Applied Dimensional Analysis And Modeling

Author : Thomas Szirtes
Publisher : Butterworth-Heinemann
Page : 856 pages
File Size : 44,9 Mb
Release : 2007-04-27
Category : Technology & Engineering
ISBN : 9780080555454

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Applied Dimensional Analysis and Modeling by Thomas Szirtes Pdf

Applied Dimensional Analysis and Modeling provides the full mathematical background and step-by-step procedures for employing dimensional analyses, along with a wide range of applications to problems in engineering and applied science, such as fluid dynamics, heat flow, electromagnetics, astronomy and economics. This new edition offers additional worked-out examples in mechanics, physics, geometry, hydrodynamics, and biometry. Covers 4 essential aspects and applications: principal characteristics of dimensional systems, applications of dimensional techniques in engineering, mathematics and geometry, applications in biosciences, biometry and economics, applications in astronomy and physics Offers more than 250 worked-out examples and problems with solutions Provides detailed descriptions of techniques of both dimensional analysis and dimensional modeling

Author : E. van Groesen,Jaap Molenaar
Publisher : SIAM
Page : 238 pages
File Size : 46,9 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898718244

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Continuum Modeling in the Physical Sciences by E. van Groesen,Jaap Molenaar Pdf

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.

Author : Qing-Ming Tan
Publisher : Springer Science & Business Media
Page : 186 pages
File Size : 46,8 Mb
Release : 2011-06-06
Category : Technology & Engineering
ISBN : 9783642192340

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Dimensional Analysis by Qing-Ming Tan Pdf

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.

Author : F. W. David,H. Nolle
Publisher : Elsevier
Page : 200 pages
File Size : 48,6 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483102023

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Experimental Modelling in Engineering by F. W. David,H. Nolle Pdf

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 : Clive L. Dym,Elizabeth S. Ivey
Publisher : Unknown
Page : 284 pages
File Size : 48,8 Mb
Release : 1980
Category : Computers
ISBN : MINN:31951D013949703

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Principles of Mathematical Modeling by Clive L. Dym,Elizabeth S. Ivey Pdf

Author : Don S. Lemons
Publisher : Cambridge University Press
Page : 115 pages
File Size : 53,6 Mb
Release : 2017-03-16
Category : Science
ISBN : 9781107161153

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A Student's Guide to Dimensional Analysis by Don S. Lemons Pdf

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 : Josef Kuneš
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 46,9 Mb
Release : 2012-04-05
Category : Technology & Engineering
ISBN : 9781907343780

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Similarity and Modeling in Science and Engineering by Josef Kuneš Pdf

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.

Author : Alberto N. Conejo
Publisher : Springer Nature
Page : 384 pages
File Size : 49,6 Mb
Release : 2021-05-31
Category : Technology & Engineering
ISBN : 9789811616020

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Fundamentals of Dimensional Analysis by Alberto N. Conejo Pdf

This is the first book which systematically describes an integral approach on dimensional analysis. The amount of textbooks on dimensional analysis is huge, however most of the books start with the definition of the relevant variables. When the variables are given to the reader without prior knowledge on each problem it has serious consequences: the usefulness of dimensional analysis is not appreciated, is not possible to understand the real challenges of this subject and the result, which is a general relationship with dimensionless groups is useless. This book closes the hole in previous books because in addition to describe step by step how to reach the general relationship with dimensionless groups, which creates solid basis of different metallurgical problems to understand the role of the relevant variables. It provides a full description on how to obtain the experimental data and applies the experimental data to transform the general relationship in a particular solution. Once the reader learns how to design the experimental work and uses that information to define the particular solution, it is possible to asses if the selection of variables was adequate or not. The book is useful for both undergraduate and graduate students.

Author : Sandro G. Longo
Publisher : Springer Nature
Page : 447 pages
File Size : 53,5 Mb
Release : 2022-02-04
Category : Mathematics
ISBN : 9783030792176

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Principles and Applications of Dimensional Analysis and Similarity by Sandro G. Longo Pdf

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 : W.M. Grudzewski
Publisher : IOS Press
Page : 152 pages
File Size : 48,8 Mb
Release : 2013-08-20
Category : Business & Economics
ISBN : 9781614992806

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Application of Dimensional Analysis in Economics by W.M. Grudzewski Pdf

The modeling of economic phenomena and processes, in terms of their static and dynamic features and with regard to the characteristics of their course, is a major methodological trend in studies of the nature, properties and functioning of contemporary management systems. Models describing management systems must be of a multi-aspect nature, entailing aspects such as technical, economic and sociological factors on the one hand, and forecasting, planning, leading, controlling etc., on the other. Developing a method for incorporating such diverse data into a system of analysis is, needless to say, a complex process. Dimensional analysis is a tool which might be useful in this process, but one which, up to now, has been little explored in the economic sciences. This book explores the application of dimensional analysis in the field of economics. It has been structured in a way which corresponds to the formulation of economic quantities, and is divided into five sections: measuring of economic quantities, modeling of economic processes, principles of dimensional analysis, building of quantified dimensional models, and experiment and practical verification.

