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Dimensional analysis
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== References == * {{citation | first = G. I. | last = Barenblatt | author-link = Grigory Barenblatt | year = 1996 | title = Scaling, Self-Similarity, and Intermediate Asymptotics | location=Cambridge, UK | publisher = Cambridge University Press | bibcode = 1996sssi.book.....B | isbn=978-0-521-43522-2 }} * {{citation | last1 = Bhaskar | first1 = R. | last2 = Nigam | first2 = Anil | year = 1990 | title = Qualitative Physics Using Dimensional Analysis | journal = Artificial Intelligence | volume = 45 | issue = 1β2 | pages = 73β111 | doi = 10.1016/0004-3702(90)90038-2 }} * {{citation | last1 = Bhaskar | first1 = R. | last2 = Nigam | first2=Anil | year = 1991 | title = Qualitative Explanations of Red Giant Formation | journal = The Astrophysical Journal | volume = 372 | pages = 592β6 | doi = 10.1086/170003 | bibcode=1991ApJ...372..592B| doi-access = free }} * {{citation | last1 = Boucher | last2 = Alves | year = 1960 | title = Dimensionless Numbers | journal = Chemical Engineering Progress | volume = 55 | pages = 55β64 }} * {{citation | first = P. W. | last = Bridgman | author-link = Percy Williams Bridgman | year = 1922 | title = Dimensional Analysis | publisher = Yale University Press | isbn = 978-0-548-91029-0 }} * {{citation | first = Edgar | last = Buckingham | author-link = Edgar Buckingham | year = 1914 | title = On Physically Similar Systems: Illustrations of the Use of Dimensional Analysis | journal = Physical Review | volume = 4 | pages = 345β376 | doi = 10.1103/PhysRev.4.345|url=https://babel.hathitrust.org/cgi/pt?id=uc1.31210014450082&view=1up&seq=905 | bibcode = 1914PhRv....4..345B | issue = 4 | hdl = 10338.dmlcz/101743 | hdl-access = free }} * {{citation | first=S. | last=Drobot | title=On the foundations of dimensional analysis | journal=Studia Mathematica | year=1953β1954 | volume=14 |pages=84β99 | url=http://matwbn.icm.edu.pl/ksiazki/sm/sm14/sm1418.pdf | url-status=live | archive-url=https://web.archive.org/web/20040116160647/http://matwbn.icm.edu.pl/ksiazki/sm/sm14/sm1418.pdf | archive-date=2004-01-16 | doi=10.4064/sm-14-1-84-99 |doi-access=free }} * {{citation | last=Fourier | first=Joseph | title=Theorie analytique de la chaleur | url=https://books.google.com/books?id=TDQJAAAAIAAJ&pg=PR3 | year=1822 | place=Paris | publisher=Firmin Didot | language=fr }} * {{citation | last = Gibbings | first = J.C. | year = 2011 | title = Dimensional Analysis | publisher = Springer | isbn = 978-1-84996-316-9 }} * {{citation | last=Hart |first=George W. |author-link=George W. Hart | date=1994 | chapter=The theory of dimensioned matrices | chapter-url=https://books.google.com/books?id=NeWVeylbeiQC&pg=PA186 | editor-last=Lewis | editor-first=John G. | title=Proceedings of the Fifth SIAM Conference on Applied Linear Algebra | publisher=SIAM | isbn=978-0-89871-336-7 | pages=186β190 }} As [http://www.georgehart.com/research/tdm.ps postscript] * {{citation | last = Hart | first = George W. | date = 1995 | title = Multidimensional Analysis: Algebras and Systems for Science and Engineering | publisher = Springer-Verlag | isbn = 978-0-387-94417-3 | url = http://www.georgehart.com/research/multanal.html }} * {{citation | last = Huntley | first = H. E. | year = 1967 | title = Dimensional Analysis | publisher = Dover | ol = 6128830M | id = LOC 67-17978 |oclc=682090763 | url=https://openlibrary.org/books/OL6128830M }} * {{citation | first = A. | last = Klinkenberg | year = 1955 | title = Dimensional systems and systems of units in physics with special reference to chemical engineering: Part I. The principles according to which dimensional systems and systems of units are constructed | journal = Chemical Engineering Science | volume = 4 | issue = 3 | pages = 130β140, 167β177 | doi = 10.1016/0009-2509(55)80004-8 | bibcode = 1955ChEnS...4..130K }} * {{citation | first = Henry L. | last = Langhaar |author-link = Henry L. Langhaar | year = 1951 | title = Dimensional Analysis and Theory of Models | publisher = Wiley | isbn = 978-0-88275-682-0 }} * {{citation | first1=P.F. | last1=Mendez | first2=F. | last2=OrdΓ³Γ±ez | title=Scaling Laws From Statistical Data and Dimensional Analysis | journal=Journal of Applied Mechanics | date=September 2005 | volume=72 | issue=5 | pages=648β657 | doi=10.1115/1.1943434 | bibcode = 