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Quantities having dimension one, dimensionless quantities, regularly occur in sciences, and are formally treated within the field of dimensional analysis.In the 19th century, French mathematician Joseph Fourier and Scottish physicist James Clerk Maxwell led significant developments in the modern concepts of dimension and unit.
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.
A quantity that has only both a ≠ 0 and b ≠ 0 is known as a kinematic quantity. A quantity that has only all of a ≠ 0, b ≠ 0, and c ≠ 0 is known as a dynamic quantity. [3] A quantity that has all exponents null is said to have dimension one. [2] The unit chosen to express a physical quantity and its dimension are related, but not ...
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.
Time for a quantity to decay to half its initial value s T: Heat: Q: Thermal energy: joule (J) L 2 M T −2: Heat capacity: C p: Energy per unit temperature change J/K L 2 M T −2 Θ −1: extensive Heat flux density: ϕ Q: Heat flow per unit time per unit surface area W/m 2: M T −3: Illuminance: E v: Wavelength-weighted luminous flux per ...
The metabolic cost of transport includes the basal metabolic cost of maintaining bodily function, and so goes to infinity as speed goes to zero. [1] A human achieves the lowest cost of transport when walking at about 6 kilometres per hour (3.7 mph), at which speed a person of 70 kilograms (150 lb) has a metabolic rate of about 450 watts. [1]
The original Standard Model of particle physics from the 1970s contained 19 fundamental dimensionless constants describing the masses of the particles and the strengths of the electroweak and strong forces. In the 1990s, neutrinos were discovered to have nonzero mass, and a quantity called the vacuum angle was found to be indistinguishable from ...
Choose judiciously the definition of the characteristic unit for each variable so that the coefficients of as many terms as possible become 1; Rewrite the system of equations in terms of their new dimensionless quantities. The last three steps are usually specific to the problem where nondimensionalization is applied.