Table of Contents

Preface xi

About the Companion Website xii

1 Continuum Mechanics 1
2 Thermodynamics 14
3 Vector Calculus and Index Notation 26
4 Kinematics of Local Fluid Motion 50
5 Basic Laws 69
6 Newtonian Fluids and the Navier–Stokes Equations 105
7 Some Incompressible Flow Patterns 121
8 Dimensional Analysis 149
9 Elements of Compressible Flow 178
10 Incompressible Flow 191
11 Some Solutions of the Navier–Stokes Equations 212
12 Streamfunctions and the Velocity Potential 256
13 Vorticity Dynamics 278
14 Flows at Moderate Reynolds Numbers 314a
15 Asymptotic Analysis Methods 360
16 Characteristics of High-Reynolds-Number Flows 393
17 Kinematic Decomposition of Flow Fields 413
18 Ideal Flows in a Plane 422
19 Three-Dimensional Ideal Flows 483
20 Boundary Layers 512
21 Flow at Low Reynolds Numbers 584
22 Lubrication Approximation 626
23 Surface Tension Effects 645
24 Introduction to Microflows 681
25 Stability and Transition 711
26 Turbulent Flows 743
27 Gas Dynamics 796

Problems 842
References 843
Index 859

This textbook offers a detailed study of fluid dynamics. Equal emphasis is given to physical concepts, mathematical methods, and illustrative flow patterns. The book begins with a precise and careful formulation of physical concepts followed by derivations of the laws governing the motion of an arbitrary fluid, the Navier-Stokes equations. Throughout, there is an emphasis on scaling variables and dimensional analysis. Incompressible flow is presented as an asymptotic expansion of solutions to the Navier-Stokes equations with low Mach numbers and arbitrary Reynolds numbers. The different physical behaviors of flows with low, medium, and high Reynolds number are thoroughly investigated. Additionally, several special introductory chapters are provided on lubrication theory, flow stability, and turbulence.

In the Fifth Edition, a chapter on gas dynamics has been added. Gas dynamics is presented as Navier-Stokes solutions for high Reynolds Number at arbitrary Mach number with a perfect gas as the fluid. The existence of several excellent, and free, compressible flow calculators on the internet has been used in the presentation and the homework. With this chapter the textbook becomes a survey of the entire field of fluid dynamics.