About: Buckingham π theorem

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In engineering, applied mathematics, and physics, the Buckingham π theorem is a key theorem in dimensional analysis. It is a formalization of Rayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically meaningful equation involving a certain number n of physical variables, then the original equation can be rewritten in terms of a set of p = n − k dimensionless parameters π1, π2, ..., πp constructed from the original variables. (Here k is the number of physical dimensions involved; it is obtained as the rank of a particular matrix.)

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rdfs:label	Buckingham π theorem (en)
rdfs:comment	In engineering, applied mathematics, and physics, the Buckingham π theorem is a key theorem in dimensional analysis. It is a formalization of Rayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically meaningful equation involving a certain number n of physical variables, then the original equation can be rewritten in terms of a set of p = n − k dimensionless parameters π1, π2, ..., πp constructed from the original variables. (Here k is the number of physical dimensions involved; it is obtained as the rank of a particular matrix.) (en)
sameAs	Buckingham π theorem
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Cite_news dbt:Cite_web dbt:Em dbt:Pi dbt:Portal dbt:Refbegin dbt:Refend dbt:Reflist dbt:Sfn dbt:Short_description
Subject	Articles containing proofs Dimensional analysis Physics theorems
Link from a Wikipage to an external page	https://zenodo.org/record/1429603 http://www.gidropraktikum.narod.ru/pi-theorem-history.htm https://archive.org/details/transactionsof37amer https://archive.org/details/transactionsof37amer/page/263 https://babel.hathitrust.org/cgi/pt%3Fid=uc1.31210014450082&view=1up&seq=905 https://babel.hathitrust.org/cgi/pt%3Fid=uiug.30112098055970&view=1up&seq=31 http://www.georgehart.com/research/multanal.html http://www.mcs.vuw.ac.nz/~vignaux/docs/maxent.pdf http://www.msu.edu/~sheppa28/constants/constants.html http://www.math.ntnu.no/~hanche/notes/buckingham/buckingham-a4.pdf
thumbnail	wiki-commons:Special:FilePath/Edgar_Buckingham_by_Pach_Brothers_c1886.jpg?width=300
foaf:depiction
gold:hypernym	Theorem
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Buckingham_π_theorem?oldid=1070748485&ns=0
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Link from a Wikipage to another Wikipage	Nondimensionalization Proceedings of the Royal Society Proportionality (mathematics) Row echelon form Small-angle approximation Unit of measurement Ampere Applied mathematics Blast wave Boyle's law Buckingham π theorem Candela Articles containing proofs Dimensional analysis Physics theorems Joseph Bertrand Dimensional analysis Dimensionless quantity Dimitri Riabouchinsky Metre Physical Review Physics Second Zero of a function Clearing denominators Kilogram Linear map Edgar Buckingham Reynolds number Engineering Gaussian elimination Identity (mathematics) Kelvin Kernel (linear algebra) Pendulum (mechanics) Scientific law International System of Units John William Strutt, 3rd Baron Rayleigh Mole (unit) Vector space Standard gravity Theorem Matrix (mathematics) Natural units Nature (journal) Rank (linear algebra) Rank–nullity theorem Rational number Rayleigh's method of dimensional analysis Similarity (geometry) Similitude dbr:Annales_Télégraphiques dbr:Transactions_of_the_American_Society_of_Mechanical_Engineers
has abstract	In engineering, applied mathematics, and physics, the Buckingham π theorem is a key theorem in dimensional analysis. It is a formalization of Rayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically meaningful equation involving a certain number n of physical variables, then the original equation can be rewritten in terms of a set of p = n − k dimensionless parameters π1, π2, ..., πp constructed from the original variables. (Here k is the number of physical dimensions involved; it is obtained as the rank of a particular matrix.) The theorem provides a method for computing sets of dimensionless parameters from the given variables, or nondimensionalization, even if the form of the equation is still unknown. The Buckingham π theorem indicates that validity of the laws of physics does not depend on a specific unit system. A statement of this theorem is that any physical law can be expressed as an identity involving only dimensionless combinations (ratios or products) of the variables linked by the law (for example, pressure and volume are linked by Boyle's law – they are inversely proportional). If the dimensionless combinations' values changed with the systems of units, then the equation would not be an identity, and the theorem would not hold. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Buckingham_π_theorem
is Wikipage redirect of	Buckingham Pi Buckingham p-theorem Buckingham p theorem Buckingham's Pi Theorem Buckingham's pi theorem Buckingham's Π (Pi) Theory Buckingham-Pi theorem

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