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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.
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] In chemistry , state properties and ratios such as mole fractions concentration ratios are dimensionless.
For example, if x is a quantity, then x c is the characteristic unit used to scale it. As an illustrative example, consider a first order differential equation with constant coefficients: + = (). In this equation the independent variable here is t, and the dependent variable is x.
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.
The compressibility factor is a dimensionless quantity which is equal to 1 for ideal gases and deviates from unity for increasing levels of non-ideality. [ 9 ] Several non-ideal models exist, from the simplest cubic equations of state (such as the Van der Waals [ 4 ] [ 10 ] and the Peng-Robinson [ 11 ] models) up to complex multi-parameter ones ...
In fluid dynamics, the Taylor number (Ta) is a dimensionless quantity that characterizes the importance of centrifugal "forces" or so-called inertial forces due to rotation of a fluid about an axis, relative to viscous forces. [1] In 1923 Geoffrey Ingram Taylor introduced this quantity in his article on the stability of flow. [2]
A quantity of dimension one is historically known as a dimensionless quantity (a term that is still commonly used); all its dimensional exponents are zero and its dimension symbol is . Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension.
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).