Froude number and flow regime
The Froude number compares inertial effects with gravity effects. It is central to free-surface flow classification and dynamic similarity for hydraulic models.
The characteristic length must match the application. In open-channel work, hydraulic depth is commonly used; other problems may use water depth, vessel length, or another defined scale.
How to use the Froude number calculator
- Choose the unknown: Select Froude number, velocity, or characteristic length.
- Define the length scale: Use the length definition appropriate to your hydraulic or similarity problem.
- Enter the known values: All input values must be positive for this magnitude-based equation.
- Interpret in context: Use the result with the geometry and flow assumptions of the application.
Formula and variables
The calculator uses standard gravity g = 9.80665 m/s² and solves for any one of Fr, v, or L.
Fr = v / √(gL)- Fr — Froude number
- Ratio of inertia to gravity effects (dimensionless)
- v — Velocity
- Representative flow speed (m/s)
- g — Gravity
- Standard gravitational acceleration (m/s²)
- L — Characteristic length
- Application-specific length scale (m)
One-meter characteristic depth
A flow travels at 3.13156 m/s with a characteristic length of 1 m.
- Velocity
- 3.13156 m/s
- Length
- 1 m
- Fr = 3.13156 / √(9.80665 × 1)
Result: Froude number is approximately 1.00.
With an appropriate open-channel length definition, this is near the critical condition.
Understanding your results
Open-channel interpretation
For the conventional open-channel definition, Fr indicates how surface disturbances relate to the flow.
- Fr < 1 is commonly described as subcritical flow.
- Fr = 1 is the ideal critical condition.
- Fr > 1 is commonly described as supercritical flow.
Assumptions
- Standard gravity is appropriate.
- Velocity and characteristic length are representative and consistently defined.
- The simple gravity-inertia scaling is appropriate to the problem.
Limitations
- Does not calculate hydraulic depth from channel geometry.
- Does not include viscosity, surface tension, compressibility, or channel-resistance effects.
- Flow classification can require a section-specific Froude definition in nonrectangular channels.
Common mistakes
- Using wetted depth when the required definition is hydraulic depth.
- Mixing feet and meters with metric gravity.
- Treating Fr = 1 as an exact field threshold despite measurement uncertainty and nonuniformity.
- Using a length scale that does not match the compared model or prototype.
Practical use cases
Open-channel screening
Classify flow after selecting the correct hydraulic length.
Physical model similarity
Compare gravity-dominated behavior between geometrically similar systems.
Frequently asked questions
What length should I use?
Use the length specified by the governing formulation. Hydraulic depth is common for open-channel cross sections, while other applications use different scales.
What does a Froude number of 1 mean?
In the ideal open-channel interpretation it represents critical flow, where flow velocity matches the relevant gravity-wave speed.
Is Froude number dimensionless?
Yes. Consistent units cancel in the ratio v/√(gL).
Sources and review
- Basic Hydraulic Principles of Open-Channel Flow — U.S. Geological Survey. Accessed 2026-07-13.
Reviewed 2026-07-13.