A homogeneous slurry is to be filtered at a constant rate of 5 cfm in a Kelly leaf press. Tests made under constant pressure conditions indicate that the cake has a compressibility coefficient a of 0.5 and that at a pressure of 50 psi the volume of filtrate in cubic feet at any given time in minutes is represented by the equation V2 = 15,000 t. The time of the constant-rate cycle is 300 min. Specify the horsepower of the motor required. What is the theoretical work done by the pump per cycle