Froude Number Calculator

Compare flow inertia with gravity and determine whether open-channel flow is subcritical, critical, or supercritical.

🌊 Open-Channel Flow📐 Fr = v/√(gL)🚢 Similarity

Fr = v√(gL)

FrFroude numberdimensionless

vmean flow velocitym/s

ggravitational accelerationm/s²

Lcharacteristic length or hydraulic depthm

Velocity v (m/s)

Characteristic length L (m)

Gravity g (m/s²)

Enter valid positive values in every field.

Froude number Fr

What the Formula Means

Froude number measures the ratio of characteristic flow speed to the speed of gravity waves. It is central to rivers, spillways, canals, hydraulic jumps, ship wakes, and free-surface model testing.

For open-channel flow, Fr < 1 is subcritical: gravity waves can travel upstream. Fr > 1 is supercritical: the flow outruns upstream-moving disturbances. Fr = 1 marks critical flow. The correct characteristic length depends on the problem; hydraulic depth is commonly used for non-rectangular channels.

Formula Reference

Quantity	Equation	Meaning
Froude number	Fr = v/√(gL)	dimensionless
Critical velocity	v_c = √(gL)	Fr = 1
Characteristic length	L = v²/(gFr²)	m

Worked Examples

Canal flow

v = 2 m/s, hydraulic depth L = 0.5 m: Fr = 2/√(9.81×0.5) = 0.903.

✓ Subcritical flow

Fast shallow chute

v = 5 m/s, L = 0.25 m: Fr = 5/√(9.81×0.25) = 3.19.

✓ Supercritical flow

Assumptions and Common Mistakes

Choose the correct characteristic length. In open channels this is often hydraulic depth A/T, not necessarily geometric depth.

Do not use pipe-flow Reynolds thresholds. Fr classifies gravity-wave behavior, not laminar versus turbulent flow.

Similarity may require several dimensionless groups. Matching Froude number alone does not automatically match viscous effects.

Connected Formulas

companion dimensionless group →Reynolds Number uses mean velocity from →Flow Rate uses gravitational acceleration from →Free Fall

Frequently Asked Questions

What does Froude number compare?▾

It compares inertial effects with gravitational effects in free-surface flow.

What does Fr less than 1 mean?▾

Subcritical flow: surface disturbances can propagate upstream as well as downstream.

What does Fr greater than 1 mean?▾

Supercritical flow: disturbances cannot travel upstream against the flow.

What is critical flow?▾

Critical flow occurs at Fr = 1, the boundary between subcritical and supercritical behavior.

Is Froude number the same as Reynolds number?▾

No. Reynolds number compares inertia with viscosity; Froude number compares inertia with gravity. Both may matter in model testing.