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BUCKINGHAM'S PI THEOREM

The dimensions in the previous examples are analysed using Rayleigh's Method. Alternatively, the relationship between the variables can be obtained through a method called Buckingham's π. Buckingham ' s Pi theorem states that: If there are n variables in a problem and these variables contain m primary dimensions (for example M, L, T) the equation relating all the variables will have (n-m) dimensionless groups. Buckingham referred to these groups as π groups. The final equation obtained is in the form of : πl = f(π2, π3 ,….. πn-m ) The π groups must be independent of each other and no one group should be formed by multiplying together powers of other groups. This method offers the advantage of being more simple than the method of solving simultaneous equations for obtaining the values of the indices (the exponent values of the variables). In this method of solving the equation, there are 2 conditions: a. Each of the fundamental dimensions must appear in at least one of the m variables b. It must not be possible to fom1 a dimensionless group from one of the variables within a recurring set. A recurring set is a group of variables forming a dimensionless group

Documents

File:Buckinghamforlect1.pdf

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