GATE AG 2012 • Q40 MCQ • 2 Marks

Section 5: Irrigation and Drainage Engineering

Irrigation Water Conveyance and Application Methods

Subtopic: Design of irrigation channels and underground pipelines

Question Statement:

A trapezoidal canal with bottom width 5.0 m and side slope 1H:1V carries a discharge of 20 m³/s. The critical depth, in m, is:

Options:

  • (A) 1.09
  • (B) 1.18
  • (C) 2.12
  • (D) 2.62

Official Answer Key:

A

Step-by-Step Solution & Explanation

Critical flow condition: Q²T/(gA³) = 1, where for trapezoidal section with b=5, side slope 1:1: A = (b+d)d = (5+d)d, T = b+2d = 5+2d. Trial d=1.09: A=(6.09)(1.09)=6.638 m², T=5+2.18=7.18 m. Check Q²T/(gA³) = 400×7.18/(9.81×292.4) = 2872/2868 ≈ 1.0 ✓. Answer: A (d_c ≈ 1.09 m).

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