Question

A channel bed slope 0.0009 carries a discharge of $30m^3/s$ when the depth of flow is 1.0 m. What is the discharge carried by an exactly similar channel at the same depth of flow if the slope is decreased to 0.0001?

• A. $90m^3/s$
• B. $15m^3/s$
• C. $10m^3/s$
• D. $60m^3/s$

Answer 1

The correct option is C

$10m^3/s$

(a)
Exactly similar channel means that area and wetted perimeter are same i.e

$\frac{Q_2}{Q_1}=\sqrt{\frac{S_2}{S_1}}$

$\Rightarrow Q_2=\sqrt{\frac{0.0001}{0.0009}}\times 30=10m^3/s$