Difference between revisions of "Pi theorem"

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<div class="definition"><div class="short_definition">(<br/>''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''(''&#x003c0;''<sub>1</sub>, ''&#x003c0;''<sub>2</sub>, . . . , ''&#x003c0;''<sub>''m'' &minus; ''n''</sub>) = 0 where ''Q''<sub>''i''</sub> are ''m'' dimensional parameters,  numbers, and [[variables]]; &#x003c0;<sub>''i''</sub> are ''m'' &minus; ''n'' nondimensional quantities; and ''n'' is the number of fundamental  dimensional units.</div><br/> </div>
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<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''(''&#x003c0;''<sub>1</sub>, ''&#x003c0;''<sub>2</sub>, . . . , ''&#x003c0;''<sub>''m'' - ''n''</sub>) = 0 where ''Q''<sub>''i''</sub> are ''m'' dimensional parameters,  numbers, and [[variables]]; &#x003c0;<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


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.


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