id stringlengths 15 145 | text stringlengths 2 241k | title stringclasses 1
value |
|---|---|---|
hydrostatic_equilibrium/Hydrostatic_equilibrium1_4.txt | �азақшаNederlands日本語Norsk bokmålNorsk nynorskPolskiPortuguêsRomânăРусскийSimple EnglishSlovenčinaSlovenščinaСрпски / srpskiSrpskohrvatski / српскохрватскиSvenskaไทยTürkç | |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_17.txt |
)
=
−
| |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states2_7.txt | a negative sign is incorporated in the mathematical expression to indicate a drop in pressure with height. Hydrostatic Equilibrium and BuoyancyThe stability of a floating or submerged body in a fluid is based on hydrostatic equilibrium conditions. When an object is fully or partially submerged in a liquid, hydrostatic... | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states1_2.txt | Design Reuse and Productivity
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hydrostatic_equilibrium/Hydrostatic_equilibrium5_7.txt |
D
2
=
k
T
D
m
D
.
{\displaystyle \sigma _{D}^{2}={\frac {kT_{D}}{m_{D}}}.}
The central density ratio
ρ
B
(
0
)
/
ρ
M
(
0
)
{\displaystyle \rho _{B}(0)/\rho _{M | |
hydrostatic_equilibrium/Hydrostatic_equilibrium3_7.txt | fourths the centrifugal force at the equator.[5] In 1742, Colin Maclaurin published his treatise on fluxions, in which he showed that the spheroid was an exact solution. If we designate the equatorial radius by
r
e
,
{\displaystyle r_{e},}
the polar radius by
r
p
,
{\displaystyle r_{p},}
and th... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium3_4.txt | hydrostatic balance is a particular balance for weighing substances in water. Hydrostatic balance allows the discovery of their specific gravities. This equilibrium is strictly applicable when an ideal fluid is in steady horizontal laminar flow, and when any fluid is at rest or in vertical motion at constant speed. ... | |
hydrostatic_equilibrium/hydrostat_html4_0.txt |
First, let's assume the density of the Earth does not change with radius.
Then we can express M(r) for the Earth as:
So that the equation of hydrostatic equilibrium becomes:
Now, let's integrate this from the center of the Earth to the surface:
To end up with an expression for the pressure at the cent... | |
hydrostatic_equilibrium/node54_html1_0.txt |
Hydrostatic equilibrium of the atmosphere
Next: The isothermal atmosphere
Up: Classical thermodynamics
| |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_6.txt | \phi }
(including the effect of centrifugal force) is
g
(
ϕ
)
=
g
p
(
1
−
f
)
1
−
(
2
f
−
f
2
)
sin
2
ϕ
.
{\displaystyle g(\phi )={\frac {g_{p}(1-f)}{\sqrt {1-(2f-f^{2 | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states3_3.txt | to regulated DC output.
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hydrostatic_equilibrium/Hydrostatic_equilibrium2_6.txt | }{c^{4}}}\left(T_{\mu \nu }-{\frac {1}{2}}g_{\mu \nu }T\right)}
and using the conservation condition
∇
μ
T
μ
ν
=
0
{\displaystyle \nabla _{\mu }T^{\mu \nu }=0}
one can derive the Tolman–Oppenheimer–Volkoff equation for the structure of a static, spherically symmetric relativistic star | |
hydrostatic_equilibrium/Hydrostatic_equilibrium3_14.txt |
The gravitational attraction on the equator (not including centrifugal force) is
g
e
=
3
2
(
1
r
e
r
p
−
ϵ
r
e
−
r
p
arctan
(
ϵ
r
e
/
r
p
)
ϵ
| |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states1_5.txt |
PCB Design from Start to Finish
| |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_9.txt | _{M}(0)\propto (1+z)^{2}\left({\frac {\theta }{s}}\right)^{3/2}}
where
θ
{\displaystyle \theta }
is the angular width of the cluster and
s
{\displaystyle s}
the proper distance to the cluster. Values for the ratio range from.11 to.14 for various surveys.[11]
Planetary geology[edit]
See also: List o... | |
hydrostatic_equilibrium/node54_html5_0.txt |
(326)
Next: The isothermal atmosphere
Up: Classical thermodynamics
Previous: Isothermal and adiabatic expansion
Richard Fitzpatrick
2006-02-02
| |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_25.txt | .; Molnár, L.; et al. (March 2024). "The visible and thermal light curve of the large Kuiper belt object (50000) Quaoar". Astronomy & Astrophysics. 684: A50. arXiv:2401.12679. Bibcode:2024arXiv240112679K. doi:10.1051/0004-6361/202348054.
