What is the Froude number?

The Froude number (Fr) is a dimensionless ratio of inertial forces to gravitational forces in a free-surface flow: Fr = V / √(g · D), where V is mean velocity, g is gravitational acceleration, and D is hydraulic depth.

What is hydraulic depth?

Hydraulic depth (D) equals the cross-sectional flow area divided by the top water-surface width (A / T). For a rectangular channel it equals the water depth directly.

What do subcritical, critical, and supercritical mean?

Subcritical flow (Fr 1) is rapid; disturbances cannot travel upstream and a hydraulic jump may form downstream.

When does a hydraulic jump occur?

A hydraulic jump forms when supercritical flow (Fr > 1) transitions to subcritical flow, dissipating kinetic energy as turbulence. The jump location depends on downstream channel conditions.

Is the Froude number the same as the Mach number?

They are analogous — the Mach number does the same job in compressible gas dynamics (speed vs. sound speed) as the Froude number does in open-channel hydraulics (speed vs. gravity-wave speed). Both equal 1 at critical conditions.

Froude Number Calculator

Enter flow velocity and hydraulic depth to compute the Froude number and instantly classify the flow regime.

Flow Parameters

Unit System

Mean Flow Velocity (m/s)

Average velocity across the channel cross-section

Hydraulic Depth D (m)

For rectangular channels: water depth. In general: A / T (area / top width)

Flow Regime Reference

Fr < 1 Subcritical tranquil / slow

Fr = 1 Critical minimum energy

Fr > 1 Supercritical rapid / shooting

Enter velocity and depth, then click Calculate

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Summary

Enter flow velocity and hydraulic depth to compute the Froude number and instantly classify the flow regime.

How it works

Enter the mean flow velocity in the channel (m/s or ft/s).
Enter the hydraulic depth — cross-sectional area divided by top width (m or ft).
Select your unit system (SI or Imperial).
The calculator applies Fr = V / √(g · D) and displays the result.
A color-coded badge shows the flow regime: subcritical (Fr < 1), critical (Fr = 1), or supercritical (Fr > 1).

Use cases

Classify open-channel flow for hydraulic engineering design.
Check whether a river or spillway section operates below or above critical depth.
Determine the likelihood of a hydraulic jump forming downstream.
Validate physical model similarity in Froude-scaled laboratory flume tests.
Support dam and weir overflow analysis.
Solve undergraduate fluid mechanics and hydraulics coursework problems.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu