Froude Number Calculator
Calculate Froude number for open channel flow from velocity, depth, and gravity to classify subcritical and supercritical flow.
What Is the Froude Number?
The Froude number (Fr) is a dimensionless quantity that compares inertial forces to gravitational forces in open-channel and free-surface flow. It helps classify whether flow is subcritical (tranquil), critical, or supercritical (rapid). It is widely used in hydraulic engineering, ship design, and river modeling.
Froude Number Formula
Fr = V / √(g × L), where V is flow velocity, g is gravitational acceleration, and L is a characteristic length. For open channels, L is typically the hydraulic depth or flow depth. When Fr < 1, flow is subcritical; when Fr > 1, flow is supercritical; at Fr = 1, flow is critical.
Flow Classification
- Subcritical (Fr < 1): Disturbances propagate upstream. Depth is relatively large compared to velocity.
- Critical (Fr = 1): Minimum specific energy for a given discharge. Transition between regimes.
- Supercritical (Fr > 1): Rapid, shallow flow. Disturbances cannot propagate upstream.
Related tools: Flow Rate Calculator and Reynolds Number Calculator.
Frequently Asked Questions
What is critical velocity?
Critical velocity is V = √(gL), the speed at which Fr = 1. Below this speed flow is subcritical; above it, supercritical.
What length should I use for L?
For rectangular open channels, use the flow depth. For complex sections, use hydraulic depth A/T, where A is cross-sectional area and T is top width.
How is Froude number used in ship design?
Ship hulls are compared using Fr based on waterline length. High Fr indicates wave-making resistance dominates, which matters for speed and fuel efficiency.
Is Froude number the same as Reynolds number?
No. Reynolds number compares inertial to viscous forces. Froude number compares inertial to gravitational forces. Both are important but describe different physics.
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