What are the limitations and assumption made in Buckingham Pi Theorem for non dimensional analysis. Comment on the accuracy over Rayleigh’s method
I suggest to have a look at Wikipedia (see the link below). The information there answers your question pretty well in my opinion, also regarding the Rayleigh method.
The theorem describes a general procedure - on the basis of a proper identification of the relevant physical quantities. In the example of the pendulum discussed in the link, a further dimensionless quantity like the maximum swing angle changes the result of the theorem obtained for the limit of small angles. Thus, to apply the theorem requires a lot of physical insight.
http://en.wikipedia.org/wiki/Buckingham_pi_theorem
\\What are the limitations and assumption made in Buckingham Pi Theorem for non dimensional analysis\\
The most important is to know the influential quantities on the physical phenomena, this is if you do not know the mathematical laws.
You should specify the repeating groups to describe many different dimensions.
For example do not use length and width as repeating groups but length and material property and so on !
You can visit my profile because I put many quesyions regarding this topic and answers may help you.
Best Regards;
Read this about Rayligh's method:
http://books.google.com.eg/books?id=Q6iflrgVaWcC&pg=PA69&dq=Rayleigh%E2%80%99s+method+non+dimensional+analysis&hl=en&sa=X&ei=Ni0YVLzsB5CTuASYroK4Ag&ved=0CCsQ6AEwAzgK#v=onepage&q=Rayleigh%E2%80%99s%20method%20non%20dimensional%20analysis&f=false
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