Fig. P$3\mathrm{.}11$ Hydroelectric installation.

$11.$ Hydroelectric installation $-M.$ Fig. P$3\mathrm{.}11$ shows a small hydroelectric installation. Water from the large mountain reservoir flows steadily through a steel pipe of $12-$in$.$ nominal diameter and effective length $1,500ft$ into a turbine. The water is ultimately discharged through a short length of $12-$in$.$ pipe to the atmosphere, where the elevation is $600$ ft below the surface of the reservoir.

If the water flow rate is $12\mathrm{.}5f\frac{t^3}{s},$ and the turbine$/$generator produces $425$ kW of useful electrical power, estimate the following:

$($a$)$ The efficiency of the turbine$/$generator combination.

$($b$)$ The pressure $($psig$)$ at the inlet to the turbine.

$($c$)$ The power $($ kW $)$ dissipated by pipe friction.

$($d$)$ The velocity gradient $(s^{-1})$ at the pipe wall.