Buckingham  Theorem http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...
8.2 Buckingham  Theorem
In 1915 Buckingham 1 showed that the number of independent dimensionless groups of variables
(dimensionless parameters) needed to correlate the variables in a given process is equal to n - m, where n is the
number of variables involved and m is the number of basic dimensions included in the variables.
Buckingham referred to the dimensionless groups as , which is the reason the theorem is called the  theorem.
Henceforth dimensionless groups will be referred to as Ä„-groups. If the equation describing a physical system
has n dimensional variables and is expressed as
then it can be rearranged and expressed in terms of (n - m) Ä„-groups as
Thus if the drag force F of a fluid flowing past a sphere is known to be a function of the velocity V, mass
density Á, viscosity µ, and diameter D, then five variables (F, V, Á, µ, and D) and three basic dimensions (L, M,
and T) are involved.* By the Buckingham  theorem there will be 5 - 3 = 2 Ä„-groups that can be used to
correlate experimental results in the form
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