Question Bank • QB_SWCE_ERS_003 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Soil and Water Erosion

Subtopic: Vegetative waterways

Question Statement:

A parabolic grassed waterway is designed to carry a peak discharge $Q = 3.6\text{ m}^3\text{/s}$ at a maximum permissible velocity $v = 1.2\text{ m/s}$. The design central water depth is $y = 0.60\text{ m}$. For a parabolic cross-section where flow area is given by $A = \frac{2}{3} T y$ (with top width $T$), the required top width $T$ in metres is ________ (round off to 1 decimal place).

Answer Key:

7.5

Step-by-Step Solution & Explanation

1. Required cross-sectional flow area: $A = \frac{Q}{v} = \frac{3.6\text{ m}^3\text{/s}}{1.2\text{ m/s}} = 3.0\text{ m}^2$ 2. Geometry of parabolic section: $A = \frac{2}{3} T y$ $3.0 = \frac{2}{3} \times T \times 0.60 = 0.40 T$ $T = \frac{3.0}{0.40} = 7.5\text{ m}$
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