Assume, a physical phenomenon is described by m number of independent variables like x₁ , x₂ , x₃ , ..., x_m

The phenomenon may be expressed analytically by an implicit functional relationship of the controlling variables as

Now if n be the number of fundamental dimensions like mass, length, time, temperature etc ., involved in these m variables, then according to Buckingham's p theorem -

The phenomenon can be described in terms of (m - n) independent dimensionless groups like π₁ ,π₂ , ..., π_m-n , where p terms, represent the dimensionless parameters and consist of different combinations of a number of dimensional variables out of the m independent variables defining the problem.

Therefore. the analytical version of the phenomenon given by Eq. (19.2) can be reduced to

(19.3)

according to Buckingham's pi theorem

• This physically implies that the phenomenon which is basically described by m independent dimensional variables, is ultimately controlled by (m-n) independent dimensionless parameters known as π terms.