# Froude Number

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Related to Froude Number: Reynolds number, Euler number

## 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 ?
The results of applying GEP model indicate that the discharge coefficient of trapezoidal side weir, are closely affected by downstream weir Froude number. Moreover, the sensitivity analysis indicates that the other important parameters affecting Cd for trapezoidal side weir, are h1/p and L/b ratios.
Symbols c: Specific heat capacity (J/(kg x K)) m: Mass (kg) AT: Temperature drop (K) h: Convective heat transfer coefficient (W/([m.sup.2] x K)) [epsilon]: Emissivity [gamma]: Wavelength (m) [sigma]: Surface tension (N/m) [omega]: Relative velocity (m/s) [rho]: Density (kg/[m.sup.3]) [We.sub.c]: Critical Weber number L: Breakup length (m) d: Droplet diameter (m) D: Jet diameter (m) Fr: Froude number V: Velocity (m/s) p: Percentage q: Heat flux (W/[m.sup.2]) g: Acceleration of gravity (m/[s.sup.2]) [C.sub.0]: Blackbody radiation coefficient (W/(m x K)) [E.sub.0]: Epstein factor.
Equation (8) clearly shows that, as the Froude number decreases (i.e., the form drag decreases), the length of a ship increases when the speed is constant.
The large Froude Number depicts no sea water intrusion into the outfall pipe as higher exit velocity of sewage from the outfall into the sea bed prevents outfall pipe chocking.
Four discharges of 17, 20, 23 and 27 liters per second were chosen in a way in which according to the fixed depth, the Froude number in all experiments was less than one and flow was the subcritical condition.
The characteristics of Free-Surface Shock Waves are governed by the Froude number based on draft, Fd.
Figure 2, showing relative velocity in horizontal pipe, is available for those conditions for which the Froude number is in the range of 0.02-0.2.
and analogously for the vertical Froude number. In Table 2, we give the Brunt-Vaisala frequency evaluated in the photosphere following the VAL C atmosphere model and considering the gas of neutral hydrogen which is the most dense with respect to the free electrons and ions.
Reference [26] plotted the Shields number as a function of Froude number for the classification of bed forms in their flume experiments.
The final expression accounts for skin and shape roughness in a nontrivially additive way, and for the free surface undulation as a function of Froude number; the intrinsically nonstationary phenomenon of the flow separation near the dune crest is evaluated in terms of resistance resorting to an equivalent steady flow configuration.
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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