This follows from Buckingham's Pi theorem and is more of a conceptual problem... I'm doing fluid mechanics 101, so everything's kinda new to me. They say that one reason dimensional analysis is so useful - I'm referring to grouping n variables into n-m dimensionless parameters, where m is the number of fundamental units etc. etc - is because it allows the experimenter to limit the scope of his investigation to those dimensionless parameters only. So for example, one could simply plot Reynold's number against the drag coefficient, instead of varying and holding constant consecutively, each density, velocity, viscosity, diameter and area. What I'm wondering is, what's to stop us from randomly selecting variables and experimenting on them. Why must they be dimensionless? If in the context of similarity (models), then I understand that dimensionless groups have their uses. But I have problem accepting the former. Can someone please clarify?