Question Bank • QB_SWCE_ADV_147 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 constructed in a stabilized gully has a rectangular weir crest length of $L = 5.0\text{ m}$ and carries a design peak flood discharge of $Q = 8.0\text{ m}^3/\text{s}$. The vertical drop from crest to horizontal apron floor is $Y = 3.0\text{ m}$. Taking $g = 9.81\text{ m/s}^2$, the critical depth of flow $y_c$ over the crest in meters is ________ (round off to two decimal places). ``` Headwater ──┐ Crest (Weir length L = 5 m) │ Drop Height Y = 3 m │ │ └────────────┴───── Apron Floor (Stilling basin) Apron Length La ```

Answer Key:

0.64

Step-by-Step Solution & Explanation

**Method 1: Critical Depth Formulation** 1. Discharge per unit crest length ($q$): $q = \frac{Q}{L} = \frac{8.0\text{ m}^3/\text{s}}{5.0\text{ m}} = 1.60\text{ m}^2/\text{s}$ 2. Critical depth in a rectangular cross-section: $y_c = \left( \frac{q^2}{g} \right)^{1/3} = \left( \frac{(1.60)^2}{9.81} \right)^{1/3} = \left( \frac{2.56}{9.81} \right)^{1/3} = (0.260958)^{1/3} = 0.63899\text{ m} \approx 0.64\text{ m}$ **Method 2: Verification of Unit Critical Energy** $E_c = 1.5 y_c = 1.5 \times 0.639 = 0.9585\text{ m}$ $V_c = \sqrt{g y_c} = \sqrt{9.81 \times 0.639} = 2.5037\text{ m/s}$ $q = y_c V_c = 0.639 \times 2.5037 = 1.60\text{ m}^2/\text{s}$
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