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 = 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 ?
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.
The depths of flow are 10 to 12 m leading to low Froude numbers between 3 and 6 [2].
In these studies, the maximum scour depth under steady flow conditions is related to the hydrodynamic and sediment parameters, Froude number and spur dike location and among others.
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.
bs] Black screen diameter (mm) F Filling ratio (%) Fr Froude number g Acceleration due to gravity (m/[s.
Bubbly flow measurements in hydraulic jumps with small inflow Froude numbers, International Journal of Multiphase Flow, 37: 555-564.
The analysis of the literature at low Froude numbers typical of condensing furnace vapor plume characteristics shows fair agreement with CFD modeling of the cases studied in this paper with straight vent terminations.
The fore part of the hull form has been optimized for a single speed corresponding to the Froude number Fr = 0.
Complex hydraulic variables (shear velocity, roughness shear velocity, inferred boundary Reynolds number, Reynolds number, Froude number, shear stress), substrate roughness, relative roughness, and physicochemical variables (water temperature, conductivity and pH) were used in order to identify those significantly related with the distribution of macroinvertebrate assemblages.
A qualitative approach can be adopted for combustor development by simulating Froude number corresponding to combustor inlet Mach number and carrying out the flow pattern analysis.
The number of conventional ferry sailings at low Froude numbers was about 20 per day.