### Hydrostatic Equilibrium

**(Hydrostatic Balance)**
(state of a fluid body when forces are such that the fluid is at rest)

**Hydrostatic Equilibrium** (**Hydrostatic Balance**) in
a body of fluid (e.g., gas) is the state
such that forces cancel and the fluid remains still.
A calm lake is at hydrostatic equilibrium. In astrophysics, a gas
ball (e.g., star) or a planetary Atmosphere is at hydrostatic
equilibrium where at each level, Gravity (toward the center)
matches the upward pressure, i.e., for a spherical symmetric
star:

dP M_{r}ρ
—— = -G ———
dr r²

- r - "radius", i.e., distance from the center of the star.
- P - pressure (dependent on r).
- ρ - density (dependent on r).
- M
_{r} - mass within the spherical volume of radius r.
- G - Gravitational Constant.

Other forces (inertia, if the body
is spinning, magnetic force, a nearby object's gravity)
can be additional factors.
A Protoplanetary Disk can take a
flared torus shape in hydrostatic equilibrium due to the star's
heating and Radiation Pressure.

An example of something not at hydrostatic equilibrium could
be a gas cloud in the midst of collapse or expansion.

For many purposes, such as modeling stars,
the state of a volume of material can be sufficiently close to
hydrostatic equilibrium that it can be assumed for simplicity's sake.
In other words, movement is trivially slow in the scheme of things.

(*physics,statics,fluid mechanics*)
http://en.wikipedia.org/wiki/Hydrostatic_equilibrium

**Referenced by:**

Eddington Luminosity

Gravitational Collapse

Hydrodynamic Equations

Lane-Emden Equation

Partial Ionization Zone

Pulsating Star

Stellar Structure

Turbulent Pressure

Vogt-Russell Theorem

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