Hydraulic Jump Calculator

About the Hydraulic Jump Calculator

A hydraulic jump occurs when supercritical flow (Fr > 1) rapidly transitions to subcritical flow (Fr < 1). The jump is an extremely turbulent, energy-dissipating phenomenon used in stilling basins downstream of spillways, weirs, and sluice gates to protect channel beds from erosion.

This calculator applies the momentum equation to compute the downstream (sequent) depth y₂ from the upstream depth y₁ and velocity V₁. For rectangular channels, the classic Bélanger equation gives y₂/y₁ = ½(√(1 + 8Fr₁²) − 1). The calculator also extends to trapezoidal, triangular, and circular cross-sections.

Key outputs include the Froude numbers before and after the jump, energy loss, jump type classification (undular, weak, oscillating, steady, or strong), estimated jump length, roller length, and the power dissipated. These values are commonly used to size stilling basins and check whether downstream structures can tolerate the remaining energy. They also help you judge whether a jump is likely to form where you expect or whether tailwater conditions will shift or drown it out.

When This Page Helps

Use this calculator to estimate sequent depth, jump length, and energy dissipation before committing to a basin layout or checking whether tailwater conditions can hold the jump in place. It is most useful as a first-pass design check for spillways, gates, and channels where uncontrolled supercritical flow could otherwise damage the downstream bed or structure.

How to Use the Inputs

1. Select the channel cross-section shape (rectangular, trapezoidal, triangular, or circular).
2. Enter the upstream (supercritical) depth y₁ in meters.
3. Enter the upstream velocity V₁ in m/s.
4. Enter the channel width (bottom width for trapezoidal, top width for others).
5. For trapezoidal or triangular shapes, enter the side slope z (horizontal:vertical).
6. Click a preset for common scenarios like spillway basins or irrigation canals.
7. Read the sequent depth, energy loss, jump type, and power dissipated.

Example Calculation

Tips & Best Practices

• For USBR stilling basin design, use the Type II basin for Fr₁ = 4.5–9 and Type III for Fr₁ = 2.5–4.5.
• Jump efficiency improves with higher Fr₁ — but so does structural loading and air entrainment.
• Air entrainment in strong jumps can cause cavitation damage to concrete surfaces; use aeration ramps.
• In practice, measure Fr₁ from the flow depth and discharge, not from velocity (which is hard to measure in shallow supercritical flow).
• A submerged jump (tailwater above y₂) loses less energy. Unsubmerged jumps are more effective dissipators.

Interpreting The Jump

The upstream Froude number largely determines the kind of jump you should expect. Weak and undular jumps dissipate little energy, while steady and strong jumps create the turbulence that designers rely on in stilling basins. If the flow lands in the oscillating range, the jump can be unstable and hard to control.

Design Use

A sequent-depth calculation is only the start. In practice you still need to compare the predicted downstream depth with available tailwater, basin geometry, appurtenances such as chute blocks or end sills, and scour protection downstream. The calculator is best used as a screening and concept-design tool.

Common Failure Modes

The most common mistakes are using velocity where discharge-based section properties are needed, assuming the rectangular formula applies to every section, and ignoring submergence. If tailwater is too high, the jump can drown out and dissipate less energy than the free-jump estimate suggests.

Frequently Asked Questions

• What happens if Fr₁ ≤ 1?

  No hydraulic jump forms — the flow is already subcritical. A jump requires supercritical approach flow (Fr > 1). The calculator will flag this condition.

• What are the jump types?

  Fr < 1.7: undular (standing waves, little dissipation). 1.7–2.5: weak jump. 2.5–4.5: oscillating (unstable, avoid in design). 4.5–9: steady (most efficient for stilling). > 9: strong (very turbulent, rough surface).

• How long is a hydraulic jump?

  Empirically, L_j ≈ 6.1 × y₂ for a free jump in a rectangular channel. This is an estimate — USBR and other agencies publish refined curves by Froude number.

• Where does the jump occur?

  The jump positions itself where downstream conditions force the flow depth to match the sequent depth. In design, sill blocks and end sills in stilling basins help anchor the jump location.

• How much energy is dissipated?

  Energy loss increases dramatically with Fr₁. At Fr₁ = 3, about 25% of energy is lost. At Fr₁ = 9, roughly 70% is dissipated. At Fr₁ = 20, over 85% is consumed by turbulence.

• Does channel shape matter?

  Yes. Non-rectangular channels have different momentum balances. The Bélanger equation is exact only for rectangular sections. For trapezoidal channels, iterative or graphical solutions are needed.