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Buckingham π theorem

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In engineering, applied mathematics, and physics, the Buckingham theorem is a key theorem in dimensional analysis. [1]

29 relations: Blast wave, Clearing denominators, Dimensional analysis, Dimensionless quantity, Dimitri Riabouchinsky, Edgar Buckingham, Gaussian elimination, John William Strutt, 3rd Baron Rayleigh, Joseph Bertrand, Kernel (linear algebra), Linear map, Matrix (mathematics), Natural units, Nature (journal), Nondimensionalization, Physical Review, Proceedings of the Royal Society, Rank (linear algebra), Rank–nullity theorem, Rational number, Rayleigh's method of dimensional analysis, Row echelon form, Similarity (geometry), Similitude (model), Small-angle approximation, Standard gravity, Theorem, Vector space, Zero of a function.

Blast wave

In fluid dynamics, a blast wave is the increased pressure and flow resulting from the deposition of a large amount of energy in a small, very localised volume.

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Clearing denominators

In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions.

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Dimensional analysis

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed.

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Dimensionless quantity

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned.

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Dimitri Riabouchinsky

Dimitri Pavlovitch Riabouchinsky (6 November 1882– 22 August 1962) was a Russian fluid dynamicist noted for his discovery of the Riabouchinsky solid technique.

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Edgar Buckingham

Edgar Buckingham (July 8, 1867 in Philadelphia, Pennsylvania – April 29, 1940 in Washington DC) was an American physicist.

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Gaussian elimination

In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.

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John William Strutt, 3rd Baron Rayleigh

John William Strutt, 3rd Baron Rayleigh, (12 November 1842 – 30 June 1919) was a physicist who, with William Ramsay, discovered argon, an achievement for which he earned the Nobel Prize for Physics in 1904.

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Joseph Bertrand

Joseph Louis François Bertrand (11 March 1822 – 5 April 1900) was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, economics and thermodynamics.

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Kernel (linear algebra)

In mathematics, and more specifically in linear algebra and functional analysis, the kernel (also known as null space or nullspace) of a linear map between two vector spaces V and W, is the set of all elements v of V for which, where 0 denotes the zero vector in W. That is, in set-builder notation,.

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Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Natural units

In physics, natural units are physical units of measurement based only on universal physical constants.

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Nature (journal)

Nature is a British multidisciplinary scientific journal, first published on 4 November 1869.

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Nondimensionalization

Nondimensionalization is the partial or full removal of units from an equation involving physical quantities by a suitable substitution of variables.

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Physical Review

Physical Review is an American peer-reviewed scientific journal established in 1893 by Edward Nichols.

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Proceedings of the Royal Society

Proceedings of the Royal Society is the parent title of two scientific journals published by the Royal Society.

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Rank (linear algebra)

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns.

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Rank–nullity theorem

In mathematics, the rank–nullity theorem of linear algebra, in its simplest form, states that the rank and the nullity of a matrix add up to the number of columns of the matrix.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Rayleigh's method of dimensional analysis

Rayleigh's method of dimensional analysis is a conceptual tool used in physics, chemistry, and engineering.

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Row echelon form

In linear algebra, a matrix is in echelon form if it has the shape resulting from a Gaussian elimination.

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Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.

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Similitude (model)

Similitude is a concept applicable to the testing of engineering models.

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Small-angle approximation

The small-angle approximation is a useful simplification of the basic trigonometric functions which is approximately true in the limit where the angle approaches zero.

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Standard gravity

The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by or, is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth.

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Theorem

In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

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References

[1] https://en.wikipedia.org/wiki/Buckingham_π_theorem

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