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Input interpretation:

Buckingham pi theorem (physical principle)


Description:

The Buckingham pi theorem states that an equation involving n physical variables expressible in terms of k independent fundamental units is equivalent to an equation involving a set of p = n - k dimensionless variables constructed from the original variable.


Alternate description:

Given an equation such as f(q_1, q_2, ..., q_n) = 0, where the q_i are n variables which are expressed in terms of k independent fundamental units, then the above equation can be restated as F(pi_1, pi_2, ..., pi_p) = 0, where the pi_i are dimensionless parameters constructed from the q_i by p = n - k equations of the form pi_i = q_1^(m_1)q_2^(m_2)...q_n^(m_n), where the exponents m_i are rational numbers.


History:

formulation date | 1914 (104 years ago)\nformulator | Edgar Buckingham


Associated equation:

F(pi_1, pi_2, ..., pi_p) = 0

Source information
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