Buckingham Pi-theorem

Consider ‘n' number of independent variables for a physical option:

Or

The theorem may be interpreted to state that one can form independent dimensionless groups of variables so that are the dimensionless groups, and M (mass), L (length) and T (time) are the primary dimensions used to describe the system. For some systems, angle may also be taken as a primary group, for which one can have (n-4) independent dimensionless groups. We explain the utility of this method in the following examples:

1. Reconsider the previous example of drag on a sphere immersed in a flowing fluid. From the physics of the problem, the independent variables that govern the drag are identified as . Therefore,

As per the Buckingham Pi-theorem, the number of dimensionless groups that can be formed is .

Therefore,