The Buckingham \(π\) technique is a formal "cookbook" recipe for determining the dimensionless parameters formed by a list of variables

The symbol \(π\) is used as a placeholder, similar to how we use \(x\), \(y\), or \(z\) for unknowns, and has nothing to do with circles

The process of dimensional analysis is presented here as a series of six steps that should be followed by a seventh whenever possible

Step 1. Select Variables and Parameters
Step 2. Create the Dimensional Matrix
Step 3. Determine the Rank of the Dimensional Matrix
Step 4. Determine the Number of Dimensionless Groups
Step 5. Construct the Dimensionless Groups
Step 6. State the Dimensionless Relationship
Step 7. Use Physical Reasoning or Additional Knowledge to Simplify the Dimensionless Relationship

Step 4 is often the most difficult or mysterious step. It takes practice to know which repeating variables to choose wisely

¹Fluid Mechanics: Fundamentals and Applications Fourth Edition. Çengel and J. M. Cimbala, McGraw-Hill, New York (2018).

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