Hydraulic Jump Calculator
Calculate hydraulic jump sequent depths, Froude number, and energy loss in open channel flow.
What Is a Hydraulic Jump?
A hydraulic jump is a sudden rise in water depth when supercritical flow transitions to subcritical flow. It dissipates kinetic energy as turbulence and is common below spillways, sluice gates, and channel drops. Civil engineers use jump calculations to size stilling basins and protect downstream channels from scour.
Froude Number and Sequent Depth
The upstream Froude number for a rectangular channel is:
$$Fr = \frac{v}{\sqrt{g \cdot y_1}}$$The sequent depth ratio for a horizontal, rectangular channel is:
$$\frac{y_2}{y_1} = \frac{1}{2}\left(\sqrt{1 + 8 Fr^2} - 1\right)$$A Froude number above 1 indicates supercritical flow. When \(Fr > 1\), a hydraulic jump can form and the downstream sequent depth \(y_2\) is greater than the upstream depth \(y_1\).
Related tools: Hydraulic Gradient Calculator, Hydraulic Radius Calculator, and Hydrostatic Pressure Calculator.
Frequently Asked Questions
When does a hydraulic jump occur?
A jump forms when fast, shallow supercritical flow (Fr greater than 1) meets slower, deeper subcritical conditions. Energy is lost as turbulence at the jump face.
What is sequent depth?
Sequent depth is the conjugate downstream depth paired with a given upstream depth for the same discharge in a horizontal rectangular channel. It satisfies momentum conservation across the jump.
Can I use flow rate instead of velocity?
Yes. For a rectangular channel, velocity equals flow rate divided by the product of depth and width: \(v = Q / (y_1 \times b)\). Enter discharge and channel width and the calculator derives velocity.
Does this apply to circular pipes?
The standard sequent depth formula assumes a horizontal rectangular channel. For other cross sections, use the hydraulic depth in the Froude number and consult section-specific conjugate depth relations.
What Froude number triggers a strong jump?
Weak jumps appear near Fr = 1 to 1.7. Oscillating and steady jumps occur up to about Fr = 9. Very high Froude numbers produce strong, air-entraining jumps with significant energy loss.
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