{{위키데이터 속성 추적}}
'''차원 해석'''(Dimensional analysis)은 공학 및 과학에서 기본 수량(예: 길이, 질량, 시간 및 전류)과 측정 단위(예: 미터 및 그램)를 식별하고 이러한 치수를 추적하여 서로 다른 물리량 간의 관계를 분석하는 것이다. 계산 또는 비교가 수행될 때. 차원 해석이라는 용어는 과학적 공식을 평가하는 데 사용할 수 있는 한 차원 단위에서 다른 차원 단위로 단위를 변환하는 것을 의미하기도 한다.

측정 가능한 물리량은 같은 종류이고 같은 차원을 가지며 다른 측정 단위로 표현되더라도 서로 직접 비교할 수 있다. 예: 미터 및 피트, 그램 및 파운드, 초 및 연도. 통약 불가능한 물리량은 종류도 다르고 차원도 다르며, 어떤 단위로 표현되든 직접 비교할 수 없다. 미터와 그램, 초와 그램, 미터와 초. 예를 들어 1그램이 1시간보다 큰지 묻는 것은 의미가 없다.

물리적으로 의미가 있는 모든 방정식 또는 부등식은 차원 동질성으로 알려진 속성인 왼쪽과 오른쪽의 차원이 동일해야 한다. 차원 동질성을 확인하는 것은 파생 방정식 및 계산에 대한 타당성 확인 역할을 하는 차원 해석의 일반적인 적용이다. 또한 더 엄격한 유도가 없는 경우 물리적 시스템을 설명할 수 있는 방정식을 유도할 때 가이드 및 제약 조건 역할을 한다.

물리적 차원과 차원 해석의 개념은 1822년 [[조제프 푸리에]]에 의해 소개되었다.

== 같이 보기 ==
* [[페르미 문제]]
* [[단위계]]
* [[벡터의 공변성 및 반변성]]
* [[외대수]]
* [[기하적 대수학]]

== 출처 ==
* {{인용
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 | year = 1996
 | title = Scaling, Self-Similarity, and Intermediate Asymptotics
 | publisher = Cambridge University Press
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* {{인용
 | last1 = Bhaskar
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 | year = 1990
 | title = Qualitative Physics Using Dimensional Analysis
 | journal = Artificial Intelligence
 | volume = 45 | issue = 1–2 | pages = 73–111
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 | first1 = R.
 }}
* {{인용
 | last1 = Bhaskar
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 | year = 1991
 | title = Qualitative Explanations of Red Giant Formation
 | journal = The Astrophysical Journal
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| bibcode=1991ApJ...372..592B}}
* {{인용
 | last1 = Boucher
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 | year = 1960
 | title = Dimensionless Numbers
 | journal = Chemical Engineering Progress
 | volume = 55 | pages = 55–64
 }}
* {{인용
 | 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
 }}
* {{인용
 | 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 = 345–376
 | 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
 }}
* {{인용|first=S. |last=Drobot |title=On the foundations of dimensional analysis |journal=Studia Mathematica |year=1953–1954 |volume=14 |pages=84–99 |url=http://matwbn.icm.edu.pl/ksiazki/sm/sm14/sm1418.pdf |archive-url=https://web.archive.org/web/20040116160647/http://matwbn.icm.edu.pl/ksiazki/sm/sm14/sm1418.pdf |archive-date=2004-01-16 |url-status=live|doi=10.4064/sm-14-1-84-99 |doi-access=free }}
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* {{인용
| last =  Gibbings
| first =  J.C.
| year = 2011
| title = Dimensional Analysis
| publisher = Springer
| isbn = 978-1-84996-316-9 }}
* {{인용
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 |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=186–190}} As [http://www.georgehart.com/research/tdm.ps postscript]
* {{인용
 | 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
 }}
* {{인용
 | 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
 }}
* {{인용
 | 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 | pages = 130–140, 167–177
 | doi = 10.1016/0009-2509(55)80004-8
 | issue = 3 | bibcode = 1955ChEnS...4..130K
 }}
* {{인용
 | 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
 }}
* {{인용|first1=P.F. |last1=Mendez |first2=F. |last2=Ordóñez |title=Scaling Laws From Statistical Data and Dimensional Analysis |journal=Journal of Applied Mechanics |date=September 2005 |volume=72 |issue=5 |pages=648–657 |doi=10.1115/1.1943434 |bibcode = 2005JAM....72..648M |citeseerx=10.1.1.422.610 }}
* {{인용
 | 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
 }}
* {{인용
 | first = N. F. | last = Murphy
 | year = 1949
 | title = Dimensional Analysis
 | journal = Bulletin of the Virginia Polytechnic Institute
 | volume = 42 | issue = 6
 }}
* {{인용
 | first = J. H. | last = Perry
 | 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
 |display-authors=etal}}
* {{인용| first = Peter | last = Pesic | year = 2005 | title = Sky in a Bottle | publisher = MIT Press | pages = [https://archive.org/details/skyinbottle00pesi/page/227 227–8] | isbn = 978-0-262-16234-0 | url-access = registration | url = https://archive.org/details/skyinbottle00pesi/page/227 }}
* {{인용
 | 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 | pages = 1067–76
 | doi = 10.1002/spe.401
 | issue = 11
 | s2cid = 206506776
 }}
* {{인용
 | first = Alfred W. | last = Porter
 | year = 1933
 | title = The Method of Dimensions
 | publisher = Methuen |url=https://books.google.com/books?id=SxguAQAAIAAJ |edition=3rd}}
* {{인용
 | last = 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
 | pages = 66–8
 | doi = 10.1038/095066c0
 |bibcode = 1915Natur..95...66R
 | issue=2368| doi-access = free
 }}
* {{인용
 | first = Donald | last = Siano
 | year = 1985 | ref={{harvid|Siano|1985-I}}
 | title = Orientational Analysis – A Supplement to Dimensional Analysis – I
 | journal = Journal of the Franklin Institute
 | issue = 6 | pages = 267–283
 | doi = 10.1016/0016-0032(85)90031-6
 | volume = 320
 }}
* {{인용
 | 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 – II
 | journal = Journal of the Franklin Institute
 | issue = 6 | pages = 285–302
 | doi = 10.1016/0016-0032(85)90032-8
 | volume = 320
 }}
* {{인용
 | 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
* {{웹 인용
 | 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
 }}
* {{인용
 | 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 = A–34 }}
* {{인용
 | first = H.  | last = Whitney
 | year = 1968
 | title = The Mathematics of Physical Quantities, Parts I and II
 | journal = American Mathematical Monthly
 | volume = 75 | pages = 115–138, 227–256
 | doi = 10.2307/2315883
 | issue = 2
 | jstor = 2315883
 }}
* {{인용
 |first = GA
 |last = Vignaux
 |chapter = Dimensional Analysis in Data Modelling
 |editor = 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 }}
* {{인용
 |first1 = Wacław
 |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 }}

{{전거 통제}}

[[분류:차원 해석| ]]
[[분류:측정]]
[[분류:단위 변환]]
[[분류:화학공학]]
[[분류:기계공학]]
[[분류:환경공학]]