Dimensional Analysis
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 analys
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J.C. Gibbings
Dimensional Analysis
123
Emeritus Reader J.C. Gibbings University of Liverpool Department of Engineering Brownlow Hill Liverpool L69 3GH UK
ISBN 978-1-84996-316-9 e-ISBN 978-1-84996-317-6 DOI 10.1007/978-1-84996-317-6 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library © Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher and the authors make no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: eStudioCalamar, Girona/Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
. . . – a University, taken in its bare idea – has this object –. It educates the intellect to reason well in all matters, to reach out towards truth and to grasp it. Cardinal J.H. Newman
Dimensional analysis combines great utility with a demanding intellectual rigour; this is its delight. Together with the idea of similitude, it has a long and honourable history. It was developed by the greatest of scientists and mathematicians; such included Newton, Fourier, D’Arcy Thompson, Vaschy, Rayleigh, Buckingham, Riabouchinsky, Einstein, Bridgman and Sedov. It is remarkable for its universality of application, increasingly so in recent times. This book is for engineers and scientists as a student’s learning volume, as a lecturer’s text, as a graduate’s reference handbook and, as it contains much that is new from the author’s work, as a research publication. In serving students it is designed to give instruction both to undergraduates and, in its more advanced applications, it could form the basis of postgraduate courses. A selection of the very elementary elements would be suitable for school pupils of science. Since the definitive Franklin Institute conference of 1971, there have been significant developments in setting out the totality and ordering of the fundamental logic, in a resolution of outstanding problems basic to the analysis and in deriving a general and rigorous statement of the theorem upon which the analysis rests, as well as further contri
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