Fluid Mechanics Second Edition - Apresentação

Fluid Mechanics

Second Edition

Joseph H. Spurk ? Nuri Aksel

Fluid Mechanics

Second Edition

123

Professor Dr. Joseph H. Spurk (em.) TU Darmstadt Institut f?r Technische Str?mungslehre Petersenstra?e 30 64287 Darmstadt Germany

Professor Dr. Nuri Aksel Universit?t Bayreuth Lehrstuhl f?r Technische Mechanik und Str?mungsmechanik Universit?tsstra?e 30 95447 Bayreuth Germany

ISBN 978-3-540-73536-6

e-ISBN 978-3-540-73537-3

DOI 10.1007/978-3-540-73537-3 Library of Congress Control Number: 2007939489 ? 2008, 1997 Springer-Verlag Berlin Heidelberg

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law.

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

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987654321



Preface to the First English Edition

This textbook is the translation of the fourth edition of Str?mungslehre, Einf?hrung in die Theorie der Str?mungen. The German edition has met with a favorable reception in German-speaking countries, showing that there was a demand for a book that emphazises the fundamentals. In the English literature there are books of the same nature, some excellent, and these have indeed influenced me to write this book. However, they cover different ground and are not aimed primarily at mechanical engineering students, which this book is. I have kept the original concept throughout all editions and there is little to say that has not been said in the preface to the first German edition. There is now a companion volume Solved Problems in Fluid Mechanics, which alleviates the drawback of the first German edition, namely the absence of problem exercises.

The book has been translated by Katherine Mayes during her stay in Darmstadt, and I had the opportunity to work with her daily. It is for this reason that I am solely responsible for this edition, too. My thanks also go to Prof. L. Crane from Trinity College in Dublin for his assistance with this book. Many people have helped, all of whom I cannot name, but I would like to express my sincere thanks to Ralf M?nzing, whose dependable and unselfish attitude has been a constant encouragement during this work.

Darmstadt, January 1997

J. H. Spurk

Preface to the Second English Edition

The first English edition was the translation of the fourth German edition. In the meantime the textbook has undergone several additions, mostly stimulated by consulting activities of the first author. Since the textbook continues to receive favourable reception in German speaking countries and has been translated in other languages as well, the publisher suggested a second English edition. The additions were translated for the most part by Prof. L. Crane from Trinity College in Dublin, who has accompanied this textbook from the very beginning. Since the retirement of the first author, Prof. N. Aksel from the University of Bayreuth, Germany, the second author, was actively engaged in the sixth and the seventh edition. The additions were written by the first author who accepts the responsibility for any mistakes or omissions in this book.

Contents

1 The Concept of the Continuum and Kinematics . . . . . . . . . . 1 1.1 Properties of Fluids, Continuum Hypothesis . . . . . . . . . . . . . . . 1 1.2 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Material and Spatial Descriptions . . . . . . . . . . . . . . . . . . 7 1.2.2 Pathlines, Streamlines, Streaklines . . . . . . . . . . . . . . . . . 10 1.2.3 Differentiation with Respect to Time . . . . . . . . . . . . . . . 14 1.2.4 State of Motion, Rate of Change of Line, Surface and Volume Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2.5 Rate of Change of Material Integrals . . . . . . . . . . . . . . . 29

2 Fundamental Laws of Continuum Mechanics . . . . . . . . . . . . . . 35 2.1 Conservation of Mass, Equation of Continuity . . . . . . . . . . . . . . 35 2.2 Balance of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.3 Balance of Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.4 Momentum and Angular Momentum in an Accelerating Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.5 Applications to Turbomachines . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.6 Balance of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 2.7 Balance of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2.8 Thermodynamic Equations of State . . . . . . . . . . . . . . . . . . . . . . . 71

3 Constitutive Relations for Fluids . . . . . . . . . . . . . . . . . . . . . . . . . 75

4 Equations of Motion for Particular Fluids . . . . . . . . . . . . . . . . 95 4.1 Newtonian Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.1.1 The Navier-Stokes Equations . . . . . . . . . . . . . . . . . . . . . . 95 4.1.2 Vorticity Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.1.3 Effect of Reynolds' Number . . . . . . . . . . . . . . . . . . . . . . . 100 4.2 Inviscid Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.2.1 Euler's Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.2.2 Bernoulli's Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.2.3 Vortex Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.2.4 Integration of the Energy Equation . . . . . . . . . . . . . . . . . 138 4.3 Initial and Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.4 Simplification of the Equations of Motion . . . . . . . . . . . . . . . . . . 145

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