Question Bank • QB_SWCE_ADV_001 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 carries a design peak discharge of $6\text{ m}^3/\text{s}$ through a rectangular weir crest of length $4\text{ m}$. The drop height from crest to apron floor is $2.5\text{ m}$. Using $g = 9.81\text{ m/s}^2$, the critical depth of flow $y_c$ over the spillway floor is ________ $\text{m}$ (round off to two decimal places).

Answer Key:

0.61

Step-by-Step Solution & Explanation

1. Discharge per unit width ($q$): $q = \frac{Q}{B} = \frac{6\text{ m}^3/\text{s}}{4\text{ m}} = 1.5\text{ m}^2/\text{s}$ 2. Critical depth for a rectangular channel: $y_c = \left( \frac{q^2}{g} \right)^{1/3} = \left( \frac{1.5^2}{9.81} \right)^{1/3} = \left( \frac{2.25}{9.81} \right)^{1/3} = (0.22936)^{0.3333} = 0.6121\text{ m} \approx 0.61\text{ m}$
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