Civil Engineering > GATE 2026 SET-1 > Open Channel Flow
For a hydraulic jump formed in a rectangular horizontal channel, the sequent depth ratio is 2. The Froude number of supercritical stream is
Correct : a
The sequent depth ratio for a hydraulic jump in a rectangular horizontal channel is given by the Belanger equation: y₂/y₁ = (1/2)[√(1 + 8Fr₁²) − 1], where Fr₁ is the Froude number of the incoming supercritical stream.
Substituting y₂/y₁ = 2:
2 = (1/2)[√(1 + 8Fr₁²) − 1]
4 = √(1 + 8Fr₁²) − 1
√(1 + 8Fr₁²) = 5
1 + 8Fr₁² = 25
Fr₁² = 3
Fr₁ = √3
This confirms the flow is supercritical (Fr₁ > 1) before the jump and subcritical after, which is consistent with how a hydraulic jump forms — a rapid transition from supercritical to subcritical flow with energy dissipation.
Correct answer: A — √3 ✓
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