Principles and Applications of Dimensional Analysis and Similarity

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.

Introduction.- Dimensional Analysis.- Handling dimensionless groups in Dimensional Analysis.- Symmetry and affine transformations.- The theory of similarity and applications to models.- Applications in Fluid Mechanics and Hydraulics.- Applications to Heat Transfer Problems.- Applications to problems of forces and deformations.- Applications in Geotechnics.- Applications in wind tunnels technology.- Physical models in River Hydraulics.- Physical models with sediment transport.

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.