Water is flowing into the top of an open cylindrical tank (which has a diameter D) at a volume flow rate of Qi and the water flows out through a hole in the bottom at a rate of Qo. The tank is constructed from wood that is old and has become very porous so that water leaks out through the walls at a rate of q per unit of wetted surface area. The initial depth of the water in the tank is Z1. a) Derive an equation for the depth of water in the tank at any time.
b) If Qi = 10 gpm, Qo = 5 gpm, D = 5 ft, q = 0.1 gpm/ft2, and Z1 = 3 ft, is the level in the tank rising or falling?