Mechanical equilibrium of fluids

This equation places a restriction on the body forces. Mechanical equilibrium can exist only if the body force field satisfies the above equation. It is clear that this condition can be satisfied by all conservative body forces, i.e. those which can be derived from a scalar potential such as

Therefore, the equipotential surfaces coincide with the isobaric surfaces. The pressure distribution for a gas at rest is easily determined, since pressure and density are directly related variables