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GATE 2018 CE (CE2) – Question 44

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

In a 5 m wide rectangular channel, vertical velocity distribution is $u=1.25y^{1/6}$, with y measured from the bed. At depth 2 m, discharge per unit width is ______.

  1. 2.40 m³/s/m
  2. 2.80 m³/s/m
  3. 3.27 m³/s/m
  4. 12.02 m³/s/m

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Show answer and explanation

Correct answer: (A) 2.40 m³/s/m

Explanation

Discharge per unit width is $$q=\int_0^2u\,dy=1.25\int_0^2y^{1/6}\,dy=1.25\frac67\,2^{7/6}=2.40528\ \mathrm{m^3/s/m}.$$ Closest choice: 2.40 (A). Multiplying by channel width would give total discharge.