A single acting reciprocating pump has a stroke length of 37.5 and a cylinder of diameter 22.5 cm…

A single acting reciprocating pump has a stroke length of
37.5 and a cylinder of diameter 22.5 cm. The suction pipe is 12 m long and has
a diameter of 15 cm. The water level in the sump is 3.0 m below the level of
the cylinder. If the speed of the pump is 20 rpm, determine the pressure head
on the piston at the beginning of the suction stroke (1) when no air vessel is
fitted and (2) when an air vessel is fitted to the suction pipe at the level of
the cylinder and at a distance of 1.5 m from the cylinder. Take Darcy–Weisbach
friction factor f = 0.02.