2005JAM....72..648M | citeseerx=10.1.1.422.610 }} * {{citation | first = L. F. | last = Moody | year = 1944 | title = Friction Factors for Pipe Flow | journal = Transactions of the American Society of Mechanical Engineers | volume = 66 | issue = 671 | pages = 671β678 | doi = 10.1115/1.4018140 }} * {{citation | first = N. F. | last = Murphy | year = 1949 | title = Dimensional Analysis | journal = Bulletin of the Virginia Polytechnic Institute | volume = 42 | issue = 6 }} * {{citation | first = J. H. | last = Perry | display-authors=etal | year = 1944 | title = Standard System of Nomenclature for Chemical Engineering Unit Operations | journal = Transactions of the American Institute of Chemical Engineers | volume = 40 | issue = 251 }} * {{citation | first = Peter | last = Pesic | year = 2005 | title = Sky in a Bottle | publisher = MIT Press | pages = [https://archive.org/details/skyinbottle00pesi/page/227 227β8] | isbn = 978-0-262-16234-0 | url-access = registration | url = https://archive.org/details/skyinbottle00pesi/page/227 }} * {{citation | first = G. W. | last = Petty | year = 2001 | title = Automated computation and consistency checking of physical dimensions and units in scientific programs | journal = Software: Practice and Experience | volume = 31 | issue = 11 | pages = 1067β76 | doi = 10.1002/spe.401 | s2cid = 206506776 }} * {{citation | first = Alfred W. | last = Porter | year = 1933 | title = The Method of Dimensions | publisher = Methuen | url = https://books.google.com/books?id=SxguAQAAIAAJ | edition = 3rd }} * {{citation | author = ((J. W. Strutt (3rd Baron Rayleigh))) | author-link = John William Strutt, 3rd Baron Rayleigh | year = 1915 | title = The Principle of Similitude | journal = Nature | volume = 95 | issue=2368 | pages = 66β8 | doi = 10.1038/095066c0 | bibcode = 1915Natur..95...66R | doi-access = free }} * {{citation | first = Donald | last = Siano | year = 1985 | ref={{harvid|Siano|1985-I}} | title = Orientational Analysis β A Supplement to Dimensional Analysis β I | journal = Journal of the Franklin Institute | volume = 320 | issue = 6 | pages = 267β283 | doi = 10.1016/0016-0032(85)90031-6 }} * {{citation | first = Donald | last = Siano | year = 1985 | ref ={{harvid|Siano|1985-II}} | title = Orientational Analysis, Tensor Analysis and The Group Properties of the SI Supplementary Units β II | journal = Journal of the Franklin Institute | volume = 320 | issue = 6 | pages = 285β302 | doi = 10.1016/0016-0032(85)90032-8 }} * {{citation | first1 = I. H. | last1 = Silberberg | last2 = McKetta |first2=J. J. Jr. | year = 1953 | title = Learning How to Use Dimensional Analysis | journal = Petroleum Refiner | volume = 32 | issue = 4 | page = 5 }}, (5): 147, (6): 101, (7): 129 * {{cite web | first = Terence | last = Tao | author-link = Terence Tao | title = A mathematical formalisation of dimensional analysis | url = https://terrytao.wordpress.com/2012/12/29/a-mathematical-formalisation-of-dimensional-analysis/ | year = 2012 }} * {{citation | first = E. R. | last = Van Driest | date = March 1946 | title = On Dimensional Analysis and the Presentation of Data in Fluid Flow Problems | journal = Journal of Applied Mechanics | volume = 68 | issue = Aβ34 }} * {{citation | first = H. | last = Whitney | year = 1968 | title = The Mathematics of Physical Quantities, Parts I and II | journal = American Mathematical Monthly | volume = 75 | issue = 2 | pages = 115β138, 227β256 | doi = 10.2307/2315883 | jstor = 2315883 }} * [[Edwin Bidwell Wilson|Wilson, Edwin B.]] (1920) [https://archive.org/details/aeronautics00wilsgoog/page/n197/mode/2up "Theory of Dimensions"], chapter XI of ''Aeronautics'', via [[Internet Archive]] * {{citation | first = GA | last = Vignaux | chapter = Dimensional Analysis in Data Modelling | editor1 = Erickson, Gary J. | editor2 = Neudorfer, Paul O. | title = Maximum entropy and Bayesian methods: proceedings of the Eleventh International Workshop on Maximum Entropy and Bayesian Methods of Statistical Analysis, Seattle, 1991 | publisher = Kluwer Academic | year = 1992 | isbn = 978-0-7923-2031-9 }} * {{citation | first1 = WacΕaw | last1 = Kasprzak | first2 = Bertold | last2 = Lysik | first3 = Marek | last3 = Rybaczuk | title = Dimensional Analysis in the Identification of Mathematical Models | publisher = World Scientific | year = 1990 | isbn = 978-981-02-0304-7 }}
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