GATE AG 2015 • Q18 NAT • 1 Mark

Section 3: Farm Power

Farm Power

Subtopic: Thermodynamic principles of I.C. engines

Question Statement:

A steady discharge of 60 m³ s⁻¹ is passing through a trapezoidal irrigation channel with a bottom width of 5 m, bed slope of 0.01% and Manning's roughness coefficient of 0.025. The conveyance of the channel in m³ s⁻¹ is _____.

Official Answer Key:

6000

Step-by-Step Solution & Explanation

By definition, the conveyance K of a channel section relates discharge and bed slope through Q = K·√S₀, i.e. K = Q/√S₀ — this relation does not require the individual channel geometry (area, hydraulic radius) once Q and S₀ are known. S₀ = 0.01% = 0.0001. K = Q/√S₀ = 60/√0.0001 = 60/0.01 = 6000 m³/s. Matches the official key exactly.

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