Question

The sequent depth ratio of a hydraulic jump in a rectangular channel is 12. What would be the corresponding Froude number at the beginning of the jump?
1. 4.42
2. 8.84
3. 3.26
4. 9.54

Answer 1

Correct Answer - Option 2 : 8.84

Concept:

Relation between pre jump, post-jump and Froude number is given by,

\(\frac{{{y_2}}}{{{y_1}}} = \frac{1}{2}\left[ {\sqrt {1 + 8F_{r1}^2} - 1} \right] \)

Where,

y2 = Post jump depth

y1 = Pre-jump depth

F1 = Froude number before the jump

Calculation:

Given,

y₂/y₁ = 12

\(\frac{{{y_2}}}{{{y_1}}} = \frac{1}{2}\left[ {\sqrt {1 + 8F_{r1}^2} - 1} \right] = 12\)

 25² = 1 + 8 F_r²

∴ Fr1 = 8.831