Principle of dimensional analysis, Vaschy-Buckingham theorem

Principle of dimensional analysis, Vaschy-Buckingham theorem 

Consider a phenomenon involving n variables. Let those n variables, in turn, involve p units. The phenomenon can then be described by a relation hnking (n-p) dimensionless numbers. 

Dimensional analysis, therefore, enables a reduction of the number of variables in the functional relation linking the physical quantities that describe the behavior of a system. To understand the Vaschy Buckingham theorem, let us return to the example of the pipe flow. Initially, the system s parameters include the following  

The first five parameters are set by the user who wishes to make a fluid, whose properties he/she specifies, flow inside a chosen pipe. The sixth one, i.e. the velocity, is set based on the values of the previous five. It is this quantity (the unknown of the problem) that we want to determine based on the knowledge of 

Let us retain all these parameters. We thus wish to express the velocity as a function of the other parameters, i.e. a functional of the form 

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