Question

The flow rate in a wide rectangular open channel is 2.0 $m^3/s$ per metre width. The channel bed slope is 0.002. Manning's roughness coefficient is 0.012. The slope of the channel is classified as

• A. Steep
• B. Horizontal
• C. Mild
• D. Critical

Answer 1

The correct option is A Steep

The critical depth for a rectangular channel is given by

$y_c={\left(\frac{q^2}{g}\right)}^{1/3}={\left(\frac{(2{)}^2}{9.81}\right)}^{1/3}=0.74m$

Using Manning's equation, we get

$q=\frac{1}{n}(y_n{)}^{5/3}\sqrt{S}$

$\Rightarrow q=\frac{1}{0.012}\times (Y_n{)}^{5/3}\times \sqrt{0.002}$

$=y_n=0.69m$

$Forsteepslopes{y}_n<y_c$.