$($b$)$ A pipeline $1400m$ long supplies water to $4$ single jet Pelton wheels. The head above the nozzle is $400m.$ The velocity coefficient for the nozzle is $0\mathrm{.}98$ and the coefficient of friction for the pipeline is $0\mathrm{.}025.$ The turbine efficiency based on the head at the nozzle is $0\mathrm{.}85.$ The specific speed of each turbine is $18\mathrm{.}2($in $m,kW,$ r$.$p$.$m$,$ units$)$ and the head lost due to friction in the pipeline is $22m$ of water. If the operating speed of each turbine is $600$ r$.$p$.$m$.,$ determine:

$($i$)$ the total power developed.

$($ii$)$ volume of water used per second

$($iii$)$ the diameter of each nozzle.

$($iv$)$ the diameter of the pipeline.