Enhanced descriptions from Syndetics:

How can the drag coefficient of a car be reduced? What factors govern the variation in the shape of the Earth's magnetosphere? What is the basis of weather prediction? These are examples of problems that can only be tackled with a sound knowledge of the principles and methods of fluid dynamics. This important discipline has applications which range from the study of the large-scale properties of the galaxies to the design of high precision engineering components. This book introduces the subject of fluid dynamics from the first principles. The first eleven chapters cover all the basic ideas of fluid mechanics, explaining carefully the modelling and mathematics needed. The last six chapters illustrate applications of this material to linearised sound and water waves, to high speed flow of air, to non-linear water waves on channels, and to aerofoil theory. Over 350 diagrams have been used to illustrate key points. Exercises are included to help develop and reinforce the reader's understanding of the material presented. References at the ends of each chapter serve not only to guide readers to more detailed texts, but also list where alternative descriptions of the salient points in the chapter may be found. This book is an undergraduate text for second or third year students of mathematics or mathematical physics, who are taking a first course in fluid dynamics.

Table of contents provided by Syndetics

• Preface (p. ix)
• Introduction (p. 1)
• 1 Fluid dynamics (p. 1)
• 2 Structure of the text (p. 3)
• 3 Method of working (p. 4)
• Reference (p. 5)
• I Mathematical preliminaries (p. 7)
• 1 Background knowledge (p. 7)
• 2 Polar coordinate systems (p. 10)
• 3 The vector derivative, [down triangle, open] (p. 13)
• 4 Cartesian tensor methods (p. 14)
• 5 Integration formulae (p. 17)
• 6 Formulae in polar coordinates (p. 19)
• Exercises (p. 22)
• References (p. 24)
• II Physical preliminaries (p. 25)
• 1 Background knowledge (p. 25)
• 2 Mathematical modelling (p. 25)
• 3 Properties of fluids (p. 27)
• 4 Dimensional reasoning (p. 29)
• Exercise (p. 30)
• III Observational preliminaries (p. 32)
• 1 The continuum model (p. 32)
• 2 Fluid velocity and particle paths (p. 34)
• 3 Definitions (p. 37)
• 4 Streamlines and streaklines (p. 39)
• Exercises (p. 42)
• References (p. 43)
• IV Mass conservation and stream functions (p. 45)
• 1 The continuity equation (p. 45)
• 2 The convective derivative (p. 46)
• 3 The stream function for two-dimensional flows (p. 48)
• 4 Some basic stream functions (p. 53)
• 5 Some flow models and the method of images (p. 58)
• 6 The (Stokes) stream function for axisymmetric flows (p. 62)
• 7 Models using the Stokes stream function (p. 64)
• Exercises (p. 68)
• References (p. 70)
• V Vorticity (p. 71)
• 1 Analysis of the motion near a point (p. 71)
• 2 Simple model flows (p. 77)
• 3 Models for vortices (p. 80)
• 4 Definitions and theorems for vorticity (p. 83)
• 5 Examples of vortex lines and motions (p. 89)
• Exercises (p. 92)
• References (p. 94)
• VI Hydrostatics (p. 95)
• 1 Body forces (p. 95)
• 2 The stress tensor (p. 96)
• 3 The form of the stress tensor (p. 99)
• 4 Hydrostatic pressure and forces (p. 102)
• Exercises (p. 108)
• References (p. 110)
• VII Thermodynamics (p. 111)
• 1 Basic ideas and equations of state (p. 111)
• 2 Energy and entropy (p. 115)
• 3 The perfect gas model (p. 118)
