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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.
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 .
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.
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The final column lists some special properties that some of the quantities have, such as their scaling behavior (i.e. whether the quantity is intensive or extensive), their transformation properties (i.e. whether the quantity is a scalar, vector, matrix or tensor), and whether the quantity is conserved.
This relationship leaves Strouhal dimensionless, although a dimensionless approximation is often used for C 3, resulting in units of pulses/volume (same as K-factor). This relationship between flow and frequency can also be found in the aeronautical field. Considering pulsating methane-air coflow jet diffusion flames, we get
In continuum mechanics, the Péclet number (Pe, after Jean Claude Eugène Péclet) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is defined to be the ratio of the rate of advection of a physical quantity by the flow to the rate of diffusion of the same quantity driven by an appropriate gradient.
The Knudsen number is a dimensionless number defined as =, where = mean free path [L 1], = representative physical length scale [L 1].. The representative length scale considered, , may correspond to various physical traits of a system, but most commonly relates to a gap length over which thermal transport or mass transport occurs through a gas phase.
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