Download or read book Dimensional Analysis and Self Similarity Methods for Engineers and Scientists written by Bahman Zohuri and published by Springer. This book was released on 2015-04-15 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Student s Guide to Dimensional Analysis written by Don S. Lemons and published by Cambridge University Press. This book was released on 2017-03-16 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Street Fighting Mathematics written by Sanjoy Mahajan and published by MIT Press. This book was released on 2010-03-05 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
Download or read book Dimensional Analysis written by Jeffrey H. Williams and published by IOP Publishing Limited. This book was released on 2022-03-15 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dimensional analysis is a powerful method to analyse complex physical phenomena, including those for which we cannot pose, much less solve governing equations. Its use in science and engineering is ubiquitous and has been central to the work of greats such as Lord Rayleigh, Bohr and Einstein. It offers a method for reducing complex physical problems to their simplest forms and provides a powerful tool for checking whether or not equations are dimensionally consistent and suggests plausible equations when we know which quantities are involved. Every scientist and engineer should have this tool at their command, and this book provides an accessible, modern, self-contained and systematic overview. It outlines the principles of similitude and presents the tools of dimensional analysis for both scientists and engineers and how it can be applied practically to aid not only a greater understanding of theoretical concepts but in designing experiments and analysing experimental data. With examples relevant to a wide range of students and not limited to the physical and engineering sciences, but encompasses the biological and life sciences. The technique has, for example, been used to estimate the running speed of a hungry Tyrannosaurus rex, a comparison of the flights of mosquitos and jet airliners, and the energy released by an atomic weapon. Key Features Draws on and presents examples across the physical, chemical and life sciences, as well as engineering applications Emphasises the technique as a tool and empowers readers to apply the method in developing their own experiments and theoretical understanding Includes methods, history and applications An engaging, accessible, self-contained and systematic resource.
Download or read book Worked Examples in Turbomachinery written by S. L. Dixon and published by Elsevier. This book was released on 2014-05-23 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Worked Examples in Turbomachinery (Fluid Mechanics and Thermodynamics) is a publication designed to supplement the materials in Fluid Mechanics, Thermodynamics of Turbomachinery, Second Edition. The title provides detailed solution for the unanswered problems from the main textbook. The text first covers dimensional analysis, and then proceeds to tackling thermodynamics. Next, the selection discusses two-dimensional cascades. The text also talks about axial flow turbines and compressors, along with the three-dimensional flow in axial turbo machines. Chapter 7 covers centrifugal compressor and pumps, while Chapter 8 tackles radial flow turbines. The book will be of great use to students of mechanical engineering, particularly those who have access to the main textbook.
Download or read book Scaling Self similarity and Intermediate Asymptotics written by G. I. Barenblatt and published by Cambridge University Press. This book was released on 1996-12-12 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dimensional Analysis Beyond the Pi Theorem written by Bahman Zohuri and published by Springer. This book was released on 2016-11-02 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Similitude and Modelling written by E. Szücs and published by Elsevier. This book was released on 2012-12-02 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Similitude and Modeling describes the theoretical aspects and application of similitude method using mathematical apparatus. This book is organized into two parts encompassing 13 chapters, and begins with an introduction to a simple technological problem in similitude modeling. The first part deals with the concept, physical fundamentals, dimensional analysis, and approximate and partial modeling of similitude. This part explores also the preparation and evaluation of similitude experiments, as well as the general types of similitude invariants. The second part highlights the application areas of similitude modeling, including heat conduction and diffusion, fluid dynamics, elastic deformation, and chemical reactions. This book will prove useful to plant and design engineers.
Download or read book Symmetry and Integration Methods for Differential Equations written by George Bluman and published by Springer Science & Business Media. This book was released on 2008-01-10 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.
Download or read book Similarity and Dimensional Methods in Mechanics written by L. I. Sedov and published by Academic Press. This book was released on 2014-05-12 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied Dimensional Analysis and Modeling written by Thomas Szirtes and published by Butterworth-Heinemann. This book was released on 2007-04-27 with total page 853 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Introduction to Fluid Mechanics Sixth Edition written by William S. Janna and published by CRC Press. This book was released on 2020-03-31 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Fluid Mechanics, Sixth Edition, is intended to be used in a first course in Fluid Mechanics, taken by a range of engineering majors. The text begins with dimensions, units, and fluid properties, and continues with derivations of key equations used in the control-volume approach. Step-by-step examples focus on everyday situations, and applications. These include flow with friction through pipes and tubes, flow past various two and three dimensional objects, open channel flow, compressible flow, turbomachinery and experimental methods. Design projects give readers a sense of what they will encounter in industry. A solutions manual and figure slides are available for instructors.
Download or read book Fluid Mechanics Through Problems written by R. J. Garde and published by New Age International. This book was released on 2006 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Is An Outcome Of Authors Over Thirty Years Of Teaching Fluid Mechanics To Undergraduate And Postgraduate Students. The Book Is Written With The Purpose That, Through This Book, Student Should Appreciate The Strength And Limitations Of The Theory, And Also Its Potential For Application In Solving A Variety Of Engineering Problems Of Practical Importance. It Makes Available To The Students, Appearing For Diploma And Undergraduate Courses In Civil, Chemical And Mechanical Engineering, A Book Which Briefly Introduces The Necessary Theory, Followed By A Set Of Descriptive/Objective Questions.In Seventeen Chapters The Book Covers The Broad Areas Of Fluid Properties, Kinematics, Dynamics, Dimensional Analysis, Laminar Flow, Boundary Layer Theory, Turbulent Flow, Forces On Immersed Bodies, Open Channel Flow, Compressible And Unsteady Flows, And Pumps And Turbines.
Download or read book Scaling written by G. I. Barenblatt and published by Cambridge University Press. This book was released on 2003-11-13 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Similarity and Modeling in Science and Engineering written by Josef Kuneš and published by Springer Science & Business Media. This book was released on 2012-04-07 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Theory and Applications of Heat Transfer in Humans 2 Volume Set written by Devashish Shrivastava and published by John Wiley & Sons. This book was released on 2018-07-02 with total page 897 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative guide to theory and applications of heat transfer in humans Theory and Applications of Heat Transfer in Humans 2V Set offers a reference to the field of heating and cooling of tissue, and associated damage. The author—a noted expert in the field—presents, in this book, the fundamental physics and physiology related to the field, along with some of the recent applications, all in one place, in such a way as to enable and enrich both beginner and advanced readers. The book provides a basic framework that can be used to obtain ‘decent’ estimates of tissue temperatures for various applications involving tissue heating and/or cooling, and also presents ways to further develop more complex methods, if needed, to obtain more accurate results. The book is arranged in three sections: The first section, named ‘Physics’, presents fundamental mathematical frameworks that can be used as is or combined together forming more complex tools to determine tissue temperatures; the second section, named ‘Physiology’, presents ideas and data that provide the basis for the physiological assumptions needed to develop successful mathematical tools; and finally, the third section, named ‘Applications’, presents examples of how the marriage of the first two sections are used to solve problems of today and tomorrow. This important text is the vital resource that: Offers a reference book in the field of heating and cooling of tissue, and associated damage. Provides a comprehensive theoretical and experimental basis with biomedical applications Shows how to develop and implement both, simple and complex mathematical models to predict tissue temperatures Includes simple examples and results so readers can use those results directly or adapt them for their applications Designed for students, engineers, and other professionals, a comprehensive text to the field of heating and cooling of tissue that includes proven theories with applications. The author reveals how to develop simple and complex mathematical models, to predict tissue heating and/or cooling, and associated damage.
