Tutorial prob#$1$

A generator is driven by a small, single$-$jet Pelton turbine designed to have a power specific speed ${}_{sp}=,$ The effective head at nozzle inlet is $120$ m and the nozzle velocity coefficient is $0\mathrm{.}985.$ The runner rotates at $880$ rpm $,$ the turbine overall efficiency is $88\%,$ and the mechanical efficiency is $96\%.$ If the blade speed to jet speed ratio, $v=0\mathrm{.}47,$ determine: $($assume density of water, $={10}^{3}k\frac{g}{m^3})$

a$.$ the shaft power output of the turbine;

b$.$ the volume flow rate;

c$.$ the ratio of the wheel diameter to jet diameter.