Force and Torque on a Dam. A dam has the shape of a rectangular solid. The side facing the lake has area A and height H. The surface of the freshwater lake behind the dam is at the top of the dam.
(a) Show that the net horizontal force exerted by the water on the dam equals ½ pgHA-that is, the average gauge pressure across the face of the dam times the area (see Problem 14.49).
(b) Show that the torque exerted by the water about an axis along the bottom of the dam is pgH'A/6.
(c) How do the force and torque depend on the size of the lake?