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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] In chemistry, state properties and ratios ...
The dimension of a physical quantity is more fundamental than some scale or unit used to express the amount of that physical quantity. For example, mass is a dimension, while the kilogram is a particular reference quantity chosen to express a quantity of mass. The choice of unit is arbitrary, and its choice is often based on historical precedent.
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.
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.
Although named for Edgar Buckingham, the π theorem was first proved by the French mathematician Joseph Bertrand in 1878. [1] Bertrand considered only special cases of problems from electrodynamics and heat conduction, but his article contains, in distinct terms, all the basic ideas of the modern proof of the theorem and clearly indicates the theorem's utility for modelling physical phenomena.
For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures, while SG H 2 O = 1.000 000 (20 °C/20 °C), it is also the case that SG H 2 O = 0.998 2008 ⁄ 0.999 9720 = 0.998 2288 (20 °C/4 °C).
siemens (S = Ω −1) L −2 M −1 T 3 I 2: scalar Electrical conductivity: σ: Measure of a material's ability to conduct an electric current S/m L −3 M −1 T 3 I 2: scalar Electric potential: φ: Energy required to move a unit charge through an electric field from a reference point volt (V = J/C) L 2 M T −3 I −1: extensive, scalar ...