$4\mathrm{.}41.$ Consider the flow conditions in the concrete channel shown in Figure $4\mathrm{.}30,$ where the flow rate in the channel is $16\frac{m^3}{s}.$ The bottom width of the channel is to be contracted at a short distance downstream of the section shown in Figure $4\mathrm{.}30.($a$)$ State the equations that must be satisfied in order for choking to occur at the downstream section; simplify your equations as much as possible. $($b$)$ Will the flow be choked at the downstream section when the bottom width of the channel is reduced to zero? What is the depth of flow in the downstream section under this condition?

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Chapter $4.$ Fundamentals of Flow in Open Channels

Figure $4\mathrm{.}30$: Flow in pre$-$contracted section