Dimensional Analysis Beyond The Pi Theorem

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Dimensional Analysis Beyond The Pi Theorem

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Author : Bahman Zohuri
language : en
Publisher: Springer
Release Date : 2016-11-02

Dimensional Analysis Beyond The Pi Theorem written by Bahman Zohuri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-02 with Technology & Engineering categories.

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.

Dimensional Analysis And Self Similarity Methods For Engineers And Scientists

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Author : Bahman Zohuri
language : en
Publisher: Springer
Release Date : 2015-04-15

Dimensional Analysis And Self Similarity Methods For Engineers And Scientists written by Bahman Zohuri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-15 with Technology & Engineering categories.

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 And Machinery

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Author : Dr.P.Maniiarasan
language : en
Publisher: RK Publication
Release Date : 2024-09-20

Fluid Mechanics And Machinery written by Dr.P.Maniiarasan and has been published by RK Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-20 with Science categories.

Fluid Mechanics and Machinery is a comprehensive exploration of the principles governing fluid behavior and the machinery utilized in fluid systems. Fundamental concepts of fluid mechanics, including fluid properties, dynamics, and statics, while also delving into the design, operation, and analysis of various fluid machinery such as pumps, turbines, and compressors. Through detailed illustrations and real-world applications, it equips readers with a solid understanding of fluid dynamics and the engineering practices necessary for effective fluid management in diverse industrial contexts.

The Pi Theorem

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Author : L.P. Yarin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-21

The Pi Theorem written by L.P. Yarin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-21 with Technology & Engineering categories.

This volume presents applications of the Pi-Theorem to fluid mechanics and heat and mass transfer. The Pi-theorem yields a physical motivation behind many flow processes and therefore it constitutes a valuable tool for the intelligent planning of experiments in fluids. After a short introduction to the underlying differential equations and their treatments, the author presents many novel approaches how to use the Pi-theorem to understand fluid mechanical issues. The book is a great value to the fluid mechanics community, as it cuts across many subdisciplines of experimental fluid mechanics.

Dimensional Analysis

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Author : Percy Williams Bridgman
language : en
Publisher: Legare Street Press
Release Date : 2022-10-26

Dimensional Analysis written by Percy Williams Bridgman and has been published by Legare Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-26 with History categories.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Chemical Engineering

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Author : Tanase Gh. Dobre
language : en
Publisher: John Wiley & Sons
Release Date : 2007-06-18

Chemical Engineering written by Tanase Gh. Dobre and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-18 with Science categories.

A description of the use of computer aided modeling and simulation in the development, integration and optimization of industrial processes. The two authors elucidate the entire procedure step-by-step, from basic mathematical modeling to result interpretation and full-scale process performance analysis. They further demonstrate similitude comparisons of experimental results from different systems as a tool for broadening the applicability of the calculation methods. Throughout, the book adopts a very practical approach, addressing actual problems and projects likely to be encountered by the reader, as well as fundamentals and solution strategies for complex problems. It is thus equally useful for student and professional engineers and chemists involved in industrial process and production plant design, construction or upgrading.

Continuum Modeling In The Physical Sciences

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Author : E. van Groesen
language : en
Publisher: SIAM
Release Date : 2007-01-01

Continuum Modeling In The Physical Sciences written by E. van Groesen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.

Mathematical modeling - the ability to apply mathematical concepts and techniques to real-life systems has expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts. Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the challenging problems sections found at the ends of several chapters.

Similitude And Approximation Theory

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Author : S.J. Kline
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Similitude And Approximation Theory written by S.J. Kline and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.

There are a number of reasons for producing this edition of Simili tude and Approximation Theory. The methodologies developed remain important in many areas of technical work. No other equivalent work has appeared in the two decades since the publication of the first edition. The materials still provide an important increase in understanding for first-year graduate students in engineering and for workers in research and development at an equivalent level. In addition, consulting experiences in a number of industries indi cate that many technical workers in research and development lack knowledge of the methodologies given in this work. This lack makes the work of planning and controlling computations and experiments less efficient in many cases. It also implies that the coordinated grasp of the phenomena (which is so critical to effective research and develop ment work) will be less than it might be. The materials covered in this work focus on the relationship between mathematical models and the physical reality such models are intended v vi Preface to the Springer Edition to portray. Understanding these relationships remains a key factor in simplifying and generalizing correlations, predictions, test programs, and computations. Moreover, as many teachers of engineering know, this kind of understanding is typically harder for students to develop than an understanding of either the mathematics or the physics alone.

Principles Of Mathematical Modeling

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Author : Clive Dym
language : en
Publisher: Academic Press
Release Date : 2004-06-21

Principles Of Mathematical Modeling written by Clive Dym and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-21 with Mathematics categories.

This book provides a readable and informative introduction to the development and application of mathematical models in science and engineering. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools (dimensional analysis, scaling techniques, and approximation and validation techniques). The second half then applies these foundational tools to a broad variety of subjects, including exponenttial growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. An extensive collection of more than 360 problems offer ample opportunity in both a formal course and for the individual reader. (Midwest).

Applied Dimensional Analysis And Modeling

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Author : Thomas Szirtes
language : en
Publisher: Butterworth-Heinemann
Release Date : 2007

Applied Dimensional Analysis And Modeling written by Thomas Szirtes and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Learn to apply the "dimensional method" to facilitate the design and testing of engineering and physical systems;and greatly accelerate the development of products. This is the first book to offer a practical approach to modeling and dimensional analysis, emphasizing the interests and problems of the engineer and applied scientist. Packed with illustrations, graphs, numeric tables, and concrete case studies, this in-depth reference work explains both dimensional analysis and scale modeling...concisely describes constructions of dimensional systems, including SI (metric) and Imperial (U.S.)...and provides over 250 worked-out examples drawn from engineering, applied physics, biomechanics, astronomy, geometry, and economics .