Question

In wide rectangular channel, an increase in the normal depth by 20% corresponds to how much (approximate) increase in discharge?

• A. 36%
• B. 12%
• C. 48%
• D. 20%

Answer 1

The correct option is A 36%

The Manning's equation for a wide rectangular channel is given as

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

$\text{Therefore, For same value of n, B and}{S}_0$
We get,

$Q\propto y^{5/3}$

$\Rightarrow \frac{Q_1}{Q_2}={\left(\frac{y_1}{y_2}\right)}^{5/3}$

$=\frac{100}{Q_2}={\left(\frac{100}{120}\right)}^{5/3}$

$\Rightarrow Q_2=\frac{100}{0.738}$

$\Rightarrow Q_2=136$

$\therefore$ Increase in discharge

$=Q_2-Q_1=136-100=36\%$