Reynolds number correlations

Figure 5-14. Reynolds number correlation for propellers. By permission, Rushton, J. H. ef a/. [18],...

Fig. 9.6 Power number-Reynolds number correlation in an agitator with four baffles (each 0. 1DT). (Rushton, et al., 1950)...

Figure 9.6 shows Power number-Reynolds number correlation in an agitator with four baffles (Rushton et al., 1950) for three different types of impellers. The power number decreases with an increase of the Reynolds number and reaches a constant value when the Reynolds number is larger than 10,000. At this point, the power number is independent of the Reynolds number. For the normal operating condition of gas-liquid contact, the Reynolds number is usually larger than 10,000. For example, for a 3-inch impeller with an agitation speed of 150 rpm, the impeller Reynolds number is 16,225 when the liquid is water. Therefore, Eq. (9.54) is simplified to... 

Figure 7-14. Power number versus Reynolds number correlation for common impellers. (Source Ruchton et al., Chem. Eng. Prog., 46, No. 8, 495, 1950. Reprinted with permission of AlChE. Copyright 1950. All rights reserved.)...

Fig. 3. Power number—Reynolds number correlation for a 12-in. propeller in a tank without baffles. Tank diameter = 54 in. Liquid depth = 54 in. Data of Rushton et al. (R13).

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 ... 

Laity and Treybal also measured power consumption with four baffles in the vessel, each baffle being % of the tank diameter in width. With single liquids, they found the same power number-Reynolds number correlation as given in Section III for normal baffled operations with the presence of an air-liquid interface at the surface. Again, with two-phase systems, the same relation correlated the data provided that an effective mean viscosity calculated as follows was used ... 

Fig. 1. Power number-Reynolds number correlation in Newtonian fluids, for disk-type 6-bladed impellers [after Metzner et al. (MI2)].

This equation neglects the effect of stream turbulence. If the butk stream Row has Re > 2100, then the drop settling velocity should exceed die velocity of turbulent eddies, which can be estimated by K K Ifi2)l/ , whete/is the friction factor determined from a Reynolds number correlation. 

Figure 9.14 shows the power number-Reynolds number correlation for a six-blade turbine impeller in pseudoplastic fluids. The dashed curve is taken from Fig. 9.12 and applies to newtonian fluids, for which = nDlpJix. The solid curve is for pseudoplastic liquids, for which is given by Eqs. (9.25) and... 

Friction Factor/Reynolds Number Correlation for Flow Around Spheres. The magnitude of the dynamic force exerted across the tlnid-solid interface provides the basis for macroscopic momentum transfer correlations. The component of this dynamic force in the primary flow direction. 

Nusselt number number of samples number of striations Prandtl number pressure drop Reynolds number correlation coefficient distance... 

Expansion index—terminal Reynolds number correlation,... 

Drag coefficient. From the previous discussions it is evident that the geometry of the immersed solid is a main factor in determining the amount of total drag force exerted on the body. Correlations of the geometry and flow characteristics for solid objects suspended or held in a free stream (immersed objects) are similar in concept and form to the friction factor-Reynolds number correlation given for flow inside conduits. In flow... 

It is possible to develop a friction factor-modified Reynolds number correlation for power law fluids. The correlation is given in Fig. 3-14, where... 

The friction-factor-Reynolds-number correlation can be expressed for smooth pipe as (Bird et al., 1960, p. 186)... 

By using the foregoing approach, a friction-factor-modified Reynolds number correlation (Figure 4-3) can be developed. Note that a number of lines exist in the turbulent region (i.e., one for each value of n ). 

Figure 4-5 gives the power number versus Reynolds number correlation for different types of agitators. The pitch referred to is the axial distance that a free propeller would move in a nonyielding liquid in one revolution. 

Figure 16-7 Nusselt-Prandtl-Reynolds number correlations for heat transfer.

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