Froude number and critical discharge

Top: behaviour of the discharge depth h of an open-channel fl ow with permanent disturbance, bottom: propagation of a surface wave after a momentary disturbance (red dot, blue lines = disturbance fronts)

1 subcritical discharge, 2 critical discharge, 3 supercritical discharge

Subcritical discharge

Disturbances in the discharge behaviour are noticeable upstream. The flow velocity v is less than the propagation velocity c of a surface wave. Subcritical discharge usually has a large discharge depth h at low flow velocity v.


Critical discharge

Disturbances in the discharge behaviour are not noticeable upstream. The flow velocity v is equal to the propagation velocity c of a surface wave.


Supercritical discharge

Disturbances in the discharge behaviour are not noticeable upstream. The flow velocity v is greater than the propagation velocity c of a surface wave.


The Froude number describes the ratio of flow velocity v to propagation velocity c of a surface wave and therefore serves as a measure of subcritical or supercritical discharge. The same Froude number means a dynamically similar open-channel flow.

Fr < 1: subcritical

Fr = 1: critical

Fr > 1: supercritical

Specific energy diagram with Froude number

h discharge depth, E specific energy, Fr Froude number

Open-channel flow has many similarities with compressible flow. In both cases there is a dimensionless number (Froude or Mach) that characterises the flow. Many of the differences between subcritical and supercritical discharge have analogies in subsonic and supersonic flow.

Critical discharge (Froude number = 1)

At the minimum specific energy Emin, the discharge depth h corresponds to the critical depth hc. At this point, the Froude number is Fr = 1, there is a prevailing critical discharge and the propagation velocity c is equal to the flow velocity v. Also, at this point the specific force F in the flume is minimal.

Examples where critical depths (critical discharge) may occur

1 critical depth near free overfall,

2 change in the bottom slope,

3 flow over a broad-crested weir,

4 hydraulic jump

Illustration of the hydraulic jump at different Froude numbers