Discussion
A trapezoidal channel carries 5 m3.s−1 of water under uniform flow condition. The channel has a bottom width of 2 m, side slope of 2:1 (horizontal: vertical), and a bed slope of 1%. If the Manning roughness coefficient is 0.03, the conveyance of the channel, in m3.s−1, is
Answer: D
The conveyance is 50 m3.s−1.
Conveyance \(K\) is defined through Manning's equation as \(Q = K\sqrt{S_{0}}\), where \(K = \frac{1}{n} A R^{2/3}\) collects everything that depends on the section. Under uniform flow the discharge and bed slope are known, so
\[ \begin{aligned} K &= \frac{Q}{\sqrt{S_{0}}} = \frac{5}{\sqrt{0.01}} \\ &= \frac{5}{0.1} = 50 \end{aligned} \]
The bottom width, side slope and Manning's \(n\) are not needed for this step. 5 is the discharge itself, as if the slope term were 1, and 2 is the bottom width; neither 2 nor 15 follows from dividing the discharge by the square root of the slope.
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