$(15$ marks$)$ Consider a rectangular channel with a constant bed elevation $($horizontal$).$ The flow

rate through the channel is steady state at $18$ m$3/$s$.$

The upstream end of the channel has a width of $6$ m and a flow depth of $2$ m$.$ It passes through a

gradual contraction to a channel width of $4$ m$.$

a$)(9$ marks$)$ Neglecting head losses, does the contraction cause the flow to choke? If flow

does not choke, what is the minimum width to ensure flow does not choke?

b$)(4$ marks$)$ Neglecting head losses, what is the depth in the narrow section downstream?

For this question do not use a cubic equation solver. You are to determine which grouping of

depth solutions below satisfies the cubic equation produced by the energy equation.

You must show that the depth chosen satisfies your cubic equation when choosing the

appropriate depth $($negative$,$ supercritical, or subcritical$).$ If you do not show that the depth

satisfies the energy equation you will not get marks for choosing correctly.

Downstream depth, y$2($m$)$

Option $1-0\mathrm{.}30760\mathrm{.}36172\mathrm{.}0610$

Option $2-0\mathrm{.}31000\mathrm{.}36622\mathrm{.}0202$

Option $3-0\mathrm{.}61490\mathrm{.}93541\mathrm{.}7945$

Option $4-0\mathrm{.}61880\mathrm{.}96261\mathrm{.}7326$

c$)(2$ marks$)$ Draw a sketch of the Specific Energy Diagram, showing the points on the

diagram associated with both upstream and downstream locations. The plot does not have

to be to scale or contain the actual values of E$,$ y$,$ or q$.$ This sketch it just to show the relative

change in E$,$ y$,$ and q $($as applicable$)$ across the transition.