dimensionless
Adjective
Meaning
Without dimensions; having no appreciable or noteworthy extent.
Source: Webster's dictionarySynonyms
Antonyms
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Examples
Although polar and spherical coordinates use radians to describe coordinates in two and three dimensions, the unit is derived from the radius coordinate, so the angle measure is still dimensionless.
Angles are, by convention, considered to be dimensionless variables, and so the use of angles as physical variables in dimensional analysis can give less meaningful results.
A simple problem illustrates how a proportion may be a dimensionless quantity.
As the Mach number is a dimensionless quantity rather than a unit of measure, with Mach, the number comes after the unit; the second Mach number is "Mach 2" instead of "2 Mach" (or Machs).
Building on Rayleigh's method of dimensional analysis, Edgar Buckingham proved the π theorem (independent of French mathematician Joseph Bertrand 's previous work) to formalize the nature of dimensionless quantities.
But, in natural convection the Grashof number is the dimensionless parameter that governs the fluid flow.