# hydrostatic equilibrium simple definition

is Boltzmann's constant and 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.

A star with an angular velocity above the critical angular velocity becomes a Jacobi (scalene) ellipsoid, and at still faster rotation it is no longer ellipsoidal but piriform or oviform, with yet other shapes beyond that, though shapes beyond scalene are not stable.[5]. B

Therefore, in the nonrelativistic limit the Tolman–Oppenheimer–Volkoff equation reduces to Newton's hydrostatic equilibrium: (we have made the trivial notation change h=r and have used f(Ρ,ρ)=0 to express ρ in terms of P). and differentiating with respect to The smallest object that appears to have an equilibrium shape is the icy moon Mimas at 396 km, whereas the largest object known to have an obviously non-equilibrium shape is the rocky asteroid Vesta at 525 km (573 × 557 × 446 km). An extreme example of this phenomenon is the star Vega, which has a rotation period of 12.5 hours.

of the cluster and is given by, where

=

( The isotropic gravitational field compresses the star into the most compact shape possible.

This qualification means that the object is symmetrically rounded into an ellipsoid shape, where any irregular surface features are due to a relatively thin solid crust. If the star has a massive nearby companion object then tidal forces come into play as well, distorting the star into a scalene shape when rotation alone would make it a spheroid.

(

{\displaystyle \theta } hydrostatic equilibrium (countable and uncountable, plural hydrostatic equilibria) (physics) The state in which a solid or liquid body has relaxed into the shape that it …

B is some function of temperature and fundamental constants.

=

{\displaystyle m_{B}} {\displaystyle \rho _{D}=\rho _{M}-\rho _{B}} Instead, it is rather in a strange walnut-like shape due to its unique equatorial ridge.

yields, If we make the assumption that cold dark matter particles have an isotropic velocity distribution, then the same derivation applies to these particles, and their density

Density changes with pressure, and gravity changes with height, so the equation would be: Note finally that this last equation can be derived by solving the three-dimensional Navier–Stokes equations for the equilibrium situation where, Then the only non-trivial equation is the This qualification typically means that the object is Λ

B This means the sum of the forces in a given direction must be opposed by an equal sum of forces in the opposite direction. =
0

https://en.wikipedia.org/w/index.php?title=Hydrostatic_equilibrium&oldid=979865432, Articles needing additional references from May 2010, All articles needing additional references, Creative Commons Attribution-ShareAlike License, This page was last edited on 23 September 2020, at 06:54. Strobel, Nick. of the dark matter, which is given by, The central density ratio

ρ This qualification typically means that the object is symmetrically rounded into a spheroid or ellipsoid shape, where any irregular surface features are due to a relatively thin solid crust .

However, Mimas is not actually in hydrostatic equilibrium for its current rotation.

-equation, which now reads. = d Also, the purported dwarf planet Haumea is scalene due to its rapid rotation, though it may not currently be in equilibrium. m

At 1,469 km the moon is neither spherical or ellipsoid. 2

B

This page was last edited on 26 September 2017, at 12:56. θ If the density is ρ, the volume is V and g the standard gravity, then: The volume of this cuboid is equal to the area of the top or bottom, times the height — the formula for finding the volume of a cube. {\displaystyle r}

ρ

A rotating star in hydrostatic equilibrium is an oblate spheroid up to a certain (critical) angular velocity.

), Definition from Wiktionary, the free dictionary, https://en.wiktionary.org/w/index.php?title=hydrostatic_equilibrium&oldid=47577783, Creative Commons Attribution-ShareAlike License.

) {\displaystyle \theta }

B {\displaystyle T_{B}}

In fluid mechanics, hydrostatic equilibrium or hydrostatic balance (also known as hydrostasy) is the condition of a fluid or plastic solid at rest. [3] For instance, the pressure-gradient force prevents gravity from collapsing Earth's atmosphere into a thin, dense shell, whereas gravity prevents the pressure gradient force from diffusing the atmosphere into space. P / (That is, the body as a whole can be considered to be in hydrostatic equilibrium even if the crust is not.

It flattens the surface of undisturbed liquids.

