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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.
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.
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.
The Q factor is a parameter that describes the resonance behavior of an underdamped harmonic oscillator (resonator). Sinusoidally driven resonators having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the ...
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
Transfer of momentum per unit time newton (N = kg⋅m⋅s −2) L M T −2: extensive, vector Frequency: f: Number of (periodic) occurrences per unit time hertz (Hz = s −1) T −1: scalar Half-life: t 1/2: Time for a quantity to decay to half its initial value s T: Heat: Q: Thermal energy: joule (J) L 2 M T −2: Heat capacity: C p: Energy ...
Replace each of them with a quantity scaled relative to a characteristic unit of measure to be determined; Divide through by the coefficient of the highest order polynomial or derivative term; Choose judiciously the definition of the characteristic unit for each variable so that the coefficients of as many terms as possible become 1;