Table of Contents
What Is the Froude Number?
The Froude number is a dimensionless number comparing the flow inertia to the gravitational effects. Named after William Froude, it is critical in hydraulic engineering, naval architecture, and open channel flow analysis. It determines whether gravity waves can travel upstream against the flow.
When Fr < 1 (subcritical flow), disturbances can propagate upstream. When Fr > 1 (supercritical flow), the flow moves faster than gravity waves, and upstream conditions cannot influence the downstream flow. The transition at Fr = 1 is critical flow, analogous to the sound barrier in aerodynamics.
Formula
Where v is flow velocity, g is gravitational acceleration, and L is the characteristic length (water depth for open channels, waterline length for ships).
Flow Regime Classification
| Froude Number | Regime | Characteristics |
|---|---|---|
| Fr < 1 | Subcritical | Slow, deep, tranquil flow |
| Fr = 1 | Critical | Unstable transitional state |
| Fr > 1 | Supercritical | Fast, shallow, shooting flow |
Frequently Asked Questions
How is the Froude number used in ship design?
In naval architecture, the Froude number based on waterline length determines wave-making resistance. Ships operating near Fr = 0.4-0.5 create maximum wave drag. Ship model testing uses Froude scaling to ensure wave patterns in scale models match full-size vessels, which requires matching the Froude number between model and prototype.
What is a hydraulic jump?
A hydraulic jump occurs when supercritical flow transitions to subcritical flow. Energy is dissipated as turbulence. This is visible below dam spillways and weirs, where fast shallow water abruptly becomes slow deep water with significant turbulence and air entrainment.