^ Cowen, R. (2007). Idiosyncratic Iapetus, Science News vol. 172, pp. | |
hydrostatic_equilibrium/Isostasy1.txt |
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hydrostatic_equilibrium/Hydrostatic_equilibrium4_13.txt |
Λ
(
T
)
{\displaystyle \Lambda (T)}
is some function of temperature and fundamental constants. The baryonic density satisfies the above equation
d
P
=
−
ρ
g
d
r
{\displaystyle dP=-\rho g\,dr}
:
p
B
(
r
+
d
r
)
−
p
B
(
r
)
=
− | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_5.txt |
(
r
)
ρ
D
(
r
)
m
D
)
]
=
−
4
π
G
r
2
ρ
M
(
r
)
.
{\displaystyle {\frac {d}{dr}}\left[{\frac {r^{2}}{\rho _{D}(r)}}{\frac {d}{dr}}\left({\frac {kT_{D}(r)\ | |
hydrostatic_equilibrium/Hydrostatic_equilibrium2_3.txt | v={\frac {\partial p}{\partial x}}={\frac {\partial p}{\partial y}}=0}
Then the only non-trivial equation is the
z
{\displaystyle z}
-equation, which now reads
∂
p
∂
z
+
ρ
g
=
0
{\displaystyle {\frac {\partial p}{\partial z}}+\rho g=0}
Thus, hydrostatic balance can be regarded | |
hydrostatic_equilibrium/Hydrostatic_equilibrium1_13.txt | the volume of a cube.
F
weight
=
−
ρ
g
A
h
{\displaystyle F_{\text{weight}}=-\rho gAh}
By balancing these forces, the total force on the fluid is
∑
F
=
F
bottom
+
F
top
+
F
weight
=
P
bottom
A
−
P
top
A
−
ρ | |
hydrostatic_equilibrium/Hydrostatic_equilibrium1_1.txt |
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1Mathematical consideration
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1.1Der... | |
hydrostatic_equilibrium/hydrostat_html2_1.txt | , plus the pressure from the
stuff below pressing up. So the net pressure is
| |
hydrostatic_equilibrium/Hydrostatic_equilibrium1_3.txt |
Hydrostatic equilibrium
39 languages
AfrikaansالعربيةБългарскиBosanskiCatalàČeštinaDanskDeutschEspañolEuskaraفارسیFrançais한국어Հայերենहिन्दीIgboBahasa IndonesiaItalianoעברית� | |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_7.txt | })\sin ^{2}\phi }}}.}
This spheroid solution is stable up to a certain (critical) angular momentum (normalized by
M
G
ρ
r
e
{\displaystyle M{\sqrt {G\rho r_{e}}}}
), but in 1834 Carl Jacobi showed that it becomes unstable once the eccentricity reaches 0.81267 (or
f
{\displaystyle f}
reaches 0.3... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium2_9.txt | left(1+{\frac {4\pi r^{3}P(r)}{M(r)c^{2}}}\right)\left(1-{\frac {2GM(r)}{rc^{2}}}\right)^{-1}}
In practice, Ρ and ρ are related by an equation of state of the form f(Ρ,ρ) = 0, with f specific to makeup of the star. M(r) is a foliation of spheres weighted by the mass density ρ(r), with the largest sphere having | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states1_0.txt |
Hydrostatic Equilibrium and Its States | System Analysis Blog | Cadence
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hydrostatic_equilibrium/Hydrostatic_equilibrium5_23.txt | .; Thomas, P. C. (2007). "Iapetus' geophysics: Rotation rate, shape, and equatorial ridge". Icarus. 190 (1): 179–202. Bibcode:2007Icar..190..179C. doi:10.1016/j.icarus.2007.02.018.
