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.

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.

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.

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.

Fluid Mechanics of the Atmosphere presents the fundamental equations which govern most of the flow problems studied by atmospheric scientists. The equations are derived in a systematic way that is intended to facilitate critical evaluation. The goal of this text is twofold. First the book supplies the student a background familiarity in the underlying physics behind the mathematics. Second it explores some systematic methods of relating these physics to atmospheric problems, including rotating frames of reference effects, vorticity dynamics, and turbulence effects on closure. Stresses vorticity, principles of scaling, and turbulence Extensively illustrated Includes end-of-chapter summaries and problem sets Classroom tested for five years

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.

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.

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.