Question

What is the normal depth in a wide rectangular channel $0.5m^3/s$ discharge at a bed slope of 0.0004 and Manning's n = 0.01?

• A. 0.43 m
• B. 0.50 m
• C. 0.13 m
• D. 0.32 m

Answer 1

The correct option is A 0.43 m

For a wide rectangular channel, the hydraulic radius (R) is approximately equal to the depth of flow. By Manning's equation, we have

$Q=\frac{1}{n}A{R}^{2/3}{S}_0^{1/2}$

Here, A = By
R = y

$\therefore Q=\frac{1}{n}\times By\times y^{2/3}\times S_0^{1/2}$

$\Rightarrow \frac{Q}{B}=\frac{1}{n}\times y^{2/3}\times S_0^{1/2}$

$\Rightarrow q=\frac{1}{n}\times y^{5/3}\times S_0^{1/2}$

$\Rightarrow \frac{0.5\times 0.01}{{\left(0.0004\right)}^{1/2}}=y^{5/3}$

$\Rightarrow$ y = 0.43 m