Froude Number Calculator

The Froude number compares inertial to gravitational forces in a flow.

How the Math Works

The Froude Number (Fr) is calculated using the formula Fr = v ÷ √(g·L), where v is the flow velocity, g is gravitational acceleration (typically 9.81 m/s²), and L is a characteristic length such as channel depth or ship length. This dimensionless quantity compares inertial forces to gravitational forces in fluid flow, determining whether the flow is subcritical (Fr < 1), critical (Fr = 1), or supercritical (Fr > 1). The square root of g·L represents the gravitational velocity head, which quantifies how gravity influences the flow's kinetic energy.

Practical Applications

Engineers use the Froude Number to analyze open-channel flows in rivers, canals, or spillways, ensuring structures like dams or weirs operate safely. For ship design, it predicts wave-making resistance and hull speed limits, helping optimize propulsion efficiency. Coastal engineers also apply it to assess wave interactions with breakwaters or harbor entrances, preventing excessive erosion or storm damage through precise flow modeling.

Day-to-Day Use

Understanding the Froude Number impacts daily life by improving water management systems that supply cities with clean water or prevent floods. It ensures ships travel efficiently and safely by minimizing drag and fuel use. Additionally, it aids in designing recreational facilities like swimming pools or theme park water rides, where controlling water flow dynamics enhances safety and user experience.

Worked example

3 m/s over 1 m depth → Fr ≈ 0.96 (just subcritical).

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