Subtopic: Planning, design and layout of surface and sub-surface drainage systems
Question Statement:
A hydraulically efficient trapezoidal drainage channel with a side slope of 2:1 has been designed in a sandy loam soil for a catchment of 600 ha. Taking a drainage coefficient of 16 mm, the flow velocity in mm s⁻¹ in the drainage channel with a flow depth of 1 m is
Options:
(A) 427
(B) 450
(C) 497
(D) 527
Official Answer Key:
B
Step-by-Step Solution & Explanation
Design discharge Q = drainage coefficient × catchment area (as a daily depth-volume, converted to steady flow) = 0.016 m × 600×10,000 m² /86,400 s = 96,000 m³/day / 86,400 s/day = 1.111 m³/s. For a hydraulically most-efficient trapezoidal section with side slope z=2 (H:V), the optimum bed width b = 2y(√(1+z²) − z) = 2(1)(√5−2) = 0.472 m. Flow area A = (b + zy)y = (0.472 + 2×1)×1 = 2.472 m². Velocity V = Q/A = 1.111/2.472 = 0.4495 m/s = 449.5 mm/s ≈ 450 mm/s, matching option (B).
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