Author : Jonathan Worstell
Publisher : Butterworth-Heinemann
Page : 160 pages
File Size : 54,8 Mb
Release : 2014-03-05
Category : Technology & Engineering
ISBN : 9780128012550

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Dimensional Analysis by Jonathan Worstell Pdf

Practical Guides in Chemical Engineering are a cluster of short texts that each provides a focused introductory view on a single subject. The full library spans the main topics in the chemical process industries that engineering professionals require a basic understanding of. They are ‘pocket publications’ that the professional engineer can easily carry with them or access electronically while working. Each text is highly practical and applied, and presents first principles for engineers who need to get up to speed in a new area fast. The focused facts provided in each guide will help you converse with experts in the field, attempt your own initial troubleshooting, check calculations, and solve rudimentary problems. Dimensional Analysis provides the foundation for similitude and for up and downscaling. Aeronautical, Civil, and Mechanical Engineering have used Dimensional Analysis profitably for over one hundred years. Chemical Engineering has made limited use of it due to the complexity of chemical processes. However, Chemical Engineering can now employ Dimensional Analysis widely due to the free-for-use matrix calculators now available on the Internet. This book shows how to apply matrices to Dimensional Analysis. Practical, short, concise information on the basics will help you get an answer or teach yourself a new topic quickly Supported by industry examples to help you solve a real world problem Single subject volumes provide key facts for professionals

Author : Josef Kuneš
Publisher : Springer Science & Business Media
Page : 451 pages
File Size : 41,9 Mb
Release : 2012-04-07
Category : Mathematics
ISBN : 9781907343773

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Similarity and Modeling in Science and Engineering by Josef Kuneš Pdf

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.

Author : Kolumban Hutter,Klaus Jöhnk
Publisher : Springer Science & Business Media
Page : 645 pages
File Size : 53,8 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783662064023

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Continuum Methods of Physical Modeling by Kolumban Hutter,Klaus Jöhnk Pdf

The book unifies classical continuum mechanics and turbulence modeling, i.e. the same fundamental concepts are used to derive model equations for material behaviour and turbulence closure and complements these with methods of dimensional analysis. The intention is to equip the reader with the ability to understand the complex nonlinear modeling in material behaviour and turbulence closure as well as to derive or invent his own models. Examples are mostly taken from environmental physics and geophysics.

Author : Frederick Y. M. Wan
Publisher : SIAM
Page : 404 pages
File Size : 46,6 Mb
Release : 2018-03-20
Category : Computers
ISBN : 9781611975277

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Mathematical Models and Their Analysis by Frederick Y. M. Wan Pdf

A great deal can be learned through modeling and mathematical analysis about real-life phenomena, even before numerical simulations are used to accurately portray the specific configuration of a situation. Scientific computing also becomes more effective and efficient if it is preceded by some preliminary analysis. These important advantages of mathematical modeling are demonstrated by models of historical importance in an easily understandable way. The organization of Mathematical Models and Their Analysis groups models by the issues that need to be addressed about the phenomena. The new approach shows how mathematics effective for one modeled phenomenon can be used to analyze another unrelated problem. For instance, the mathematics of differential equations useful in understanding the classical physics of planetary models, fluid motion, and heat conduction is also applicable to the seemingly unrelated phenomena of traffic flow and congestion, offshore sovereignty, and regulation of overfishing and deforestation. The formulation and in-depth analysis of these and other models on modern social issues, such as the management of exhaustible and renewable resources in response to consumption demands and economic growth, are of increasing concern to students and researchers of our time. The modeling of current social issues typically starts with a simple but meaningful model that may not capture all the important elements of the phenomenon. Predictions extracted from such a model may be informative but not compatible with all known observations; so the model may require improvements. The cycle of model formulation, analysis, interpretation, and assessment is made explicit for the modeler to repeat until a model is validated by consistency with all known facts.

Author : Guillaume Delaplace,Karine Loubière,Fabrice Ducept,Romain Jeantet
Publisher : Elsevier
Page : 358 pages
File Size : 41,5 Mb
Release : 2015-09-18
Category : Technology & Engineering
ISBN : 9780081004876

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Dimensional Analysis of Food Processes by Guillaume Delaplace,Karine Loubière,Fabrice Ducept,Romain Jeantet Pdf

This book deals with the modeling of food processing using dimensional analysis. When coupled to experiments and to the theory of similarity, dimensional analysis is indeed a generic, powerful and rigorous tool making it possible to understand and model complex processes for design, scale-up and /or optimization purposes. This book presents the theoretical basis of dimensional analysis with a step by step detail of the framework for applying dimensional analysis, with chapters respectively dedicated to the extension of dimensional analysis to changing physical properties and to the use of dimensional analysis as a tool for scaling-up processes. It includes several original examples issued from the research works of the authors in the food engineering field, illustrating the conceptual approaches presented and strengthen the teaching of all. Discusses popular dimensional analysis for knowledge and scaling-up tools with detailed case studies Emphasises the processes dealing with complex materials of a multiphase nature Introduces the concept of chemical or material similarity and a framework for analysis of the functional forms of the propoerty