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GATE 2020 CE (CE1) – Question 46

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

A hydraulic jump occurs in a 6 m wide rectangular channel carrying 12 m³/s, with upstream depth 30 cm. Take g = 9.81 m/s² and water density 1000 kg/m³. Find the rate of energy loss.

  1. 114.2 kW
  2. 114.2 MW
  3. 141.2 hp
  4. 141.2 J/s

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Correct answer: (A) 114.2 kW

Explanation

Upstream velocity is $V_1=12/(6\cdot0.3)=6.6667$ m/s. Compute $Fr_1^2=V_1^2/(gy_1)$ and $y_2=y_1[\sqrt{1+8Fr_1^2}-1]/2\approx1.506$ m. Jump loss is $\Delta E=(y_2-y_1)^3/(4y_1y_2)\approx0.970$ m. Power lost is $\rho gQ\Delta E\approx114.2$ kW. **A**.