Question Bank • QB_SWCE_EXP_032 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Soil and Water Erosion

Subtopic: Gully control structures – drop, drop inlet and chute spillways

Question Statement:

A straight drop spillway with a rectangular weir crest of length $L = 3.5\text{ m}$ carries a design peak flood discharge under a total head of $0.80\text{ m}$. Using the standard broad-crested weir equation $Q = 1.77 L H^{3/2}$, the design discharge capacity in $\text{m}^3\text{/s}$ is ________ (round off to 2 decimal places).

Answer Key:

4.43

Step-by-Step Solution & Explanation

Weir discharge formula: $Q = 1.77 L H^{3/2}$ Given: • $L = 3.5\text{ m}$ • $H = 0.80\text{ m}$ $H^{3/2} = (0.80)^{1.5} = \sqrt{0.80^3} = \sqrt{0.512} \approx 0.71554$ $Q = 1.77 \times 3.5 \times 0.71554 = 6.195 \times 0.71554 \approx 4.433\text{ m}^3\text{/s} \approx 4.43\text{ m}^3\text{/s}$
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