This is more of a dimensional analysis or unit analysis problem than a basic analysis problem. So if I didn't post this thread in the right forum, please delete it. Moving on, I'm having trouble grasping the concepts behind the Buckingham Pi Theorem. After reading some textbooks and doing some research on the internet, I've found out that is a theorem that correlates mathematics with physical science. Mathworld defines the Buckingham Pi Theorem like this: physical laws are independent of the form of the units; therefore, acceptable laws of physics are homogeneous in all dimensions. Now, here's where I'm having troubles. Since the function becomes homogeneous, do you have to use Euler's Homogeneous Function Theorem? Or is there another way to do the problem once factored? When applying the Buckingham Pi Theorem, will you always end up with a homogeneous function on the way to your answer? Does the theorem ever "fail"? Sorry if I'm missing something here, but I'm trying to learn advanced mathematics on my own so I get a better understanding of aerodynamics. So please, if I'm misinterpreting something, let me know. Any help is greatly appreciated.