Question Bank • QB_SWCE_FM_009 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Flow in open channels

Question Statement:

A most hydraulically efficient rectangular open channel has a flow depth $y = 1.0\text{ m}$ (so bottom width $B = 2y = 2.0\text{ m}$ and hydraulic radius $R = y/2 = 0.50\text{ m}$). The longitudinal bed slope is $S_0 = 0.0009$ and Manning's roughness coefficient is $n = 0.015$. The uniform discharge conveyed by the channel in $\text{m}^3\text{/s}$ is ________ (round off to 2 decimal places).

Answer Key:

2.52

Step-by-Step Solution & Explanation

1. Wetted area $A = B \times y = 2.0 \times 1.0 = 2.0\text{ m}^2$ 2. Hydraulic radius $R = 0.50\text{ m} \implies R^{2/3} = (0.50)^{2/3} \approx 0.62996$ 3. Bed slope $S_0 = 0.0009 \implies \sqrt{S_0} = 0.03$ 4. Using Manning's formula: $Q = \frac{1}{n} A R^{2/3} S_0^{1/2} = \frac{1}{0.015} \times 2.0 \times 0.62996 \times 0.03$ $Q = \frac{0.06}{0.015} \times 0.62996 = 4.0 \times 0.62996 = 2.5198\text{ m}^3\text{/s} \approx 2.52\text{ m}^3\text{/s}$
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