^ Garrick-Bethell, I.; Wisdom, J; Zuber, MT (4 August 2006). "Evidence for a Past High-Eccentricity Lunar Orbit". Science. 313 (5787): 652... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium3_9.txt |
r
e
ϵ
r
e
−
r
p
arctan
(
ϵ
r
e
/
r
p
)
ϵ
3
G
ρ
=
3
ϵ
r
e
−
r
p
arctan
(
ϵ
r
e
| |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_3.txt | }{15}}f}
Maclaurin showed (still in the case of uniform density) that the component of gravity toward the axis of rotation depended only on the distance from the axis and was proportional to that distance, and the component in the direction toward the plane of the equator depended only on the distance from that plane... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_30.txt | policy
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hydrostatic_equilibrium/Hydrostatic_equilibrium3_10.txt |
/
r
p
)
ϵ
3
r
e
3
G
M
{\displaystyle {\begin{aligned}g_{p}&=4\pi {\frac {r_{p}}{r_{e}}}{\frac {\epsilon r_{e}-r_{p}\arctan(\epsilon r_{e}/r_{p})}{\epsilon ^{3}}}G\rho \\&=3{\frac | |
hydrostatic_equilibrium/Hydrostatic_equilibrium2_10.txt | radius r:
M
(
r
)
=
4
π
∫
0
r
d
r
′
r
′
2
ρ
(
r
′
)
.
{\displaystyle M(r)=4\pi \int _{0}^{r}dr'\,r'^{2}\rho (r').}
Per standard procedure in taking the nonrelativistic limit, we let c → ∞ | |
hydrostatic_equilibrium/node54_html3_0.txt | the gas, and is the acceleration due to gravity. In follows that the
force balance condition can be written
(322)
which reduces to
(323)
This is called the equation of hydrostatic equilibrium for the atmosphere.
We can write the density of a gas in the following form,
| |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_8.txt | }(0)}
is dependent on the redshift
z
{\displaystyle z}
of the cluster and is given by
ρ
B
(
0
)
/
ρ
M
(
0
)
∝
(
1
+
z
)
2
(
θ
s
)
3
/
2
{\displaystyle \rho _{B}(0)/\rho | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_24.txt | . Bibcode:2006Sci...313..652G. doi:10.1126/science.1128237. PMID 16888135. S2CID 317360.
^ Sean Solomon, Larry Nittler & Brian Anderson, eds. (2018) Mercury: The View after MESSENGER. Cambridge Planetary Science series no. 21, Cambridge University Press, pp. 72–73.
^ Kiss, C.; Müller, T. G.; Marton, G.; Szakáts, R.; ... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_15.txt | tidal forces from its moon Weywot.[16] If so, this would resemble the situation of Iapetus, which is too oblate for its current spin.[17][18] Iapetus is generally still considered a planetary-mass moon nonetheless,[19] though not always.[20]
Solid bodies have irregular surfaces, but local irregularities may be consist... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_18.txt | . (14 March 2019). Ocean Circulation in Three Dimensions. Cambridge University Press. ISBN 9780521768436.
^ Zee, A. (2013). Einstein gravity in a nutshell. Princeton: Princeton University Press. pp. 451–454. ISBN 9780691145587.
^ Propositions X-XXIV (Motions of celestial bodies and the sea), Propositions XIX and XX. ... | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states1_1.txt |
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hydrostatic_equilibrium/Hydrostatic_equilibrium5_28.txt | External links[edit]
Strobel, Nick. (May, 2001). Nick Strobel's Astronomy Notes.
