P$1.(50$ points$)$ Hydrostatic Transmission, Steady State Characteristics

A hydraulic pump drives a hydraulic motor supplying $3\mathrm{.}7$ kW at $500re\frac{v}{m}in$ to a mechanical

load. The pressure rise across the pump is $5\mathrm{.}2$ MPa and there is a pressure drop of $20$ kPa in each

of the lines joining the pump to the motor. Assuming volumetric efficiencies of $90\%$ and

mechanical efficiencies of $90\%$ for both pump and motor determine:

a$)$ The displacement of the motor,

b$)$ The input flow rate at the motor,

c$)$ The power required to drive the pump.