Section $12\mathrm{.}4\mathrm{.}2$ Pump Performance Characteristics

$12\mathrm{.}11$ Water is pumped with a centrifugal pump, and measurements made on the pump indicate that for a flowrate of $240$ gpm the required input power is $6$ hp $.$ For a pump efficiency of $62\%,$ what is the actual head rise of the water being pumped?

$12\mathrm{.}10$ A centrifugal radial water pump has the dimensions shown in Fig. P$12\mathrm{.}10.$ The volume rate of flow is $0\mathrm{.}25f\frac{t^3}{s},$ and the absolute inlet velocity is directed radially outward. The angular velocity of the impeller is $960$ rpm $.$ The exit velocity as seen from a coordinate system attached to the impeller can be assumed to be tangent to the vane at its trailing edge. The hydraulic efficiency is $82\%$ and the mechanical efficiency is $96\%.$ Calculate the power required to drive the pump.