# Theory on test with world in miniature

November 27, 2008

Dimensional Analysis and Intelligent Experimentation

Author: Andrew C. Palmer

Edition: First

Publisher: World Scientific

Price: £25.00 and £17.00

Pages: 164

ISBN 97898108182 and 8199

This is a brief guide to deriving scientific relationships through practical experiments and, of course, dimensional analysis. Crudely put, dimensional analysis is a method of relating some of the variables in a system in terms of others so that their units cancel each other out and a dimensionless group is formed; for example, Froude number or Reynolds number.

The book begins by explaining the concept of units before demonstrating how to form dimensionless groups. The first chapters are a relaxed introduction to the concept. This led me to believe that the rest of the book would be the same, which was not the case.

Once the familiar science was out the way, the pace rapidly quickened. The principle of dimensional analysis is outlined briefly, after which the focus immediately shifts to examples where dimensional analysis has been used to solve problems. Many of these examples were obscure, and the author's use of dimensional analysis to help with his research interest of underwater piping is used too often. From here onwards, the same principle of creating dimensionless groups is used to solve more complicated problems. The simplicity of the early chapters is left behind and complex mathematics requires the reader to have a good knowledge of principles such as differential equations, matrices and systems analysis to keep up.

Towards the end of the book, intelligent experimentation describes the important aspects required to help to design useful tests. Because dimensional analysis takes advantage of dimensionless groups, and hence size is not an issue, it can be used to calculate the real-world effects using miniature models. This is explored using historical scenarios. In these examples, intelligent experimentation and dimensional analysis are used to solve problems in structural analysis, aerodynamics, hydraulics and geotechnics.

Between the theory and examples are problems for the reader to solve, most of which are potential real-world representations. Solutions are given, with each question's major difficulties explained. There are enough problems to keep even the most interested reader busy for a long time.

Overall, the book describes the ideas and processes of dimensional analysis in a concise way, from first principles through to complex equation derivation. It is most suitable for students or academics undertaking research projects that require new scientific relationships. It would also be an excellent core text on courses relating to dimensional analysis because of the number of practice problems. But without assistance from lectures, the content can be difficult to follow.

Who is it for? Research students or academics.

Presentation: Clear layout with appropriate diagrams and equations.

Would you recommend it? Only to those with a keen interest in the subject or who need it for research.

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