Section 4: Soil and Water Conservation Engineering
Open Channel Hydraulics & Manning Equation
Subtopic: Manning discharge in rectangular channel
Question Statement:
A rectangular lined open channel has a bed width of $2.0\text{ m}$, flow depth of $1.0\text{ m}$, bed slope $S_0 = 1/1000$, and Manning's roughness coefficient $n = 0.02$. The discharge capacity of the channel is ________ $\text{m}^3/\text{s}$ (round off to two decimal places).
Answer Key:
1.99
Step-by-Step Solution & Explanation
Flow area $A = b \times y = 2.0 \times 1.0 = 2.00\text{ m}^2$.
Wetted perimeter $P = b + 2y = 2.0 + 2(1.0) = 4.0\text{ m}$.
Hydraulic radius $R = \frac{A}{P} = \frac{2.00}{4.0} = 0.5000\text{ m}$.
Using Manning's equation:
$Q = \frac{1}{n} A R^{2/3} S_0^{1/2} = \frac{1}{0.02} \times 2.00 \times (0.5000)^{2/3} \times \sqrt{0.001} = 1.99\text{ m}^3/\text{s}$