Applied dimensional analysis and modeling

Abstract

This rather large book (of 815 pages) presents a very thorough treatment of dimensional analysis and modeling, covering a broad range of engineering fields. Professor Rozsa has written the first chapter on mathematical preliminaries, which contains a brief discussion of matrices, determinants, and systems of linear equations. Chapters 2–5 discuss the formats for physical relations, dimensional systems, and dimensions. Chapter 6 discusses dimensional homogeneity. The structure of physical relations is discussed at great length in Chap. 7. Chapter 8 shows the development of an efficient method for the construction of dimensionless parameters and introduces a few examples from fluid mechanics. Chapter 9 presents several theorems dealing with the transformations of dimensionless parameters. Chapter 10 discusses the number of dimensionless products of variables with illustrative problems. Chapter 11 presents a discussion on the relevancy of the variables, along with some techniques for identifying physically irrelevant variables. The effectiveness of graphical presentation is discussed in Chap. 12, and forms of the dimensionless relations are discussed in Chap. 13 as to whether the relation between the dimensionless parameters is monomial or non-monomial. If such a monomial relation exists, then some arguments are presented to find the exponents in such a relation. Chapter 14 gives some useful rules and guidelines for sequencing the physical variables in a dimensional set. Chapter 15 discusses problems where dimensions other than mass or force, length, and time occur. One interesting problem is the determination of the optimal location density and location patterns for retail shops. Chapter 16 introduces three ideas to reduce the number of dimensionless groups: (i) reducing the number of physical variables, (ii) increasing the number of dimensions, and (iii) fusing the dimensionless parameters. Chapter 17 looks at dimensional modeling, discussing geometric, kinematic, dynamic, and thermal similarities. This chapter also looks at modeling laws for a whole range of problems, including roasting time for a turkey and comfortable walking speeds for humans and dinosaurs. Chapter 18 presents 43 additional applications, dealing with problems such as axial tensions in a rotating ring, the maximum velocity of an electron in a vacuum tube, the buckling load of a hinged column, existence criteria for black holes, the lateral natural frequency of a cantilever, the diameter of a soap bubble, the velocity of collapse of a row of dominoes, and jamming a circular plug into a non-smooth circular hole. The list of references includes 148 items. There are 8 appendices dealing respectively with (i) recommended names and symbols for some physical quantities, (ii) some more important physical constants, (iii) some more important named dimensionless variables, (iv) notes attached to figures, (v) acronyms, (vi) solutions to problems, (vii) proofs of selected theorems and equations, and (viii) a blank modeling data table. There is also a subject index followed by a surname index. Appendix 3 includes dimensionless numbers such as Beaufort number, Nusselt number, Fourier number, Gratz number, Grashof number, Peclet number, Prandtl number, Rayleigh number, Reynolds number, Schmidt number, Stanton number, Cowling number, Euler number, Froude number, Hartman number, Knudsen number, Strouhal number, Weber number, Snellen number, Mach number, and Cauchy number. This is indeed a rigorous treatment of dimensional analysis, covering vast areas of engineering and physics. Reading the book, one is continuously touched by the contagious enthusiasm and intriguing insight of the author and is entertained by so many interesting anecdotes, quotations, and amusing problems. The treatment of the different topics is very thorough. This reviewer teaches and works in the areas of fluid mechanics and hydraulic engineering and uses dimensional analysis and hydraulic modeling in his work and enjoyed reading this book. Generally, undergraduate students in civil engineering, in their course in fluid mechanics, are introduced to dimensional analysis and then study the principles of hydraulic modeling. Most texts in fluid mechanics have a chapter dealing with these two topics and as such a book like this is perhaps not suitable for them. Even graduate students might find this book far too extensive. But researchers and engineers might find all kinds of interesting problems in this book and as such would benefit from studying this book. This book would be an excellent addition to engineering libraries and consulting offices.