Hydrostatic equilibrium

In fluid mechanics, a fluid is said to be in hydrostatic equilibrium or hydrostatic balance when it is at rest, or when the flow velocity at each point is constant over time. This occurs when external forces such as gravity are balanced by a pressure gradient force. 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.

Hydrostatic equilibrium is the current distinguishing criterion between dwarf planets and small Solar System bodies, and has other roles in astrophysics and planetary geology. 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. There are 31 observationally confirmed such objects (apart from the Sun), sometimes called planemos, in the Solar System, seven more that are virtually certain, and a hundred or so more that are likely.

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.

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