$4.$ A trapezoidal channel has a bottom width, b$,$ of $5$ m and a side slope ratio of $2\mathrm{.}8$:$1.$ The Manning's n of the channel is $0\mathrm{.}03,$ and it is laid on a slope of $0\mathrm{.}002.$ If the channel ends in a free overfall, compute the water surface profile for a discharge of $40$ m$\%$ with excel spreadsheet for comparison. $(30$ points$)$