Question Bank • QB_SWCE_ERS_004 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 has a rectangular crest length $L = 4.0\text{ m}$. The design head over the weir crest is $H = 0.81\text{ m}$. Using the discharge formula $Q = 1.77 L H^{3/2}$, the peak design discharge conveyed through the structure in $\text{m}^3\text{/s}$ is ________ (round off to 2 decimal places).

Answer Key:

5.16

Step-by-Step Solution & Explanation

From the straight drop weir equation: $Q = 1.77 \cdot L \cdot H^{3/2}$ Given: • $L = 4.0\text{ m}$ • $H = 0.81\text{ m} \implies H^{3/2} = (0.81)^{1.5} = (0.9)^3 = 0.729$ $Q = 1.77 \times 4.0 \times 0.729 = 7.08 \times 0.729 = 5.16132\text{ m}^3\text{/s} \approx 5.16\text{ m}^3\text{/s}$
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