# 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

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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 = v2gl, 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.

References in periodicals archive ?
It is found that the laboratory data for Flint River modeling with b/[d.sub.50] = 18.8 agree well with Melville's and Sheppard et al.'s formula, while HEC-18 overpredicts the scour depth for two small Froude numbers as shown in Figure 8.
Parameters mentioned above render Froude number Fr = v/[square root of gR] = 0.39, relative distance [epsilon] = h/R = 1.25, and T = vt/h, which are the same as those used by Greenhow and Moyo [25] and Lin [26].
Jiang and Lu [19] measured the burning rate and flame angle of wind-blown pool fires and demonstrated that flame tilt was a function of Froude number (Fr).
Inspired by the success of the non-space-filling multispeed model, the capability of their space-filling counterpart will be investigated on simulating flows with finite Froude number. Specifically, two space-filling models will be derived by matching hydrodynamic moments (see, e.g., [1, 22, 24]) and then tested by using two typical shallow water problems.
Although these ferries are capable of speeds up to ~ 25 knots, they normally run at reduced speeds in the shallowest coastal areas, hence the depth Froude number [F.sub.d] is well below the critical level for these ships.
The depths of flow are 10 to 12 m leading to low Froude numbers between 3 and 6 [2].
[7] studied the temporal evolution of clear-water pier and abutment scour and found that the principal parameter influencing the scour process is the densimetric particle Froude number so suggested an logarithmic formula.
It was shown that the wave pattern depended on the Froude number Fn (non-dimensional parameter of speed with reference to the ship's length, Fn = U/ [square root of](gL)], where U is the ship speed, g the gravity acceleration and L the ship's length) and the hull-form configuration, contrary to the theory of linear, dispersive waves.
To sustain observations made on the variation of riverbed material, a Shields diagram as a function of Reynolds number and as a function of Froude number was utilized.
The range of Froude number was fixed between 0.017 and 0.7, because these conditions were found to represent the limits of the rolling regime determined experimentally (visual observation).

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