Impellers power

When macro-scale variables are involved, every geometric design variable can affect the role of shear stresses. They can include such items as power, impeller speed, impeller diameter, impeller blade shape, impeller blade width or height, thickness of the material used to make the impeller, number of blades, impeller location, baffle location, and number of impellers. 

Pumps No Discharge head Input rate and power Impeller size >100 1 10 1 10... 

Trifluoroacetates of carbohydrates have been prepared 80), These substances, which are quite sensitive to hydrolysis, show some promise as intermediates in synthetic work. Trifluoroacetic anhydride is a powerful impelling reagent for the acetylation of polysaccharides 80),... 

For design calculations, impeller power must be a calculated quantity, unless power has been measured on a previously built, identical mixer. Impeller power calculations based on empirical laboratory measurements can be used successfully for most mixer design. However, as a good design practice, total calculated impeller power should not be more than about 85 or 90% of motor power. Impeller power can be as little as 50% of motor power for a conservative design with uncertain process conditions. 

Until recently most industrial scale, and even bench scale, bioreactors of this type were agitated by a set of Rushton turbines having about one-thind the diameter of the bioreactor (43) (Fig. 3). In this system, the air enters into the lower agitator and is dispersed from the back of the impeller blades by gas-fiUed or ventilated cavities (44). The presence of these cavities causes the power drawn by the agitator, ie, the power requited to drive it through the broth, to fall and this has important consequences for the performance of the bioreactor with respect to aeration (35). k a has been related to the power per unit volume, P/ U, in W/m and to the superficial air velocity, in m/s (20), where is the air flow rate per cross-sectional area of bioreactor. This relationship in water is... 

Each equation is independent of impeller type. As pointed out eadier, the absolute kpi values vary considerably from Hquid to Hquid. However, similar relationships have been found for other fluids, including fermentation broths, and also for hold-up, 8. Therefore, loss of power reduces the abiHty of the Rushton turbines to transfer oxygen from the air to the broth. 

The velocity head JT in a pipe flow is related to Hquid velocity hy H = I Qc The Hquid velocity in a mixing tank is proportional to impeller tip speed 7zND. Therefore, JTin a mixing tank is proportional to The power consumed by a mixer can be obtained by multiplying and H and is given... 

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... 

Theoretically, be correlated to interfacial tension, continuous-phase density, and power per unit mass swept by the impeller ... 

Fig. 4. Chart for efficiency estimates and curve shapes, where (a) represents curve shapes showing the relationship between efficiency (Eff), head (H), and power (P) as a function of flow (b) specific speed, where the numbers represent flow in nr /s and (c) impeller profiles.

Correlations of nucleation rates with crystallizer variables have been developed for a variety of systems. Although the correlations are empirical, a mechanistic hypothesis regarding nucleation can be helpful in selecting operating variables for inclusion in the model. Two examples are (/) the effect of slurry circulation rate on nucleation has been used to develop a correlation for nucleation rate based on the tip speed of the impeller (16) and (2) the scaleup of nucleation kinetics for sodium chloride crystalliza tion provided an analysis of the role of mixing and mixer characteristics in contact nucleation (17). Pubhshed kinetic correlations have been reviewed through about 1979 (18). In a later section on population balances, simple power-law expressions are used to correlate nucleation rate data and describe the effect of nucleation on crystal size distribution. 

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. 

Gassed Impeller Power Sensei et al. (op. cit.) have developed the following correlation for six-bladed disk impellers. 

FIG. 15-23 Power for agitation impellers immersed in single-phase liquids, baffled vessels with a gas-liquid surface [except curves (c) and (g)]. Curves correspond to (a) marine impellers, (h) flat-blade turbines, w = dj/5, (c) disk flat-blade turbines witb and without a gas-liquid surface, (d) curved-blade turbines, (e) pitcbed-blade turbines, (g) flat-blade turbines, no baffles, no gas-liquid interface, no vortex. 

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