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This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers , dimensionless ratios, or dimensionless physical constants ; these topics are discussed in the article.
Dimensionless quantities, or quantities of dimension one, [1] are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. [ 2 ] [ 3 ] Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units .
Dimensionless quantities (2 C, 9 P) R. Ratios (11 C, 59 P) T. Dimensionless numbers of thermodynamics (21 P) U. Dimensionless units (1 C, 4 P) ... Statistics; Cookie ...
Parts-per notations are all dimensionless quantities: in mathematical expressions, the units of measurement always cancel. In fractions like "2 nanometers per meter" (2 n m / m = 2 nano = 2×10 −9 = 2 ppb = 2 × 0.000 000 001), so the quotients are pure-number coefficients with positive values less than or equal to 1.
Nondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution of variables.This technique can simplify and parameterize problems where measured units are involved.
A United States Navy Aviation boatswain's mate tests the specific gravity of JP-5 fuel. Relative density, also called specific gravity, [1] [2] is a dimensionless quantity defined as the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material.
The particles could be the grains in a metallurgical or ceramic microstructure, or the microorganisms in a culture, for example. The dimensionless quantities often represent the degree of deviation from an ideal shape, such as a circle, sphere or equilateral polyhedron. [1] Shape factors are often normalized, that is, the value ranges from zero ...
Similitude has been well documented for a large number of engineering problems and is the basis of many textbook formulas and dimensionless quantities. These formulas and quantities are easy to use without having to repeat the laborious task of dimensional analysis and formula derivation.
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