Dimensionless quantity
A dimensionless quantity is a physical quantity that can be represented by a pure number without unit. Even for these sizes of clarity are sometimes used for units, see auxiliary units.
In ISO 80000, the term " dimensionless " as is " outdated " means. Recommended instead, the term " size of the number of dimensions ".
The term is here meant by dimension in the sense of dimension (size System) to understand such as " length", not in the sense of dimension (mathematics) as in " three-dimensional space."
Examples
Examples of quantities of dimension number are:
- Information in ratio units such as percent, per mille, ppm
- Numbers, even though they are shown in a counting measure such as dozen
- Dimensionless numbers (also called parameters ) as the Mach number
- Plane angle and solid angle ( SI auxiliary unit radian and steradian )
- Logarithmic ratios, as Bel, Napier, Phon
- Quantum numbers
- Ratios, ie quotient of two dimensionless same sizes, such as the Avogadro number
- Probabilities
Ratios are related quantities whose reference each of the same size type (eg efficiency).
Important are the dimensionless coefficients ( parameters ) of the fluid dynamics and thermal hydraulics as intensive quantities, by which one can predict the behavior or enable a comparison between different systems ( different dimensions ). This includes, for example, the Reynolds number, the flow quality (laminar / turbulent) characterized.
An example from another field is the Sommerfeld fine structure constant, which is composed of electrical elementary charge, Planck's quantum of action and the speed of light. Its value is approximately 1 / 137th This constant was introduced by Arnold Sommerfeld in 1916, in order to calculate the conditional by magnetic fine structure splitting of spectral lines.
Designation
According to DIN 5485 Designation principles of physical quantities; Compound words with property and basic words, the rules for renaming of physical quantities contains, there is no name for which is provided for non-dimensional variables:
- Share
- Rate coefficient
- Factor
- Degree
- Rate
- Number
In the scientific and technical everyday, there are still many names that do not follow these criteria and dimensionless physical quantities are often, but not always, identified by the extension number. Even the ending coefficient referred to sometimes, but not always a dimensionless quantity. Examples:
- Refractive index ( " index " instead of " number " )
- Permeability ( not dimensionless)
- Friction coefficient ( " coefficient " instead of " rate coefficient " )
- Coefficient of Thermal Expansion ( not dimensionless)
Commonly used for the naming of dimensionless variables is also the ending
- Module
Theoretical background
In the metrology size has the dimension number if it is not associated with dimension of the selected size system. This is shown, for example, the fact that in the representation of the corresponding dimension of the product of powers of the basic dimensions of each dimension exponent is zero. That one size no dimension belongs can in principle have three reasons:
Example: In a multivariable system with only the two basic dimensions of length and mass, the length, the dimension.
Basically, it depends on the basis chosen for a sizing system from which derived quantities have the dimension, and thus which variables ( except the quotient of equal dimensions sizes) have the dimension number. Thus, in electrostatic cgs systems electric capacity and length of the same dimension. Therefore, any quotient of these quantities given the dimension of the number one.
As you can see, according to the theory of relativity, time and length as one and the same size type, can also speed up as the dimensionless ratio size view. This takes place in the system of natural units, which is used in many branches of physics. In the SI system, however, time and length are separate base sizes, and speed as their quotient has the unit.