Dimensionless Quantities

Dimensionless Quantities

 

derived physical quantities which are independent of the simultaneous variation of quantities that are chosen to be fundamental. If, for example, one chooses length L, mass M, and time T as the fundamental quantities and their simultaneous variations have no effect on the value of a given quantity, then the dimensionality of such a quantity is equal to L0M0T0 = 1, and the quantity is dimensionless in this system of quantities. For example, a plane angle, defined as the ratio of the length of the arc of a circle enclosed between two radii to the length of the radius, is a dimensionless quantity in the LMT system, because it is independent of the length of the radius. All relative quantities—that is, relative density (the density of an object in relation to the density of water), relative elongation, relative magnetic and dielectric permeability, and the like—as well as similarity criteria (Reynolds number and Prandtl number), are also considered dimensionless quantities. Dimensionless quantities are expressed in abstract units. Relative quantities are also expressed in percent (%) and in parts per thousand (‰).

K. P. SHIROKOV

References in periodicals archive ?
By introducing the dimensionless quantities [mathematical expression not reproducible] and [mathematical expression not reproducible], Equation 4 can be expressed as a function of [mathematical expression not reproducible] and t* only.
For general expression we introduce dimensionless quantities:
[23], dimensionless quantities are introduced to obtain the similarity solutions:
We proceed in the equations (1) to dimensionless quantities (2):
The differential equation (12) of motion for cable-beam coupled vibrations is derived by using dimensionless method, and the following dimensionless quantities are defined [15-17]:
Subsequently, the flow equations are normalized by means of dimensionless quantities to demonstrate the effect of Reynolds number on the flow characteristics:
In order to make all dimensionless quantities independent of the axial dimensionless coordinate [zeta], it is relevant to use the centerline velocity and scalar distributions, obtained from (41) and (42):
Horizontal axis, x [m]; vertical axis, dimensionless quantities [THETA], Y, [[rho].sub.f] and u.
8 data in terms of the dimensionless quantities of Table 1.
By forming these dimensionless quantities, the multitude of fan curves shown in Figure 3 was compressed into a single curve for each impeller, as shown in Figure 2.
Therefore we can define the dimensionless quantities [M.sub.C], x, and [[phi].sub.C] by the replacement:
(2)), have dimensionless quantities. The modal amplitude problem is obtained in a general form.