Conditions at the inlet to the nozzle of a Pelton wheel are \(p=700 \mathrm{psig}\) and \(V=15 \mathrm{mph}\). The jet diameter is \(d=7.5 \mathrm{in}\). and the nozzle loss coefficient is \(K_{\text {nozle }}=0.04\). The wheel diameter is \(D=8 \mathrm{ft}\). At this operating condition, \(\eta=0.86\). Calculate

(a) the power output,

(b) the normal operating speed,

(c) the approximate runaway speed,

(d) the torque at normal operating speed, 

(e) the approximate torque at zero speed.