Discussion
In a rectangular channel of width 4 m and depth 2 m, water is running full. The bed slope is 1 in 3600. Find the velocity of the flow of water if Chezy's constant C = 60.
Answer: A
The channel is running full, so the area is 4 x 2 = 8 m\(^2\) and the wetted perimeter is 4 + 2 + 2 = 8 m (the free surface is not part of it). The hydraulic mean depth is \(m = A/P = 8/8 = 1\) m. By Chezy's formula:
\[ \begin{aligned} V = C\sqrt{mS} \\ &= 60\sqrt{1 \times \tfrac{1}{3600}} \\ &= 60 \times \tfrac{1}{60} = 1\ \text{m/s} \end{aligned} \]The velocities of 2, 3 and 4 m/s would result from using too large a hydraulic mean depth, for example taking the whole perimeter as only the bed width.
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