( / θ r B T

Finally, the weight of the volume element causes a force downwards. {\displaystyle p_{B}=kT_{B}\rho _{B}/m_{B}} z

The baryonic density satisfies the above equation ) If this were the case, … In the atmosphere, the pressure of the air decreases with increasing altitude. The smallest body confirmed to be in hydrostatic equilibrium is the dwarf planet Ceres, which is icy, at 945 km, whereas the largest body known body to have a noticeable deviation from hydrostatic equilibrium is Iapetus (moon) being made of mostly permeable ice and almost no rock [7].

Values for the ratio range from .11 to .14 for various surveys.[6]. 2

ρ Hydrostatic Equilibrium For the majority of the life of a star, the gravitational force (due to the mass of the star) and the gas pressure (due to energy generation in the core of the star) balance, and the star is said to be in ‘ hydrostatic equilibrium ’. B

This pressure difference causes an upward force called the pressure-gradient force.

The fact that identical hydrostatic pressures form in the equilibrium state is also shown by the fact that pressures in liquids act equally in all directions. )

(

{\displaystyle \rho _{B}(0)/\rho _{M}(0)}

This occurs when external forces such as gravity are balanced by a pressure-gradient force. k Only baryonic matter (or, rather, the collisions thereof) emits X-ray radiation. ρ

, the index i runs for the coordinates r and

This phenomenon is why Earth's atmosphere neither dissipates into space nor collapses into a thin, dense shell, and is also what gives large celestial objects their ellipsoidal shape. t However, in the cases of moons in synchronous orbit, nearly unidirectional tidal forces create a scalene ellipsoid.

)

ϕ Often the equilibrium shape is an oblate spheroid, as is the case with Earth.

θ

The balance of these two forces is known as the hydrostatic balance. For example, the massive base of the tallest mountain on Earth, Mauna Kea, has deformed and depressed the level of the surrounding crust, so that the overall distribution of mass approaches equilibrium. {\displaystyle {\mathcal {L}}_{X}=\Lambda (T_{B})\rho _{B}^{2}}

B

The absolute X-ray luminosity per unit volume takes the form The force of gravity balances this out, keeping the atmosphere bound to Earth and maintaining pressure differences with altitude.

In fluid mechanics, hydrostatic equilibrium or hydrostatic balance (also known as hydrostasy)[1][2] is the condition of a fluid or plastic solid at rest.

By saying these changes are infinitesimally small, the equation can be written in differential form.

p and Using the ideal gas law D Under planetary conditions, "solid" rock and ice are actually fluid, and will lapse into hydrostatic equilibrium if the body is massive or warm enough. By balancing these forces, the total force on the fluid is. There are 3 forces: the force downwards onto the top of the cuboid from the pressure, P, of the fluid above it is, from the definition of pressure, Similarly, the force on the volume element from the pressure of the fluid below pushing upwards is. {\displaystyle (t,r,\theta ,\phi )} B

s satisfies the non-linear differential equation, With perfect X-ray and distance data, we could calculate the baryon density at each point in the cluster and thus the dark matter density. This short article about physics can …

Solid bodies have irregular surfaces, but local irregularities may be consistent with global equilibrium.

The balance of these two forces is known as the hydrostatic balance.

is dependent on the redshift

M In addition to the Sun, there are a dozen or so equilibrium objects confirmed to exist in the Solar System, with others possible. r ρ To put it simply, hydrostatic equilibrium is the balance struck between pressure-gradient force and gravity.

{\displaystyle z} ρ

This occurs when external forces such as gravity are balanced by a pressure-gradient. Some icy bodies may be in equilibrium at least partly due to a subsurface ocean, which is not the definition of equilibrium used by the IAU (gravity overcoming internal rigid-body forces). B [4] A similar equation can be computed for rotating, axially symmetric stars, which in its gauge independent form reads: Unlike the TOV equilibrium equation, these are two equations (for instance, if as usual when treating stars, one chooses spherical coordinates as basis coordinates )

We could then calculate the velocity dispersion ρ : The integral is a measure of the total mass of the cluster, with

T

{\displaystyle z} It flattens the surface of undisturbed liquids. (May, 2001).

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