Vectors, Tensors and the Basic Equations of Fluid Mechanics

by Rutherford Aris

Book Overview

This excellent text develops and utilizes mathematical concepts to illuminate physical theories. Directed primarily to engineers, physicists, and applied mathematicians at advanced undergraduate and graduate levels, it applies the mathematics of Cartesian and general tensors to physical field theories and demonstrates them chiefly in terms of the theory of fluid mechanics. Essentially an introductory text, intended for readers with some acquaintance...

• Format: Paperback
• Language: English
• ISBN: 0486661105
• ISBN13: 9780486661100
• Release Date: January 1990
• Publisher: Dover Publications
• Length: 320 Pages
• Weight: 0.77 lbs.
• Dimensions: 0.7" x 5.4" x 8.3"

Customer Reviews

a necessary book for working on fluid dynamics

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.

Very complete introduction to tensor analysis in 3 dimensions.

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.

Aris on fluid dynamics

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

Not for the weakhearted!

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:)

Too good!

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!