Method and variables
This calculator uses Fr = V/√(gD), where V is mean flow velocity, g is gravitational acceleration and D is hydraulic depth. Hydraulic depth is the flow area divided by the free-surface top width.
Worked example
With mean velocity V = 2 m/s, hydraulic depth D = 1 m and g = 9.80665 m/s², Fr = 2/√(9.80665 × 1) ≈ 0.639. That is subcritical open-channel flow.
How to read the result
For the standard open-channel interpretation, Fr < 1 is subcritical (tranquil), Fr = 1 is critical and Fr > 1 is supercritical (rapid). This compares mean flow with shallow-water wave celerity; it is not a turbulence classification.
Important limits
Use the hydraulic depth appropriate to the cross section and the same representative reach for velocity and depth. This simple screening form does not capture nonuniform velocity, rapidly varied flow, hydraulic jumps, nonhydrostatic effects, sediment transport, air entrainment or a complex channel/structure geometry. Do not apply its open-channel regime label to a fully pressurized pipe.
References
- U.S. FHWA: Froude number and open-channel flow regimes
- U.S. Army Corps of Engineers: hydraulic depth and Froude-number interpretation
Related tools
Reynolds Number Calculator · Pipe Flow Rate & Velocity Calculator · Dimensionless Numbers Calculators
Frequently asked questions
What does Froude number indicate in open-channel flow?
It compares mean flow speed with shallow-water wave speed. In the usual open-channel interpretation, Fr below 1 is subcritical, Fr equal to 1 is critical and Fr above 1 is supercritical.
What depth should I enter?
Use hydraulic depth, cross-sectional flow area divided by free-surface top width. For a wide rectangular channel, it is approximately the water depth.
Can I use this for a pressurized pipe?
Not for the usual open-channel regime interpretation. A full pipe has no free surface, so use pipe-flow, Reynolds-number and pressure-loss tools instead.