Enter the flow velocity and hydraulic depth (or characteristic length) to calculate the Froude number for open channel flow or ship hydrodynamics. You can also solve for velocity or depth when the Froude number is known. Results include the Fr value, flow regime classification (subcritical, critical, or supercritical), and a visual breakdown.
Froude Number (Fr)
--
Flow Regime
--
Flow Velocity (V)
--
Hydraulic Depth / Length (L)
--
The Froude number (Fr) is a dimensionless value that expresses the ratio of a fluid's inertial forces to gravitational forces. It is widely used in open-channel hydraulics and ship hydrodynamics to characterize the nature of flow. A Froude number less than 1 indicates subcritical (tranquil) flow, equal to 1 is critical flow, and greater than 1 is supercritical (rapid) flow.
The formula is Fr = V / √(g × L), where V is the flow velocity, g is gravitational acceleration (9.81 m/s² on Earth), and L is the hydraulic depth for open channels or hull length for ships. Simply divide the velocity by the square root of the product of gravity and the characteristic length.
When Fr ≈ 1, the flow is at or near the critical state. This is a sensitive condition where small changes in channel geometry or flow rate can cause significant changes in flow behavior, including hydraulic jumps. Engineers typically design channels to avoid operating near Fr = 1 unless a hydraulic jump is intentionally desired.
For open-channel flow (rivers, spillways, weirs), use the hydraulic depth — the cross-sectional flow area divided by the top water surface width. For ship or vessel applications, the hull waterline length is used as the characteristic length instead.
Both are dimensionless numbers used in fluid mechanics, but they describe different force ratios. The Froude number compares inertial forces to gravitational forces and is critical for free-surface flows. The Reynolds number compares inertial forces to viscous forces and is used to determine laminar vs. turbulent flow. Open-channel and naval engineers primarily rely on the Froude number.
No. Since the Froude number is defined as the ratio of speed (a scalar magnitude) to the square root of a positive quantity, it is always non-negative. A value of zero would indicate no flow. Negative velocities in a physical context are typically handled by convention in directional analyses, but the Froude number itself remains ≥ 0.
Most natural rivers and designed channels operate with Fr between 0.1 and 0.8 (subcritical). Spillways and fast-moving floodwaters can exceed Fr = 1 (supercritical). Ships typically operate at Fr between 0.1 and 0.5, and planing hulls can exceed 0.5. Hydraulic jumps occur when flow transitions from supercritical back to subcritical.
The calculator uses the standard formula Fr = V / √(g × L) and is mathematically exact given your inputs. Accuracy in real applications depends on how precisely you measure velocity and hydraulic depth. For irregular cross-sections, the hydraulic depth should be computed as flow area divided by top width rather than simply using channel depth.