Engineering calculator reviewed for preliminary design use · Last updated: March 2026
Calculate Froude number Fr = v/√(gL). Fr < 1 indicates subcritical (tranquil) flow; Fr > 1 indicates supercritical flow. Apply to open channel flow, tank drainage, and two-phase flow design.
What this calculator is used for
The Froude number is a dimensionless parameter that compares inertial forces to gravitational
forces in a flowing fluid. It is essential for analyzing open-channel flows, free-surface
hydraulics, and vertical or inclined two-phase systems where gravity effects are significant.
Typical engineering use cases
Open channel and spillway design in hydraulic engineering
Flow regime assessment in vertical gas-liquid systems
Slug flow risk screening in multiphase pipelines
Free-surface stability evaluation in tanks and channels
Ship and marine structure design
Governing equation and methodology
The Froude number is defined as:
Fr = v / √(g · L)
Where L is a characteristic length such as hydraulic depth or pipe diameter.
Engineering assumptions and limitations
Gravity-dominated flow conditions
Appropriate selection of characteristic length
Does not predict detailed multiphase flow patterns
Practical design notes
When Fr < 1, gravity effects dominate and flow disturbances can propagate upstream
(subcritical flow). When Fr > 1, inertia dominates and the flow is supercritical.
For complete flow characterization, evaluate Froude number together with Reynolds number.
Result: Fr ≈ 0.68 — below 1, so the flow is subcritical (tranquil).
Interpretation: Subcritical means disturbances travel upstream and the surface is controlled by downstream conditions — important for sizing overflow weirs and gravity drain headers. As Fr approaches 1 expect a hydraulic jump or surface instability, so keep gravity lines comfortably below critical.
Common Mistakes & Misuse
Picking the characteristic length L inconsistently — hydraulic depth, diameter, or impeller diameter give different Fr, and the regime threshold only applies to the matching definition.
Using the plain Froude number for gas–liquid systems where a densimetric Froude (with the density ratio) is the meaningful group.
Reading Fr = 1 as a numeric curiosity rather than the critical condition where a hydraulic jump or flow-regime change can occur.
Applying open-channel subcritical/supercritical logic to fully pressurised pipe flow, where Froude is not the controlling parameter.
Frequently Asked Questions
What does the Froude number tell us?
Fr = v/√(gL) compares inertia to gravity. Fr < 1 means gravity dominates (subcritical / tranquil flow). Fr > 1 means inertia dominates (supercritical / rapid flow). Fr = 1 is the critical condition.
Where is Froude number used in practice?
Open channel design, weir flow, tank drainage, ship hull design, mixing vessel surface vortex evaluation, and two-phase flow regime determination. In process engineering, it helps assess free-surface flow behavior.
For preliminary estimation and educational use only. Results may depend strongly on assumptions, input data, fluid or material properties, and the range of validity of the underlying equation. Verify critical calculations independently and follow the applicable code, specification, and formal engineering review process before using any result for design, procurement, fabrication, operation, or safety decisions.