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.
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.
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.
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.
Periods of waves of ships, sailing over 12 m/s (~45 km/h or ~24 knots), match those of wind waves in strong storms whereas ships sailing faster than about 50 km/h may excite waves of periods that are extremely seldom found under natural conditions in Tallinn Bay, even if they sail at low depth Froude numbers over the deepest part of the bay.
This scaled bridge deck is optimal to produce values ranging from low to high flows, all at subcritical Froude numbers (less than 1) in the upstream flow.
d] is the jet Reynolds number and Fr the Froude number.
A common effect of sailing at moderate and high depth Froude numbers (equivalently, in relatively shallow water) is the formation of a depression region (often called Bernoulli wake) in the ship's vicinity (Akylas, 1984; Grimshaw and Smyth, 1986; Lee et al.
The objectives of the present work are to investigate the effect of the bottom baffle and its angle on the performance of an irrigation sedimentation basin experimentally and numerically, and then to study the effects of Froude number on the sediment removal efficiency.