Regime turbulent

The power number depends on impeller type and mixing Reynolds number. Figure 5 shows this relationship for six commonly used impellers. Similar plots for other impellers can be found in the Hterature. The functionality between and Re can be described as cc Re in laminar regime and depends on p. N in turbulent regime is constant and independent of ]1. 

Pressure drop in catalyst beds is governed by the same principles as in any flow system. Consequently, at very low flow, pressure drop is directly proportional to velocity, and at very high flow, to the square of velocity. These conditions correspond to the laminar and turbulent regimes of the flow. 

The turbulent regime for Cq is characterized by the section of line almost parallel to the x-axis (at the Re" > 500). In this case, the exponent a is equal to zero. Consequently, viscosity vanishes from equation 46. This indicates that the friction forces are negligible in comparison to inertia forces. Recall that the resistance coefficient is nearly constant at a value of 0.44. Substituting for the critical Reynolds number, Re > 500, into equations 65 and 68, the second critical values of the sedimentation numbers are obtained ... 

For the same case of n = 1200 rpm and r = 0.5, we obtain u,/Ug = 800, whereas for the turbulent regime the ratio was only 28. This example demonstrates that the centrifugal process is more effective in the separation of small particles than of large ones. Note that after the radial velocity u, is determined, it is necessary to check whether the laminar condition. Re < 2, is fulfilled. For the transition regime, 2 < Re < 500, the sedimentation velocity in the gravity field is ... 

This ratio represents an average between similar ratios for the laminar and turbulent regimes. In the most general case, u, = f(D, Pp, p, /r, r, w), and hence we may ignore whether the particle displacement is laminar, turbulent or within the transition regime. This enables us to apply the dimensionless Archimedes number (recall the derivation back in Chapter 5) ... 

This model is referred to as the axial dispersed plug flow model or the longitudinal dispersed plug flow model. (Dg)j. ean be negleeted relative to (Dg)[ when the ratio of eolumn diameter to length is very small and the flow is in the turbulent regime. This model is widely used for ehemieal reaetors and other eontaeting deviees. 

Turbulent Regime In the turbulent regime, GrxPr > 2.3x10, and = 1 /3. This regime may occur only when the area of evaporating liquid is very large (tens of square meters). 

Clift and Gauvin modified Schiller and Nauman s Eq. (14.26) to represent the drag force throughout the transitional and turbulent regimes ... 

Tlie equation of Hawtliome, Wenddell, and Hottel can be used to predict the flaine lengtli in the turbulent regime. 

D,-or = Impeller diameter for turbulent regime, corrected for viscosity effect, in. 

Leung, J. C., Overpressure During Emergency Relief Venting In Bubbly and Churn-Turbulent Regimes, AIChEJ, 33 (6), 952-958, June 1987. 

Since the Reynolds number is greater than 104, therefore the flow is turbulent. Based on a power number defined in the turbulent regime, the power number is defined as about 6 (from Figure 6.6). 

The mass transfer coefficient for non-coalescing air bubbled in the fermentation broth in turbulent regime is frequently discussed in the literature.6 The volumetric mass transfer coefficient is defined by the following correlation ... 

Read Np from Figure 6.6, Chapter 6, power versus Re, for a turbulent regime, Np = 6... 

The friction correlations in the turbulent regime are compared against conventional correlations in Fig. 2.20b. Predictions for nitrogen flow by Choi et al. (1991) agree very well with conventional results the Wu and Little (1984) correlation is similar to those two in its trend, but the predicted values are much higher in mag-... 

The heat transfer correlations are considered separately in the laminar and turbulent regimes in Figs. 2.21 and 2.22, respectively. The dependence of the Nusselt number on the Reynolds number is stronger in all the micro-channel predictions compared to conventional results, as indicated by the steeper slopes of the former Choi et al. (1991) predict the strongest variation of Nusselt number with Re. The predictions for all cases by Peng et al. (1996) also fall below those for a conventional channel. 

The mechanism in the fully turbulent regime is less clear. 

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