Principles And Applications Of Dimensional Analysis And Similarity
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Author | : Sandro G. Longo |
Publisher | : Springer Nature |
Total Pages | : 447 |
Release | : 2022-02-04 |
Genre | : Mathematics |
ISBN | : 303079217X |
The book provides a summary of the historical evolution of dimensional analysis, and frames the problem of dimensions, systems of units and similarity in a vision dominated by the conventions that formalise even the exact sciences. The first four chapters address the definitions, with few dimensional analysis theorems and similarity criteria. There is also the analysis of self-similarity, both of first and second kind, with a couple of completely solved problems, framed within the group theory. From chapter 5 onward, the focus is on applications in some of the engineering sectors. The number of topics is necessarily limited, but, almost always, there are details, calculations and treatment of assumptions. The book contains descriptions of some of the experimental apparatuses currently used for the realisation of physical models, such as the wind tunnel, the shaking table, the centrifuge, and with the exclusion of many others, which can be found in specialist monographies. Measurement techniques and instrumentation and statistical data processing is also available in other books. Some more specific notions, required by the context, are reported in the appendix, where appears also the description of numerous dimensionless groups, all of engineering interest, but with the exclusion of many others related to physical processes of electrical nature or physics of particles. A glossary lists the meaning of some specific terms typical of dimensional analysis and used in the book.
Author | : Bahman Zohuri |
Publisher | : Springer |
Total Pages | : 278 |
Release | : 2016-11-02 |
Genre | : Technology & Engineering |
ISBN | : 3319457268 |
Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First and Second kind. Such solutions are not newly discovered; they have been identified and named by Zel’dovich, a famous Russian Mathematician in 1956. They have been used in the context of a variety of problems, such as shock waves in gas dynamics, and filtration through elasto-plastic materials. Self-Similarity has simplified computations and the representation of the properties of phenomena under investigation. It handles experimental data, reduces what would be a random cloud of empirical points to lie on a single curve or surface, and constructs procedures that are self-similar. Variables can be specifically chosen for the calculations.
Author | : Don S. Lemons |
Publisher | : Cambridge University Press |
Total Pages | : 115 |
Release | : 2017-03-16 |
Genre | : Mathematics |
ISBN | : 1107161150 |
This introduction to dimensional analysis covers the methods, history and formalisation of the field. Utilising topics including mechanics, hydro- and electrodynamics, and thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis, making it perfect for students on introductory courses in physics, engineering and mathematics.
Author | : Bahman Zohuri |
Publisher | : Springer |
Total Pages | : 379 |
Release | : 2015-04-15 |
Genre | : Technology & Engineering |
ISBN | : 3319134760 |
This ground-breaking reference provides an overview of key concepts in dimensional analysis, and then pushes well beyond traditional applications in fluid mechanics to demonstrate how powerful this tool can be in solving complex problems across many diverse fields. Of particular interest is the book’s coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering. Numerous practical examples of dimensional problems are presented throughout, allowing readers to link the book’s theoretical explanations and step-by-step mathematical solutions to practical implementations.
Author | : F. W. David |
Publisher | : Elsevier |
Total Pages | : 200 |
Release | : 2013-10-22 |
Genre | : Technology & Engineering |
ISBN | : 1483102025 |
Experimental Modelling in Engineering presents the principles of experimental modeling methodically and in such a generalized manner that they may lend themselves to application in practically all fields of technology. The book covers related topics such as modeling based on conditions of similarity; units and dimensions; the applications of homogeneity and dimensionally homogenous equations in the field; and the selection of variables in dimensional analysis. Also covered in the book are topics such as the use of models in experiments; the principle of similarity; examples in experimental modeling; and problems in dimensional analysis and model design. The text is recommended for engineers who would like to know more about the principles, concepts, behind experimental modeling, as well as its applications in engineering and other related fields.
