A hydropower storage station $($i$.$e$.$ reservoir$)$ has a storage capacity of $6$x$106$ m$3,$ which can be

released for generating electricity over a $3-$hour period. If the effective head is $300$m$,$ and the

generator efficiency is $92\%,$

a$)$ Calculate the average power output and the total electrical energy produced in $3$ hours.

b$)$ The reservoir above is part of a pumped storage scheme. It takes $4\mathrm{.}5$ hours to refill the

reservoir. Because of frictional drag, the effective head when pumping is $320$m$.$ For pumps

having an energy efficiency of $87\%,$ calculate the input power to the pumps.