Hydraulic Jump Calculator

Calculate the downstream depth after a hydraulic jump: y2 = (y1/2) * (sqrt(1 + 8*Fr1^2) - 1), where Fr1 is the upstream Froude number.

m
m/s

Upstream Froude Number

2.2580

Downstream Depth (y2)1.3661 m
Energy Head Loss0.2378 m

Upstream Froude Number vs Upstream Depth (y1)

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Formule

## Hydraulic Jump A hydraulic jump occurs when supercritical flow (fast, shallow) abruptly transitions to subcritical flow (slow, deep). ### Downstream Depth **y2 = (y1/2) * [sqrt(1 + 8 Fr1^2) - 1]** where Fr1 = v1 / sqrt(g y1) is the upstream Froude number (must be > 1 for a jump to occur). Energy is dissipated in the turbulent roller, making hydraulic jumps useful for energy dissipation in spillways.

Exemple Résolu

y1 = 0.5 m, v1 = 5 m/s.

  1. 01Fr1 = 5 / sqrt(9.807 * 0.5) = 5 / 2.214 = 2.259
  2. 02y2 = (0.5/2) * (sqrt(1 + 8*5.103) - 1)
  3. 03y2 = 0.25 * (sqrt(41.82) - 1)
  4. 04y2 = 0.25 * (6.467 - 1) = 1.367 m