# Buckingham pi theory

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## Buckingham Pi theory

A systematic method of dimensional analysis, whereby variables that are relevant to a particular atmospheric situation are formed into dimensionless groups called Pi groups.

Because the number of dimensionless groups equals the original number of variables minus the number of fundamental dimensions present in all the variables, this analysis reduces the degrees of freedom for the physical situation and can be used to guide the design of measurement programs. Buckingham Pi theory is often used in similarity theory to identify the relevant dimensionless groups. Fundamental dimensions are length, mass, time, temperature, electric current, and luminous intensity. All other dimensions can be formed from combinations of these fundamental dimensions.

*See*Pi theorem.Stull, R. B. 1988. An Introduction to Boundary Layer Meteorology. 666 pp.