Buckingham Pi Theorem

Buckingham Pi Theorem relies on the identification of variables involved in a process. Further, a few of these have to be marked as "Repeating Variables". This would seem to be a major difficulty in carrying out a dimensional analysis. Let us continue with our example of drag about a cylinder. We have identified the variables involved - F (drag force), D(diameter of the cylinder), V (the fluid velocity), $\rho$ (density of the fluid), $\mu$ (viscosity of the fluid). Now we mark three of these as the Repeating Variables - V, D and $\rho$. The selection comes by practice. Some general guidelines can however be given. These variables combine with the non-repeating ones to form the non-dimensional numbers. Further, they do not form a non-dimensional number themselves. A general prescription is to consider velocity, linear dimension and density to be the Repeating Variables. But by looking at the list of variables one can often intuitively tell the Repeating Variables from the rest.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney