Water is pumped from a lake to a storage tank $10m$ above at a rate of

$50\frac{L}{s}$ while consuming $7kW$ of electric power.

Disregarding any frictional losses in the pipes and any changes in kinetic energy.

Determine:

$($a$)$ the overall efficiency of the pump$-$motor unit

$($b$)$ the pressure difference between the inlet and the exit of the pump.

Part$-2$

Water at and $=1\mathrm{.}138{10}^{-}k\frac{g}{m}-s)$ is flowing steadily in a $25-m-$long and $5-cm$ diameter horizontal pipe made of stainless steel at a rate of $9\frac{L}{s}.$

Given that the pipe has a sharp$-$edged inlet and five $90$ smooth flanged bends.

Determine

$($a$)$ the pressure drop

$($b$)$ the head loss

$($c$)$ the pumping power requirement to overcome this pressure drop.