Difference between revisions of "Pi theorem"
From Glossary of Meteorology
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| − | <div class="definition"><div class="short_definition">( | + | <div class="definition"><div class="short_definition">(''Or'' [[Buckingham Pi theory]].) The basis for [[dimensional analysis]].</div><br/> <div class="paragraph">The theorem states that an equation for a physical system that can be written ''f''(''Q''<sub>1</sub>, ''Q''<sub>2</sub>, . . . , ''Q''<sub>''m''</sub>) = 0 can also be written as ''g''(''π''<sub>1</sub>, ''π''<sub>2</sub>, . . . , ''π''<sub>''m'' - ''n''</sub>) = 0 where ''Q''<sub>''i''</sub> are ''m'' dimensional parameters, numbers, and [[variables]]; π<sub>''i''</sub> are ''m'' - ''n'' nondimensional quantities; and ''n'' is the number of fundamental dimensional units.</div><br/> </div> |
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Latest revision as of 15:50, 20 February 2012
Pi theorem
(Or Buckingham Pi theory.) The basis for dimensional analysis.
The theorem states that an equation for a physical system that can be written f(Q1, Q2, . . . , Qm) = 0 can also be written as g(π1, π2, . . . , πm - n) = 0 where Qi are m dimensional parameters, numbers, and variables; πi are m - n nondimensional quantities; and n is the number of fundamental dimensional units.
