A single acting reciprocating pump has a piston area of 1.5 ft2 and a stroke of 12in. The cross sectional area of delivery pipe is 0.3 ft2 and water is lifted through a total height of 40 ft. If the speed of the pump in 60 r.p.m, and the actual quantity of water lifted 550 gal/min, find the slip, the coefficient of discharge, and the theoretical horse power required to derive the pump.