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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.
In differential geometry, the use of dimensionless parameters is evident in geometric relationships and transformations. Physics relies on dimensionless numbers like the Reynolds number in fluid dynamics, [6] the fine-structure constant in quantum mechanics, [7] and the Lorentz factor in relativity. [8]
Listed below are all conversion factors that are useful to convert between all combinations of the SI base units, and if not possible, between them and their unique elements, because ampere is a dimensionless ratio of two lengths such as [C/s], and candela (1/683 [W/sr]) is a dimensionless ratio of two dimensionless ratios such as ratio of two volumes [kg⋅m 2 /s 3] = [W] and ratio of two ...
As a dimensionless constant which does not seem to be directly related to any mathematical constant, the fine-structure constant has long fascinated physicists. Arthur Eddington argued that the value could be "obtained by pure deduction" and he related it to the Eddington number , his estimate of the number of protons in the universe. [ 68 ]
In differential geometry, the use of dimensionless parameters is evident in geometric relationships and transformations. Physics relies on dimensionless numbers like the Reynolds number in fluid dynamics, [7] the fine-structure constant in quantum mechanics, [8] and the Lorentz factor in relativity. [9]
For example, if "x" represented mass, the letter "m" might be an appropriate symbol to represent the dimensionless mass quantity. In this article, the following conventions have been used: t – represents the independent variable – usually a time quantity.
These include the Boltzmann constant, which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant, which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless).
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.