Froude Number Calculator
Compute Fr = v / √(g · L) — 3-way solver (Fr, velocity, characteristic length), flow regime classification, and ship vs open-channel context. 100% runs in your browser.
Formulas
Fr = v / √(g · L)
Fr is dimensionless: the ratio of inertial force to gravitational force in free-surface flow. The surface wave speed (which is also the critical speed) is c = √(g·L).
| Fr value | Regime | Meaning |
|---|
| Fr < 1 | Subcritical | Tranquil flow; disturbances can travel upstream |
| Fr = 1 | Critical | Minimum specific energy; hydraulic control condition |
| Fr > 1 | Supercritical | Rapid flow; disturbances swept downstream |
Scope limits vs other calculators
This tool is a dedicated Froude number calculator with a 3-way solver (Fr ↔ v ↔ L), regime classification, and ship (LWL) plus open-channel (hydraulic depth) context interpretation. The open-channel-flow (#444) calculator computes the Froude number as part of Manning flow analysis (normal/critical depth of rectangular, trapezoidal, triangular, circular sections) — it does not solve Fr from v & L in general, has no inverse mode, and does not cover ship context. Use this tool when you want purely the Froude number; use #444 when analyzing channel sections with the Manning equation.
Frequently asked questions
What is the Froude number?
The Froude number (Fr) is a dimensionless number comparing inertial force to gravitational force in free-surface flow. Its formula is Fr = v / √(g · L), where v is flow velocity, g is gravitational acceleration, and L is the characteristic length. This value determines the flow regime: subcritical, critical, or supercritical.
How do you compute the Froude number? Example?
Divide velocity by the square root of g times the characteristic length: Fr = v / √(g · L). Ship example: LWL 10 m, speed 5 m/s, g = 9.80665 m/s² → Fr = 5 / √(9.80665 × 10) ≈ 0.5049. Since Fr < 1, the flow is subcritical.
What do Fr < 1, Fr = 1, and Fr > 1 mean?
Fr < 1 means subcritical (tranquil) flow: surface waves can travel upstream against the current. Fr = 1 means critical: minimum specific energy and the hydraulic control point. Fr > 1 means supercritical (rapid) flow: disturbances are swept downstream, and the transition back to subcritical forms a hydraulic jump.
What is the characteristic length L for a ship?
For a ship, L is the waterline length (LWL), the length of hull submerged in water. This is the length scale controlling bow wave formation. A ship with LWL 10 m sailing at 5 m/s produces Fr ≈ 0.5049.
What is the characteristic length L for an open channel?
For an open channel, L is the hydraulic depth: wetted cross-sectional area divided by free-surface width (L = A / T). For a wide rectangular section, hydraulic depth equals water depth. Example: hydraulic depth 0.8 m at 1.5 m/s → Fr ≈ 0.5355 (subcritical).
How do you compute velocity from the Froude number?
Invert the formula: v = Fr × √(g · L). Example: target Fr = 0.8 with L = 10 m → v = 0.8 × √(9.80665 × 10) ≈ 7.9223 m/s. The "Compute v" mode on the calculator above does it automatically, including knot, km/h, and ft/s unit conversion.
How do you compute characteristic length from Fr and v?
Use L = (v / Fr)² / g. Example: v = 8 m/s with target Fr = 1.2 → L = (8 / 1.2)² / 9.80665 ≈ 4.5321 m. The "Compute L" mode on the calculator above solves it directly.
How does the Froude number relate to a ship’s hull speed?
Hull speed — the speed at which wave resistance rises sharply — occurs around Fr ≈ 0.4. For LWL 10 m: v = 0.4 × √(9.80665 × 10) ≈ 3.9611 m/s (≈ 7.70 knots). Above Fr ≈ 0.4 a displacement ship needs enormous power; planing hulls are designed to punch through to Fr > 1.
What units does this calculator support?
Velocity: m/s, km/h, knot, ft/s, mph. Length: m, cm, mm, km, ft, in. Gravity: 9.80665 m/s² (SI standard), 32.174 ft/s² (US customary), or a custom value — e.g. Moon or Mars gravity for other-planet case studies. The Froude number itself is dimensionless, so it is consistent across all unit systems.
How does this tool differ from the open-channel-flow calculator?
This tool focuses purely on the Froude number: 3-way solver (Fr, v, L), regime classification, and ship plus channel context. The open-channel-flow calculator computes the Froude number only as one output of Manning analysis for specific channel sections. Choose this tool for the Fr itself; choose open-channel-flow for channel section design.
Free tool by NRTechStudio