# Dimensional Analysis: Buckingham Pi Theorem

I am studying for a fluids quiz and I am having a few problems relating to dimensional analysis but for the time being fundamentally I have a problem selecting the repeating variables. Like does anyone know an effective way of determining them or an approximate list one should start with?

In particular if one looks here

I don't understand two things:

1. How do you choose what repeating variables to use - my assumption based on what I've read in the text and online is you want something that is not dimesionless, that is the variable must not be and when you put it all together it cannot be dimessionless.

2. Now assuming I understand that correctly, do you always just set it equal to $F^0L^0T^0$?

Sidenote - so one thing I couldn't have done is chosen D and l as repeating variables, because they are the same thing basically. Apart from that I could have done, any combination of $\mu, V, D, or \sigma$ correct?

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## 2 Answers

If you think of the exponents of the base units as forming a vector, you want to choose a set of repeating variables which are linearly independent and span the space.

The pi variables are dimensionless by definition, so you set the exponents of each unit to 0.

But yes, there can be more than one correct combination of variables.

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OK, thanks alot. –  eWizardII Dec 4 '11 at 6:16

Look at this page , explained very well

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Hi Bob, welcome to Physics.SE. We expect answers to be able to mostly stand on their own and provide enough information that the link isn't strictly needed. In this case, your link would work better as a comment. –  Brandon Enright May 31 '13 at 22:25

## protected by Qmechanic♦May 31 '13 at 21:43

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