Supercritical flow

A supercritical flow is a flow whose velocity is larger than the wave velocity. The analogous condition in gas dynamics is supersonic.

Information travels at the wave velocity. This is the velocity at which waves travel outwards from a pebble thrown into a lake. The flow velocity is the velocity at which a leaf in the flow travels. If a pebble is thrown into a supercritical flow then the ripples will all move down stream whereas in a subcritical flow some would travel up stream and some would travel down stream. It is only in supercritical flows that hydraulic jumps (bores) can occur. In fluid dynamics, the change from one behaviour to the other is often described by a dimensionless quantity, where the transition occurs whenever this number becomes less or more than one. One of these numbers is the Froude number:

• $Fr \ \stackrel{\mathrm{def}}{=}\ \frac{U}{\sqrt{gh}}$,

where

• U = velocity of the flow
• g = acceleration due to gravity (9.81 m/s² or 32.2 ft/s²)
• h = depth of flow relative to the channel bottom

If $Fr < 1$, we call the flow subcritical; if $Fr > 1$, we call the flow supercritical. If $Fr \approx 1$, it is critical.

See also

• Supercritical vs. subcritical flow
• Supersonic
• Hypersonic

The Hydraulics of Open Channel Flow: An Introduction. Physical Modelling of Hydraulics Chanson, Hubert (1999)