Relevance list intermediate quantities

Many engineering problems involve several parameters, that impede the elaboration of the pi space. Fortunately, in some cases, a closer look at a problem (or previous experience) facilitates reduction of the number of physical quantities in the relevance list. This is the case when some relevant variables affect the process by way of a so-called intermediate quantity. Assuming that this intermediate variable can be measured experimentally, it should be included in the problem relevance list, if this facilitates the removal of more than one variable from the list. 

The impact that the introduction of intermediate quantities can have on the relevance list will be demonstrated in the following elegant example. 

By introducing these intermediate quantities v and p, the nine-parametric relevance list, Equation (15) reduces by three parameters to a six-parametric one... 

The fluid velocity v in pipes—or the superficial gas velocity vq in mixing vessels or in bubble columns—presents a well-known intermediate quantity. Its introduction into the relevance list removes two others (throughput q and diameter D), because v qlD and va qcID, respectively. 

The impact, which the introduction of intermediate quantities can have on the relevance list, will be demonstrated in the following by one elegant example. Example 3 Mixing-Time Characteristics for Liquid Mixtures with Differences in Density and Viscosity. The mixing time 0 necessary to achieve a molecular homogeneity of a liquid mixture—normally measured by decolorizatiorr methods—depends, in material systems without differences in density and viscosity, on only four parameters stirrer diameter d, density p, kinematic viscosity v, rotational speed ti ... 

By the introduction of the intermediate quantities p and p the relevance list (5.3) is reduced by three parameters ... 

This relevance list, which is certainly incomplete with respect to physical properties, can be streamlined significantly by introducing two intermediate quantities ... 

The impact, which the introduction of intermediate quantities can have on the relevance list, is convincingly demonstrated by the treatment of the homogenisation characteristic for mixtures with density and viscosity differences, c.f [616] and section 3.4.2. 

Wgg is an intermediate material quantity, whose incorporation in the relevance list replaces more than one of the previously listed parameters (i.e. lUgg instead of dp and see the determination equations for iVgg in section 5.3.3.1). 

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