Dimensional Analysis and buckingham pi

[GBA13]

Homework Statement

Hi Guys,

I am a bit confused concerning one part of this topic. Specifically when trying to find non dimensional groups. My problem is a small thing in the finding of the indices.

So, for example, your are trying to find a pi group when finding the drag on a car.
so you have D,A,V,rho.

then you find indices by doing [M][L][T]^-2 ([L]^2)^a ...

and then do [L]: 0 = 1 + 2a...

but sometimes I have seen in solution people doing

[L]: 1 = 2a...

This obviously gives a different answer to the one above. as a = 1/2 for the bottom one and -1/2 for the other. I am confused about which one we are supposed to use for what

Homework Equations

The Attempt at a Solution

One thing I am finding is that often when it is like

[L]: 1= 2a.. that is because the pi group has been labelled D = kA^aV^b rho^c or something like that while then it looks like

[L]: 0 = 1 + 2a... it is normall labeled DA^aV^b rho^c. I am not sure what the difference is but the two methods give different numbers and I'm not sure when one should be used or not. I'm not sure why k is in the group above and isn't in the one below etc..

All I am tyring to do is form a functional relationship with things.

Thanks, I'm sorry if this is a bit disjointed I am struggling to explain it!

I would really appreciate someone setting me straight.

 

[GBA13]

Actually I think I may have just solved it! I'm thinking it means the same thing, and when rearranged they are the same, just different ways of doing the same thing! If I'm wrong please jump in! :)