Book Review of Eric Lauga’s Fluid Mechanics: A Very Short Introduction
Fluid Mechanics: A Very Short Introduction, by Eric Lauga (Oxford University Press, 2022). Very Short Introductions, vol. 708. Reviewed by Christopher Tong, October 2022.
The technical literature on fluid mechanics is vast, and blessed with many writers of varying styles. However, there is a notable gap in the literature for readers who would like some exposure to the field before they’ve mastered vector calculus. The classic little book by Ascher Shapiro, Shape and Flow (1961), and the little-known, album-sized volume by Hans Lugt, Vortex Flow in Nature and Technology (1983), both require only high school level algebra, and ably serve as nontechnical introductions to fluid flow. Unfortunately both are long out of print. Since the demise of those volumes, only the delightful tome by Philip Ball, Flow (2009), which doesn’t require any mathematics at all, has been available…until now.
A new entry in Oxford University Press’s venerable Very Short Introductions series has just appeared, Fluid Mechanics by Eric Lauga. In my view, this book may be read by anyone with a working knowledge of the first semester of introductory physics. The author freely uses reasoning based on Newton’s laws of motion, force balance, and mechanical energy conservation, for example. All calculations are at a high-school algebra level, and calculus is stated to be beyond the scope of the book.
Lauga’s book is limited by the format of the Very Short Introductions series: the 140-or-so pages are small, but illustrations are plentiful. The small size helps make the book friendly, of course. Though it is probably more mathematical than most VSIs, it is as readable as the best of them, in my opinion. Good writing is essential for a book of this type, and the author doesn’t disappoint.
The first chapter outlines the macroscopic, continuum approach taken in the book, and covers hydrostatics, surface tension, and wetting. The second chapter introduces the Eulerian velocity field, flow kinematics, forces of a fluid parcel, and viscosity. Chapter 3 is on “Pipes”, which covers Poiseuille flow, the transition to turbulence, blood flow, and industrial applications. Chapter 4 is a primer on dimensional analysis, taking the reader on a tour of key flows characterized by nondimensional numbers such as the Reynolds, Froude, and Rossby numbers. Chapter 5 is on boundary layers and separation, with the obligatory discussion of D’Alembert’s paradox. Chapter 6 introduces vortex dynamics, including Helmholtz’s vortex laws, aerodynamic lift, and the Magnus effect. Chapter 7 provides a tour of hydrodynamic instabilities, including the Rayleigh-Taylor, Rayleigh-Plateau, Taylor-Couette, Saffman-Taylor, and Kelvin-Helmholtz instabilities. The final chapter mentions a number of fields of contemporary research in hydrodynamics. Overall the author has made a reasonable choice of topics to cover; specialist readers such as myself will disagree on which omissions are the most egregious, as we inevitably would for any book of this length.
The author is an applied mathematician, and at the time of publication, co-lead editor of Physical Review Fluids, a major journal in the field, and a faculty member at Cambridge University’s famous “DAMTP” (Dept. of Applied Mathematics and Theoretical Physics). This book fits neatly between the completely nontechnical one by Ball (2009) and the more mathematical sampler dish by Worster (2009), which requires vector calculus and differential equations, and while not a textbook, shows you some serious fluid dynamical calculations and problem solving. Indeed, Lauga cites both of these earlier works in his brief but well-curated “Further reading” list.
References
Philip Ball, 2009: Flow. Part 2 of Nature’s Patterns: A Tapestry in Three Parts. Oxford University Press.
Hans J. Lugt, 1983: Vortex Flow in Nature and Technology. Wiley-Interscience. (Reprinted by Krieger, 1995.)
Ascher H. Shapiro, 1961: Shape and Flow: The Fluid Dynamics of Drag. Science Study Series, S21. Doubleday Anchor.
Grae Worster, 2009: Understanding Fluid Flow. AIMS Library Series. Cambridge University Press.
Disclaimers
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(c) 2022 by Christopher Tong