infinitesimal. If one displacement is much much greater than the other, then that displacement will effectively be half rotation and ha... | 872 |
fluid dynamics | Why jets entrain mass? | https://physics.stackexchange.com/questions/244864/why-jets-entrain-mass | <p><a href="https://i.sstatic.net/FztW0.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FztW0.jpg" alt="enter image description here"></a></p>
<p>This very beautiful picture shows a jet of fuel in the combustion chamber of a diesel engine. Does anydody could explain me what is the physical reason that t... | <p>Your many questions shows remarkable effort on questioning. You seem to note the point.</p>
<blockquote>
<p>Does anydody could explain me what is the physical reason that the jet entrains <strong>air</strong>? </p>
</blockquote>
<p><strong>"Diffusion"</strong> is now given as an answer. But If that would be true... | 873 |
fluid dynamics | I want to increase pressure of water in a closed vessel | https://physics.stackexchange.com/questions/249734/i-want-to-increase-pressure-of-water-in-a-closed-vessel | <p>I am trying to make a high pressure water jet using DIY hand pump which pushes water into a sealed vessel with non-return valve at the inlet. I am planning to do it by first closing the valve to the nozzle until i pump in enough water into the vessel so that pressure is created.then after open the nozzle valve to cr... | <p>I recommend that you add some air in your system. Water is mostly incompressible - so while you can raise the pressure to 100 psi quite easily, the moment you open the nozzle and a little bit of water leaves, the pressure will drop right down. As you add air, the air will expand and maintain pressure in the vessel (... | 874 |
fluid dynamics | Efficient way to move water pumping vs circulation | https://physics.stackexchange.com/questions/249742/efficient-way-to-move-water-pumping-vs-circulation | <p>I have a basic question about efficiency of pumping. </p>
<p>If I have a well of 100 meters depth, but water filled till top, and I want to circulate the water. What will be most energy efficient. A) Pumping the water to 100 meters head and then discharging the water at top of that well but below water level or B... | <p>Both will be of the same efficiency. It only matters how far you raise water above the surface. Where you take it from within the bulk of the water is irrelevant.</p>
| 875 |
fluid dynamics | How does a fluid force behave at different angles? | https://physics.stackexchange.com/questions/249805/how-does-a-fluid-force-behave-at-different-angles | <p>I have a mock exam problem that deals with fluid forces acting at different angles. Here are the scans:
<a href="https://i.sstatic.net/PE9AW.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/PE9AW.png" alt="enter image description here"></a>
<a href="https://i.sstatic.net/vAu0n.png" rel="nofollow norefe... | <p>The solution to part (B) is not same as part (a) because the fluid pressure along YZ plane would vary as $$P=P_o+\rho(gh)$$ <br><br>Thus<br><br>$force_{yz}=\int_{y}^{z}(P_o+\rho(gy))Zdy$<br><br>$$force_{yz}=P_o(Z)(Z-Y)+\frac{\rho(g)(Z)(Z^2-Y^2)}{2}$$
Therefore force on YZ plane would have to found by integration.<br... | 876 |
fluid dynamics | How much load does an aqueduct support? | https://physics.stackexchange.com/questions/250104/how-much-load-does-an-aqueduct-support | <p>Recently, I found out about /r/InfrastructurePorn, and I found a particularly interesting photo of the Gouwe Aqueduct in Gouda, NE: </p>
<p><a href="https://i.sstatic.net/HG7Wi.jpg" rel="noreferrer"><img src="https://i.sstatic.net/HG7Wi.jpg" alt="enter image description here"></a></p>
<p>It seems like the bridge t... | <p>The ship is floating and so is supported by the upthrust due to the water and so the weight of water displaced by the ship.<br>
If the ship travels very slowly so that the level of water does not rise but rather flows away then the weight supported by the aqueduct does not change between the ship present and no ship... | 877 |
fluid dynamics | A question about droplets formation | https://physics.stackexchange.com/questions/251934/a-question-about-droplets-formation | <p><a href="https://i.sstatic.net/Eptst.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Eptst.jpg" alt="enter image description here"></a></p>
<p>This picture shows a fuel ejector of a diesel engine that propels ships.</p>
<p>When the fuel line pressure exceeds 380 bars, the tension of the spring is ov... | 878 | |
fluid dynamics | Pressure drop through a flat vs. pleated filter | https://physics.stackexchange.com/questions/254754/pressure-drop-through-a-flat-vs-pleated-filter | <p>Consider two identical pipes where two identical air flows take place. The pipes are "obstructed" by two filters made of the same fabric, one flat, the other pleated as shown in the following picture.</p>
