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February 10th, 2014, 06:07 AM   #1
Joined: Feb 2014

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Tricky dimensional analysis


I have a problem related to dimensional analysis. I have 6 variables and they are: Ac [kg m^-3 s^-2], C [kg m^-3 s^-2], Pave [kg m^-1 s^-2], Pg [kg s^-2 m^-2], Pgk [kg s^-2 m^-2], Vk [m s^-1]. In this problem Vk is dependent variable or I could say the variable I want to solve for. Basic dimension in this problem are M (for kg), L (for m) and T (for s). However, since M T^-2 is in all terms, I believe that M and T are not independent dimensions which complicates the problem. The additional problem is that Ac and C have the same dimensions, as well as Pg and Pgk.

My concern in this problem is how many Pi groups I should have and what should be my repeating variables?

Thank you very much!
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