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|Additional Physical Format:||Print version:
Lectures on fluid mechanics.
Mineola, N.Y. : Dover Publications, 2012
|Material Type:||Document, Internet resource|
|Document Type:||Internet Resource, Computer File|
|All Authors / Contributors:||
|Notes:||Originally published: New York : Gordon and Breach, 1973.|
|Description:||1 online resource (xiii, 222 pages) : illustrations.|
|Contents:||Cover Page; Title Page; Copyright Page; Dedication; Preface; Contents; PART I SETTING THE SCENE; Introduction; CHAPTER 1 The equations of motion; 1 Notation; 2 The transport theorem; 3 Conservation of probability; Exercises; 4 The conservation equations. Definition of a fluid; Exercises; 5 The Stokes hypothesis; Exercise; 6 Boundary conditions. A theorem of Grad; Exercise; 7 Fluid mechanical derivation of the conservation equations; CHAPTER 2 Potential flow; 1 Ideal fluids; 2 The good fairy strikes!; 3 Lagrange's theorem; Exercises; 4 Some examples of potential flow; Exercise. CHAPTER 3 Some properties of potential flows1 Introduction; 2 Gauss's theorem; Exercise; 3 The maximum principle; 4 The minimum principle for the pressure; 5 A variational principle for potential flows; 6 Uniqueness of potential flows; Exercises; 7 Uniqueness of ideal fluid flows; Exercise; CHAPTER 4 Potential flows in two dimensions; 1 Introduction; 2 Examples of two-dimensional potential flows; 3 Existence of potential flows; Exercises; 4 Examples of two-dimensional potential flows (continued); Exercises; CHAPTER 5 d'Alembert's paradox and early attempts at its resolution; 1 Introduction. 2 The d'Alembert paradox3 Cavity flows; Exercises; 4 Discussion of the result; 5 Water waves; CHAPTER 6 Flows with circulation; 1 The stream function; 2 Circulation; 3 Circulatory flow past an airfoil; 4 Lift. Blasius' theorem; 5 Joukowski's hypothesis. Goodbye to all that; Exercise; CHAPTER 7 Viscous fluids; 1 The Stokes hypothesis again; Exercise; 2 The equations of motion; 3 The stream function; 4 The energy equation; 5 The existence question; CHAPTER 8 Examples of viscous fluid flow; 1 Introduction; 2 Steady flow between parallel planes; 3 Steady flow in a pipe. 4 Steady flow past a moving plane5 Unsteady flow past a moving plane; 6 Viscous flow due to a source; Exercises; CHAPTER 9 Various approximations; 1 Introduction; 2 Stokes flow; Exercise; 3 Oseen flow; 4 Boundary layer flow; Part II A TASTE OF THE MODERN THEORY; Introduction; CHAPTER 10 Preliminaries; 1 To start; 2 Spaces of functions; Exercises; 3 Functions of time; Table of Spaces Defined; CHAPTER 11 The weak solution; 1 Definition of the weak solution; Exercise; 2 The Lax-Milgram lemma; 3 The quantized Navier-Stokes equations; 4 The Navier-Stokes equations in a bounded domain; Exercises. 5 Some properties of weak solutionsExercises; CHAPTER 12 Uniqueness of weak solutions; 1 Introduction; 2 Uniqueness of classical solutions; 3 Uniqueness of weak solutions; Exercises; CHAPTER 13 Strong solutions; 1 Introduction; 2 Some preliminaries; 3 Uniqueness of strong solutions; 4 Some a priori inequalities; 5 Existence of strong solutions; Exercise; 6 Smoothness and uniqueness of weak solutions; CHAPTER 14 A reproductive property of the Navier-Stokes equations; 1 Preliminary remarks; 2 The reproductive property; Exercise; 3 Periodic solutions and stability; Index; Back Cover.|
|Series Title:||Dover books on physics.|