Demonstration on YouTube by Richard Pogge, Ohio State University, Department of Astronomy
Portals: Physics Astronomy Stars Outer space
Retrieved from "https://en.wikipedia.org/w/index.php?title=Hydrostatic_equilibrium&oldid=1217662134"... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_14.txt | larger bodies deviate from hydrostatic equilibrium, although they are ellipsoidal: examples are Earth's Moon at 3,474 km (mostly rock),[14] and the planet Mercury at 4,880 km (mostly metal).[15]
In 2024, Kiss et al. found that Quaoar has an ellipsoidal shape incompatible with hydrostatic equilibrium for its current sp... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium1_2.txt | –Stokes equations
1.3Derivation from general relativity
2Applications
Toggle Applications subsection
2.1Fluids
2.2Astrophysics and planetary science
2.3Planetary geology
2.4Atmospheric modeling
3See also
4References
5External links
Tog... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_17.txt | experiment
References[edit]
^ White, Frank M. (2008). "Pressure Distribution in a Fluid". Fluid Mechanics. New York: McGraw-Hill. pp. 63, 66. ISBN 978-0-07-128645-9.
^ Vallis, Geoffrey K. (6 November 2006). Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation. Cambridge University Press.... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium3_15.txt |
3
r
e
2
r
p
| |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states2_9.txt | on the relative position of the center of gravity and the center of buoyancy, the equilibrium state differs between:
Stable equilibrium: The weight and buoyant force are equal and opposite. Under this condition, if the center of buoyancy lies above the center of gravity, it is in a stable state of equilibrium.
Unst... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium3_11.txt | {\epsilon r_{e}-r_{p}\arctan(\epsilon r_{e}/r_{p})}{\epsilon ^{3}r_{e}^{3}}}GM\\\end{aligned}}}
where
G
{\displaystyle G}
is the gravitational constant,
ρ
{\displaystyle \rho }
is the (uniform) density, and
M
{\displaystyle M}
is the total mass. The ratio of this to | |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_10.txt | flattening (
f
{\displaystyle f}
) and the ratio at the equator of centrifugal force to gravitational attraction. (Compare with the exact relation above for the case of uniform density.) Clairaut's theorem is a special case, for an oblate spheroid, of a connexion found later by Pierre-Simon Laplace between the s... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium2_4.txt | as a particularly simple equilibrium solution of the Navier–Stokes equations.
Derivation from general relativity[edit]
By plugging the energy–momentum tensor for a perfect fluid
T
μ
ν
=
(
ρ
c
−
2
+
P
)
u
μ
u
ν
+
P
g
μ
ν
{\displaystyle T^{\mu \nu }=\left(\r | |
hydrostatic_equilibrium/Hydrostatic_equilibrium1_10.txt |
Derivation from force summation[edit]
Further information: Mechanical equilibrium
Newton's laws of motion state that a volume of a fluid that is not in motion or that is in a state of constant velocity must have zero net force on it. This means the sum of the forces in a given direction must be opposed by an equal sum... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_5.txt |
∼
4
5
f
g
e
.
{\displaystyle g_{e}-{\frac {r_{p}}{r_{e}}}g_{p}\sim {\frac {2}{5}}\epsilon ^{2}g_{e}\sim {\frac {4}{5}}fg_{e}.}
Defining the latitude to be the angle between a tangent to the meridian and axis of rotation, the total gravity felt at latitude
ϕ
{\displaystyle | |
hydrostatic_equilibrium/Hydrostatic_equilibrium3_12.txt |
g
0
,
{\displaystyle g_{0},}
the gravity if the fluid is not rotating, is asymptotic to
g
p
/
g
0
∼
1
+
1
15
ϵ
2
∼
1
+
2
15
f
{\displaystyle g_{p}/g_{0}\sim 1+{\frac {1}{15}}\epsilon | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_22.txt | . (July 2010). "Sizes, shapes, and derived properties of the saturnian satellites after the Cassini nominal mission" (PDF). Icarus. 208 (1): 395–401. Bibcode:2010Icar..208..395T. doi:10.1016/j.icarus.2010.01.025. Archived from the original (PDF) on 23 December 2018.
