Problem XIV$-2$

A Pelton wheel is required to generate $3,750kW$ under an effective head of $400$ m $.$ Find the total volumetric flow rate, wheel diameter and jet diameter, if the generator and turbine efficiencies are $95\%$ and $80\%,$ respectively. Let $C_v=0\mathrm{.}97$ and speed ratio of $0\mathrm{.}46.$ If the wheel$-$jet diameter ratio is $10,$ determine the synchronous speed and number of poles at $60$ Hz $.$