Discussion
The correct conditions for which the hydraulically efficient rectangular channel will deliver maximum discharge are
P - depth of water is equal to half the breadth of channel
Q - depth of water is equal to breadth of channel
R - depth of water is equal to twice the breadth of channel
S - hydraulic radius is equal to half the depth of water
Answer: C
The conditions are P and S.
For a rectangular channel of breadth b and depth y, the most efficient section for a given area has the least wetted perimeter, \(P = b + 2y\). Minimising it with \(A = by\) fixed gives \(b = 2y\), so the depth equals half the breadth (P).
The hydraulic radius is then \(R = \frac{by}{b + 2y} = \frac{2y^{2}}{4y} = \frac{y}{2}\), half the depth (S).
Q (depth equal to breadth) and R (depth twice the breadth) give deeper, narrower sections with a larger wetted perimeter for the same area, so every option containing Q or R is wrong.
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