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 ?
1) The characteristics of ship-generated waves are highly dependent on the depth Froude number [F.
The team presented the experimental and simulation results in dimensionless form for various Froude numbers (which characterize the open-channel flow) and the inundation ratio (which characterizes the flooding height).
The inlet Froude number for a particular test is determined from the measurement of depth of water at the inlet as well as the flow rate.
The Bond number represents the ratio between the surface tension and the gravity force, and the Froude number represents the mean flow velocity relative to the velocity of the long wave.
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.
The results and discussion are presented in four parts; the first part discusses the effect of the vertical baffle installed at the bottom of the basin, the second part deals with the angle of the baffle and the last two parts describes the effects of Froude number and flow depth on sediment removal efficiency.
As can be seen in Figure 8, by increasing gates' opening, Froude number decreases, and this is because with increasing Froude number flow rate increases, also in all the openings by increasing Froude number jump length increases.
d] is the jet Reynolds number and Fr the Froude number.
Results show that in high Reynolds numbers, the flow field and baffle position are not affected by the inlet Froude number.
The second group, the ratio of inertial to gravity forces, important when the liquid surface is wavy or curved, as with a vortex, is the Froude number that defined as Fr = [d.
These parameters are include the Reynolds number, A special case of the Euler number, Densitometry froude number, internal angle of the jet, submergence number, geometrical parameter of the nozzle and relative velocity [8].
Also, the effects of Froude number and sediment concentration on the sediment removal efficiency of the sedimentation basin with a baffle were investigated in this study.