An $80-$percent$-$efficient pump with a power input of $36\mathrm{.}00hp$ is pumping water from a lake to a nearby pool at a rate of $1\mathrm{.}5f\frac{t^3}{s}$ through a constant$-$diameter pipe. The free surface of the pool is $80ft$ above that of the lake. Determine the mechanical power used to overcome frictional effects in piping.

We take the density of water to be $=62\mathrm{.}4lb\frac{m}{f}{t}^3.$

The mechanical power used to overcome frictional effects in piping is hp$.$