Hydraulic Jump Calculator
Analyzes hydraulic jump characteristics in open channel flow, including sequent depth, energy loss, and jump length. Used by hydraulic engineers designing spillways, stilling basins, and irrigation channels.
About this calculator
A hydraulic jump is an abrupt transition from supercritical (fast, shallow) to subcritical (slow, deep) open-channel flow, dissipating energy as turbulence. The upstream Froude number governs the jump: Fr₁ = V₁ / √(g × y₁), where V₁ is upstream velocity, g is gravitational acceleration, and y₁ is upstream depth. When Fr₁ > 1, a hydraulic jump forms. The sequent (downstream) depth is: y₂ = (y₁ / 2) × (−1 + √(1 + 8·Fr₁²)). Energy loss across the jump is: ΔE = (y₂ − y₁)³ / (4 × y₁ × y₂). Jump length is estimated empirically as: L ≈ 6 × (y₂ − y₁). These relationships allow engineers to size stilling basins that safely absorb excess energy below dams and weirs.
How to use
Suppose upstream velocity V₁ = 6 m/s, upstream depth y₁ = 0.5 m, and g = 9.81 m/s². 1. Froude number: Fr₁ = 6 / √(9.81 × 0.5) = 6 / 2.214 = 2.71 2. Sequent depth: y₂ = (0.5 / 2) × (−1 + √(1 + 8 × 2.71²)) = 0.25 × (−1 + √(58.79 + 1)) = 0.25 × (−1 + 7.73) = 1.68 m 3. Depth difference: Δy = 1.68 − 0.5 = 1.18 m 4. Energy loss: ΔE = (1.18)³ / (4 × 0.5 × 1.68) = 1.643 / 3.36 = 0.489 m 5. Jump length: L = 6 × 1.18 = 7.08 m
Frequently asked questions
What is a hydraulic jump and when does it occur in open channel flow?
A hydraulic jump is a sudden rise in water surface that occurs when supercritical flow (Froude number > 1) transitions to subcritical flow (Froude number < 1). It commonly occurs downstream of sluice gates, spillways, weirs, and steep chutes where fast-moving water meets slower conditions. The jump is accompanied by intense turbulence, surface rollers, and significant energy dissipation. Engineers deliberately induce hydraulic jumps in stilling basins to protect downstream channels from erosion caused by high-velocity flow. The location and intensity of the jump depend on the upstream Froude number and downstream water level (tailwater).
How does the Froude number determine the type and strength of a hydraulic jump?
The Froude number Fr₁ classifies hydraulic jumps into distinct types based on their intensity. For Fr₁ between 1.0 and 1.7, an undular or weak jump forms with little energy loss. Between 1.7 and 2.5, a weak jump with small rollers occurs. For Fr₁ from 2.5 to 4.5, an oscillating jump develops that can cause downstream wave problems. The most efficient and stable jump — the steady jump — occurs between Fr₁ of 4.5 and 9.0, dissipating 45–70% of energy. Above 9.0, a strong jump forms with up to 85% energy dissipation. Stilling basin design aims to achieve a steady jump within the basin for maximum energy absorption.
Why is energy loss in a hydraulic jump important for hydraulic structure design?
Energy dissipation is the primary purpose of an engineered hydraulic jump. Without controlled energy removal, high-velocity flow exiting a dam spillway or sluice gate can scour the downstream riverbed and undermine foundations. The energy loss formula ΔE = (y₂ − y₁)³ / (4 × y₁ × y₂) quantifies how much head is converted to turbulent heat within the jump. Knowing this value lets engineers confirm that the stilling basin is long enough and that tailwater depth is correctly set to anchor the jump. If too little energy is dissipated, protective riprap or additional dissipators must be added to prevent structural damage downstream.