$($c$)$ A rectangular channel $15m$ wide and $20km$ long has a slope of ${10}^{-4}$ and connects two lakes. The water depths at the upstream and downstream ends of the channel are $2\mathrm{.}0m$ and $1\mathrm{.}5$ ni respectively. Find the discharge in the channel assuming Manning' $N=00,015$ using varied flow function.