Number pumping

The pumping number is a function of impeller type, the impeller/tank diameter ratio (D/T), and mixing Reynolds number Re = pND /p.. Figure 3 shows the relationship (2) for a 45° pitched blade turbine (PBT). The total flow in a mixing tank is the sum of the impeller flow and flow entrained by the hquid jet. The entrainment depends on the mixer geometry and impeller diameter. For large-size impellers, enhancement of total flow by entrainment is lower (Fig. 4) compared with small impellers. 

Fig. 3. Pumping numbers, N, vs mixing Ke for a pitched blade turbine. The numbers on the curves represent the ratio D/T.

Impellers are sometimes viewed as pumping devices the total volumetric flow rate Q discharged by an impeller is made dimensionless in a pumping number ... 

Dimensionless pumping number and blend time are independent of Reynolds number under fully turbulent conditions. The magnitude of concentration fluctuations from the final well-mixed value in batch mixing decays exponentially with time. 

The primary pumping capacity of an impeller is determined by the impeller diameter, the Pumping number, and the rotational speed. The Pumping number Nq is defined by [13]... 

The Pumping number is used to determine the pumping rate Qp of an impeller,... 

Hicks et al. [8] developed a correlation involving the Pumping number and impeller Reynolds number for several ratios of impeller diameter to tank diameter (D /D ) for pitched-blade turbines. From this coiTclation, Qp can be determined, and thus the bulk fluid velocity from the cross-sectional area of the tank. The procedure for determining the parameters is iterative because the impeller diameter and rotational speed N appear in both dimensionless parameters (i.e., Npe and Nq). 

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.)...

Thus, during geometric scale-up, the characteristic velocity is held constant by holding NqND constant. Qp is determined from the Pumping number and Figure 7-15. is a linear function of the characteristic velocity and is determined by... 

This is probably the most important dimensionless group used to represent the actual flow during mixing in a vessel. Flow Number, Nq (or pumping number) ... 

Figure 5-11 [28] presents an analysis of pumping number versus Reynolds Number for various vessel dimensional relationships, for turbine mixers. 

Figure 5-11. Pumping number is the basis for design procedures involving blending and motion. By permission, Hicks, R. W., ef. a/., Chem. Eng., Apr. 26,1976, p. 104 [26].

Process results, 316, 323, 324 Pumping number, 400 Radial flow, 291 Reynolds number, 299, 303 Scale up, 312-318 Shear rate, 315... 

Proceeding further, obtain the value of the terminal pumping number in the R D pilot process by using the following formula ... 

Equation 13 is the empirical relationship obtained by the linear regression between D/T and terminal pumping numbers (4). It is important to note that a family of curves exists for each D/T ratio when Nq (pumping number) is plotted versus the impeller Reynolds number (5). In the turbulent range (iVRe > 2000), the Nq curves flatten out and thus are independent of the Reynolds number. 

The terminal pumping number, iVq/Re > 2000, plotted against the D/T ratio results in Equation (13). 

Because the value of the Reynolds number is >2000, Equation (13) is used to obtain the pumping number. The pumping number is inserted into Equation (15) to obtain the effective pumping capacity. 

Figure 1 Pumping number versus impeller Reynolds number for turbine and marine type propeller agitators.

Figure 1 Various dimensionless parameters [dimensionless velocity, v = v/ND pumping number, Nq = Q/ND power number, Np=[Pgc/pN D ) and dimensionless mixing time, f = as a function of the Reynolds number for the analysis of turbine-agitator systems. Source Adapted from Ref. 22.

Earlier, the analysis established that the mixing of this product occurs in the turbulent flow regime because the Reynolds number obtained far exceeds the minimally required 2000. Therefore, the pumping number can be calculated for the 3780-L tank by using Eq. (8) to obtain... 

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