Topic

# Dimensionless quantity

About: Dimensionless quantity is a research topic. Over the lifetime, 3757 publications have been published within this topic receiving 78590 citations. The topic is also known as: dimensionless parameter & quantity of dimension one.

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TL;DR: In this paper, two general classes of descriptive numbers are presented: linear scale measurements and dimensionless numbers, usually angles or ratios of length measures, whereby the shapes of analogous units can be compared irrespective of scale.

Abstract: Quantitative geomorphic methods developed within the past few years provide means of measuring size and form properties of drainage basins. Two general classes of descriptive numbers are (1) linear scale measurements, whereby geometrically analogous units of topography can be compared as to size; and (2) dimensionless numbers, usually angles or ratios of length measures, whereby the shapes of analogous units can be compared irrespective of scale.
Linear scale measurements include length of stream channels of given order, drainage density, constant of channel maintenance, basin perimeter, and relief. Surface and crosssectional areas of basins are length products. If two drainage basins are geometrically similar, all corresponding length dimensions will be in a fixed ratio.
Dimensionless properties include stream order numbers, stream length and bifurcation ratios, junction angles, maximum valley-side slopes, mean slopes of watershed surfaces, channel gradients, relief ratios, and hypsometric curve properties and integrals. If geometrical similarity exists in two drainage basins, all corresponding dimensionless numbers will be identical, even though a vast size difference may exist. Dimensionless properties can be correlated with hydrologic and sediment-yield data stated as mass or volume rates of flow per unit area, independent of total area of watershed.

4,480 citations

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TL;DR: In this paper, it was shown that the fundamental constants of physics, such as c the velocity of light, h Planck's constant, e the charge and m mass of the electron, and so on, provide a set of absolute units for measurement of distance, time, mass, etc.

Abstract: THE fundamental constants of physics, such as c the velocity of light, h Planck's constant, e the charge and m mass of the electron, and so on, provide for us a set of absolute units for measurement of distance, time, mass, etc. There are, however, more of these constants than are necessary for this purpose, with the result that certain dimensionless numbers can be constructed from them. The significance of these numbers has excited much interest in recent times, and Eddington has set up a theory for calculating each of them purely deductively. Eddington's arguments are not always rigorous, and, while they give one the feeling that they are probably substantially correct in the case of the smaller numbers (the reciprocal fine-structure constant hc/e2 and the ratio of the mass of the proton to that of the electron), the larger numbers, namely the ratio of the electric to the gravitational force between electron and proton, which is about 1039, and the ratio of the mass of the universe to the mass of the proton, which is about 1078, are so enormous as to make one think that some entirely different type of explanation is needed for them.

1,234 citations

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TL;DR: In this paper, the correlation energy per particle of an electron gas expressed in rydbergs is computed for small values of rs (high density) and found to be given by ec=Alnrs+C+O(rs).

Abstract: The quantity ec is defined as the correlation energy per particle of an electron gas expressed in rydbergs. It is a function of the conventional dimensionless parameter rs, where rs-3 is proportional to the electron density. Here ec is computed for small values of rs (high density) and found to be given by ec=Alnrs+C+O(rs). The value of A is found to be 0.0622, a result that could be deduced from previous work of Wigner, Macke, and Pines. An exact formula for the constant C is given here for the first time; earlier workers had made only approximate calculations of C. Further, it is shown how the next correction in rs can be computed. The method is based on summing the most highly divergent terms of the perturbation series under the integral sign to give a convergent result. The summation is performed by a technique similar to Feynman's methods in field theory.

985 citations

01 Oct 1976

TL;DR: The influence of the ellipticity parameter and the dimensionless speed U, load W, and material G on minimum film thickness was investigated in this paper, where conditions corresponding to the use of solid materials of bronze, steel, and silicon nitride and lubricants of paraffinic and naphthenic mineral oils were considered.

Abstract: The influence of the ellipticity parameter and the dimensionless speed U, load W, and material G parameters on minimum film thickness was investigated. The ellipticity parameter k was varied from 1 (a ball-on-plate configuration) to 8 (a configuration approaching a line contact). The dimensionless speed parameter was varied over a range of nearly two orders of magnitude. And the dimensionless load parameter was varied over a range of one order of magnitude. Conditions corresponding to the use of solid materials of bronze, steel, and silicon nitride and lubricants of paraffinic and naphthenic mineral oils were considered in obtaining the exponent on the dimensionless material parameter.

764 citations

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TL;DR: In this paper, a large number of turbulence observations were made under stable conditions along a meteorological mast at Cabauw, The Netherlands, and they were used to present and organize these data and turn to the parameterized equations for the turbulent variances and covariances.

Abstract: A large number of turbulence observations were made under stable conditions along a meteorological mast at Cabauw, The Netherlands. To present and organize these data we turn to the parameterized equations for the turbulent variances and covariances. In a dimensionless form these equations lead to a local scaling hypothesis. According to this hypothesis, dimensionless combinations of variables which are measured at the same height can be expressed as a function of a single parameter z/Λ. Here, Λ is called a local Obukhov length and is defined as Λ=−τ3/2T/(kgwθ) where τ and wθ) are the kinematic momentum and heat flux, respectively. Note that, in general, Λ may vary across the boundary layer, because τ and wθ are still unknown functions of height. The observations support local scaling. In particular, they agree with the limit condition for z/Λ→∞, which predicts that locally scaled variables approach a constant value. The latter result is called z-less stratification. An important application of z...

751 citations