Similarity parameters

C. G. Sinclair [Chem. Process. E/ig., 47, 147 (1966)] has considered similar parameters to the (EMIP) and (IRP) based on a cumulative-discounted-cash-flow curve. 

Strictly speaking, these are all phasor quantities but only their magnitudes are considered for ease of illustration, as quantities of similar parameters such as /f. hi and f,2 fall almost in phase with each other. 

This will be carried out under similar parameters of room condition and the type of test voltage wave to those for a switchgear assembly (Section 14.3.5). The current in each phase should be within 2% of the specified test value (rated current). 

Turbomachines can be compared with each other by dimensional analysis. This analysis produces various types of geometrically similar parameters. Dimensional analysis is a procedure where variables representing a physical situation are reduced into groups, which are dimensionless. These dimensionless groups can then be used to compare performance of various types of machines with each other. Dimensional analysis as used in turbomachines can be employed to (1) compare data from various types of machines—it is a useful technique in the development of blade passages and blade profiles, (2) select various types of units based on maximum efficiency and pressure head required, and (3) predict a prototype s performance from tests conducted on a smaller scale model or at lower speeds. 

When using dimensional analysis in computing or predicting performance based on tests performed on smaller-scale units, it is not physically possible to keep all parameters constant. The variation of the final results will depend on the scale-up factor and the difference in the fluid medium. It is important in any type of dimensionless study to understand the limit of the parameters and that the geometrical scale-up of similar parameters must remain constant. 

Thermal analysis is really no more diffieult than Ohm s Taw. There are similar parameters to voltage, resistanee, nodes, and branehes. For the majority of elee-tronie applieations, the thermal eireuit models are quite elementary and if enough is known of the thermal system, values ean be ealeulated in a matter of minutes. If one has a temperature-measuring probe, the thermal eomponents ean also easily be measured and ealeulated. 

Newby et al. 6 also studied a steam/TCR cycle with similar parameters and steam/air ratio. They calculated an efficiency of 48.7%, compared with 35.7% for a comparable CBT plant, 45.6% for a STIG plant and 56.8% for a CCGT plant, all for similar pressure ratios and top temperatures. 

Thus, the ratios of the various forces occurring in mixing vessels can be expressed as the above dimensionless groups which, in turn, serve as similarity parameters for scale-up of mixing equipment. It can be shown that the existence of geometric and dynamic similarities also ensures kinematic similarity. 

After performing this exercise you will get similar parameters to those obtained by more elaborated free-energy calculations and summarized in Table 8.1. A similar procedure can be used for the second step where the... 

Although the conductivity change Aa [relation (8)] of microwave conductivity measurements and the Ac of electrochemical measurements [relation (1)] are typically not identical (owing to the theoretically accessible frequency dependence of the quantities involved), the analogy between relations (1) and (8) shows that similar parameters are addressed by (photo)electrochemical and photoinduced microwave conductivity measurements. This includes the dynamics of charge carriers and dipoles, photoeffects, flat band and capacitive behavior, and the effect of surface states. 

The isopropoxy compound 25f reacts about an order of magnitude faster than 25a, 25c and 25g. A measurably larger AS is consistent with additional relief of steric compression in the transition state the protonated intermediate (Fig. 14a) would be sp3 hybridised at nitrogen while the alkoxynitrenium ion (Fig. 14c) would be sp2 hybridised at nitrogen. The isobutoxy compound 25g, in which the branching is one methylene removed from the oxygen atom has similar parameters to straight chain substrates 25a and 25c. 

The same analysis can be performed on the effect of the similar parameters k, rmax, 1 > k2 and rmax - The steady-state flux increases when any of them increases. As seen in Figure 5f for the particular case of rmax,i variation, there are two asymptotic limits for J s given by the fixed Ju>2 (at low rm lX)i) and by the fixed limiting diffusion value (see equation (16) and Figure 5e). 

If this model is selected, one must then decide what variables to use for the ordinate and the abscissa. The parameters must be dose-sensitive, free of confounding variables, easily determined and preferably linear. We have evaluated this approach for estimating the bioavailability of calcium in mechanically deboned meat products (11). Typically, correlations between various bone parameters and dietary calcium are very high (r = 0.943 to 0.999). This is consistent with what others have found for similar parameters (46,47). These correlations are also similar to the those (r = 0.947 to 0.982) between the amount of calcium consumed and calcium retained (11) a good index procedure. 

A next-level assay is usually an isolated heart/cardiac tissue preparation. The canine Purkinje fiber assay (GLP) measures several action potential parameters, like resting membrane potential, upstroke velocity, action potential duration and shape, but also if a drug acts reverse-use dependently [72]. Based on changes of the action potential shape it is possible to conclude which ion channels are modulated (e.g., L-type calcium channel block would abolish the plateau phase). The papillary muscle assay (e.g., guinea pigs) determines similar parameters [73]. 

There are three techniques of developing the dimensionless similarity parameters. The use of Buckingham s pi theorem can be found in most fluid mechanics books, where the variables of importance are used to determine the number of dimensionless parameters that should describe an application and help to identify these parameters. One difficulty with Buckingham s pi theorem is the unspecified form of the dimensionless numbers, which can result in unusual combinations of parameters. 

Mean value and other similar parameters Distribution spread... 

Dimensionless correlations based on momentum-or energy-balances and using the Lockhart and Martinelli parameter, Xc, or some similar parameter. The practical relevance of such correlations is limited since their use requires the knowledge of the single-phase pressure drop of both gas and liquid furthermore, the influence of the geometry of the bed is not always well described by these single-phase pressure drops alone. 

EPR parameters for the Cu(R2Dtc)2 complexes in frozen solutions (515, 595) or in host lattices of Ni(R2Dtc)2 or Zn(R2Dtc)2 have been obtained for various guest/host ratios (167, 450b). Similar parameters have been obtained for the Ag(R2Dtc)2 complexes (605, 606). 

The effect of pressure on burner flames is related to the burner diameter the parameter Uo/pd correlates blow-off data for various fuel concentrations (40). In other words, for a given burner and mixture, the blow-off velocity is proportional to the pressure. Quite similar parameters serve for supported flames as well (Table IV). 

It is clear that this method cannot be based on the use of similarity parameters since reactive molding in common with other chemical engineering processes, involves nonlinear phenomena that result in the invalidity of similarity conditions as geometric, chemical, and thermal parameters. 

All data should be inspected by calculating variable means, standard deviations, skewness and similar parameters. Even better is to plot the data in all potentially useful ways, in particular various kinds of scatterplots of, for example, intervariable correlations and residuals. These methods will not be penetrated further in this paper because they can be found easily in any... 

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