Multiple choice

Water emerges from an ogee spillway with velocity = 13.72 m/s and depth = 0.3 m at its toe. The tail water depth required to form a hydraulic jump at the toe is

  1. 6.48 m

  2. 5.24 m

  3. 3.24 m

  4. 2.24 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the hydraulic jump formula: y2 = (-y1 / 2) + sqrt((y1^2 / 4) + (2 * v1^2 * y1 / g)). Given v1 = 13.72, y1 = 0.3, g = 9.81. Froude number Fr = 13.72 / sqrt(9.81 * 0.3) = 13.72 / 1.716 = 7.99. y2 = 0.3/2 * (sqrt(1 + 8 * 7.99^2) - 1) = 0.15 * (sqrt(1 + 510.7) - 1) = 0.15 * (22.6 - 1) = 3.24 m.

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