# Froude Number

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## Froude number

The dimensionless quantity *U*(*gL*)^{-1/2}, where *U* is a characteristic velocity of flow, *g* is the acceleration of gravity, and *L* is a characteristic length. The Froude number can be interpreted as the ratio of the inertial to gravity forces in the flow. This ratio may also be interpreted physically as the ratio between the mean flow velocity and the speed of an elementary gravity (surface or disturbance) wave traveling over the water surface.

When the Froude number is equal to one, the speed of the surface wave and that of the flow is the same. The flow is in the critical state. When the Froude number is less than one, the flow velocity is smaller than the speed of a disturbance wave traveling on the surface. Flow is considered to be subcritical (tranquil flow). Gravitational forces are dominant. The surface wave will propagate upstream and, therefore, flow profiles are calculated in the upstream direction. When the Froude number is greater than one, the flow is supercritical (rapid flow) and inertial forces are dominant. The surface wave will not propagate upstream, and flow profiles are calculated in the downstream direction.

The Froude number is useful in calculations of hydraulic jump, design of hydraulic structures, and ship design, where forces due to gravity and inertial forces are governing. In these cases, geometric similitude and the same value of the Froude number in model and prototype produce a good approximation to dynamic similitude. *See* Dimensional analysis, Dimensionless groups

## Froude Number

a similarity criterion for the motion of liquids or gases, used in cases where the effect of gravity is considerable. Such cases are encountered in hydroaeromechanics— for example, during the motion of bodies in water—and in dynamic meteorology.

The Froude number characterizes the ratio of the inertial force and the gravitational force acting on a unit volume of a liquid or gas. Quantitatively, the Froude number is *Fr = v ^{2}gl*, where v is the flow velocity or the speed of a moving body,

*g*is the acceleration of gravity, and

*l*is a characteristic linear dimension of the flow of the body. The number was introduced in 1870 by the English scientist W. Froude (1810–79). The similarity requirement based on equal Froude numbers for a model and a full-scale object is used, for example, in the modeling of the motion of ships and water flows in open channels and in the testing of models of hydraulic engineering installations.