Supercritical flow

Encyclopedia

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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 jump

s (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

:

where

If , we call the flow

**supercritical flow**is when the**flow**velocity is larger than the**wave**velocity. The analogous condition in gas dynamics is supersonicSupersonic

Supersonic speed is a rate of travel of an object that exceeds the speed of sound . For objects traveling in dry air of a temperature of 20 °C this speed is approximately 343 m/s, 1,125 ft/s, 768 mph or 1,235 km/h. Speeds greater than five times the speed of sound are often...

.

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 jump

Hydraulic jump

A hydraulic jump is a phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise occurs in the liquid surface...

s (bores

Tidal bore

A tidal bore is a tidal phenomenon in which the leading edge of the incoming tide forms a wave of water that travel up a river or narrow bay against the direction of the river or bay's current...

) can occur. In fluid dynamics

Fluid dynamics

In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

, the change from one behaviour to the other is often described by a dimensionless quantity

Dimensionless quantity

In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and...

, where the transition occurs whenever this number becomes less or more than one. One of these numbers is the Froude number

Froude number

The Froude number is a dimensionless number defined as the ratio of a characteristic velocity to a gravitational wave velocity. It may equivalently be defined as the ratio of a body's inertia to gravitational forces. In fluid mechanics, the Froude number is used to determine the resistance of an...

:

- ,

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 , we call the flow

**subcritical**; if , we call the flow**supercritical**.## See also

- Subcritical vs. supercritical flow
- SupersonicSupersonicSupersonic speed is a rate of travel of an object that exceeds the speed of sound . For objects traveling in dry air of a temperature of 20 °C this speed is approximately 343 m/s, 1,125 ft/s, 768 mph or 1,235 km/h. Speeds greater than five times the speed of sound are often...
- HypersonicHypersonicIn aerodynamics, a hypersonic speed is one that is highly supersonic. Since the 1970s, the term has generally been assumed to refer to speeds of Mach 5 and above...