A $78\%$ efficient $12-$hp pump is pumping water from a lake to a nearby pool at a rate of $2f\frac{t^3}{s}$ through a constant$-$diameter pipe. The

free surface of the pool is $32$ ft above that of the lake. Determine the irreversible head loss of the piping system, in ft $,$ and the

mechanical power used to overcome it$.$ Take the density of water to be $62\mathrm{.}4lb\frac{m}{f}{t}^3.$

The irreversible head loss of the piping system is

ft$.$

The mechanical power used to overcome the head loss is

hp$.$