^ Castillo-Rogez, J. C.; Matson, D. L.; Sotin, C.; J... | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states4_3.txt |
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hydrostatic_equilibrium/Hydrostatic_equilibrium3_3.txt | if as usual when treating stars, one chooses spherical coordinates as basis coordinates
(
t
,
r
,
θ
,
φ
)
{\displaystyle (t,r,\theta,\varphi )}
, the index i runs for the coordinates r and
θ
{\displaystyle \theta }
).
Applications[edit]
Fluids[edit]
The hydrostatic equilibrium pertains to hydrostatics a... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_15.txt | 4\pi r^{2}\,\rho _{M}(r)\,dr.}
The integral is a measure of the total mass of the cluster, with
r
{\displaystyle r}
being the proper distance to the center of the cluster. Using the ideal gas law
p
B
=
k
T
B
ρ
B
/
m
B
{\displaystyle p_{B}=kT_{B}\rho | |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_4.txt |
g
p
{\displaystyle {\frac {r_{p}}{r_{e}}}g_{p}}
in order to have the same pressure at the bottom of channels from the pole or from the equator to the centre, so the centrifugal force at the equator must be
g
e
−
r
p
r
e
g
p
∼
2
5
ϵ
2
g
e | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_16.txt | Atmospheric modeling[edit]
Further information: Atmospheric model
In the atmosphere, the pressure of the air decreases with increasing altitude. This pressure difference causes an upward force called the pressure-gradient force. The force of gravity balances this out, keeping the atmosphere bound to Earth and maintaini... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_20.txt | }\theta }
but his subsequent statements are correct.
^ a b Henri Poincaré (1885). "Les formes d'équilibre d'une masse fluide en rotation". Revue Général des Sceince Pures et Appliquées.
^ "Gallery : The shape of Planet Earth". Josleys.com. Retrieved 2014-06-15.
^ Clairaut, Alexis; Colson, John (1737). "An Inquiry ... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_19.txt | 125. Maclaurin does not use modern notation but rather gives his results in geometric terms. The gravity results are in article 646. At one point he makes an erroneous statement equivalent to
d
(
tan
θ
−
θ
)
/
d
tan
θ
=
tan
2
θ
{\displaystyle d(\tan \theta -\theta )/d\tan \theta =\tan ^{2 | |
hydrostatic_equilibrium/hydrostat_html5_0.txt |
Numbers:
G = 6.67x10-11 N m2 kg-2
average density of Earth = 5500 kg m-3
radius of Earth = 6400 km = 6.4x106 m
So plugging in, we get Pc = 1.7x1011 N m-2
= 1.7x106 atmospheres
| |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states2_10.txt | and center of gravity are at the same point, the state of equilibrium is neutral, provided the weight and buoyant forces are equal and opposite.
Hydrostatic equilibrium is important when dealing with fluids and objects that are either immersed or floating in fluid. Design challenges can be overcome or balanced by ana... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_9.txt | aré was unsure what would happen at higher angular momentum, but concluded that eventually the blob would split in two.
The assumption of uniform density may apply more or less to a molten planet or a rocky planet, but does not apply to a star or to a planet like the earth which has a dense metallic core. In 1737 Alexi... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium2_1.txt | of the volume element—a change in the distance above the ground. By saying these changes are infinitesimally small, the equation can be written in differential form.
d
P
=
−
ρ
g
d
h
{\displaystyle dP=-\rho g\,dh}
Density changes with pressure, and gravity changes with height, so the equation would be:
d
... | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states4_5.txt |
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hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states2_3.txt | on a fluid and the pressure exerted by a fluid on an immersed object is called hydrostatics.
In the air, a condition arises where the pressure gradient force balances the gravitational force, called the hydrostatic equilibrium state.
