Dimensional Analysis

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.

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.

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.

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

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

Make dosage calculations easier to master with dimensional analysis. Dosage calculations can be intimidating, but they don’t need to be. Dimensional analysis is an easy, systematic approach that shows you how to master simple to complex calculations with consistency and accuracy and reduce medication errors to ensure that drugs are administered safely and documented correctly. Dimensional analysis, which can be used on virtually every dosage calculation problem, eliminates the need to use other methods or perform lengthy, multi-step calculations. It’s a method of problem-solving that organizes data in a manner that is easy to understand and apply.

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.

Derived from a course in fluid mechanics, this text for advanced undergraduates and graduate students employs symmetry arguments to illustrate the principles of dimensional analysis. 2006 edition.