Dimensional Analysis

The great principle of similitude

By (author) Jeffrey H Williams

Publication date:

14 December 2021

Length of book:

244 pages

Publisher

Institute Of Physics Publishing

Dimensions:

254x178mm
7x10"

ISBN-13: 9780750336536

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.

Preface Dr Jeffrey Huw Williams (1956-2021) – an appreciation Author Biography Introduction: The language that is science 1 The origin of units 2 A brief history of dimensional analysis: A holistic approach to physics 3 Introduction to dimensions 4 Why, and how we play with variables 5 The Buckingham Π-theorem and its application 6 Scaling and similitude 7 Rules of thumb, intuitive planning, and physical insight 8 Continuum forces 9 Why is the sky blue? 10 The equilibrium between matter and energy 11 Dimensions involving molecules and fields 12 The dynamics of atoms and molecules 13 Modelling phenomena 14 The Great Principle of Similitude in Biology and Sport 15 A miscellany of analyses by dimension

Jeffrey Williams explains how dimensional methods can be used to investigate new phenomena and obtain trends and approximate results quickly and easily. The heart of the method is Buckingham’s theorem, and this is clearly explained and illustrated, and the basic ideas of scaling and similitude and the importance of planning and physical insight are discussed, including the possibility of overcomplicating problems. The bulk of the book is taken up with examples from fluid mechanics, light scattering and radiation, atoms, molecules and fields. There are interesting illustrations of the issues which arise from applying the results of scale models (of submarines, for example) to real-life scale, as well as treatments of topics as diverse as sport, cookery, the Aeolian harp and Drake’s equation. This is a well-written book, with some interesting insights from an author who was obviously an enthusiast for the subject.

A.H. Harker, Contemporary Physics, 17 Oct 2022.