Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
Two irrigation channels are designed in the same type of alluvial soil having the channel bed slopes of 1.52×10⁻⁴ and 1.6×10⁻⁴, respectively. If the design discharge of the first channel, using Lacey's regime theory, is 30 m³ s⁻¹, then the design discharge of the second channel in m³ s⁻¹ will be
Options:
(A) 22.05
(B) 29.74
(C) 30.26
(D) 40.81
Official Answer Key:
A
Step-by-Step Solution & Explanation
In Lacey's regime theory, for channels carrying the same silt (in the same alluvial soil, i.e. same silt factor f), the regime bed slope relates to discharge as S ∝ Q^(−1/6), i.e. Q ∝ S⁻⁶, or equivalently Q₂/Q₁ = (S₁/S₂)⁶.
Q₂ = Q₁×(S₁/S₂)⁶ = 30×(1.52×10⁻⁴/1.6×10⁻⁴)⁶ = 30×(0.95)⁶ = 30×0.7351 = 22.05 m³/s. Matches option (A) exactly.
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