Dimensional analysis (fluid mechanics context)

[Kenny Lee]

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?

 

[Astronuc]

For one thing, it is the cost involved in fabricating a full size prototype - with all the materials, tooling, parts fabrication, possibly new fabrication techniques. It's much less expensive to build a scale model.

The idea of dimensional analysis allows one to build a scale model of something - car, truck, aircraft, ship, nuclear fuel assembly, rocket - and then test it over a range of thermohydraulic parameters, including flow sweep tests.

Suppose one to test at range of temperature and pressure conditions - e.g. temperatures 200 - 350°C and pressure 7 bar - 18 bar. Testing a large product requires a large (full size) testing rig. So a scale model of the prototype means a smaller testing system.

Most of the time time testing scale models works. Applying to dynamic analysis sometimes has short comings.