Question

What will be the bed width and depth of flow for the most efficient trapezoidal section carrying the discharge of $10m^3/sec$? The channel slope and n-value are $5\times {10}^{-4}$ and 0.020. The side slope is 1.5H: 1V.

• A. 1.5 m, 2.5 m
• B. 1.25 m, 2.5 m
• C. 1.5 m, 2 m
• D. 1.25 m, 2 m

Answer 1

The correct option is D 1.25 m, 2 m

Let bed width and depth of flow be B and d respectively


For most efficient trapezoidal section

(i) $B+2md=2d\sqrt{1+m^2}$

$B+2\times 1.5d=2d\sqrt{1+(1.5{)}^2}$

B = 0.605d

(ii) $R=\frac{d}{2}$

Area of flow, A = Bd + 1.5$d^2$

$=2.105d^2$

$Q=\frac{1}{n}A{R}^{2/3}{S}^{1/2}$

$10=\frac{1}{0.020}\left(2.105d^2\right){\left(\frac{d}{2}\right)}^{2/3}(5\times {10}^{-4}{)}^{1/2}$

d = 2.05 m

$\therefore B=0.605\times 2.05=1.24m$