The sequent depth ratio for hydraulic jump occurring in horizontal, frictionless and rectangular channel is given by (where, y1 and y2 are pre-jump and post-jump depth respectively and F1 is Froude’s Number of incoming flow)
- Ay2/y1 = (−1 + √(1 + 8F1²))
- By2/y1 = ½ (−1 + √(1 + F1²))
- Cy2/y1 = ¼ (−1 + √(1 + 8F1²))
- Dy2/y1 = ½ (−1 + √(1 + 8F1²))Correct
Solution
Concept
Belanger momentum equation
Formula
y₂ / y₁ = ½ [ −1 + √(1 + 8 F₁²) ]
Step-by-step solution
1. Apply the momentum equation (specific force) before and after the jump in a horizontal rectangular channel. 2. Solving the quadratic in y₂/y₁ gives y₂/y₁ = ½(√(1 + 8F₁²) − 1).
Explanation
The sequent depth ratio is obtained from the momentum principle. It is called the Belanger equation. The factor 8 and the factor ½ must both be present.
Shortcut
Belanger: ½(−1 + √(1 + 8F₁²)).
Common mistake
Forgetting the 8 or the ½.
Correct answer: D) y2/y1 = ½ (−1 + √(1 + 8F1²))