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GATE 2021 CE (CE2) – Question 41

Hydraulics · Channel hydraulics: specific energy, critical flow, uniform flow, hydraulic jump · 2 marks · Multiple choice

A 6 m wide rectangular channel carries 20 m³/s. With g=9.81 m/s², find the depth at which specific energy is minimum.

  1. 0.82 m
  2. 1.04 m
  3. 2.56 m
  4. 3.18 m

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Show answer and explanation

Correct answer: (B) 1.04 m

Explanation

Specific energy is $E=y+q^2/(2gy^2)$ with q=Q/b. Setting dE/dy=0 gives critical depth $y_c=(q^2/g)^{1/3}=[(20/6)^2/9.81]^{1/3}=1.04239$ m. Hence **1.04 m (B)**.