Dimensionless

Dimensionless quantities are often obtained as products or ratios of quantities that are not dimensionless, but whose dimensions cancel out in the mathematical operation.

However, the choice of dimensionless parameters is not unique; Buckingham's theorem only provides a way of generating sets of dimensionless parameters and does not indicate the most "physically meaningful".

Note: The erlang is a dimensionless load unit calculated as the mean arrival rate, λ, multiplied by the mean call holding time, h. See Little's law to prove that the erlang unit has to be dimensionless for Little's Law to be dimensionally sane.

Since the kernel is only defined to within a multiplicative constant, if the above dimensionless constant is raised to any arbitrary power, it will yield another equivalent dimensionless constant.

There is mathematically no natural choice of dimensionless variables; some choices of dimensionless variables are more physically meaningful, and these are what are ideally used.

This equilibrium constant is dimensionless as activity is a dimensionless quantity.

The proposal is, of course, only viable if a universe that curves out of a dimensionless point in the way Hartle and Hawking imagined naturally grows into a universe like ours.

The same goes for the giant rhinos in ’s big battle, their hooves squashed into a dimensionless rumble as they lumber toward their enemies.

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.

Celestial or cosmic music removes listeners from their ordinary acoustical surroundings by creating stereo sound images of vast, virtually dimensionless spatial environments.

Chaos may be described as having the consistency of vapor or water, dimensionless, and sometimes salty or muddy.

Combining these dimensionless equations with the momentum equations gives the following simplified equation.

Dimensionless force The ratio of the actual dynamic force to the steady momentum.

Dimensionless volumetric flow rate The ratio of the dynamic volumetric flow rate to the steady volumetric flow rate.

Each of these other units (SI derived units) is either dimensionless or can be expressed as a product of (positive or negative, but usually integral) powers of one or more of the base units.