Buckingham Pi Theorem Explained: Understanding Variables and Parameters

[whiskydelta]

Heya, I'm new here and really need help!

So I'm having trouble with the *Buckingham Pi Theorem*.

I think I've got the jist of it bar one thing...So you have a bunch of variables e.g a force, velocity, denisty, length, viscosity, speed of sound:
f(F, V, roh, L, mu, a)

Do the (N variables - M fundamental dimentions):
6-3=3
to get the number of parameters:
pi1 pi2 pi3

BUT
How do know/determine which are the reoccuring variables:
eg.
pi1 = f(roh, V, L, F)
pi2 = f(foh, V, L, mu)
pi3 = f(roh, V, L, a)

AND
How do you know/determine which of the variables within each parameter doesn't go to the power of a letter (where the letters are exponents to be found)?

eg. pi1 = roh^c V^d L^e F

I hope this makes sense :)
Thanks

 

[Navin A S]

in advance!The Buckingham Pi theorem is a way to reduce the number of variables in a system. To do this, you need to identify the fundamental dimensions (such as length, density, force, etc.) that are necessary for your system. Then you can use these fundamental dimensions to determine the number of parameters (pi1, pi2, etc.) needed for the system. For example, if you had six variables with three fundamental dimensions, you would have three parameters. To determine which variables reoccur in each parameter, you will need to look at the equation or formula that describes the system, and identify which variables are dependent on each other. For example, if you have an equation that includes force, velocity, density, length, viscosity, and speed of sound, and all of these variables are connected in the equation, then they all need to be included in each parameter. To determine which of the variables within each parameter don't go to the power of a letter, you will need to look at the equation or formula and identify which variables are not raised to a power. For example, if you have an equation such as pi1 = roh^c V^d L^e F, then the only variable that doesn't go to the power of a letter is F.