Dimensionless Physical Quantities in Science and Engineering

Dimensionless quantities, such as ?, e, and ? are used in mathematics, engineering, physics, and chemistry. In recent years the dimensionless groups, as demonstrated in detail here, have grown in significance and importance in contemporary mathematical and computer modeling as well as the traditional fields of physical modeling. This book offers the most comprehensive and up to date resource for dimensionless quantities, providing not only a summary of the quantities, but also a clarification of their physical principles, areas of use, and other specific properties across multiple relevant fields. Presenting the most complete and clearly explained single resource for dimensionless groups, this book will be essential for students and researchers working across the sciences.

Includes approximately 1,200 dimensionless quantities
Features both classic and newly developing fields
Easy to use with clear organization and citations to relevant works

Dimensionless quantities, such as p, e, and f are used in mathematics, engineering, physics, and chemistry. In recent years the dimensionless groups, as demonstrated in detail here, have grown in significance and importance in contemporary mathematical and computer modeling as well as the traditional fields of physical modeling. This book offers the most comprehensive and up to date resource for dimensionless quantities, providing not only a summary of the quantities, but also a clarification of their physical principles, areas of use, and other specific properties across multiple relevant fields. Presenting the most complete and clearly explained single resource for dimensionless groups, this book will be essential for students and researchers working across the sciences. Includes approximately 1,200 dimensionless quantitiesFeatures both classic and newly developing fieldsEasy to use with clear organization and citations to relevant works

Leseprobe
2
Physics and Physical Chemistry
The basic laws of physics and chemistry are like each other. Dmitri Ivanovich Mendeleev (1834-1907) 2.1 Physics, Mathematics and Geometry
In physics, dimensionless physical quantities and constants have been widely used, in thermodynamics, optics, radiation and other spheres of physics, especially in applications in various natural scientific and technical branches, and have become an important tool in their development. In mathematics, dimensionless quantities have their theoretical base in the theory of groups and also in linear algebra and matrix calculus. At the same time, the fundamental theorem to determine the similarity criteria is the dimensional homogeneity of equations of mathematical physics as defined by Fourier. The similarity criteria are practically important in numerical mathematics and computer modelling, e.g. not only in generalized dimensionless expressions of numerical solution stability of mathematical physics equations but also in other spheres of mathematics. Among the best known physical dimensionless quantities are the following numbers: Abbé, Fresnel and Snellen numbers in optics; Bejan, Boyle, Carnot, Gay-Lussac, Pitzer and Van der Walls numbers in thermodynamics; and the Planck number for radiation. In mathematics, for example, diverse dimensionless numbers express the stability conditions of the numerical solution, such as the Courant, Damkhler, Neumann and Péclet numbers and other mathematical and geometrical dimensionless numbers. 2.1.1 Abbé Number V
nD, nF, nC (-) - refractive indices of the material at the wavelength of the Fraunhofer D-, F- and C spectral lines (589.2, 486.1 and 656.3 nm, respectively). It is used to classify the glasses in the dispersion measurement in the visible radiation band. Low-fracture glasses have high values of V, e.g. for lead crystal glass it is V50. For heavy flint glasses, the common extent of V is about 20. Very light crown glasses have values of V up to 60. Info: [C2]. Ernst Abbé (23.1.1840-14.1.1905), German physicist and astronomer. He was engaged in physics, mathematics and meteorology but in optics and astronomy above all. He deduced the mathematical theory of a light microscope. He designed and fabricated high-quality lenses for scientific purposes. He manufactured special instruments. He was the co-founder of the Carl Zeiss works in Jena. 2.1.2 Energy Accommodation Coefficient rE, s,
Ein, Ere (J) - incident and reflected energy flux; EW (J) - reflected energy flux obtained if the molecules are in thermal equilibrium. It characterizes the mutual energetic effects of gas molecules with a solid body surface with heat passing in diluted gases. It expresses the energy of that part of the total number of gas molecules which come in contact with the surface and the energy which, after rebound or reemission, is reduced because of being accommodated to the surface temperature. Besides, it is the measure of the thermal energy transfer perfection. With the complete transfer, rE=1 is valid; and with a complete (mirrored) reflection of the energy, rE=0. Its size depends on the physical properties of the surroundings and usually does not differ very much from the number one. Info: [A33]. 2.1.3 Avogadro Number NA
The Avogadro number expresses the number of pa

Inhalt
1: Introduction 2: Physics and Physical Chemistry 3: Fluid Mechanics 4: Solid Mechanics 5: Thermomechanics 6: Electromagnetism 7: Physical Technology 8: Technology and Mechanical Engineering 9: Geophysics and Ecology

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