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GATE 2025 CE (CE2) – Question 42

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

Consider flow in a long and very wide rectangular open channel. Width of the channel can be considered as infinity compared to the depth of flow. Uniform flow depth is 1.0 m. The bed slope of the channel is 0.0001. The Manning roughness coefficient value is 0.02. Acceleration due to gravity, g can be taken as 9.81 m/s$^2$.
The critical depth (in m) corresponding to the flow rate resulting from the above conditions is ______ (round off to one decimal place).

  1. 0.4
  2. 0.3
  3. 0.6
  4. 0.1

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Correct answer: (B) 0.3

Explanation

For a very wide channel the hydraulic radius is the depth, so the discharge per unit width is $q = \frac{1}{n}y^{5/3}S^{1/2} = \frac{1}{0.02} \times 1 \times 0.01 = 0.5$ m²/s. The critical depth is $y_c = \left(\frac{q^2}{g}\right)^{1/3} = \left(\frac{0.25}{9.81}\right)^{1/3} = 0.294 \approx 0.3$ m.