When the center of buoyancy and center of gravity are at the same point, the sta... | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states5_4.txt | us
| |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states3_0.txt | OrCAD X Start Your Free Trial
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hydrostatic_equilibrium/Hydrostatic_equilibrium4_2.txt | 3}r_{e}^{3}}}GM\\\end{aligned}}}
Asymptotically we have:
g
e
/
g
0
∼
1
−
1
30
ϵ
2
∼
1
−
1
15
f
{\displaystyle g_{e}/g_{0}\sim 1-{\frac {1}{30}}\epsilon ^{2}\sim 1-{\frac {1 | |
hydrostatic_equilibrium/Isostasy2.txt |
4.3Mid-ocean ridges
4.4Basin and Range
4.5Ice sheets
4.6Lithosphere-asthenosphere boundary
5See also
6References
7Further reading
8External links
Toggle the table of contents
Isostasy
42 languages
AfrikaansالعربيةAzərbaycancaবাংলাБелар... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_14.txt |
d
r
ρ
B
(
r
)
G
r
2
∫
0
r
4
π
r
2
ρ
M
(
r
)
d
r
.
{\displaystyle p_{B}(r+dr)-p_{B}(r)=-dr{\frac {\rho _{B}(r)G}{r^{2}}}\int _{0}^{r} | |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_11.txt | it a spheroid. An example of this is Beta Lyrae.
Hydrostatic equilibrium is also important for the intracluster medium, where it restricts the amount of fluid that can be present in the core of a cluster of galaxies.
We can also use the principle of hydrostatic equilibrium to estimate the velocity dispersion of dark ... | |
hydrostatic_equilibrium/node54_html2_1.txt | starts at height above
ground level and extends to
height. The upwards force exerted on this slice from the gas below
is, where is the pressure at height.
Likewise, the downward force exerted by the gas above the slice is
. The net upward force is clearly
. In equilibrium,
this upward force must be balanced by t... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium3_1.txt | dh}
(we have made the trivial notation change h = r and have used f(Ρ,ρ) = 0 to express ρ in terms of P).[4] A similar equation can be computed for rotating, axially symmetric stars, which in its gauge independent form reads:
∂
i
P
P
+
ρ
−
∂
i
ln
u
t
+
u
t
| |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states2_5.txt | is greater than the pressure from the top. There is a pressure gradient experienced in the column of air as we go vertically upwards. The net force acting on the slice of air column upwards is due to the pressure gradient and can be given by the equation:A is the horizontal cross-sectional area of the air column and P... | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states2_12.txt |
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hydrostatic_equilibrium/hydrostat_html2_0.txt | gravity acting on the cylinder?
Now, define the quantity
(what is g(r)?)
so that we have
What balances this gravitational force? Pressure. So let's calculate the pressure acting
on the cylinder. (remember Pressure = Force/Area)
The cylinder feels the press... | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states4_2.txt |
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hydrostatic_equilibrium/Hydrostatic_equilibrium5_26.txt | 104–106. references Archived 2007-10-13 at the Wayback Machine
^ Thomas, P. C. (July 2010). "Sizes, shapes, and derived properties of the saturnian satellites after the Cassini nominal mission" (PDF). Icarus. 208 (1): 395–401. Bibcode:2010Icar..208..395T. doi:10.1016/j.icarus.2010.01.025. Archived from the original (... | |
hydrostatic_equilibrium/Isostasy5.txt | {\displaystyle P(x)}
is the load on the ocean crust. The parameter D is the flexural rigidity, defined as
D
=
E
T
c
3
/
12
(
1
−
σ
2
)
{\displaystyle D=ET_{c}^{3}/12(1-\sigma ^{2})}
where E is Young's modulus,
σ
{\displaystyle \sigma }
is Poisson's ratio, and
T
c
{\displaystyle ... | |
hydrostatic_equilibrium/node54_html4_0.txt |
(324)
where is the molecular weight of the gas,
and is equal to the mass of one mole of gas particles.
For instance, the molecular weight of Nitrogen gas is 28 grams.
The above formula for the density of a gas
combined with the ideal gas law
yields
(325)
It follows that the equation of hydrostati... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium2_12.txt |
c
2
)
−
1
→
1
{\displaystyle \left(1+{\frac {P(r)}{\rho (r)c^{2}}}\right)\left(1+{\frac {4\pi r^{3}P(r)}{M(r)c^{2}}}\right)\left(1-{\frac {2GM(r)}{rc^{2}}}\right)^{-1}\rightarrow 1}
Therefore, in the nonrelativ | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states3_4.txt | two types of co-fired ceramic fabrication processes, LTCC and HTCC, and their role in enhancing semiconductor packaging diversity.
