7R44. Hydrodynamics: Examples and Problems: A Textbook. - YA Buyevich (Deceased), DV Alexandrov (Dept of Math Phys, Ural State Univ, Lenin Ave 51, Ekaterinburg, 620083, Russia), SV Zakharov (Inst of Math and Mech, Russian Acad of Sci, Ural Branch, S Kovalevskaja St 16, Ekaterinburg, 620219 GSP-384, Russia). Begell House, New York. 2001. 331 pp. ISBN 1-56700-159-9. $67.50.

Reviewed by R Verzicco (Dept di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Via Re David 200, Bari, 70125, Italy).

This textbook addresses several basic fluid mechanics topics with a particular emphasis on mathematical aspects. The book is organized into five chapters plus six appendices and a big selection of answers to problems proposed at the end of each chapter.

Chapter 1 reviews the tensor analysis discussing covariant and contravariant vector components, derivatives, and transformations. The differencing operators are then presented in their most general form with the aim of providing the reader with the tools for the derivation of the fluid mechanics equations in every coordinate system.

Chapter 2 explains, very briefly, the foundation of dimensional analysis and, as an example, applies it to the motion of the pendulum. In the successive chapter, a short description of self-similar solutions is given, starting from the combination of independent variable to reduce a partial differential equation to an ordinary differential equation. Two sections with linear and nonlinear processes discuss simple examples.

Chapter 4 is mainly concerned with flows with negligible viscous effects: a half-page introduction to hydrostatics is given with the discussion of two examples. A simple derivation of the Bernoulli equation is then presented with the solution of two additional model problems. The rest of the chapter is devoted to the discussion of potential flows treated either with standard methods and by separation of variables.

The fifth and last chapter involves viscous flows, starting from exact solutions of the Navier-Stokes equations and Stokes flows (solved by various methods) up to boundary layers and laminar flows. The book closes with a long part (about half of the book) containing problem answers and six short appendices dealing with equations on particular coordinate systems, solutions of specific differential equations, and some tabulated functions.

A very limited list of references and a subject index are given. Each chapter contains several proposed problems which help the reader in applying the explained concepts. The figure quality is sufficient; only sketches and graphs are shown. Perhaps some experimental pictures or numerical simulation plots would have helped the explanation of some concepts.

This book introduces with a particular perspective some classical topics of fluid mechanics; this reviewer has found the presentation strongly biased toward mathematical aspects while physical interpretation is sometimes lacking. Some arguments, like dimensional analysis or hydrostatics, have been described too shortly while others, like ideal and viscous exact solutions, occupy almost all of the book. Classical topics like fluid dynamics forces and turbulence are completely disregarded.

The text could be used as a reference book by the experienced researchers or graduate students involved in fluid mechanics. In contrast, this reviewer would not advise the use of this book as a text for undergraduates owing to the inhomogeneous treatment of the arguments, the mathematical skew of the presentation, and the absence of important topics. The purchase of the book is advised for libraries.