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In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their fundamental dimensions (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms vs. grams) and tracking these dimensions as calculations or comparisons are performed. Converting from one dimensional unit to another is often somewhat complex. Dimensional analysis, or more specifically the factor-label method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra.〔(Dimensional Analysis or the Factor Label Method )〕 The concept of physical dimension was introduced by Joseph Fourier in 1822.〔Fourier, Joseph. ''Théorie analytique de la chaleur'', Firmin Didot, Paris, 1822.〕 Physical quantities that are commensurable have the same dimension; if they have different dimensions, they are incommensurable. For example, it is meaningless to ask whether a kilogram is less, the same, or more than an hour. Any physically meaningful equation (and likewise any inequality and inequation) will have the same dimensions on the left and right sides, a property known as "dimensional homogeneity". Checking this is a common application of dimensional analysis. Dimensional analysis is also routinely used as a check on the plausibility of derived equations and computations. It is generally used to categorize types of physical quantities and units based on their relationship to or dependence on other units. ==Concrete numbers and base units== Many parameters and measurements in the physical sciences and engineering are expressed as a concrete number – a numerical quantity and a corresponding dimensional unit. Often a quantity is expressed in terms of several other quantities; for example, speed is a combination of length and time, e.g. 60 miles per hour or 1.4 km per second. Compound relations with "per" are expressed with division, e.g. 60 mi/1 h. Other relations can involve multiplication (often shown with · or juxtaposition), powers (like m2 for square meters), or combinations thereof. A unit of measure that is in a conventionally chosen subset of a given system of units, where no unit in the set can be expressed in terms of the others, is known as a base unit.〔(JCGM 200:2012 ''International vocabulary of metrology – Basic and general concepts and associated terms (VIM)'' )〕 For example, units for length and time are normally chosen as base units. Units for volume, however, can be factored into the base units of length (m3), thus being derived or compound units. Sometimes the names of units obscure that they are derived units. For example, an ampere is a unit of electric current, which is equivalent to electric charge per unit time and is measured in coulombs (a unit of electrical charge) per second, so . One newton is 1 kg⋅m/s2. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「dimensional analysis」の詳細全文を読む スポンサード リンク
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