$($c$)$ A rectangular channel with a bottom width of $4$ m and a bottom slop of $0\mathrm{.}0008$ has a discharge of $1\mathrm{.}5\frac{m^3}{sec}.$ Compute the backwater profile created by a dam which backs up the water to a depth of $5$ ft $.$ immediately behind the dam. Given energy coefficient $=1\mathrm{.}10.$ Compute the flow profile of the prismatic channel.