Author | : L. I. Sedov |
Publisher | : CRC Press |
Total Pages | : 498 |
Release | : 2018-05-04 |
Genre | : Science |
ISBN | : 1351416561 |
Similiarity and Dimensional Methods in Mechanics, 10th Edition is an English language translation of this classic volume examining the general theory of dimensions of physical quantities, the theory of mechanical and physical similarity, and the theory of modeling. Several examples illustrate the use of the theories of similarity and dimensions for establishing fundamental mechanical regularities in aviation, explosions, and astrophysics, as well as in the hydrodynamics of ships. Other interesting areas covered include the general theory of automodel motions of continuum media, the theory of propagation of explosion waves in gases, the theory of one-dimensional nonestablished motion in gases, the fundamentals of the gas-dynamics theory of atom-bomb explosion in the atmosphere and the theory of averaging of gaseous flows in channels. Aspects of modeling include the dimensionless characteristics of compressor operation, the theories of engine thrust, and efficiency of an ideal propeller for subsonic and supersonic speeds. Similiarity and Dimensional Methods in Mechanics, 10th Edition is an ideal volume for researchers and students involved in physics and mechanics.
Author | : |
Publisher | : |
Total Pages | : 592 |
Release | : 1974 |
Genre | : Mechanics, Applied |
ISBN | : |
Author | : P.S. Westine |
Publisher | : Elsevier |
Total Pages | : 397 |
Release | : 2012-12-02 |
Genre | : Technology & Engineering |
ISBN | : 0444598138 |
Here is the second revised and updated edition of probably the most practical sourcebook on similarity methods and modeling techniques available. Written by leading authorities who incorporate many of the latest advances in the field, this new work maps out techniques for modeling as well as instrumentation and data analysis for an extremely wide array of problems in engineering dynamics. This practical reference uses experimental test data on various engineering problems demonstrating exactly how and why these similarity methods work. The problems involve spread of oil slicks, explosive cratering, car crashes, space vehicle heat exchange, explosive forming, and more. The spectrum of topics covered and number of examples are far greater than in other texts. Of particular importance are the dissimilar material modeling techniques which bring new versatility and freedom to the modeler in structural dynamics. The book also contains a clear, in-depth discussion of the theory underlying modeling and includes alternate methods for developing model laws. The work will undoubtedly prove invaluable to every professional involved in testing or design of dynamic experiments.
Author | : Rattan Lal |
Publisher | : CRC Press |
Total Pages | : 699 |
Release | : 2004-05-28 |
Genre | : Technology & Engineering |
ISBN | : 0824751272 |
Principles of Soil Physics examines the impact of the physical, mechanical, and hydrological properties and processes of soil on agricultural production, the environment, and sustainable use of natural resources. The text incorporates valuable assessment methods, graphs, problem sets, and tables from recent studies performed around the globe and offers an abundance of tables, photographs, and easy-to-follow equations in every chapter. The book discusses the consequences of soil degradation, such as erosion, inhibited root development, and poor aeration. It begins by defining soil physics, soil mechanics, textural properties, and packing arrangements . The text continues to discuss the theoretical and practical aspects of soil structure and explain the significance and measurement of bulk density, porosity, and compaction. The authors proceed to clarify soil hydrology topics including hydrologic cycle, water movement, infiltration, modeling, soil evaporation, and solute transport processes. They address the impact of soil temperature on crop growth, soil aeration, and the processes that lead to the emission of greenhouse gases. The final chapters examine the physical properties of gravelly soils and water movement in frozen, saline, and water-repellant soils. Reader-friendly and up-to-date, Principles of Soil Physics provides unparalleled coverage of issues related to soil physics, structure, hydrology, aeration, temperature, and analysis and presents practical techniques for maintaining soil quality to ultimately preserve its sustainability.
Author | : L. I. Sedov |
Publisher | : CRC Press |
Total Pages | : 496 |
Release | : 2018-05-04 |
Genre | : Science |
ISBN | : 135141657X |
Similiarity and Dimensional Methods in Mechanics, 10th Edition is an English language translation of this classic volume examining the general theory of dimensions of physical quantities, the theory of mechanical and physical similarity, and the theory of modeling. Several examples illustrate the use of the theories of similarity and dimensions for establishing fundamental mechanical regularities in aviation, explosions, and astrophysics, as well as in the hydrodynamics of ships. Other interesting areas covered include the general theory of automodel motions of continuum media, the theory of propagation of explosion waves in gases, the theory of one-dimensional nonestablished motion in gases, the fundamentals of the gas-dynamics theory of atom-bomb explosion in the atmosphere and the theory of averaging of gaseous flows in channels. Aspects of modeling include the dimensionless characteristics of compressor operation, the theories of engine thrust, and efficiency of an ideal propeller for subsonic and supersonic speeds. Similiarity and Dimensional Methods in Mechanics, 10th Edition is an ideal volume for researchers and students involved in physics and mechanics.