Irrigation Water Conveyance and Application Methods
Subtopic: Design of irrigation channels and underground pipelines
Question Statement:
A regime channel carrying 25 m³/s is designed using Lacey's regime theory. Side slope ½H:1V, Lacey's silt factor f = 1. The bottom width and depth of flow, in m, respectively are:
Options:
(A) 20.26, 1.38
(B) 20.26, 1.56
(C) 23.75, 1.56
(D) 32.78, 1.56
Official Answer Key:
B
Step-by-Step Solution & Explanation
Lacey's regime equations (f=1): Velocity V = [Qf²/140]^(1/6) = [25×1/140]^(1/6) = (0.1786)^(1/6) = 0.749 m/s. Regime area A = Q/V = 25/0.749 = 33.38 m². Hydraulic radius R = (5/2)(V²/f) = 2.5×0.749²/1 = 1.402 m. Perimeter P = 4.75√Q = 4.75×5 = 23.75 m. Using A = (b + 0.5d)d = 33.38 and P = b + d√(1+0.25²)... solving with trapezoidal side slope ½H:1V simultaneously with P≈23.75 and A≈33.38 gives depth d ≈ 1.56 m and bed width b ≈ 20.26 m. Answer: B.
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