Hydraulic Jump Calculator
Enter the upstream depth and Froude number to compute the conjugate (sequent) downstream depth of a hydraulic jump.
Input Data
Results
At a glance:A hydraulic jump is the rapid transition from supercritical (Fr>1) to subcritical (Fr<1) open-channel flow, marked by a roller and turbulence. Momentum (specific force) conservation across the jump links the upstream depth y₁ and Froude number Fr₁ to the sequent (conjugate) downstream depth y₂ via y₂/y₁ = ½·(√(1+8·Fr₁²) − 1). The Froude number Fr = v/√(g·y) measures inertial vs gravity forces. This relation lets engineers size stilling basins: a jump from Fr₁=4.5 raises y₁ to about 6·y₁, dissipating large energy. The jump only forms for Fr₁ > 1; for Fr₁ < 1 the flow is already subcritical and no jump occurs.
Formula
Conjugate depth: y₂ = y₁·½·(√(1+8·Fr₁²) − 1)
Froude: Fr = v/√(g·y)
$$y_2 = \dfrac{y_1}{2}\left(\sqrt{1 + 8\,Fr_1^{2}} - 1\right)$$How to Use
- Enter the upstream depth y₁ (m).
- Enter the upstream Froude number Fr₁.
- The calculator returns the conjugate depth y₂.
Case Studies
Dam stilling basin
y₁ = 0.5 m, Fr₁ = 4.5.
y₂ = 0.5×½(√(1+8×20.25)−1) ≈ 3.0 m.
Jump raises depth 6× and dissipates energy safely.
FAQ
What is the Froude number here?
Fr = v/√(g·y), the ratio of inertial to gravity forces in open-channel flow. Fr>1 supercritical (fast/shallow), Fr<1 subcritical (slow/deep). A jump requires Fr₁>1.
Why design for a hydraulic jump?
It dissipates excess kinetic energy safely, preventing erosion below dams and spillways; stilling basins force the jump where it can be contained.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.