<p><a href="https://i.sstatic.net/u7WKp.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/u7WKp.pn... | <p>In a first approximation, and if you have a laminar flow in the pipes, the flux will be $Q=\frac{-\kappa A}{\mu} \frac{(p_b - p_a)}{L}$, from <a href="https://en.wikipedia.org/wiki/Fluid_flow_through_porous_media" rel="nofollow">Darcy's law</a>, see notations there. So increasing the area $A$ will increase the flux ... | 879 |
fluid dynamics | Why is the velocity of fluid on top a hydrofoil higher than that on the bottom? What keeps enlarging the difference in these 2 velocities? | https://physics.stackexchange.com/questions/258858/why-is-the-velocity-of-fluid-on-top-a-hydrofoil-higher-than-that-on-the-bottom | <p>I am trying to learn how hydrofoil works. A big part of it is Bernoulli's principles.</p>
<p>I found this <a href="http://web.mit.edu/2.972/www/reports/hydrofoil/hydrofoil.html" rel="nofollow noreferrer">article</a> on MIT website.</p>
<p>There are two explanation for how it works:</p>
<ol>
<li>The conservation o... | 880 | |
fluid dynamics | Attractive force between hose and floor when a pool is filled | https://physics.stackexchange.com/questions/262495/attractive-force-between-hose-and-floor-when-a-pool-is-filled | <p>I was filling a rubber pool for my baby using a hose. But I noticed that if I put the hose outlet directly with the floor there is an attractive force!
This is strange, because the hose is throwing water, and by action/reaction it should experiment a repulsive force upward (...I noticed this repulsive force when the... | <p>An apparently simple situation can be extremely complex (effects from nozzle on tube, possible helical flow inside tube, ram pump effect, cavitation...), but the most common attractive force in this situation is the <strong>Venturi effect</strong>.
Please check <a href="https://en.wikipedia.org/wiki/Venturi_effect" ... | 881 |
fluid dynamics | How does an hydraulic ram pump work? | https://physics.stackexchange.com/questions/264398/how-does-an-hydraulic-ram-pump-work | <p>Hydraulic ram (<a href="https://en.wikipedia.org/wiki/Hydraulic_ram" rel="nofollow noreferrer">wikipedia</a>)(<a href="https://www.youtube.com/results?search_query=ram%20pump" rel="nofollow noreferrer">youtube</a>) uses the water hammer (<a href="https://en.wikipedia.org/wiki/Water_hammer" rel="nofollow noreferrer">... | <p>I doubt if the person who made that animated gif knew how the pump works. It's not at all clear why the valves open and close, and the regular movement of the water is nothing like an actual ram pump. It's more likely to confuse than enlighten people imo. </p>
<p><a href="https://i.sstatic.net/PSWtD.gif" rel="noref... | 882 |
fluid dynamics | How much input fluid is needed to fully replace the contents of my inline chamber | https://physics.stackexchange.com/questions/272878/how-much-input-fluid-is-needed-to-fully-replace-the-contents-of-my-inline-chambe | <p>I have built a simple inline chamber for my irrigation system. I have made it so I can add powdered fertilizer to the chamber which will then be pumped through the system to the drip feed sprinklers. What I need to know now is how many liters of water must enter the chamber to replace the original contents. The insi... | <p>The answer will really depend on the degree of mixing that happens. If there is "no" mixing in the chamber, then the entire volume $V$ will be replaced by pushing just $V$ additional fluid through. But the question is more interesting when you have perfect mixing - so let's set up that problem and do the math:</p>
... | 883 |
fluid dynamics | Question about a fountain | https://physics.stackexchange.com/questions/299136/question-about-a-fountain | <p><img src="https://i.sstatic.net/GnUeT.jpg" alt="enter image description here"></p>
<p>There's this fountain where I work. I haven't really studied fluid dynamics, so my question is about how it works. </p>
<p>The way the fountain is designed, is that there is one long big pipe that runs down the middle of the foun... | <p>There would be a slight difference in height, but obviously they design these to be negligible.</p>
<p>The key issue is the drag on the water from the inside surface of the pipe. If you were to explore this system in a static situation (no water movement), you would find the pressure at the outlets of each fountai... | 884 |
fluid dynamics | Why the excess pressures are equated in hydraulic press? | https://physics.stackexchange.com/questions/302454/why-the-excess-pressures-are-equated-in-hydraulic-press | <p>Let's say we have a closed chamber filled with incompressible liquid and there are two area's(smaller(a) and larger(A)) where we can apply force or keep objects.We keep an object of weight W on larger area.Due to this,pressure at every point in a liquid will increase by W/A ,according to pascal's law.The situation i... | <p>This equality is a equilibrium condition, i.e. a condition for the fluid to be in rest. In general, inertia force terms must be added if the fluid is not in equilibrium.</p>
