$(35$ points$)$ The pump in the figure below delivers water at $3\frac{f{t}^3}{s}$ from a very large reservoir $($standard atmospheric pressure$)$ to a machine located $20$ ft higher than the reservoir surface and operating at a vacuum pressure of $4\mathrm{.}7$ psi $.$ The piping system loses are given by $h_L=\frac{V^2}{2g},$ where $=7\mathrm{.}5($dimensionless$).$ Assuming a kinetic correction factor of $=1\mathrm{.}07$ and $3$ in pipe diameter, find the horsepower required to drive the pump if its efficiency is $80\%.$

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