$(40$ pts$)$ A pump moves water from one reservoir to another as sketched. The

elevation difference between the two reservoir surfaces is $h_R=30\mathrm{.}5m.$ The

reservoirs are very large, and thus the elevations of the water at their surfaces

changes by a negligible amount. The pipe diameter is $D=15\mathrm{.}2cm.$ The desired

volume flow rate is $0\mathrm{.}156\frac{m^3}{s},$ and the total irreversible head loss through the

pipes and valves, etc. is proportional to the square of the average flow speed $V$

through the pipe, i$.$e$.,h_L=41\mathrm{.}3\frac{V^2}{2g}.[$Note: Later on in the course $($Chapter $8),$

you will learn how to estimate the irreversible head loss; for now, it is given to

you.$]$ If the pump is $82\mathrm{.}5\%$ efficient, calculate the power $($in kW and in hp $)$

required to rotate the pump shaft.