Froude Number Calculator

Your details

Choose which quantity to solve for.
Mean cross-sectional flow velocity.
m/s
Hydraulic depth = cross-sectional area / top width (equals actual depth for a wide rectangular channel).
m
Discharge per unit width of a rectangular channel, used to compute critical depth. Leave blank to skip.
m²/s
Gravitational acceleration. Default is standard gravity 9.806 65 m/s². Override for other planets or unit systems.
m/s²
Froude Number (Fr)Critical
0.8745

Ratio of inertial to gravitational forces; < 1 subcritical, = 1 critical, > 1 supercritical.

Flow RegimeCritical
Wave Celerity (c)3.43m/s
Critical Depth (hc)0.861m
Critical Velocity (Vc)2.905m/s
Specific Energy (E)1.659m
0.8745
Subcritical<0.85Critical0.85-1.15Supercritical1.15+

Fr = 0.875, Critical.

  • Near-critical flow: the channel is close to the critical point where wave celerity equals flow velocity.
  • Critical flow is hydraulically unstable and is deliberately avoided in most channel designs except at control structures such as weirs and flumes.
  • Wave celerity (shallow-water wave speed) is 3.43 m/s at this depth.
  • For the given unit discharge, critical depth is 0.86 m and critical velocity is 2.91 m/s.

Next stepFor channel design, keep Fr well below 1 (ideally under 0.6) to avoid waves and instability at the transition.

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