$(20$ points$)$ A trapezoidal channel has a bed width of $4ft$ and side slopes of $4$:$1.$ The

channel is paved with smooth cement surface with $n=0\mathrm{.}011.$ If the channel is laid on a

slope of $0\mathrm{.}001$ and carries a uniform flow of depth $1\mathrm{.}0ft,$ determine the discharge.