| 885 |
fluid dynamics | Manometer Reading from Fluid Dynamics | https://physics.stackexchange.com/questions/305140/manometer-reading-from-fluid-dynamics | <p>so I have been working on this problem :</p>
<ol>
<li>Diameter1 at wide end: 8cm || V1 = 1.56m/s</li>
<li>Diameter2 at narrow end: 3cm || V2 = 11.094m/s</li>
</ol>
<p><strong><em>Find the manometer reading</em></strong></p>
<p><a href="https://i.sstatic.net/ZKpT0.jpg" rel="nofollow noreferrer"><img src="htt... | <p>For a problem like this, you first calculate the velocity in the two sections - the ratio of the velocities is the inverse of the ratio of the areas for an incompressible fluid.</p>
<p>The manometer will read a pressure that depends on the difference in density between mercury and water, so</p>
<p>$$\Delta p = \De... | 886 |
fluid dynamics | Simplest model of simplest organism swimming in fluid | https://physics.stackexchange.com/questions/313395/simplest-model-of-simplest-organism-swimming-in-fluid | <p>(Hopefully this question isn't too elementary for this StackExchange.)</p>
<p>Given a micro-organism we'll define as two "cells" (which are the
atomic things in this model):</p>
<ol>
<li>A "main" larger cell: <code>O</code></li>
<li>A "tail" smaller cell: <code>o</code></li>
</ol>
<p>The <code>o</code> is connect... | 887 | |
fluid dynamics | Expressions for Analytical Solutions of the Sedov blast wave problem? | https://physics.stackexchange.com/questions/601690/expressions-for-analytical-solutions-of-the-sedov-blast-wave-problem | <p>There is a large amount of expository material out there about the self similar solution to the Sedov Blast wave problem, and I am interested in obtaining the analytical expression so I can code it up and compare it to my numerical results.</p>
<p>From Chapter 17 of Shu's "The Physics of Astrophysics (Vol 2)&qu... | 888 | |
fluid dynamics | Is the pressure of an incompressible fluid discontinuous or continuous across an aperture, like the nozzle of a hose? | https://physics.stackexchange.com/questions/607513/is-the-pressure-of-an-incompressible-fluid-discontinuous-or-continuous-across-an | <p>Is the pressure of an incompressible fluid discontinuous or continuous across an aperture? E.g. inside the fire hose water is at high pressure, outside of it it's at 1atm, but what does the transition look like at the aperture of the nozzle?</p>
<p>Since water is only <em>mostly</em> incompressible I'm sure there's ... | <p>The flow in and around a fire hose can be modelled in a similar way to a jet in the vicinity of a wing - a configuration studied by Carl Shollenberger and Peter Lissamon in 1971.</p>
<p><a href="https://thesis.library.caltech.edu/6018/" rel="nofollow noreferrer">Shollenberger_PhDThesis</a></p>
<p>In this idealizatio... | 889 |
fluid dynamics | Is dropping water from a cup in a dry bucket an incompressible flow? | https://physics.stackexchange.com/questions/608793/is-dropping-water-from-a-cup-in-a-dry-bucket-an-incompressible-flow | <p>I'm learning hydrodynamics by googling stuff so forgive me if the question is super simple.</p>
<p>Imagine that I'm holding a cup of water, which I proceed to drop in a bucket laying next to my feet. The water will splash, and after some movement it will spread across the bottom of the bucket forming a thin layer.</... | <blockquote>
<p>[...] when it is clearly changing density [...]</p>
</blockquote>
<p>The shape the water is in has nothing to do with its density. It is changing shape, not density. Fill a cube of 1 m side length with water. Now put the same water in a cube with 10 m side length. The water will fill the larger cube onl... | 890 |
fluid dynamics | Would birds be able to fly if the air had no viscosity? | https://physics.stackexchange.com/questions/610126/would-birds-be-able-to-fly-if-the-air-had-no-viscosity | <p>There are already many answers to the general question of why birds or planes can fly. But my question is more specific: I would like to understand the relative importance of the viscosity. The air has a very low viscosity, so I am wondering whether it really makes a difference that the viscosity is non-zero. Or cou... | 891 | |
fluid dynamics | If a fluid element defined by the fluid particle it contains, it becomes useless for turbulent flow, doesn't it? | https://physics.stackexchange.com/questions/610408/if-a-fluid-element-defined-by-the-fluid-particle-it-contains-it-becomes-useless | <p>In the book of Batchelor, <em>Introduction to Fluid Mechanics</em>, at page 71 the author defines the fluid/material elements as a volume that contains the same fluid particles all the time. In other words, the fluid elements defined by the fluid particles that they contain.</p>
