Why This Textbook Still Shows Up in Every Fluids Course
I ran into a grad student last week who had somehow been assigned Fay's book for a computational fluid dynamics class, which is an odd pairing since Fay writes from a very traditional physical perspective. It happens more often than you'd think. Professors assign it because it's cheap, it's clear, and it doesn't waste time on frivolous derivations. It also means the student ends up confused about why their professor keeps saying "just trust the chapter on dimensional analysis" when they're trying to set up ANSYS. The book itself, formally titled Introduction to Fluid Mechanics by James A. Fay, covers roughly the same ground as Munson, Young, and Okiishi or White, but with a different pacing. Fay spends more time on the physical intuition behind equations before deriving them. That approach works well if you're seeing these concepts for the first time. It works less well if you already have some background and want to get to turbulence modeling.
Getting Started With Introduction To Fluid Mechanics By James A Fay
Start with chapters 1 through 3. Those cover dimensions, fluid properties, and pressure distribution. The pressure chapter is where most people hit their first wall. Fay derives the hydrostatic equation efficiently but doesn't spend enough time on piezometer and manometer configurations that show up in practically every exam problem. I remember grading a set of reports where students consistently failed because they couldn't handle an inclined manometer with two different fluids. The math is straightforward once you draw the right control surface, but the textbook example stays at a 45-degree complexity level while the homework problems jump to 90 degrees. The workaround I tell people to use is simple: close the book and just draw every manometer problem from scratch. Label each interface, assign a pressure variable, and walk from one open end to the other. It takes longer initially but cuts out the guessing phase that eats into exam time. One student of mine was consistently getting manometer problems wrong until she started numbering each fluid interface. She stopped missing them entirely after two weeks.
Where The Book Is Actually Useful
Chapters on conservation laws — mass, momentum, and energy — are where Fay earns his keep. The control volume approach is laid out cleanly. The Bernoulli equation derivation doesn't hide assumptions behind vague language, which is rare in introductory texts. Most books state the inviscid, incompressible, steady-flow requirements without emphasizing how easily students violate them in problem setups. Fay makes you uncomfortable about that. The boundary layer chapter is solid. Not exhaustive, but solid. If you need a deeper treatment,go to Schlichting or White. For a first pass that won't make you want to throw the book across the room, Fay works. The integral method for boundary layer analysis gets about eight pages, which is enough to understand the concept but not enough to feel confident solving a non-zero pressure gradient problem on your own. I usually supplement that section with lecture notes from MIT OpenCourseWare, specifically the 2.25 course materials from the early 2000s. They're free and they fill the gap. Dimensional analysis and similitude come later in the book. This is where the text gets genuinely good. The Buckingham Pi theorem is explained without the hand-waving that plagues most textbooks. The worked examples use real fluid mechanics problems, not contrived toy cases. I've seen students struggle with this topic for months using other books. Fay's treatment usually clears it up in a week.
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What The Book Doesn't Cover Well
Turbulence. There isn't much of it. If your course goes beyond Reynolds-averaged equations and you need something on turbulence modeling, this book will disappoint you. It touches on the concept but doesn't give you the tools to work with it computationally. You'll need to supplement with Wilcox's "Turbulence Modeling for CFD" or at minimum go through the relevant sections of Pope's "Turbulent Flows" if you're doing serious work. Computational methods are essentially absent. Fay wrote this book for a pre-CFD era audience, even though later editions tried to acknowledge numerical methods. If you're in a program that expects you to code a finite difference solver for the Navier-Stokes equations, this textbook won't prepare you. Pair it with Tannehill, Anderson, and Pletcher, or just learn the numerics from your lecture notes and move on. The problem sets at the end of each chapter are fine but not challenging. They test procedure more than insight. I found myself giving students additional problems from Holman's "Fluid Mechanics for Engineers" when I wanted them to really struggle with a concept. The Holman problems force you to combine ideas from different chapters, which is closer to what actually happens in practice.
Practical Tips For Using This Book
Don't read it cover to cover. Work through a chapter, do the problems, and move on. The book is structured so that each chapter builds on the previous one, but the later chapters on compressible flow and open channel flow can be approached somewhat independently if your course lets you skip around. Keep a separate notebook for derivations. Fay's derivations are concise, sometimes too concise. When he skips a step in the momentum equation for a control volume, it's easy to nod along and then realize three pages later that you don't actually know how he got there. Writing out the missing steps yourself takes about ten minutes per derivation but prevents a cascade of confusion later. The appendix with property tables is adequate. I've used it for quick lookups throughout my career. If you need high-precision viscosity data for water at unusual temperatures, go to the NIST database instead. The book's tables are rounded and will introduce small errors in sensitive calculations.
Where To Find It
The book is widely available through major retailers and academic suppliers. Older editions circulate freely on campus bulletin boards and in secondhand bookshops. Edition differences are minor — the core content hasn't changed substantially between the 2000s reprints and later versions. If you're on a budget, an older edition will serve you just as well as the latest print run. The problem numbers may differ slightly, but the concepts are identical. I've recommended this text to undergraduates for over a decade. It's not the most comprehensive fluid mechanics book out there, and it's certainly not the most rigorous. But it's accessible, it doesn't talk down to you, and it respects your time. That combination is harder to find than people think.
