# Hydraulic Jump Calculator

URL: https://speedycalculator.com/calculators/physics/hydraulic-jump/
Last updated: 2026-10-30

> The hydraulic jump calculator finds the conjugate (downstream) depth, velocities, Froude numbers, energy loss, jump height, length and efficiency of a hydraulic jump in a rectangular channel.

## Inputs

- Channel width B (m, cm, mm, km, in, ft, yd, mi)
- Flow rate Q (m³/s, L/s, ft³/s)
- Upstream depth y₁ (m, cm, mm, km, in, ft, yd, mi)
- Gravitational acceleration g (m/s², ft/s², g, cm/s²)

## Results

- Upstream velocity v₁
- Upstream Froude number
- Downstream depth y₂
- Downstream velocity v₂
- Downstream Froude number
- Depth ratio y₂/y₁
- Head loss
- Jump length
- Jump height
- Efficiency E₂/E₁
- Jump type

## 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)
```

## Explanation

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

FieldWhat to enterChannel width BUnits: m, cm, mm, km, in, ft …Flow rate QUnits: m³/s, L/s, ft³/sUpstream depth y₁Units: m, cm, mm, km, in, ft …Gravitational acceleration gUnits: 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)2.55.51583.753.613552.66326.252.09377.51.7146101.242

## 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.

## FAQ

**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.


## Sources

- [Fluid Mechanics (F. M. White) – reference text](https://www.mheducation.com/highered/product/fluid-mechanics-white-chul/M9781260258318.html)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)