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Hydrostatic equilibrium occurs when compression due to gravity is balanced by a pressure gradient which creates a pressure gradient force in the opposite direction. The balance of these two forces is known as the hydrostatic balance.
Mathematical consideration
Fluids The hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids. A hydrostatic balance is a particular balance for weighing substances in water. Hydrostatic balance allows the discovery of their specific gravities. Astrophysics Hydrostatic equilibrium is the reason stars don't implode, or explode. In astrophysics, in any given layer of a star, there is a balance between the thermal pressure (outward) and the weight of the material above pressing downward (inward). This balance is called hydrostatic equilibrium. A star is like a balloon. In a balloon, the gas inside the balloon pushes outward and the elastic material supplies just enough inward compression to balance the gas pressure. In the case of a star, the star's internal gravity supplies the inward compression. The isotropic gravitational field compresses the star into the most compact shape possible: a sphere. Note however that a star becomes a sphere only in the ideal case where only its own self-gravity is involved. In real situations there are other forces at play that alter the outcome, most notably centrifugal force from a star's rotation. A rotating star becomes an oblate spheroid when in hydrostatic equilibrium. An extreme example of this is the star Vega, which has a rotation period of 12.5 hours and is about 20% fatter at the equator than at the poles because of it. If the star has a massive nearby companion object then tidal forces come into play as well, further distorting the star into an ellipsoidal shape. For an example of this see Beta Lyrae. 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 enacted by the International Astronomical Union in 2006, planets and dwarf planets are objects that have sufficient gravity to overcome their own rigidity and assume hydrostatic equilibrium. Since the terrestrial planets and dwarf planets have rough surfaces and so are not perfectly in equilibrium this definition evidently has some flexibility, but as of yet a specific means of quantifying an object's shape by this standard has not been announced. Atmospherics Hydrostatic equilibrium can explain why the Earth's atmosphere does not collapse to a very thin layer on the ground. In the atmosphere, the pressure of air decreases with increasing altitude. This causes an upward force, called the pressure gradient force, which tries to smooth over pressure differences. The force of gravity, on the other hand, almost exactly balances this out, keeping the atmosphere bound to the earth and maintaining pressure differences with altitude. Without the pressure gradient force, the atmosphere would collapse to a much thinner shell around the earth, and without the force of gravity, the pressure gradient force would diffuse the atmosphere into space, leaving earth with hardly any atmosphere. See also | ||||||||||
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