Your Answer : (Not Answered)

Correct 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.

Your Answer : (Not Answered)

Correct 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.