Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Flow in open channels
Question Statement:
A hydraulically efficient trapezoidal drainage channel has to be designed for draining 400 ha of land with a drainage coefficient of 20 mm. If the recommended side slope and depth are 2:1 and 1.06 m respectively, the bottom width is
Options:
(A) 0.25 m
(B) 0.50 m
(C) 0.75 m
(D) 1.00 m
Official Answer Key:
B
Step-by-Step Solution & Explanation
For the most hydraulically efficient (min. wetted perimeter) trapezoidal section with side slope z (H:V = z:1): b = 2d(√(1+z²) − z). With z=2, d=1.06 m: b = 2(1.06)(√5 − 2) = 2.12×0.2361 = 0.50 m. (The 400 ha / 20 mm data determine the design discharge for a subsequent depth/velocity check, not the b–d relation itself.)
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