Question

In a river, discharge is $173{\text{m}}^3/\text{s}$; water surface slope is 1 in 6000; and stage at the gauge station is $10.0m$. If during a flood, the stage at the gauge station is same and the water surface slope is 1 in 2000, the flood discharge in ${\text{m}}^3/\text{s}$, is approximately

• A. 371
• B. 100
• C. 519
• D. 300

Answer 1

The correct option is D 300

Using Manning's equation
$Q=\frac{1}{n}A{R}^{\frac{2}{3}}{S}^{\frac{1}{2}}$

Given, stage is same in both cases
$Q\propto \sqrt{S}$
$\frac{Q_1}{Q_2}=\sqrt{\frac{S_1}{S_2}}$
$\frac{173}{Q_2}=\sqrt{\frac{\frac{1}{6000}}{\frac{1}{2000}}}$
$Q_2=300{\text{m}}^3/\text{s}$