Governing variable

In applying dimensional analysis, it is first necessary to be able to identify the variables that govern a particular physical phenomenon. The naming of the governing variables requites some prior knowledge of a particular branch of physics involved. This may include analytical studies, experimental observations, or both. Whatever the source, there must be some prior knowledge upon which a selection can be made. 

The governing variables are accurately known, are independent of each other (orthogonal) and span wide value ranges. 

In view of the extreme importance of the impinging velocity, n(), in the implementation of impinging stream technology, in all the investigations worked by the author of this book u0 is employed as the governing variable, as was done in the chapter on absorption. 

As mentioned above, to determine one value for fM needs an experimental curve of X, versus u0 for the case where the impinging velocity m() is taken as the governing variable. The plot of a set of typical data is indicated in Fig. 10.12. From the curve the critical point at which Xs turns from a varying value to a small constant is found at u -0.184 m/s. With the known reaction rate constant at 298 K, the micromixing time can be calculated as... 

While we do not want to give a sophisticated model including all the effects found in the mechanical behavior of polymers, we restrict ourselves to the simplest case, namely to an elastic small-strain model at constant temperature. Therefore, the governing variables are the linear strain tensor [Eq. (13)] derived from the spatial gradient of the displacement field u, and the microstructural parameter k and its gradient. The free energy density is assumed to be a function of the form of Eq. (14). 

M.K. Atesmen, Everyday heat transfer problems sensitivities to governing variables (2009)... 

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