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Dimensionless quantity. 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.
List of dimensionless quantities. 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 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.
Relative density ( ) or specific gravity ( ) is a dimensionless quantity, as it is the ratio of either densities or weights where is relative density, is the density of the substance being measured, and is the density of the reference. (By convention , the Greek letter rho, denotes density.) The reference material can be indicated using ...
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 fundamental physical constants include: α, the fine-structure constant, (≈ 1 / 137 ). This is also the square of the electron charge, expressed in Planck units, which defines the scale of charge of elementary particles with charge. The electron charge is the coupling constant for the electromagnetic interaction.
In fluid dynamics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. [2] At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent.
Dimensionless quantities of chemistry (4 P) Countable quantities (1 C, 4 P)