Scaling, Self-similarity, and Intermediate Asymptotics
Scaling, Self-similarity, and Intermediate Asymptotics

Author: G. I. Barenblatt

Publisher: Cambridge University Press

Published: 1996-12-12

Total Pages: 412

ISBN-13: 9780521435222

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Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.

Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists
Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists

Author: Bahman Zohuri

Publisher: Springer

Published: 2015-04-15

Total Pages: 379

ISBN-13: 3319134760

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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.

Dimensional Analysis
Dimensional Analysis

Author: J.C. Gibbings

Publisher: Springer Science & Business Media

Published: 2011-02-11

Total Pages: 302

ISBN-13: 1849963177

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For experiments, dimensional analysis enables the design, checks the validity, orders the procedure and synthesises the data. Additionally it can provide relationships between variables where standard analysis is not available. This widely valuable analysis for engineers and scientists is here presented to the student, the teacher and the researcher. It is the first complete modern text that covers developments over the last three decades while closing all outstanding logical gaps. Dimensional Analysis also lists the logical stages of the analysis, so showing clearly the care to be taken in its use while revealing the very few limitations of application. As the conclusion of that logic, it gives the author's original proof of the fundamental and only theorem. Unlike past texts, Dimensional Analysis includes examples for which the answer does not already exist from standard analysis. It also corrects the many errors present in the existing literature by including accurate solutions. Dimensional Analysis is written for all branches of engineering and science as a teaching book covering both undergraduate and postgraduate courses, as a guide for the lecturer and as a reference volume for the researcher.

Dimensional Analysis and Similarity in Fluid Mechanics
Dimensional Analysis and Similarity in Fluid Mechanics

Author: Nord-Eddine Sad Chemloul

Publisher: John Wiley & Sons

Published: 2020-11-03

Total Pages: 240

ISBN-13: 1119788021

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Dimensional analysis is the basis for the determination of laws that allow the experimental results obtained on a model to be transposed to the fluid system at full scale (a prototype). The similarity in fluid mechanics then allows for better redefinition of the analysis by removing dimensionless elements. This book deals with these two tools, with a focus on the Rayleigh method and the Vaschy-Buckingham method. It deals with the homogeneity of the equations and the conversion between the systems of units SI and CGS, and presents the dimensional analysis approach, before addressing the similarity of flows. Dimensional Analysis and Similarity in Fluid Mechanics proposes a scale model and presents numerous exercises combining these two methods. It is accessible to students from their first year of a bachelorÂs degree.

A Dictionary of Mechanical Engineering
A Dictionary of Mechanical Engineering

Author: Tony Atkins

Publisher: OUP Oxford

Published: 2013-04-25

Total Pages: 450

ISBN-13: 0191044962

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A Dictionary of Mechanical Engineering is one of the latest additions to the market leading Oxford Paperback Reference series. In over 8,500 clear and concise A to Z entries, it provides definitions and explanations for mechanical engineering terms in the core areas of design, stress analysis, dynamics and vibrations, thermodynamics, and fluid mechanics. Topics covered include heat transfer, combustion, control, lubrication, robotics, instrumentation, and measurement. Where relevant, the dictionary also touches on related subject areas such as acoustics, bioengineering, chemical engineering, civil engineering, aeronautical engineering, environmental engineering, and materials science. Useful entry-level web links are listed and regularly updated on a dedicated companion website to expand the coverage of the dictionary. Cross-referenced and including many line drawings, this excellent new volume is the most comprehensive and authoritative dictionary of its kind. It is an essential reference for students of mechanical engineering and for anyone with an interest in the subject.

Principles and Applications of Dimensional Analysis and Similarity
Principles and Applications of Dimensional Analysis and Similarity

Author: Sandro G. Longo

Publisher: Springer Nature

Published: 2022-02-04

Total Pages: 447

ISBN-13: 303079217X

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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.

Similarity and Modeling in Science and Engineering
Similarity and Modeling in Science and Engineering

Author: Josef Kuneš

Publisher: Springer Science & Business Media

Published: 2012-04-07

Total Pages: 451

ISBN-13: 1907343776

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The present text sets itself in relief to other titles on the subject in that it addresses the means and methodologies versus a narrow specific-task oriented approach. Concepts and their developments which evolved to meet the changing needs of applications are addressed. This approach provides the reader with a general tool-box to apply to their specific needs. Two important tools are presented: dimensional analysis and the similarity analysis methods. The fundamental point of view, enabling one to sort all models, is that of information flux between a model and an original expressed by the similarity and abstraction Each chapter includes original examples and applications. In this respect, the models can be divided into several groups. The following models are dealt with separately by chapter; mathematical and physical models, physical analogues, deterministic, stochastic, and cybernetic computer models. The mathematical models are divided into asymptotic and phenomenological models. The phenomenological models, which can also be called experimental, are usually the result of an experiment on an complex object or process. The variable dimensionless quantities contain information about the real state of boundary conditions, parameter (non-linearity) changes, and other factors. With satisfactory measurement accuracy and experimental strategy, such models are highly credible and can be used, for example in control systems.

Scaling
Scaling

Author: G. I. Barenblatt

Publisher: Cambridge University Press

Published: 2003-11-13

Total Pages: 187

ISBN-13: 0521826578

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The author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural consequences of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists.

Dimensional Analysis
Dimensional Analysis

Author: Qing-Ming Tan

Publisher: Springer Science & Business Media

Published: 2011-06-06

Total Pages: 199

ISBN-13: 3642192343

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Dimensional analysis is an essential scientific method and a powerful tool for solving problems in physics and engineering. This book starts by introducing the Pi Theorem, which is the theoretical foundation of dimensional analysis. It also provides ample and detailed examples of how dimensional analysis is applied to solving problems in various branches of mechanics. The book covers the extensive findings on explosion mechanics and impact dynamics contributed by the author’s research group over the past forty years at the Chinese Academy of Sciences. The book is intended for research scientists and engineers working in the fields of physics and engineering, as well as graduate students and advanced undergraduates of the related fields. Qing-Ming Tan is a former Professor at the Institute of Mechanics, the Chinese Academy of Sciences, China.

Similarity and Dimensional Methods in Mechanics
Similarity and Dimensional Methods in Mechanics

Author: L. I. Sedov

Publisher: Academic Press

Published: 2014-05-12

Total Pages: 386

ISBN-13: 1483225917

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Similarity and Dimensional Methods in Mechanics provides a complete development of the basic concepts of dimensional analysis and similarity methods, illustrated by applications to a wide variety of problems in mechanics. This book shows the power of dimensional and similarity methods in solving problems in the theory of explosions and astrophysics. Organized into five chapters, this book begins with an overview of the fundamental ideas behind similarity and dimensional methods. This text then provides a series of examples of application of the methods. Other chapters consider the use of similarity and dimensional analysis in developing fundamental contributions to viscous fluid theory. This book discusses as well the various theories of isotropic turbulence. The final chapter deals with the applications to the theory of the luminosity and internal structure of stars. This book is a valuable resource for students who wish to learn dimensional analysis and similarity methods for the first time. Readers who are connected with the many aspects of gas dynamics, including space technology, astrophysics, and atomic energy will also find this book useful.