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hydrostatic_equilibrium/Hydrostatic_equilibrium5_0.txt |
ρ
B
(
r
)
G
r
2
∫
0
r
4
π
r
2
ρ
M
(
r
)
d
r
.
{\displaystyle {\frac {d}{dr}}\left({\frac {kT_{B}(r)\rho _{B}(r)}{m_{B}}}\right)=-{\frac {\rho _{B}(r | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_4.txt |
ρ
D
=
ρ
M
−
ρ
B
{\displaystyle \rho _{D}=\rho _{M}-\rho _{B}}
satisfies the non-linear differential equation
d
d
r
[
r
2
ρ
D
(
r
)
d
d
r
(
k
T
D | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_27.txt | Emily Lakdawalla et al., What Is A Planet? Archived 2022-01-22 at the Wayback Machine The Planetary Society, 21 April 2020
^ Chen, Jingjing; Kipping, David (2016). "Probabilistic Forecasting of the Masses and Radii of Other Worlds". The Astrophysical Journal. 834 (1): 17. arXiv:1603.08614. doi:10.3847/1538-4357/834/1... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium4_12.txt |
=
Λ
(
T
B
)
ρ
B
2
{\displaystyle {\mathcal {L}}_{X}=\Lambda (T_{B})\rho _{B}^{2}}
where
T
B
{\displaystyle T_{B}}
and
ρ
B
{\displaystyle \rho _{B}}
are the temperature and density of the baryonic matter, and
| |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_2.txt |
[
r
2
ρ
B
(
r
)
d
d
r
(
k
T
B
(
r
)
ρ
B
(
r
)
m
B
)
]
=
−
4
π
G
r
2
ρ
M
(
r
)
.
{\displaystyle {\ | |
hydrostatic_equilibrium/Hydrostatic_equilibrium1_12.txt | displaystyle F_{\text{bottom}}=P_{\text{bottom}}A}
Finally, the weight of the volume element causes a force downwards. If the density is ρ, the volume is V and g the standard gravity, then:
F
weight
=
−
ρ
g
V
{\displaystyle F_{\text{weight}}=-\rho gV}
The volume of this cuboid is equal to the area of the... | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states2_1.txt |
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hydrostatic_equilibrium/Hydrostatic_equilibrium1_6.txt | Download QR codeWikidata item
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State of balance between external forces on a fluid and internal pressure gradient
For broader coverage of this topic, se... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_10.txt | rounded objects of the Solar System
Further information: Clairaut's theorem (gravity)
The concept of hydrostatic equilibrium has also become important in determining whether an astronomical object is a planet, dwarf planet, or small Solar System body. According to the definition of planet adopted by the International ... | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states2_0.txt |
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hydrostatic_equilibrium/Hydrostatic_equilibrium3_5.txt | to both stars and objects like planets, which may have been fluid in the past or in which the solid material deforms like a fluid when subjected to very high stresses.
In any given layer of a star there is a hydrostatic equilibrium between the outward-pushing pressure gradient and the weight of the material above pres... | |
hydrostatic_equilibrium/Hydrostatic_equilibrium5_12.txt | mass to attain hydrostatic equilibrium than rocky objects. The smallest object that appears to have an equilibrium shape is the icy moon Mimas at 396 km, whereas the largest icy object known to have an obviously non-equilibrium shape is the icy moon Proteus at 420 km, and the largest rocky bodies in an obviously non-e... | |
hydrostatic_equilibrium/node54_html2_0.txt | Up: Classical thermodynamics
Previous: Isothermal and adiabatic expansion
Hydrostatic equilibrium of the atmosphere
The gas which we are most familiar with in everyday life is, of course, the Earth's
atmosphere. In fact, we can use the isothermal
and adiabatic gas laws to
explain most of the observable
feature... | |
hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states3_2.txt |
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hydrostatic_equilibrium/msa2022_hydrostatic_equilibrium_and_its_states1_4.txt | Capture and Circuit Simulation
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