Froude Number Calculator

Froude Number - Perform scientific calculations with precision and accuracy.

Froude Number Calculator

Froude Number Calculator

Analyze open channel flow regimes and ship hydrodynamics

m/s
m
m/s²

Calculate the ratio of inertial to gravitational forces

What is the Froude Number?

The Froude number ($Fr$) is a dimensionless number defined as the ratio of the flow inertia to the external field (the latter in many applications simply being gravity).

Fr = v / √(gL)

In Open Channel Flow, it predicts whether flow is tranquil (subcritical) or rapid (supercritical). A hydraulic jump occurs when flow transitions from supercritical to subcritical.

In Ship Hydrodynamics, it is used to compare the wave-making resistance between hulls of various sizes and speeds.

Regimes

  • Fr < 1 (Subcritical)Slow flow. Waves can travel upstream. Controlled from downstream.
  • Fr = 1 (Critical)Minimum energy state. Flow velocity equals wave velocity.
  • Fr > 1 (Supercritical)Fast flow. Waves cannot travel upstream. Controlled from upstream.

© 2026 Professional Physics Tools | Hydraulics

Froude Number Calculator Guide

Understanding the Froude Number

The Froude number (Fr) is a dimensionless quantity used in fluid dynamics to indicate the ratio of inertial forces to gravitational forces. It is particularly important in analyzing open-channel flow, wave motion, and the behavior of ships.

Understanding the Froude number helps engineers and scientists predict how fluids will behave under different conditions, especially when gravity significantly influences the flow. For example, it's used to design efficient ship hulls, analyze river flows, and model hydraulic structures.

Our Froude Number Calculator helps you determine the Froude number for a given flow condition, or to understand the relationship between flow velocity, characteristic length, and gravitational acceleration. This tool is invaluable for students, civil engineers, naval architects, and hydrologists.

Key Concepts in Froude Number

Flow Velocity (v)

The average velocity of the fluid flow.

Characteristic Length (L)

A relevant length scale of the flow, such as the depth of water in a channel or the length of a ship.

Gravitational Acceleration (g)

The acceleration due to gravity, approximately 9.81 m/s² on Earth.

Dimensionless Quantity

The Froude number has no units, making it useful for comparing different flow systems.

How the Froude Number Calculator Works

1

Input Flow Velocity

The user enters the velocity of the fluid flow.

2

Input Characteristic Length

The user enters the relevant length scale for the flow (e.g., water depth).

3

Calculate Froude Number

The calculator applies the formula: Fr = v / √(gL), where 'v' is flow velocity, 'g' is gravitational acceleration, and 'L' is characteristic length.

Flow Regimes Based on Froude Number

Subcritical Flow (Fr < 1)

Flow is slow and deep, dominated by gravitational forces. Waves can propagate upstream.

Critical Flow (Fr = 1)

Flow is at a transitional state where inertial and gravitational forces are balanced.

Supercritical Flow (Fr > 1)

Flow is fast and shallow, dominated by inertial forces. Waves cannot propagate upstream.

Hydraulic Jump

A phenomenon where supercritical flow transitions to subcritical flow, often with significant energy dissipation.

Frequently Asked Questions

QWhat is the difference between Froude number and Reynolds number?

A

The Froude number compares inertial forces to gravitational forces, important for free-surface flows. The Reynolds number compares inertial forces to viscous forces, important for determining flow regime (laminar vs. turbulent).

QWhy is the Froude number important in ship design?

A

The Froude number is used to predict wave-making resistance for ships. Ships operating at similar Froude numbers will have similar wave patterns, allowing for model testing to scale up to full-size vessels.

QHow does the Froude number relate to hydraulic jumps?

A

A hydraulic jump occurs when a supercritical flow (Fr > 1) transitions to a subcritical flow (Fr < 1). The Froude number is used to characterize the conditions before and after the jump.

QIs this calculator a substitute for understanding fluid mechanics?

A

No. This calculator is a tool to assist with calculations. A solid understanding of the underlying principles of fluid mechanics, open-channel flow, and wave phenomena is essential for correctly applying the concepts of the Froude number and interpreting the results.

Calculate Froude Number with Precision

Use our Froude Number Calculator to analyze open-channel flow, wave motion, and ship hydrodynamics.

Master the dynamics of free-surface flows.

Continue with calculators that answer nearby questions and help compare the next step.