Example $10$

The pump$-$turbine system in the figure draws water from the upper reservoir in the daytime to produce power for a city. At night, it pumps water from lower to upper reservoirs to restore the situation. For a design flow rate of $975\frac{L}{s}$ in either direction, the friction head loss is $6\mathrm{.}25$ m $.$

a$.$ Estimate the power in $kW$ extracted by the turbine.

b$.$ Estimate the power in $kW$ delivered by the pump.

c$.$ If the system is $82\%$ efficient, what is the power extracted by the turbine.

$69$