Question Bank • QB_SWCE_002 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Flow in open channels

Question Statement:

Water flows uniformly at a depth of $1.5\text{ m}$ in a rectangular concrete channel of width $4.0\text{ m}$ on a bed slope of $0.0016$. Manning's roughness coefficient $n = 0.015$. The discharge through the channel in $\text{m}^3\text{/s}$ is ________ (round off to 2 decimal places).

Answer Key:

19.38

Step-by-Step Solution & Explanation

1. Flow cross-sectional area $A$: $A = B \times y = 4.0 \times 1.5 = 6.0\text{ m}^2$ 2. Wetted perimeter $P$: $P = B + 2y = 4.0 + 2(1.5) = 7.0\text{ m}$ 3. Hydraulic radius $R$: $R = \frac{A}{P} = \frac{6.0}{7.0} = 0.8571\text{ m}$ 4. Bed slope $S_0 = 0.0016 \implies \sqrt{S_0} = 0.04$ 5. Discharge via Manning's equation: $Q = \frac{1}{n} A R^{2/3} S_0^{1/2} = \frac{1}{0.015} \times 6.0 \times (0.8571)^{2/3} \times 0.04$ $(0.8571)^{2/3} \approx 0.9023$ $Q = 400 \times 6.0 \times 0.9023 \times 0.04 = 2400 \times 0.04 \times 0.9023 = 19.38\text{ m}^3\text{/s}$
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