Physics

Hydraulic Jump Calculator

Find the downstream depth after a hydraulic jump.

Upstream depth

Upstream velocity

Gravity (m/s²)

Calculated Output

Downstream depth 1.096

Upstream Froude number 2.915

Formula: y₂ = (y₁/2)·(√(1 + 8·Fr₁²) − 1)

Step-by-Step Breakdown

1. Values used:

2. Upstream depth = 0.3

3. Upstream velocity = 5

4. Gravity = 9.81 m/s²

6. Downstream depth = 1.096

7. Upstream Froude number = 2.915

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The math behind it

y₂ = (y₁/2)·(√(1 + 8·Fr₁²) − 1), where Fr₁ is the upstream Froude number. A jump occurs only when Fr₁ > 1.

0.3 m at 5 m/s (Fr ≈ 2.9) → downstream depth about 1.10 m.

Why does it form?

Supercritical flow must transition to subcritical, dissipating energy in turbulence.