Customer Reviews

Vectors, Tensors and the Basic Equations of Fluid Mechanics (Dover Books on Mathematics)

5 star:		(9)
4 star:		(3)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

The title and many of the Amazon reviews of this book are misleading in my opinion. This book should have been titled `The Mathematical Foundation of Fluid Mechanics'. This book describes, in gory detail, the fundamental mathematics of viscous fluid flow. The text is, obviously, heavy on vector and tensor calculus. The first few chapters review the basic theorems of vector and tensor calcular relevent to fluid dynamics. The basic equations of fluid dynamics are then derived, and the analysis is extended to viscous flow. Finally, Aris discusses coordinate transformation and tensor analysis (that is really more of a lead-in to GR than fluid dynamics, although it is interesting to see how this all ties together!). This is NOT a `complete' text in hydrodynamics. There is no discussion of turbulence, supersonic flow, instabilities, etc. This is a text on the mathematical (and geometrical) foundations of hydrodynamics. As such, I view this as an advanced text for a researcher who wants to understand hydrodynamics at it's most complete, fundamental mathematical level. If you are searching for any other type of hydrodynamics text, just move on. The reason that I only gave this book four stars was because I feel that hydrodynamics is a much richer discipline than what is contained within this book. Some of the most enthusiastic reviews greatly overstate the value of working through this book. You will learn quite a bit by going through this book, and it is a great text IF you want to study the foundations of hydrodynamics in great detail, but you will need (alot) more if you want to begin to appreciate fluid mechanics.

This would make a good introduction to tensors for physics students (e.g. for General Relativity), though the approach is a completely classical, using index notation; you won't find anything on manifolds or differential forms here. An interesting feature is an extensive chapter on local surface theory (e.g. Gaussian curvature, but only after introducing the full Riemann tensor), which is good for building intuition about curvature in higher dimensions. While the applications are all in n <= 3 dimensions, the mathematics is done in a way that easily generalizes to higher dimensions.

Well, I don't want to go into an endless list of superlatives which this book really deserves. I'd rather point out some of its features. It's terse, sometimes awfully so & therefore, this's not the best book to learn the "basics". Don't expect any elementary physics of fluid flow. I've only read the first half of the book and in those less-than-hundred pages, I've appreciated fluid mechanics much more than I've by any other means. However, I must say that the so-called "indices" notation for vectors and tensors can be extremely frustrating and even confusing. This notation is so extensively used in the book that it can become possibly the only reason to put the book down. The order of presentation is quite nice.

There are few problems to solve which mostly seem to fill in the details of presentation. The last chapter on mass transport is a disappointment, with nothing close to what one would expect in a book of this stature. It is however included only because "it would be unpardonable not to do so, for a book coming from Chemical Engineering dept".

The author says in his preface that the time has come to go beyond the notion that engineers don't need rigorous applied mathematics and he proves his point in every page of his book. It's a pleasure to read and work on, especially the second half of the book. With patience, paper and pencil (lots of them), one can gain a real mastery over the subject. A true graduate-level book!

This is one of those pithy classics that one needs to tread through very very carefully. The book is an uphill task, wherein rests its utility and fun. Fluid Mechanics in its simplified diluted version is served in many OTHER textbooks. This one serves it in its raw mathematical glory, and as the author says in the preface of the book, any serious engineer and fluid mechanician must realize that math must be befriended and mastered. The author makes very terse, and powerful introduction to the field. I would recommend a physicist to supplement it with a text by Faber, for Chemical Engineer to study it after the famous BSL (Transport Phenomenon), for a mathematician to pick it on any day, and for everyone in general to approach it with determination required to climb a rocky terrain. (Ah! I guess I would write an even better review if and when I finish reading it:)

this is really a nice book if you want to work on fluid mechanics. it provides you the equations of fluid mechanics in different coordinate system.

I got this book for my research. This book is amongst the more readable introductions to tensors in complicated coordinate systems. Also has a very good chapter on free surface problems that is very well written and easy to understand.

One of the smartest book in the field that made complicate stuff easy to understand

This book is simply magnificent. ANYONE interested in fluid dynamics should own it!

There is some very important information given in this book. However I still need to do much reading around tensor calculus as I feel that there were not enough worked examples using Christoffel notation.

This book comes from the author who is influenced by Clifford Truesdell(pioneer of Rational Continuum Mechanics & Thermodynamics). This book can be a good introductory material to begin study in rational mechanics. However, not so serious students may find it disappointing. One can surely learn some good tensor manipulation skills with application to fluid mechanics.