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Principles and Applications of Dimensional Analysis and Similarity

  • Textbook
  • © 2021


  • Brings to light the axioms and fundamental postulates of science, revitalising the conventions and clarifying the conceptual schemes that have allowed the evolution of scientific disciplines as they are currently practised
  • Targets researchers and graduate students in engineering and physical sciences, as well as researchers interested in a clarification of the methodology, of dimensional analysis and theory of similarity aims and purposes
  • Includes a chapter-end glossary listing the meaning of specific terms typical of dimensional

Part of the book series: Mathematical Engineering (MATHENGIN)

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About this book

The book provides a summary of the historical evolution of dimensional analysis, and frames the problem of dimensions, systems of units and similarity in a vision dominated by the conventions that formalise even the exact sciences.

The first four chapters address the definitions, with few dimensional analysis theorems and similarity criteria. There is also the analysis of self-similarity, both of first and second kind, with a couple of completely solved problems, framed within the group theory. From chapter 5 onward, the focus is on applications in some of the engineering sectors. The number of topics is necessarily limited, but, almost always, there are details, calculations and treatment of assumptions. The book contains descriptions of some of the experimental apparatuses currently used for the realisation of physical models, such as the wind tunnel, the shaking table, the centrifuge, and with the exclusion of many others, which can be found in specialist monographies. Measurementtechniques and instrumentation and statistical data processing is also available in other books.

Some more specific notions, required by the context, are reported in the appendix, where appears also the description of numerous dimensionless groups, all of engineering interest, but with the exclusion of many others related to physical processes of electrical nature or physics of particles. A glossary lists the meaning of some specific terms typical of dimensional analysis and used in the book.

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Table of contents (11 chapters)

  1. The Applications


“I really enjoyed this book. The writing is clear and eloquent, and it was fun to see a wide range of fundamental physical principles derived in a concise manner. The book is substantial with a wide scope, so should be valuable to many.” (D. J. W. Simpson, SIAM Review, Vol. 65 (3), 2023)

Authors and Affiliations

  • Department of Engineering and Architecture, University of Parma, Parma, Italy

    Sandro G. Longo

About the author

Sandro Longo is full professor of Hydraulics at the University of Parma, Italy, where he teaches Hydraulics and Environmental and Coastal Hydraulics and where he is also director of the Hydraulics Laboratory. His research interests include water wave generation and numerical modelling of sea waves, sediment transport, turbulence analysis, debris flows, soil quality management, non-Newtonian fluids in porous media and flows in poroelastic media, gravity currents, stratified flows. He is author or co-author of three books on Dimensional Analysis, Water Waves Mechanics, Measurements and Hydraulic Control Systems and of two textbooks on Exercises in Hydraulics and Fluid Mechanics. He serves in the editorial board of several international journals.

Bibliographic Information

  • Book Title: Principles and Applications of Dimensional Analysis and Similarity

  • Authors: Sandro G. Longo

  • Series Title: Mathematical Engineering

  • DOI:

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-79216-9Published: 05 February 2022

  • Softcover ISBN: 978-3-030-79219-0Published: 05 February 2023

  • eBook ISBN: 978-3-030-79217-6Published: 04 February 2022

  • Series ISSN: 2192-4732

  • Series E-ISSN: 2192-4740

  • Edition Number: 1

  • Number of Pages: XXXI, 428

  • Number of Illustrations: 13 b/w illustrations, 107 illustrations in colour

  • Topics: Analysis, Mechanical Engineering, Applications of Mathematics

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