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Dimensional analysis

In engineering and science, dimensional analysis of different physical quantities is the analysis of their physical dimension or quantity dimension, defined as a mathematical expression identifying the powers of the base quantities involved (such as length, mass, time, etc.), and tracking these dimensions as calculations or comparisons are performed. The…

History, Applications, Measurement & Technology

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Overview

Formulation

Concrete numbers and base units

Dimensional homogeneity (commensurability)

Conversion factor

Applications

History

Examples

Properties

Dimensionless concepts

Programming languages

Affine quantities

Orientation and frame of reference

Siano's extension: orientational analysis

Related areas of mathematics

Advanced semantic analysis

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Map overview Semantic statistics

Dimensional analysis

Nodes200
Edges199
Triples307
Avg. degree1.99
Density0.01
Components1

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Dimensional analysis

Top relations

related to References · 155
Dimensional analysis → Aeronautics, Alfred, Algebras, Alves, American Institute, American Mathematical Monthly, American Society, Analysis, Anil, Applied Linear Algebra, Applied Mechanics, Artificial Intelligence, As, Automated, Barenblatt, Baron Rayleigh, Bayesian, Bayesian Methods, Bertold, Bibcode
related to External links · 16
Dimensional analysis → An, Archived, Boost, Brady Haran, David, December, Dureisseix, INSA Lyon, List, Live, Nottingham, Roger, Sixty Symbols, System, University, Wayback MachineUnits
related to A simple example: period of a harmonic oscillator · 14
Dimensional analysis → Dimensional, From, G1, If, It, L/T2, M/T2, T2, T2k/m, That, The, They, This, What
related to Finance, economics, and accounting · 14
Dimensional analysis → Annual, For, From, Furthermore, GDP, GDP/money, However, In, More, Note, Of, P/E, Therefore, Velocity
related to Fluid mechanics · 13
Dimensional analysis → According, Common, Delta, Eu, Euler, Fr, Froude, In, Ma, Mach, Re, Reynolds, Using
related to Formalisms · 12
Dimensional analysis → As, Duff, Ising, It, Length, Mass, Michael, Now, Paradoxically, Such, The, Time
related to Further reading · 12
Dimensional analysis → Applications, Dimensions, Douglas, Estimating, Giancoli, Introduction, ISBN, Measurement, OCLC, Pearson, Physics, Principles
related to A third example: demand versus capacity for a rotating disc · 11
Dimensional analysis → An, As, Consider, Dimensional, However, If, Lame, M/L3, The, There, Through
related to history · 11
Dimensional analysis → Buckingham, Daviet, François Daviet, In, Joseph-Louis Lagrange, Poisson, Science, Simeon Poisson, The, This, Turin Academy
related to Affine quantities · 7
Dimensional analysis → Consider, If, In, Numbers, Some, The, While

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Important terminology

dimensional analysis quantities dimensions dimension dimensionless physical quantity time units length one unit example mass equation may form variables displaystyle

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
lengthinstance ofas illustrated in the examples below.The dimension of a physical quantity can be expressed as a product of the base physical dimensions0.80text
massinstance ofas illustrated in the examples below.The dimension of a physical quantity can be expressed as a product of the base physical dimensions0.80text
timeinstance ofas illustrated in the examples below.The dimension of a physical quantity can be expressed as a product of the base physical dimensions0.80text
each raised to an integerinstance ofas illustrated in the examples below.The dimension of a physical quantity can be expressed as a product of the base physical dimensions0.80text
the Reynolds numberinstance ofthe answer may depend on a dimensionless number0.80text
which may be interpreted by dimensional analysis.A third exampleinstance ofthe answer may depend on a dimensionless number0.80text
which may be interpreted by dimensional analysisinstance ofthe answer may depend on a dimensionless number0.80text
exponentialinstance ofThis excludes polynomials of more than one term or transcendental functions not of that form.Scalar arguments to transcendental functions0.80text
trigonometricinstance ofThis excludes polynomials of more than one term or transcendental functions not of that form.Scalar arguments to transcendental functions0.80text
logarithmic functionsinstance ofThis excludes polynomials of more than one term or transcendental functions not of that form.Scalar arguments to transcendental functions0.80text
or to inhomogeneous polynomialsinstance ofThis excludes polynomials of more than one term or transcendental functions not of that form.Scalar arguments to transcendental functions0.80text
must be dimensionless quantitiesinstance ofThis excludes polynomials of more than one term or transcendental functions not of that form.Scalar arguments to transcendental functions0.80text

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