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GATE 2022 CE (CE2) – Question 47

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

Water flows in a horizontal frictionless rectangular channel over a smooth hump whose height increases until choking. Depth on hump is y₂, upstream depth y₁. Which statements apply?

  1. In choked condition, 1y decreases if the flow is supercritical and increases if the flow is subcritical.
  2. In choked condition, 2y is equal to the critical depth if the flow is supercritical or subcritical.
  3. In unchoked condition, 1y remains unaffected when the flow is supercritical or subcritical.
  4. In choked condition, 1y increases if the flow is supercritical and decreases if the flow is subcritical.

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Show answer and explanation

Correct answer: (A) In choked condition, 1y decreases if the flow is supercritical and increases if the flow is subcritical.; (B) In choked condition, 2y is equal to the critical depth if the flow is supercritical or subcritical.; (C) In unchoked condition, 1y remains unaffected when the flow is supercritical or subcritical.

Explanation

Before choking, the hump changes local depth without changing the prescribed upstream state, so C holds. At choking, the hump section reaches minimum specific energy and is critical, so B holds.

Further hump increase requires larger upstream specific energy. On the subcritical branch this raises y₁; on the supercritical branch it lowers y₁. Thus A is true and D reverses the changes. **Answer: A,B,C**.