Froude Number
Calculate Froude number for open channel flow using Fr = u/√(g·Hd) with hydraulic depth from area and width. Classify subcritical, critical, and supercritical flow with charts.
About This Calculator
What Is the Froude Number?
The Froude number (Fr) is a dimensionless quantity in fluid mechanics that characterizes free-surface flows by comparing inertial forces to gravitational forces. Named after William Froude, a 19th-century English engineer who studied ship resistance and wave patterns, this parameter is fundamental to open channel hydraulics, hydraulic engineering, and naval architecture. The Froude number determines whether flow is subcritical (tranquil, Fr < 1), critical (Fr = 1), or supercritical (rapid, Fr > 1).
The Froude number is calculated using the formula Fr = u / √(g · Hd), where u is the flow velocity (m/s), g is the acceleration due to gravity (9.80665 m/s²), and Hd is the hydraulic depth (m). The hydraulic depth is computed as Hd = A / W, where A is the cross-sectional area of flow (m²) and W is the top width of the water surface (m).
When Fr is below 1, gravitational forces dominate and the flow is subcritical — slow, deep, and tranquil with waves that can propagate upstream. When Fr exceeds 1, inertial forces dominate and the flow is supercritical — fast, shallow, and rapid with disturbances that cannot travel upstream. At Fr = 1, the flow is critical, representing the minimum specific energy condition that governs hydraulic control sections.
Applications in Hydraulic Engineering
The Froude number is widely used in hydraulic engineering for designing open channels, spillways, weirs, culverts, and energy dissipators such as stilling basins. It predicts the occurrence and characteristics of hydraulic jumps — when supercritical flow transitions to subcritical flow, causing a sudden rise in water surface and energy dissipation. In ship hydrodynamics, the Froude number governs wave-making resistance, with the hull speed of displacement hulls corresponding to a Froude number of approximately 0.4. The Froude number is also critical for Froude scaling in physical hydraulic models, ensuring dynamic similarity between model tests and prototype structures.
Regional Notes
The Froude number formula is universal and uses SI units (m/s, m, m²) which are standard in fluid mechanics worldwide. The acceleration due to gravity is taken as 9.80665 m/s², the standard value at sea level. The classification thresholds (Fr < 1, Fr = 1, Fr > 1) are universally accepted in hydraulics across the US, UK, India, and all other regions, as defined by the fundamental physics of wave celerity in open channel flow.
Frequently Asked Questions
What is the Froude number?
The Froude number (Fr) is a dimensionless value in fluid mechanics that characterizes open channel flow by comparing inertial forces to gravitational forces. It is calculated as Fr = u/√(g·Hd) where u is flow velocity, g is gravity, and Hd is hydraulic depth. It determines whether flow is subcritical (Fr < 1), critical (Fr = 1), or supercritical (Fr > 1).
How do you calculate the Froude number?
The Froude number formula is Fr = u/√(g·Hd), where u is the flow velocity in m/s, g is the acceleration due to gravity (9.80665 m/s²), and Hd is the hydraulic depth in meters. Hydraulic depth is calculated as Hd = A/W, where A is the cross-sectional area of flow in m² and W is the channel width in meters.
What does a Froude number less than 1 indicate?
A Froude number less than 1 (Fr < 1) indicates subcritical or tranquil flow. In this regime, gravitational forces dominate over inertial forces, meaning the flow velocity is slower than the wave speed. Subcritical flow is characterized by smooth, steady water surfaces and occurs in mild-slope channels, deep rivers, and downstream of hydraulic jumps.
What does a Froude number greater than 1 mean?
A Froude number greater than 1 (Fr > 1) indicates supercritical or rapid flow. In this regime, inertial forces dominate over gravitational forces, meaning the flow velocity exceeds the wave speed. Supercritical flow occurs in steep channels, spillways, rapids, and shallow flows. It is characterized by high velocities, standing waves, and rapid water surface changes.
What is critical flow in open channels?
Critical flow occurs when the Froude number equals 1 (Fr = 1). At this point, the flow velocity exactly matches the wave celerity (speed), and the specific energy of the flow is at its minimum. Critical flow represents the boundary between subcritical and supercritical regimes and is important for hydraulic control sections in channels, weirs, and flumes.
How is the Froude number used in hydraulic engineering?
The Froude number is essential in hydraulic engineering for designing channels, spillways, weirs, and energy dissipators. It is used to predict the occurrence and characteristics of hydraulic jumps, design riprap for scour protection, model ship hydrodynamics, analyze wave behavior, and ensure proper flow conditions in open channel systems. It is the hydraulic equivalent of the Mach number in compressible flow.
What is hydraulic depth and how is it calculated?
Hydraulic depth (Hd) is the ratio of the cross-sectional area of flow (A) to the top width of the channel (W), expressed as Hd = A/W. For rectangular channels, hydraulic depth equals the actual water depth. For trapezoidal, triangular, or irregular channels, it differs from the actual depth and must be computed from the specific cross-section geometry.
What is the difference between Froude number and Reynolds number?
The Froude number compares inertial forces to gravitational forces and is used primarily for free-surface flows like open channels, rivers, and ship hydrodynamics. The Reynolds number compares inertial forces to viscous forces and determines whether flow is laminar or turbulent. Both are dimensionless, but Froude number governs wave and surface behavior while Reynolds number governs internal flow structure and friction.