When fast, shallow water meets slow, deep water it jumps up abruptly in a turbulent roller that dissipates energy. Engineers build stilling basins below spillways to force a jump and protect the riverbed.
How to use the Hydraulic Jump Calculator
- Channel width B
- Flow rate Q
- Upstream depth y₁
- Gravitational acceleration g
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the channel width, the flow rate and the upstream (supercritical) depth.
Inputs explained
| Field | What to enter |
|---|---|
| Channel width B | Units: m, cm, mm, km, in, ft … |
| Flow rate Q | Units: m³/s, L/s, ft³/s |
| Upstream depth y₁ | Units: m, cm, mm, km, in, ft … |
| Gravitational acceleration g | Units: m/s², ft/s², g, cm/s² |
What each result means
- Upstream velocity v₁ = [Flow rate Q]÷([Channel width B]×[Upstream depth y₁])
- Upstream Froude number = [Upstream velocity v₁]÷sqrt([Gravitational acceleration g]×[Upstream depth y₁])
- Downstream depth y₂ = [Upstream depth y₁]÷2×(sqrt(1 + 8×[Upstream Froude number]^2) – 1)
- Downstream velocity v₂ = [Flow rate Q]÷([Channel width B]×[Downstream depth y₂])
- Downstream Froude number = [Downstream velocity v₂]÷sqrt([Gravitational acceleration g]×[Downstream depth y₂])
- Depth ratio y₂/y₁ = [Downstream depth y₂]÷[Upstream depth y₁]
- Head loss = ([Downstream depth y₂] – [Upstream depth y₁])^3÷(4×[Upstream depth y₁]×[Downstream depth y₂])
- Jump length = 6.9×([Downstream depth y₂] – [Upstream depth y₁])
- Jump height = [Downstream depth y₂] – [Upstream depth y₁]
- Efficiency E₂/E₁ = ([Downstream depth y₂] + [Downstream velocity v₂]^2÷(2×[Gravitational acceleration g]))÷([Upstream depth y₁] + [Upstream velocity v₁]^2÷(2×[Gravitational acceleration g]))×100
Example values
How the main result changes when Channel width B changes and everything else stays at the example values above:
| Channel width B (m) | Downstream depth y₂ (m) |
|---|---|
| 2.5 | 5.5158 |
| 3.75 | 3.6135 |
| 5 | 2.6632 |
| 6.25 | 2.0937 |
| 7.5 | 1.7146 |
| 10 | 1.242 |
Formula
q = Q/B, v₁ = q/y₁, Fr₁ = v₁/√(gy₁), y₂ = (y₁/2)·(√(1 + 8Fr₁²) − 1)
ΔE = (y₂ − y₁)³/(4y₁y₂), L_j ≈ 6.9·(y₂ − y₁)
Worked example
Inputs — Channel width B: 5 m; Flow rate Q: 20 m³/s; Upstream depth y₁: 0.4 m; Gravitational acceleration g: 9.80665 m/s².
Results — Upstream velocity v₁ = 10 m/s; Upstream Froude number = 5.049; Downstream depth y₂ = 2.6632 m; Downstream velocity v₂ = 1.502 m/s; Downstream Froude number = 0.2939; Depth ratio y₂/y₁ = 6.6579; Head loss = 2.7204 m; Jump length = 15.6159 m; Jump height = 2.2632 m; Efficiency E₂/E₁ = 50.5255 %; Jump type = Steady jump.
Key terms
- Conjugate depths
- Depths before and after a hydraulic jump.
Frequently asked questions
When does a hydraulic jump form?
When supercritical flow (Fr > 1) meets subcritical flow downstream.
Why is energy lost?
Intense turbulence in the roller converts it to heat.
Which jump type is best for stilling basins?
A steady jump (Fr₁ ≈ 4.5–9).
Where can I see one?
In a kitchen sink where the water spreads out in a ring.