A multi$-$nozzle Pelton wheel develops $60,000$ hp at $400$ rpm under a

head of $1,400$ ft$.$ How many nozzles should this turbine have if the

maximum efficiency for a single$-$nozzle occurs when the turbine specific

speed is $18?$ Find the wheel diameter if the peripheral velocity factor is $0\mathrm{.}45$ at maximum efficiency? $.$ If the velocity coefficient is $0\mathrm{.}96$ with a wheel$-$jet diameter ratio of $11\mathrm{.}5$ then, calculate the efficiency?

The answers are $6$ nozzles, $1\mathrm{.}966$ m$,$ and $90\mathrm{.}27\%$ respectively pls prove this