# dimensionless number

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## dimensionless number

[də′men·chən·ləs ′nəm·bər]
(mathematics)
A ratio of various physical properties (such as density or heat capacity) and conditions (such as flow rate or weight) of such nature that the resulting number has no defining units of weight, rate, and so on. Also known as nondimensional parameter.
References in periodicals archive ?
The linear correlation coefficient, as defined by Equation 6 is a dimensionless quantity. In general, -1[less then or equal to] r [less than or equal to] 1, wherein a "+" sign indicates positive linear correlation, and a "-" sign implies negative linear correlation.
In addition to dimensionless quantity [theta], for further analysis the dimensionless variables are introduced:
is a dimensionless number group that characterizes the influence of vibration force field on the apparent viscosity of melt; [epsilon] = [A[omega]]/[[pi]D[bar.N]], called vibration impact factor, is a dimensionless quantity that represents the strength of axial vibration of screw, and [A.sub.z] = [epsilon]xtg[theta], [A.sub.z] = [epsilon]xctg[theta].
In at least one case the author conforms to accepted usage, e.g., the mass-to-charge ratio (m/z) is defined as a dimensionless quantity, although the physics of the accepted terminology are questionable because a quantity so defined cannot be used in equations of motion for charged particles.
This dimensionless quantity is defined by the equation
The modal amplitude [h.sub.n] should be found out hereinafter as a dimensionless quantity. As it follows from Equation (28), the other modal amplitudes, [V.sub.'n] and [I'.sup.n], will be dimensionless, as well.
Another important dimensionless quantity, the Janeschitz-Kriegl (Jk) number, merely follows the changes in De/St and does not increase our understanding of the problem.
The reference interval width for the W group was compared to that of the T group by using their ratio because this dimensionless quantity allows for comparisons across analytes.

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