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The unit of angular frequency is the radian per second (rad/s) but, for discrete-time signals, can also be expressed as radians per sampling interval, which is a dimensionless quantity. Angular frequency is frequency multiplied by 2 π.
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.
C = linear coefficient of expansion for the meter housing material. 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.
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 .
The Strouhal number gives the vortex shedding frequency resulting from placing an object in a steady flow, so it describes the flow unsteadiness as a result of an instability of the flow downstream of the object. Conversely, the Keulegan–Carpenter number is related to the oscillation frequency of an unsteady flow into which the object is placed.
The strain is the ratio of two lengths, so it is a dimensionless quantity (a number that does not depend on the choice of measurement units). Thus, strain rate has dimension of inverse time and units of inverse second, s −1 (or its multiples).
Measure for how the magnetization of material is affected by the application of an external magnetic field H/m L M T −2 I −2: intensive Permittivity: ε s: Measure for how the polarization of a material is affected by the application of an external electric field F/m L −3 M −1 T 4 I 2: intensive Plane angle: θ: Ratio of circular arc ...
The same law in the ISQ is: = where ε 0 is the vacuum permittivity, a quantity that is not dimensionless: it has dimension 2 2 −1 −3. Without ε 0 , the equation would be dimensionally inconsistent with the quantities as defined in the ISQ, whereas the quantity ε 0 does not appear in Gaussian equations.