Consider the gate shown in Fig. P2.79. The gate is massless and has a width \(b\) (perpendicular to the paper). The hyprostatic pressure on the vertical side creates a counterclockwise moment about the hinge, and the hydrostatic pressure on the horizontal side (or bottom) creates a clockwise moment about the hinge. Show that the net clockwise moment is

\[ \Sigma u=ho_{w} g h b\left(\frac{\ell^{2}}{2}-\frac{h^{2}}{6}\right) \]

Figure P2.79

Water, P Hinge