$($c$)$ A hydro$-$electric plant is supplied water at the rate of $500$ litres in a second, under a head of $250$ metres through a pipeline which is $3\mathrm{.}2$ km long and $520$ mm diameter. The pipeline terminates in a nozzle, which has a diameter of $180$ mm $.$ Determine the power that can be transmitted, if Darcy's coefficient for the pipe materials is $0\mathrm{.}01.$

$(6$ mks $)$