Show that the total force on a rectangular dam due to the water behind it increases with the square of the water depth. In particular, show that this force is given by F = ρgh² L/2, where ρ is the density of water, h is its depth at the dam, and L is the length of the dam. You may assume the face of the dam is vertical. (Hint: Calculate the average pressure exerted and multiply this by the area in contact with the water. (See Figure 11.39.)

F F = PA P=hpg