$4.$ A concrete rectangular channel $\backslash (($n$=0\mathrm{.}015)\backslash )$ is $10$ m wide and carries a discharge of $50$ cms $.$ Additional channel details are given in the figure below.

$\backslash [$

$\_\{0\}=$U $.$ U $3$

$\backslash ]$

a$)($hand in on paper$)$ Determine the water surface profile classification upstream of where critical depth occurs $($e$.$g$.,$ M$-2,$ S$-1).$ Show your work.

b$)($hand in on paper$)$ Determine the water surface profile classification downstream of where critical depth occurs $($e$.$g$.,$ M$-2,$ S$-1).$ Show your work.

c$)($hand in on paper$)$ Sketch the water surface profile for the entire channel $($both the upstream and downstream portions$).$