Understanding the Froude Number
The Froude number (Fr) is a dimensionless quantity used in fluid mechanics to compare the inertial force of a moving fluid or vessel to the force of gravity. It is named after the English naval engineer William Froude, who developed it in the 1860s to predict the resistance of ship hulls from scale-model tests. The formula is Fr = v / √(g·L), where v is the flow (or vessel) velocity, g is gravitational acceleration, and L is a characteristic length such as water depth, channel hydraulic depth, or waterline hull length. Because Fr is dimensionless, it lets engineers compare flows of very different sizes — a lab model and a full-scale river or ship — on equal footing.
How the calculation works
The calculator first converts your velocity and length inputs into consistent SI units (meters per second and meters). It then computes the critical wave velocity, c = √(g·L) — the speed at which a small gravity wave (a ripple or surface disturbance) travels across that depth or length. Dividing the actual flow velocity by this wave speed gives the Froude number: Fr = v / c. When Fr = 1, the flow velocity exactly equals the wave speed, which is the critical condition that separates the two flow regimes below.
Interpreting the flow regime
When Fr < 1, the flow is subcritical (or "tranquil"): gravity dominates, the flow moves slower than a surface wave, and disturbances can propagate upstream — this describes most navigable rivers, canals, and slow-moving channels. When Fr > 1, the flow is supercritical (or "rapid" / "shooting"): inertia dominates, the flow outruns its own waves, and disturbances cannot travel upstream — this describes water shooting down a spillway, a steep mountain stream, or flow just before a hydraulic jump. At Fr = 1 the flow is critical, a boundary condition that is inherently unstable in open channels.
Common uses and limitations
Naval architects use the Froude number to scale hull-resistance tests: a displacement hull's practical top speed ("hull speed") corresponds to roughly Fr ≈ 0.4 based on waterline length, beyond which wave-making drag rises sharply. Hydraulic engineers use it to design spillways, culverts, stilling basins, and to locate hydraulic jumps in open-channel flow. The main limitation is choosing the right characteristic length — hydraulic depth for channels, waterline length for ships — an inconsistent choice makes the result meaningless for comparison. The Froude number also does not account for viscous effects (that's the role of the Reynolds number) or surface-tension effects (the Weber number), so it should be paired with those where relevant.