advantages of forming dimensionless groups in dimensional analysis and study

1.

A significant reduction in the number of “variables” to be investigated; that is, each dimensionless group, containing several physical variables, may be treated as a single compound “variable,” thereby reducing the number of experiments needed as well as the time required to correlate and interpret the experimental data.

2.

Predicting the effect of changing one of the individual variables in a process (which it may be impossible to vary much in available equipment) by determining the effect of varying the dimensionless group containing this parameter (this must be done with some caution, however).

3.

Making the results independent of the scale of the system and of the system of units being used.

4.

Simplifying the scaling-up or scaling-down of results obtained with models of systems by generalizing the conditions which must exist for similarity between a system and its model.

5.

Deducing variation in importance of mechanisms in a process from the numerical values of the dimensionless groups involved; for instance, an increase in the Reynolds number in a flow process indicates that molecular (viscous) transfer mechanisms will be less important relative to transfer by bulk flow (“inertia” effects), since the Reynolds number is known to represent a measure of the ratio of inertia forces to viscous forces.