# Buckingham π theorem if there are k variables ݑଵ

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3.Buckingham πTheorem If there are k variables ݑ, ݑ, ݑ, ⋯ , ݑݑൌ ݂ሺݑ, ݑ, ⋯ , ݑwhere f is a function, then we can form (k r) πgroups ߨ, ߨ, ߨ, ⋯ , ߨ௞ି௥, so that ߨൌ ݃ሺߨ, ߨ, ⋯ , ߨ௞ି௥where r is the number of basic dimensionsand g is a different function. 4.Procedures for applying Buckingham πTheorem: a.Determine relevant variables for a given problem. b.Determine the dimensions of all variables and the number of basic dimensions. c.Determine the number of πgroups. d.Select repeating variables: e.Form πgroups. f.Check that the resulting πgroups are indeed non-dimensional. g.Express the final functional form using the πgroups. and
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