Suppose water is leaking from a tank through a circular hole of area Ah at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of the water leaving the tank per second to cAhsqrt(2gh), where c (0 < c < 1) is an empirical constant. Determine a differential equation for the height h of water at time t for the cubical tank in the figure below. The radius of the hole is 9 in., g = 32 ft/s2.
