Calculate the Froude number for open-channel flow, ship hull speed, and hydraulic engineering to determine subcritical or supercritical flow regimes.
The Froude number is a dimensionless number comparing the speed of a flow (or a body moving through fluid) to the speed of gravity waves on the surface. It is defined as Fr = V / √(gL), where V is the flow velocity, g is gravitational acceleration, and L is a characteristic length — typically the water depth for channels or the waterline length for ships.
When Fr < 1 the flow is subcritical (tranquil): surface waves can travel upstream, and the flow is deep and slow. When Fr > 1 the flow is supercritical (shooting): waves cannot propagate upstream, and the flow is fast and shallow. The transition at Fr = 1 is the critical condition, where hydraulic jumps can form.
This Froude Number Calculator serves both hydraulic engineers and naval architects. Enter a flow velocity and characteristic length to instantly determine the Froude number, flow regime, critical velocity, hull speed, and specific energy. The tool supports multiple velocity units and provides a color-coded scale for quick visual assessment. A reference table maps Froude number ranges to flow regimes and their physical descriptions.
Use this calculator to identify whether flow is subcritical, critical, or supercritical and to relate speed to wave behavior in open-channel and ship-motion problems. It is a quick way to connect a speed value to the regime change engineers and naval architects actually care about. That helps turn a raw velocity into a more meaningful design classification.
Froude Number: Fr = V / √(g × L) Critical Velocity: V_crit = √(g × L) Hull Speed: V_hull ≈ 1.34 × √(L_ft) (in knots) Specific Energy: E = y + V² / (2g)
Result: Fr = 0.361, Subcritical flow
A ship traveling at 8 m/s with a 50 m waterline has Fr = 0.361 — well below critical, operating in the efficient displacement regime.
The Froude number tells you whether gravity waves can travel upstream relative to the moving flow. In open channels, that distinction is critical because it changes how disturbances, control structures, and downstream conditions influence the flow field.
In channel flow, the characteristic length is usually hydraulic depth. For ships, the same idea helps compare vessel speed to the wave system generated by the hull. That is why the number appears in both spillway design and naval architecture even though the physical setups look very different.
Use the right characteristic length for the problem. A wrong length scale can make the regime classification meaningless. Also remember that Froude number and Reynolds number answer different questions, so one does not replace the other.
The flow speed is below the gravity-wave speed, so disturbances can propagate upstream. In open-channel terms, that usually corresponds to deeper, slower flow that remains strongly influenced by downstream conditions.
The maximum efficient speed for a displacement vessel, roughly 1.34 × √(waterline in ft) knots. Beyond this point, wave-making drag rises sharply and additional speed usually demands disproportionate power.
When supercritical flow transitions to subcritical, such as downstream of a spillway, energy is dissipated violently in a hydraulic jump. It is one of the clearest practical signs that the flow regime has changed across the channel.
Both are dimensionless, but Reynolds measures viscous vs inertial forces while Froude measures inertial vs gravitational forces. Engineers often check both because one cannot replace the other when regime changes depend on viscosity and gravity at the same time.
Yes. In density currents or stratified atmospheric flows, engineers often use a densimetric Froude number built from reduced gravity rather than the standard free-surface form. The governing idea is still the same comparison between inertial motion and gravity-driven wave behavior.
Because wave-making behavior is strongly tied to the ratio between hull speed and gravity-wave speed, Froude-based scaling is a practical way to compare vessels of different lengths. It helps model tests and full-scale predictions stay in the same gravity-wave regime.