<blockquote>
<p>Nevertheless, the not... | 892 | |
fluid dynamics | Why does measured pressure change over time in closed hose with temperature gradient | https://physics.stackexchange.com/questions/2158/why-does-measured-pressure-change-over-time-in-closed-hose-with-temperature-grad | <p>I have a 4' hose that is closed at one end and connected to a Airdata Test Set (precise control of pressure) and a high accuracy pressure monitor on the other end with a T and valve. The valve allows the Airdata Test Set connection to be closed off resulting in a hose connected to the pressure monitor and closed at... | <p>Firstly, and forgive me for asking the obvious, are you <em>certain</em> that there are no leaks anywhere in your setup? I'd suggest getting someone else to check it over in person - it may be something obvious you've overlooked that a fresh pair of eyes would see. Again, apologies if you've already tried this :-)</... | 893 |
fluid dynamics | Mixing of fluid in a rotating barrel | https://physics.stackexchange.com/questions/4038/mixing-of-fluid-in-a-rotating-barrel | <p>A barrel/drum with a diameter of 60cm is rotating at 20RPM to get a good mixing of the fluid contained (type thick oil). </p>
<p>At what RPM should a barrel of 30cm rotate to get the same mixing efficiency with the same fluid? To get the same peripheral velocity, the RPM should be 40RPM, but will this give the same... | <p>Knowing a bit about process engineers' attitude to science I would say you just need to have same Reynolds number. $U\approx\Omega R$, $L\approx R$, then $Re\approx\frac{\Omega R^2}{\nu}$ so 80RPM.</p>
| 894 |
fluid dynamics | How to pump liquid aerosol? | https://physics.stackexchange.com/questions/577913/how-to-pump-liquid-aerosol | <p>I have a use case where I want to produce fog (an aerosol) using an industrial grade high-volume fog generator and then I would like to direct the resulting fog to different locations i.e. small boxes in the same room. This way, I can have concentrated fog where I need and keep rest of the room space clear.</p>
<p>B... | 895 | |
fluid dynamics | How do fluids behave in a vacuum? | https://physics.stackexchange.com/questions/566883/how-do-fluids-behave-in-a-vacuum | <p>My textbook says that the volume of liquids is assumed to be such under atmospheric pressure. What if the atmospheric pressure is reduced? Will the liquid stop exerting pressure according to Pascal's law? Will there be an intrinsic force that the liquid will exert?</p>
| <p>If you pull a vacuum on a liquid, when the ambient pressure exerted on the liquid falls to the vapor pressure of the liquid at that temperature, the liquid starts to boil. Pulling such a vacuum very suddenly on a sample of water will cause the water to explode violently into vapor by boiling all at once.</p>
| 896 |
fluid dynamics | How would air flow inside a toroidal space station? | https://physics.stackexchange.com/questions/309124/how-would-air-flow-inside-a-toroidal-space-station | <p>The torus-shaped rotating space station, familiar from science fiction, is a way to produce artificial gravity in space. Would the fluid dynamics of gas in a rotating torus cause a person standing inside to notice any airflow?</p>
<p>It's noted (for example <a href="https://physics.stackexchange.com/questions/11235... | <p>No, the atmosphere will rotate with the space station, just like Earth's atmosphere.</p>
| 897 |
fluid dynamics | Bernoulli's principle in a closed loop? | https://physics.stackexchange.com/questions/588481/bernoullis-principle-in-a-closed-loop | <p>In most simple terms, Bernoulli's principle dictates that</p>
<ul>
<li>a fluid or gas moving in one direction exposes less pressure in orthogonal directions.</li>
<li>the sum of the pressures, in the direction of movement and otherwise, is equal the pressure as measured in rest.</li>
</ul>
<p>Essentially, we loose s... | 898 | |
fluid dynamics | Evaluating the gradient of pressure at the boundary of container | https://physics.stackexchange.com/questions/595136/evaluating-the-gradient-of-pressure-at-the-boundary-of-container | <p>In the hydrostatic case with no viscosity, we can write the gradient of the pressure inside a container of water within the gravitational field as
<span class="math-container">$$ \nabla P = g \rho$$</span></p>
<p>Moving close to a wall vertical wall, We encounter a normal force which should reduce our pressure, howe... | <p>I'm not sure why you think the normal force should reduce the pressure. The normal force on the container is a <em>reaction</em> force. The normal force on the ground when you step on it doesn't cause you to not weigh anything, it just prevents your weight from continuing to accelerate you downwards. It's similar... | 899 |
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