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Concept
Hydrostatic equilibrium
Summary
In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary physics of Earth, the pressure-gradient force prevents gravity from collapsing the planetary atmosphere into a thin, dense shell, whereas gravity prevents the pressure-gradient force from diffusing the atmosphere into outer space.
Hydrostatic equilibrium is the distinguishing criterion between dwarf planets and small solar system bodies, and features in astrophysics and planetary geology. Said qualification of equilibrium indicates that the shape of the object is symmetrically rounded, mostly due to rotation, into an ellipsoid, where any irregular surface features are consequent to a relatively thin solid crust. In addition to the Sun, there are a dozen or so equilibrium objects confirmed to exist in the Solar System.
For a hydrostatic fluid on Earth:
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 of forces in the opposite direction. This force balance is called a hydrostatic equilibrium.
The fluid can be split into a large number of cuboid volume elements; by considering a single element, the action of the fluid can be derived.
There are three 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
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:
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.
Official source
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