GATE AG 2012 • Q20 MCQ • 1 Mark

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Flow in open channels

Question Statement:

A trapezoidal grassed waterway on a 4% longitudinal gradient has cross-sectional flow area 1.52 m², wetted perimeter 12.5 m, and Manning's n = 0.04 m⁻¹/³ s. The flow through the waterway, in m³/s, is:

Options:

  • (A) 1.9
  • (B) 2.1
  • (C) 2.3
  • (D) 2.5

Official Answer Key:

A

Step-by-Step Solution & Explanation

Hydraulic radius R = A/P = 1.52/12.5 = 0.1216 m. Manning's equation: V = (1/n) R^(2/3) S^(1/2) = (1/0.04)(0.1216)^0.667 (0.04)^0.5 = 25 × 0.2429 × 0.2 = 1.215 m/s. Q = V×A = 1.215 × 1.52 = 1.85 ≈ 1.9 m³/s. Answer: A.

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