Froude Number

What is this formula?

The Froude Number is a dimensionless parameter that compares inertial forces to gravitational forces in free-surface flow.

It is one of the most important numbers in open-channel hydraulics because it determines whether flow is subcritical, critical, or supercritical.

When to use it

Use this formula when analyzing:

- Rivers

- Irrigation canals

- Spillways

- Stormwater channels

- Hydraulic structures

Flow classification:

Fr < 1 → Subcritical flow

Fr = 1 → Critical flow

Fr > 1 → Supercritical flow

Example

A rectangular channel carries water with:

v = 3.0 m/s

Dh = 1.2 m

g = 9.81 m/s²

Formula:

Fr = v/√(gDh)

Substitution:

Fr = 3.0/√(9.81×1.2)

Fr = 0.875

Result:

Fr ≈ 0.88

The flow is subcritical.

Applications

- Open-channel hydraulics

- River engineering

- Spillway design

- Hydraulic jumps

- Flood analysis

- Scale-model studies

Note

The Froude Number is particularly important for flows with a free surface where gravity strongly influences fluid motion. Different hydraulic texts may use hydraulic depth, flow depth, or another characteristic length depending on the geometry and application. For open-channel flow, hydraulic depth is generally the preferred parameter.