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A First Course In Dimensional Analysis

Dimensional Analysis
Author: Juan G. Santiago
Publisher: MIT Press
ISBN: 0262537710
Size: 37.48 MB
Format: PDF, Kindle
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An introduction to dimensional analysis, a method of scientific analysis used to investigate and simplify complex physical phenomena, demonstrated through a series of engaging examples. This book offers an introduction to dimensional analysis, a powerful method of scientific analysis used to investigate and simplify complex physical phenomena. The method enables bold approximations and the generation of testable hypotheses. The book explains these analyses through a series of entertaining applications; students will learn to analyze, for example, the limits of world-record weight lifters, the distance an electric submarine can travel, how an upside-down pendulum is similar to a running velociraptor, and the number of Olympic rowers required to double boat speed. The book introduces the approach through easy-to-follow, step-by-step methods that show how to identify the essential variables describing a complex problem; explore the dimensions of the problem and recast it to reduce complexity; leverage physical insights and experimental observations to further reduce complexity; form testable scientific hypotheses; combine experiments and analysis to solve a problem; and collapse and present experimental measurements in a compact form. Each chapter ends with a summary and problems for students to solve. Taken together, the analyses and examples demonstrate the value of dimensional analysis and provide guidance on how to combine and enhance dimensional analysis with physical insights. The book can be used by undergraduate students in physics, engineering, chemistry, biology, sports science, and astronomy.
A First Course in Dimensional Analysis
Language: un
Pages: 184
Authors: Juan G. Santiago
Categories: Technology & Engineering
Type: BOOK - Published: 2019-10-22 - Publisher: MIT Press
An introduction to dimensional analysis, a method of scientific analysis used to investigate and simplify complex physical phenomena, demonstrated through a series of engaging examples. This book offers an introduction to dimensional analysis, a powerful method of scientific analysis used to investigate and simplify complex physical phenomena. The method enables bold approximations and the generation of testable hypotheses. The book explains these analyses through a series of entertaining applications; students will learn to analyze, for example, the limits of world-record weight lifters, the distance an electric submarine can travel, how an upside-down pendulum is similar to a running velociraptor, and the number of Olympic rowers required to double boat speed. The book introduces the approach through easy-to-follow, step-by-step methods that show how to identify the essential variables describing a complex problem; explore the dimensions of the problem and recast it to reduce complexity; leverage physical insights and experimental observations to further reduce complexity; form testable scientific hypotheses; combine experiments and analysis to solve a problem; and collapse and present experimental measurements in a compact form. Each chapter ends with a summary and problems for students to solve. Taken together, the analyses and examples demonstrate the value of dimensional analysis and
A Student's Guide to Dimensional Analysis
Language: un
Pages:
Authors: Don S. Lemons
Categories: Science
Type: BOOK - Published: 2017-03-16 - Publisher: Cambridge University Press
This introduction to dimensional analysis covers the methods, history and formalisation of the field, and provides physics and engineering applications. Covering topics from mechanics, hydro- and electrodynamics to thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis. Introducing basic physics and fluid engineering topics through the mathematical methods of dimensional analysis, this book is perfect for students in physics, engineering and mathematics. Explaining potentially unfamiliar concepts such as viscosity and diffusivity, the text includes worked examples and end-of-chapter problems with answers provided in an accompanying appendix, which help make it ideal for self-study. Long-standing methodological problems arising in popular presentations of dimensional analysis are also identified and solved, making the book a useful text for advanced students and professionals.
Dimensional Analysis
Language: en
Pages: 186
Authors: Qing-Ming Tan
Categories: Technology & Engineering
Type: BOOK - Published: 2011-06-06 - Publisher: Springer Science & Business Media
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.
Infinite Dimensional Analysis
Language: un
Pages: 704
Authors: Charalambos D. Aliprantis, Kim C. Border
Categories: Business & Economics
Type: BOOK - Published: 2007-05-02 - Publisher: Springer Science & Business Media
Aimed at students and researchers, this is the very first book to present functional analysis in a unified manner, along with applications to economics, social sciences, and engineering. It is a rigorous study of modern functional analysis.
Spectral methods in infinite-dimensional analysis. 1 (1995)
Language: en
Pages: 572
Authors: I︠U︡riĭ Makarovich Berezanskiĭ, I︠U︡riĭ Grigorʹevich Kondratʹev
Categories: Degree of freedom
Type: BOOK - Published: 1995 - Publisher: Springer Science & Business Media
Books about Spectral methods in infinite-dimensional analysis. 1 (1995)
Dimensional Analysis
Language: en
Pages: 160
Authors: Jonathan Worstell
Categories: Technology & Engineering
Type: BOOK - Published: 2014-03-05 - Publisher: Butterworth-Heinemann
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
Dimensional Analysis
Language: en
Pages: 135
Authors: G. I. Barenblatt
Categories: Dimensional analysis
Type: BOOK - Published: 1987 - Publisher: Gordon & Breach Science Publishers
Books about Dimensional Analysis
Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists
Language: un
Pages: 372
Authors: Bahman Zohuri
Categories: Technology & Engineering
Type: BOOK - Published: 2015-04-15 - Publisher: Springer
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
Language: un
Pages: 297
Authors: J.C. Gibbings
Categories: Mathematics
Type: BOOK - Published: 2014-09-26 - Publisher: Springer
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 for Engineers
Language: un
Pages: 134
Authors: Volker Simon, Bernhard Weigand, Hassan Gomaa
Categories: Technology & Engineering
Type: BOOK - Published: 2017-02-09 - Publisher: Springer
This monograph provides the fundamentals of dimensional analysis and illustrates the method by numerous examples for a wide spectrum of applications in engineering. The book covers thoroughly the fundamental definitions and the Buckingham theorem, as well as the choice of the system of basic units. The authors also include a presentation of model theory and similarity solutions. The target audience primarily comprises researchers and practitioners but the book may also be suitable as a textbook at university level.