Net force on an object due to a pressure difference (11-10)

Review

As a simple example of the force produced by a pressure difference, consider an object like a door with fluid on each side. The object has area $A$, there is pressure $p_1$ on one side of the object, and there is a greater pressure $p_2$ on the \perpher side (Figure 11-10). By rearranging Equation 11-2, $p = F_\perp /A$ we can calculate the magnitude of the force that each fluid exerts perpendicular to the object's surface:

Force on side 1: magnitude $F_{\perp\ 1} = p_1A$

Force on side 2: magnitude $F_{\perp\ 2} = p_2A$

Since $p_2 >p_1$ the force $F_{\perp\ 2}$ on side 2 is greater than the force $F_{\perp\ 1}$ on side 1. These forces are in opposite directions, so the $\textbf{net}$ force on the object has magnitude

$F_{\mathrm{net}} = F_{\perp\ 2} - F_{\perp\ 1} = p_2A - p_1A$

Equation 11-8 must be satisfied for a fluid to remain at rest, so this is also called the $\textbf{equation of hydrostatic equilibrium}$.