A trapezoidal channel has a bottom width, $\backslash ($ b $\backslash ),$ of $8$ m and a sideslope of $\backslash (2$: $1\backslash )$ and carry a discharge of $\backslash (3\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$sec$\}\backslash ).$ The manning's $\backslash ($ n $\backslash )$ of the channel is $0\mathrm{.}025,$ and it is laid on a slope of $0\mathrm{.}001.$ If the channel ends in a free overfall,

$1.$ Compute and draw the water surface profile.

$2.$ Would the water surface profile change if the manning's n is reduced to half $($i$.$e$.,0\mathrm{.}0125,$ representing sand bed$)?$ Describe the change and explain why?

$3.$ In which case $($a$)$ or $($b$),$ the flow will have higher capacity to erode channel bed. Discuss your results.