Astrophysics (index)

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      Mrρ
—— = -G ———
dr      r²
  • r - "radius", i.e., distance from the center of the star.
  • P - pressure (dependent on r).
  • ρ - density (dependent on r).
  • Mr - 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)

Referenced by:
Eddington Luminosity
Lane-Emden Equation
Stellar Structure
Turbulent Pressure
Vogt-Russell Theorem