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Which is the most economical depth of flow in an open rectangular channel?
Question

Which is the most economical depth of flow in an open rectangular channel?

A.

Depth of flow equals to the width of channel

B.

Depth of flow is double the width of channel

C.

Depth of flow is half of the width of channel

D.

Depth of flow is 1/3rd the width of channel

Correct option is C

For a rectangular channel, the section is most efficient (economical) when:y=b2ory=2RThis means: The depth of flow = half the bottom width Or equivalently, depth = 2 × hydraulic radiusSo both of the following are true for the most economical rectangular channel: y=b2 y=2R\begin{aligned}&\text{For a rectangular channel, the section is most efficient (economical) when:} \\&\boxed{y = \frac{b}{2}} \quad \text{or} \quad \boxed{y = 2R} \\[1em]&\text{This means:} \\&\bullet \ \text{The \textbf{depth of flow} = half the bottom width} \\&\bullet \ \text{Or equivalently, \textbf{depth} = 2 × \textbf{hydraulic radius}} \\[1em]&\text{So both of the following are true for the most economical rectangular channel:} \\&\bullet \ y = \frac{b}{2} \\&\bullet \ y = 2R\end{aligned}​​

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