Question

A trapezoidal channel having side slope 1.5H : 1V carries 2 cumecs of water, for most efficient channel, the bed width and depth of flow respectively are: (Take n = 0.012 and s = 2×${10}^{-4}$)

• A. 0.70m, 1.1m
• B. 0.70m, 1.0m
• C. 0.65m, 1.1m
• D. 0.65m, 1.0m

Answer 1

The correct option is A 0.70m, 1.1m


When side slope is fixed, then for most efficient trapezodial channel,
Top width = 2 × (length of side slope)

$\Rightarrow B+2my=2y\sqrt{1+m^2}$

$B+(2\times 1.5)y=2y\sqrt{1+{\left(1.5\right)}^2}$

$B=0.605y$

Area of flow,

$A=By+1.5y^2$

$=2.105y^2$

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

$2=\frac{2.105y^2}{0.012}{\left(\frac{y}{2}\right)}^{2/3}{(2\times {10}^{-4})}^{1/2}$

$\Rightarrow y=1.1m$

$\therefore B=(0.605\times 1.1)=0.6655m\approx 0.7m$