Alternatively, since the pressure at any place is the same in all directions, there can be a net force per unit volume only if the pressure varies from point to point. The necessary condition is expressed by the equation of hydrostatic equilibrium that everywhere in the fluid. If the conditions for equilibrium hold for all V , the resultant force on each element of the fluid is zero. Therefore is the necessary and sufficient condition for the fluid to be in equilibrium. The restriction imposed on possible equilibrium states lies in the fact that only for certain distributions of and , viz.
Pressure increases to support the weight of fluid.
The density of an element of fluid may be affected by the pressure to which it is subjected, and also by other factors such as radiation transport, so that detailed discussion requires information about . However, when const., the solution of is simply This condition is illustrated in Fig.