Similarity criteria

Physical modeling involves searching for the same or nearly the same similarity criteria for the model and the real process. The full-scale process is modeled on an increasing scale with the principal linear dimensions scaled-up in proportion, based on the similarity principle. For relatively simple systems, the similarity criteria and physical modeling are acceptable because the number of criteria involved is limited. For complex systems and processes involving a complex system of equations, a large set of similarity criteria is required, which are not simultaneously compatible and, as a consequence, cannot be realized. 

In the set of conservation equations described earlier, the Reynolds number and the Froude number must be the same for the model and the prototype. Since most industrial operations involve turbulent flow for which the Reynolds number dependence is insignificant, part of the dynamic similarity criteria can be achieved simply by ensuring that the flow in the model is also turbulent. For processes involving hot gases (i.e., buoyancy driving forces), the Froude number similarit) yields the required prototype exhaust rate as follows. 

Pharmacoeconomics needs to address all three criteria. One reason is because effectiveness, efficiency and equity are most relevant to economic evaluations another is their intuitive appeal— we are likely to use similar criteria in spending our own personal resources and a third consideration is that they underpin public policy in many countries, including the UK. There will often be tensions between the criteria maximizing effectiveness may well not represent the most efficient use of resources, while efficiency and... 

Results with butene are not as extensive as those with propylene. Nevertheless, on the basis of the ground work laid by the more extensive propylene studies, we are able to apply similar criteria to the more limited data for butene and conclude that a x-allyl species forms. Some preliminary studies suggest that two x-allyl species form from 1-butene (65), corresponding to the syn and anti forms. The results for propylene, the fact that x-allyl species form from butene, and the fact that zinc oxide is an effective catalyst for butene isomerization strongly suggest that these x-allyls are intermediates in the isomerization reaction. 

The temperature of incubators must be uniform throughout and should not vary more than 0.2 C. The vegetative assay organism must be sensitive to the analyte, be stable (resistant to spontaneous change), be in the logarithmic growth phase (for uniformity of response), and be easily cultured, maintained and standardized. Spores suspension have similar criteria except that the spores must be capable of germinating with reasonable synchrony. 

Similar criteria apply when evaluating data obtained from the combined repeated dose toxicity study with the reproductive/developmental toxicity screening test. 

In the simplest possible case, we wish to distinguish only two objects. In optics the required specification is called a two-point resolution criterion. In spectroscopy a two-point criterion specifies the distance that must separate two spectral lines for them to be called resolved. Essentially similar criteria apply to other fields. 

The second approach consists in deliberately abandoning certain similarity criteria and checking the effect on the entire process. This technique was used by Gerhard Damkohler (1908-1944) in his trials to treat a chemical reaction in a catalytic fixed bed reactor by means of dimensional analysis. 

The principle of similarity requires geometrically similar systems to be compared at equal values of the appropriate dimensionless groups, called similarity criteria. However, in many cases, this requirement is not possible to be fulfilled, since it may be either impractical or impossible to be achieved. 

Similar criteria will be applicable when the drug is administered concomitantly with other drugs. 

When the differential equations, or in general the equations, that govern the behavior of a system are not known, such similarity criteria can be derived by means of dimensional analysis. 

Similarity criteria for scaling combustors were presented by Penner (66), who considered Damkohler s similarity groups and prescribed that the characteristic reaction frequency should decrease as the square of the engine thrust (65). Experimental evidence of combustion similarity was presented by Trent (82), who found by sampling the combustion gases at various stations in the chamber, that the local value of the charac-... 

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