Froude Number Calculator

Compute the Froude number from velocity and depth to classify flow as subcritical, critical, or supercritical.

What it does

The Froude number compares the speed of flowing water to the speed of a small wave on its surface. When water moves slowly, a ripple can travel upstream and warn the flow about what is ahead. When water moves faster than the wave speed, the ripple cannot climb back, and the flow behaves differently. That transition is what the Froude number measures.

The formula is simple: velocity divided by the square root of gravity times a length. The length is the hydraulic depth, which is the flow area divided by the top width. For a wide rectangular channel, the hydraulic depth is just the water depth. For a trapezoid, a circle, or a natural stream, it has to be computed from the cross section.

The three regimes have practical consequences. Subcritical flow is controlled from downstream, so a gate or a downstream constriction can back water up for a long distance. Supercritical flow is controlled from upstream and can form shocks and hydraulic jumps. Critical flow is the dividing line, and it is often the condition that sets the most efficient depth for a given discharge in a rectangular channel.

Froude similarity is also used in physical models. If a scale model has the same Froude number as the prototype, gravity waves and free-surface patterns scale correctly. That is why river and harbor models often match Froude number rather than Reynolds number. The model scale sets the velocity and time scales.

This page computes the Froude number, the wave speed, and the critical depth for the entered velocity. It is a point calculation for steady flow. It does not solve the water surface profile, and it does not replace a full open-channel design. Use it to classify a reach, check a model scale, or understand why a hydraulic jump forms.

How to use

1. Choose metric or imperial units.
2. Enter the mean velocity of the flow, not the velocity at the surface or the bed.
3. Enter the hydraulic depth. For a rectangular channel, use the water depth; for other shapes, divide area by top width.
4. Read the Froude number and the regime.
5. Compare the flow velocity with the gravity wave speed to see how close the reach is to critical.
6. Use the critical depth as a check, then run a full water surface profile for design work.

Formula

Fr

Froude number, dimensionless.

V

Mean flow velocity, in m/s or ft/s.

g

Gravity, 9.80665 m/s2 or 32.174 ft/s2.

L

Hydraulic depth, in m or ft, equal to flow area divided by top width.

For a rectangular channel, L equals the water depth. For a trapezoid or a natural section, compute L as area divided by top width at the water surface. Some texts use the maximum depth instead of the hydraulic depth, which gives a different number for non-rectangular sections. The regime labels use 0.99 and 1.01 as a small band around critical flow, because real measurements are never exact. The critical depth shown here is V squared divided by g, which applies to a rectangular channel with the same velocity.

Worked example

Reference table

Limits

• Assumes steady, uniform flow at a single cross section.
• Uses hydraulic depth, which must be computed correctly for non-rectangular sections.
• The critical depth shown is for a rectangular channel at the same velocity.
• Does not model waves, surges, or the water surface profile along a reach.

Common mistakes

• Using channel width instead of hydraulic depth for L.
• Mixing ft/s with meters, or m/s with feet.
• Using a surface velocity as the mean velocity.
• Forgetting that critical depth depends on unit discharge, not only on velocity.
• Treating the Froude number as a substitute for a full hydraulic design.

Try it yourself

Quick checks. Answers sit tucked under each question.

Questions

Sources

• USGS: Basic hydraulic principles of open-channel flow
• US Bureau of Reclamation: Froude number and critical flow
• University of Texas: Sub-critical and super-critical flow

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