• 4 The atmosphere (p. 122)
• Exercises (p. 125)
• References (p. 126)
• VIII The equation of motion (p. 127)
• 1 The fundamental form (p. 127)
• 2 Stress and rate of strain (p. 128)
• 3 The Navier-Stokes equation (p. 131)
• 4 Discussion of the Navier-Stokes equation (p. 133)
• Exercises (p. 138)
• References (p. 139)
• IX Solutions of the Navier-Stokes equations (p. 140)
• 1 Flows with only one coordinate (p. 140)
• 2 Some flows with two variables (p. 148)
• 3 A boundary layer flow (p. 157)
• 4 Flow at high Reynolds number (p. 160)
• Exercises (p. 165)
• References (p. 168)
• X Inviscid flow (p. 169)
• 1 Euler's equation (p. 169)
• 2 The vorticity equation (p. 170)
• 3 Kelvin's theorem (p. 177)
• 4 Bernoulli's equation (p. 180)
• 5 Examples using Bernoulli's equation (p. 186)
• 6 A model for the force on a sphere in a stream (p. 197)
• Exercises (p. 201)
• References (p. 204)
• XI Potential theory (p. 205)
• 1 The velocity potential and Laplace's equation (p. 205)
• 2 General properties of Laplace's equation (p. 209)
• 3 Simple irrotational flows (p. 214)
• 4 Solutions by separation of variables (p. 216)
• 5 Separation of variables for an axisymmetric flow: Legendre polynomials (p. 221)
• 6 Two unsteady flows (p. 228)
• 7 Bernoulli's equation for unsteady irrotational flow (p. 232)
• 8 The force on an accelerating cylinder (p. 236)
• 9 D'Alembert's paradox (p. 240)
• Exercises (p. 243)
• References (p. 247)
• XII Sound waves in fluids (p. 248)
• 1 Background (p. 248)
• 2 The linear equations for sound in air (p. 249)
• 3 Plane sound waves (p. 253)
• 4 Plane waves in musical instruments (p. 261)
• 5 Plane waves interacting with boundaries (p. 264)
• 6 Energy and energy flow in sound waves (p. 272)
• 7 Sound waves in three dimensions (p. 278)
• Exercises (p. 285)
• References (p. 288)
• XIII Water waves (p. 289)
• 1 Background (p. 289)
• 2 The linear equations (p. 290)
• 3 Plane waves on deep water (p. 293)
• 4 Energy flow and group velocity (p. 297)
• 5 Waves at an interface (p. 300)
• 6 Waves on shallower water (p. 305)
• 7 Oscillations in a container (p. 310)
• 8 Bessel functions (p. 317)
• Exercises (p. 322)
• References (p. 324)
• XIV High speed flow of air (p. 325)
• 1 Subsonic and supersonic flows (p. 325)
• 2 The use of characteristics (p. 331)
• 3 The formation of discontinuities (p. 339)
• 4 Plane shock waves (p. 350)
• Exercises (p. 359)
• References (p. 362)
• XV Steady surface waves in channels (p. 363)
• 1 One-dimensional approximation (p. 363)
• 2 Hydraulic jumps or bores (p. 370)
• 3 Changes across a hydraulic jump (p. 377)
• 4 Solitary waves (p. 382)
• Exercises (p. 392)
• References (p. 395)
• XVI The complex potential (p. 396)
• 1 Simple complex potentials (p. 396)
• 2 More complicated potentials (p. 402)
• 3 Potentials for systems of vortices (p. 410)
• 4 Image theorems (p. 413)
• 5 Calculation of forces (p. 422)
• Exercises (p. 432)
• References (p. 434)
• XVII Conformal mappings and aerofoils (p. 435)
• 1 An example (p. 435)
• 2 Mappings in general (p. 439)
• 3 Particular mappings (p. 448)
• 4 A sequence of mappings (p. 459)
• 5 The Joukowski transformation of an ellipse (p. 462)
• 6 The cambered aerofoil (p. 468)
• 7 Further details on aerofoils (p. 476)
• Exercises (p. 479)
• References (p. 482)
• Hints for exercises (p. 483)
• Answers for exercises (p. 508)
• Books for reference (p. 519)
• Index (p. 521)