Question $2(7$ points$)$

Assuming the conduit in the figure is a trapezoidal designed rock excavated open channel with bottom width of $5\text{'}$ and side slopes of $4\mathrm{.}5\text{'}$ horizontal to $2\mathrm{.}5\text{'}$ vertical, and that the flow carried must be the same as in Question $1$:

a$)$ Determine the critical depth of the flow.

b$)$ Determine the normal depth of flow based on Manning's equation.

c$)$ If we place a $65V-$notch weir at the left side of the reservoir, with the bottom of the notch $71\text{'}$ above the invert, what will be the discharge over the weir?

d$)$ Determine the size and character of the hydraulic jump occurring at the gate. $($Assume the initial depth is the depth emerging from the gate.$)$