Fluid flow Froude number

For NRc S 10, the liquid motion moves with the impeller, and off from the impeller, the fluid is stagnant [34]. The Froude number accounts for the force of gravity when it has a part in determining the motion of the fluid. The Froude numbers must be equal in scale-up situations for the new design to have similar flow when gravity controls the motion [16]. 

Laminar component of fanning friction factor fluid force normal to the direction of flow Froude number... 

Tliis is the well-known dimensionless equation for fluid flow. It represents the pressure coefficient as an unspecified function of the Reynolds and Froude groups. In geometrically similar flow systems, the pressure coefficients will be also equal, provided that the Reynolds and Froude numbers are both equal. 

The Froude number, = vP Lg, is similar to it is a measure of the inertial stress to the gravitational force per unit area acting on a fluid. Its inclusion in Eq. (11) is justified when density differences are encountered in the absence of substantive differences in density, e.g., for emulsions more so than for suspensions, the Froude term can be neglected. Dimensionless mixing time is independent of the Reynolds number for both laminar and turbulent flow regimes, as in-... 

For additional information, see Simpson (Chem. Eng., 75[6], 192-214 [1968]). A critical Froude number of 0.31 to ensure vented flow is widely cited. Recent results (Thorpe, 3d Int. Conf. Multi-phase Flow, The Hague, Netherlands, 18-20 May 1987, paper K2, and 4th Int. Conf. Multi-phase Flow, Nice, France, 19-21 June 1989, paper K4) show hysteresis, with different critical Froude numbers for flooding and unflooding of drain pipes, and the influence of end effects. Wallis, Crowley, and Hagi (Trans. ASME J. Fluids Eng., 405-413 [June 1977]) examine the conditions for horizontal discharge pipes to run full. 

In the flow of water in open channels, fluid friction is a factor as well as gravity and inertia, and apparently we face the same difficulty here. However, for flow in an open channel there is usually fully developed turbulence, so that the hydraulic friction loss is exactly proportional to V2, as will be shown later. The fluid friction is therefore independent of Reynolds number, with rare exceptions, and thus is a function of the Froude number alone. 

The letters R, F, and W stand for so-called Reynolds, Froude, and Weber numbers, respectively these are dimensionless numbers, as indicated. For example, if we make the Reynolds number the same in model and prototype, using the same fluid, the dimension of length is smaller in the model and hence the velocity v will have to be greater. In other words, the water would have to flow faster in the model. If we now consider the Froude number as the same in model and prototype, and that the same fluid is used in both, we see that the velocity would have to be less in the model than in the prototype. This may be regarded as two contradictory demands on the model. Theoretically, by using a different fluid in the model (thus changing p0 and p), it is possible to eliminate the difficulty. The root of the difficulty is the fact that the numbers are derived for two entirely different kinds of flow. In a fluid system without a free surface, dynamic similarity requires only that the Reynolds number be the same in model and prototype the Froude number does not enter into the problem. If we consider the flow in an open channel, then the Froude number must be the same in model and prototype. 

The Froude number described above is frequently used for the description of radial and axial flotvs in liquid media when the pressure difference along a mixing device is important. When cavitation problems are present, the dimensionless group (Pj — p,) /pw - called the Euler number - is commonly used. Here p is the liquid vapour saturation pressure and p is a reference pressure. This number is named after the Swiss mathematician Leonhard Euler (1707-1783) who performed the pioneering work showing the relationship between pressure and flow (basic static fluid equations and ideal fluid flow equations, which are recognized as Euler equations). 

For Newtonian fluids, the state of flow can be described by two dimensionless groups, usually the Reynolds number, Re, (inertial forces/viscous forces) and Froude number, Fr, (inertial/gravity forces). For a visco-elastic fluid, at least one additional group involving elastic forces is required. 

The Froude number is normally used to investigate the fluid flow in free surfaces ... 

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