Question $2,(30$ marks$)$

An oil pump is drawing $50$ kW of electric power while pumping gasoline with a density of with a

density of $730K\frac{g}{m^3}$ Given that the volumetric flowrate through the pump is $75\frac{L}{s},$ the speed at

the inlet and outlet of the pipe are $25\frac{m}{s}$ and $14\mathrm{.}5\frac{m}{s}$ respectively. If the change in pressure

observed at the pump is $420$ kPa and the motor efficiency is $76\%,$

Determine the:

$($i$)$ The mechanical power,

$($ii$)$ The shaft power and the overall mechanical efficiency of the pump.