A Pelton wheel develops $8000$ kW under a net head of $130$ m at a speed of $200$ r$.$p$.$m$.$ Assuming the coefficient of velocity for the nozzle $0\mathrm{.}98,$ hydraulic efficiency $87,$ speed ratio $0\mathrm{.}46$ and jet diameter to

wheel diameter ratio

$,$ determine:

$($i$)$ the discharge required

$($ii$)$ the diameter of the wheel

$($iii$)$ the diameter of the jet and number of jets required

$($iv$)$ the specific speed and the type of the turbine

Assume Mechanical efficiency as $.$