Dimensional ratios

Unfortunately the literature is rampant with data obtained from cyclones of so wide a variety of deviating dimensional ratios and ill defined particle properties, sizes and loadings, that full agreement between designers, theorists and practitioners has not yet been achieved. However, in practice, the enormous number of cyclones installed in identical industrial process applications in the petroleum and petrochemical industries (Zenz, A P I., 1975) throughout the world and spurred by a common interest in economics and environmental regulations, has led to the correlations shown as the solid curves in Figs. 2 and 3. 

Table 2. Radii and dimensional ratios formed with the molecular parameters of Table 1...

Table 5.11 Typical dimensional ratios for bioreactors with 3 multibladed impellers.

Down-pumping axial flow impellers are more appropriate for most particle-suspension operations (Perry and Green, 1984). Typical dimensional ratios are DT/Da = 2-3.3, and Za/DT = 0.25-0.5. The power can be calculated as in the case of liquid agitation (see eq. (3.107)) (Perry and Green, 1984). 

The dimensional ratios of indentations obtained with the first three, most common, indenters, taking indentation depth to be 1, are for the measured parameters 7—with the Vickers indenter 30.5—with the Knoop indenter 7.4—with the Berkovich indenter. 

Equations (6.198)-(6.200) can be arranged to show dimensionless or dimensional ratios, which express only the LM or the prototype. These dimensionless or dimensional relations are called similitude simplexes when they result from the same type of parameters and similitude multiplexes when they are composed of different types of parameters. 

Cyclone Separators. The most commonly used equipment for the separation of dust particles from an air/gas stream is the cyclone separator. The literature on design and operation of cyclones has been extensively reviewed by Rietemer and Vetver (1961), Maas (1979), Zenz (1982), and Pell and Dunson (1999). A sketch of a cyclone separator and typical dimensional ratios are found in Figure 20.1(b). The dust-laden gas stream enters near the top of the collection chamber tangentially. The force on the larger particles is greater than the force on the smaller ones because the latter... 

Let ca in cm-2 be the equilibrium number concentration of the tracer entities in the adsorption layer, and cg in cm-3 the concentration in the gaseous phase. Experimental studies have shown that a range of small ca values (in the sense of surface coverage much less than unity) always exists, over which the dimensional ratio of the concentrations fca, the distribution coefficient... 

This is consistent with our assumption that Id > V only when u/D < 1. The ratio of the diffusivity of momentum and of the diffusivity of concentration defines the Schmidt number Sc = u/D. This description also applies to temperature fluctuations in turbulent flows, when the temperature field can be approximated as a passive scalar. In that case the diffusion coefficient is replaced by the heat conduction coefficient n and the non-dimensional ratio Pr = u/n is known as the Prandtl number. 

To make up the difference between the expected expander returned power and the required compressor input power. Meruit designed an air system using a commercially available positive-displacement compressor driven by an electric motor in tandem with Meruit s turbocompressor. Meruit designed a family of compressor and expander wheels with var5dng characteristics (specific speed, dimensional ratios, etc.) representing different compromises in providing performance compatible with the DOE specifications. After extensive evaluation, a compressor wheel was chosen to provide a desired pressure curve over a wide range of mass flows, and a turbine wheel was matched to it. The chosen compressor wheel is intended to trade peak efficiency for extended turndown performance. 

Down-pumping axial flow impellers are more appropriate for most paiticle-suspension operations (Peiiy and Green, 1984). Typical dimensional ratios are = 2-3.3, and... 

Among all dimensionless numbers, the most important is the capillary number Ca based on the mean continuous phase velocity, usually ranging between 10 and 10 in most microfluidic devices, while additional dimensionless parameters are the ratio between flow rates = qjqoui between viscosities A. = p, / and the geometric dimensional ratio typically given by the ratio of channel widths wr =... 

This form is easy to remember, since the dimensional ratio y/x appears throughout. The occurrence of this ratio suggests the substitution y/x = vix). 

In a manner similar to the first order case, we attempt to rearrange certain equations into the homogeneous format, which carries the dimensional ratio... 

The typical dimensional ratios used are DJD, = 0.95, with some ratios as low as... 

Geometric similarity of two bodies of different scale is achieved by fixing corresponding dimensional ratios. 

Electrode Size and Dimensional Ratio Effect on the Resonant Characteristics of Piezoelectric Ceramic Disk... 

In this study, the vibration characteristics of a thin piezoelectric ceramic disk with different electrode size and dimensional ratio are study by the impedance analysis method. 

Two groups of samples were used in this study, one group used for electrode size study, the other group used for dimensional ratio effect. The diameter and thickness of samples used... 

Some scale-up methods emphasize geometric similarity. This refers to holding constant the impeller geometry, the impeller dimensional ratios (such as D/T, W/D, C/T), the liquid height/tank diameter ratio, and baffling. There are many situations when complete geometric similarity is not feasible for example, when the aspect ratio of commercial scale tanks needs to be larger than the laboratory tank. 

Fig. 6.27 Comparison between concentration factors k and k obtained with FE calculations and Neuber s rule, respectively, vs. the non-dimensional ratio of nominal stress (T to yield strength (jy [38]...

To use Eq. (5.2.1), we need to calculate the velocities Vrcs and vecs from Eqs. (4.2.4)-(4.2.6), following the procedure outlined in Appendix 5A. In doing this, we note that the velocities we calculate are only functions of dimensional ratios". In other words, for a constant inlet velocity the internal velocities we calculate are independent of the scale of the cyclone. 

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