P$1.$ Water, $=1\mathrm{.}94$ slugs$/$ cubic feet and $v=0\mathrm{.}000011f\frac{t^2}{s},$ is used for energy storage as shown in the diagram. The roughness ratio is $\frac{}{d}=0\mathrm{.}001.$ Turbine is used instead of pump for energy production situation. Water is pumped between the two reservoirs at $0\mathrm{.}05f\frac{t^3}{s}$ through $400$ ft $.$ of $2-$in$-$diameter pipe and several minor losses.

a$)$ Calculate the pump horsepower required if its efficiency is $85\%$

b$)$ Calculate power output of turbine if its efficiency is $85\%$

c$)$ Calculate energy storage efficiency