Discussion
A 4 m wide by 2 m deep rectangular channel is flowing fully. The bed slope of the channel is 1 in 2500. If Chezy's constant is 50, what is the discharge through the channel?
Answer: D
Running full, the cross-sectional area is \(4 \times 2 = 8\) m\(^2\) and the wetted perimeter is \(4 + 2 + 2 = 8\) m, so the hydraulic mean depth is \(m = 1\) m. Chezy's formula gives the velocity
\[ \begin{aligned} V = C\sqrt{mS} = 50\sqrt{\tfrac{1}{2500}} \\ &= 1\ \text{m/s} \\ Q = AV = 8 \times 1 = 8\ \text{m}^3/\text{s} \end{aligned} \]The options 6, 10 and 12 m\(^3\)/s come from a wrong area or a wrong velocity, such as using the whole perimeter of 12 m.
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