Buckingham Pi Theorem

The Buckingham Pi Theorem enables one to "discover" the non-dimensional numbers for a given process and is stated as

If a physical process has "n" variables and from these "k" are Repeating Variables, then the there are "n-k" independent non-dimensional numbers that can describe that process.

For the example we have been considering there are 5 variables that govern the process. So n = 5. We have marked three repeating variables, making k = 3. The theorem tells us that there are twonon-dimensional numbers.

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