Froude number mixture

It should be noted that the frictional drop was calculated by subtracting the hydrostatic head and acceleration losses from the measured total pressure-drop where void data were lacking, a homogeneous flow model was assumed. This modification of X by use of the Froude number appears very similar to the technique used by Kosterin (K2, K3) for horizontal pipes, in which the equivalent of volume-fraction of gas flowing, with mixture Froude number as the correlating parameter. 

Hughmark (Hll) has extended this approach to obtain an empirical correlation covering wide ranges of data for the air-water systems in vertical flow. Basically the correlation consists of using Eq. (70) with a variable value of the coefficient K. This coefficient was expressed by Hughmark as a function of the mixture Reynolds number, Froude number, and liquid volume-fraction. Hughmark s approach gives... 

Laity and Treybal (LI) report on experiments with a variety of two-phase systems in a covered vessel which was always run full, so that there was no air-liquid interface at the surface of the agitated material. Under these circumstances no vortex was present, even in the case of operation without baffles. Mixing Equipment Company flat-blade disk-turbines were used in 12- and 18-in. diameter vessels whose heights were about 1.07 times their diameters. Impeller diameter was one-third of tank diameter in each case. For operation without baffles, using only one liquid phase, the usual form of power-number Reynolds-number correlation fit the data, giving a correlation curve similar to that given in Fig. 6 for disk-turbines in unbaffled vessels. In this case, however, the Froude number did not have to be used in the correlation because of the absence of a vortex. For two-phase mixtures, Laity and Treybal could correlate the power consumption results for unbaffled operation by means of the same power number-Reynolds number correlation as for one-phase systems provided the following equations were used to calculate the effective mean viscosity of the mixture For water more than 40% by volume ... 

Zlokarnik [619] found no effect of a and S in measurements with a turbine stirrer of conventional design in pure liquids and in glycerine-water mixtures (coalescing material systems ). Surprisingly, the Froude number also had no effect on Ne in the industrially interesting range of Fr 0.65, so that for Re S 10 the power characteristic could just be described by Ne(Q) (Fig, 2.5). The process equation is ... 

With a more complex approach that takes into account the actual viscosity of the slur ry mixture and the density of the particles. Gillies et al, (1999) developed an equation for the Froude number Fin terms of the Archimedean number (which we wUl discuss in Sec tion 4-4-5 for stratified coarse flows) ... 

The effect of solids concentration on deposition Froude number in Figure 4 was also reported by Thomas [7]. The increase in deposition velocity with solids concentration contrasts with that which be shown later to occur for finer particles with broad size distributions. As the slurry concentration increases the slurry viscosity begins to increase rapidly at concentrations above 30% by volume. This causes the Reynolds number of the mixture flow to decrease at a given velocity, which according to Gillies and Shook [6], tends to increase the contact load. 

For liquid-liquid mixtures, the calculations of mixing time and power (or Newton) number outlined above are valid for unbaffled vessels only as long as the vortex created by the stirrer does not reach the stirrer head. Otherwise, gas entrainment occurs and the physical properties of the system change. The depth of the liquid-gas interface at the vessel axis with respect to static liquid surface level, HL, can be related to the Froude and Galileo numbers. Some of the reported relationships are summarized in Table XIV. The value of H, at which the vortex reaches the upper impeller blades level can be expressed as... 

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