Hydrostatic Pressure

where is the static fluid pressure, the mass density, the gravitational potential energy per unit mass, and the (approximately uniform) acceleration due to gravity. Now,

where is the (approximately uniform) mass density of water. Here, the comparatively small mass density of air has been neglected. Because and , it immediately follows, from Equation (2.1), that , where

We conclude that constant pressure surfaces in a stationary body of water take the form of horizontal planes. Making use of Equation (2.2), the previous equation can be integrated to give

where is atmospheric pressure at ground level (Batchelor 2000). According to this expression, pressure in stationary water increases linearly with increasing depth (i.e., with decreasing , for ). In fact, given that and (Batchelor 2000), we deduce that hydrostatic pressure in water rises at the rate of 1 atmosphere (i.e., ) every increase in depth below the surface.