Question $2(30$ marks$)$

An oil pump is drawing $50$ kW of electric power while pumping gasoline with a density of with and the volumetric flowrate through the pump is $75\frac{L}{s},$ the speed density of $730K\frac{g}{m^3}$ Given that the volumetric fowrate respectively. If the change in pressure the inlet and outlet of the pipe are $25\frac{m}{s}$ and $14\mathrm{.}5\frac{m}{s}$ resp $76\%,$ observed at the

Determine the:

$($i$)$ The mechanical power,

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