Numbers powers

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. 

Fig. 6. (a) Effect of baffling and D/T on power number relative to for standard configuration and (b) effect of dual impeller spacing on power... 

The power P drawn by the impeller is made dimensionless in a group called the power number ... 

Figure 6-40 shows power number vs. impeller Reynolds number for a typical configuration. The similarity to the friction factor vs. Reynolds number behavior for pipe flow is significant. In laminar flow, the power number is inversely proportional to Reynolds number, reflecting the dominance of viscous forces over inertial forces. In turbulent flow, where inertial forces dominate, the power number is nearly constant. 

FIG. 6-40 Dimensionless power number in stirred tanks. (Reptinted with petTwssion from Bates, Fondy, and Cotpstein, Ind. Eng. Gbem. Process Design Develop., 2, 310 [1.963].)... 

Radial-flow impellers include the flat-blade disc turbine, Fig. 18-4, which is labeled an RlOO. This generates a radial flow pattern at all Reynolds numbers. Figure 18-17 is the diagram of Reynolds num-ber/power number curve, which allows one to calculate the power knowing the speed and diameter of the impeller. The impeller shown in Fig. 18-4 typically gives high shear rates and relatively low pumping capacity. 

Power Consumption of Impellers Power consumption is related to fluid density, fluid viscosity, rotational speed, and impeller diameter by plots of power number (g P/pN Df) versus Reynolds number (DfNp/ l). Typical correlation lines for frequently used impellers operating in newtonian hquids contained in baffled cylindri-calvessels are presented in Fig. 18-17. These cui ves may be used also for operation of the respective impellers in unbaffled tanks when the Reynolds number is 300 or less. When Nr L greater than 300, however, the power consumption is lower in an unbaffled vessel than indicated in Fig. 18-17. For example, for a six-blade disk turbine with Df/D = 3 and D IWj = 5, = 1.2 when Nr = 10. This is only about... 

Power Number a dimensionless number used to describe the power dissipation of impeller and which is given by Np = Pg,/pN D where P = impeller power dissipation and g, = gravitational conversion factor. 

Np = power number, dimensionless (see Figure 20 or 21) p = fluid density at eonditions, kg/m ... 

Figure 25. Plot provides effect of baffling and D/T on the power number.

This chapter reviews the various types of impellers, die flow patterns generated by diese agitators, correlation of die dimensionless parameters (i.e., Reynolds number, Froude number, and Power number), scale-up of mixers, heat transfer coefficients of jacketed agitated vessels, and die time required for heating or cooling diese vessels. 

Experimental data on power eonsumption are generally plotted as a funetion of the Power number Np versus Reynolds number Np, that is by rearranging Equation 7-14. 

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

At high Reynolds, at which most mixing operations are performed, the Power number is constant, that is, Np P/pN D = constant. 

Rush ton et al. [10] investigated the effect of varying the tank geometrical ratios and the correlation of the Power number with Reynolds number. At high Reynolds number, it was inferred that. 

The power eonsumed by an agitator at various rotational speeds and physieal properties (e.g., viseosity and density) for a system s geometry ean be determined from the Power number eorrelation. The proeedure involves ... 

Reading the Power number Np from the appropriate eurve, and ealeulating the power P given by... 

Figure 7-15 shows plots of Pumping number Nq and Power number Np as functions of Reynolds number Np for a pitched-blade turbine and high-efficiency impeller. Hicks et al. [8] further introduced the scale of agitation, S, as a measure for determining agitation intensity in pitched-blade impellers. The scale of agitation is based on a characteristic velocity, v, defined by... 

Figure 7-15. Power number and Pumping number as functions of Reynolds number for a pitched-blade turbine and high-efficiency impeller. (Source Bakker, A., and Gates L. , Properly Choose Mechanical Agitators for Viscous Liquids," Chem. Eng. Prog., pp. 25-34, 1995.)...

Using curve 6 in Figure 7-14, the Power number is Np = 5.0. The theoretical power for mixing is... 

Studies on various turbine agitators have shown that geometrie ratios that vary from the standard design ean eause different effeets on the Power number Np in the turbulent regions [24]. 

A baffled, vertieal square tank or a horizontal eylindrieal tank has the same Power number as a vertieal eylindrieal tank. 

Knowing the value of N2, the required power ean be determined using Equation 7-17 and tlie generalized Power number eoirelation. 

Assuming that the equation is in the turbulent range, the Power numbers will be equal. The ratio of the power per unit volume (P/V) for large and small seales ean be expressed by... 

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