Fluid Mechanics

by Kundu, Pijush K.

• ISBN13: 9780124287709
• ISBN10: 0124287700
• Edition: 1st
• Format: Hardcover
• Copyright: 1990-09-01
• Publisher: Academic Pr

Summary

Written in a clear and simple style, this textbook on fluid mechanics gives equal emphasis to both geophysical and engineering fluid mechanics. For physicists, it contains chapters on geophysical fluid mechanics and gravity waves; for engineers, it has chapters on aerodynamics and compressible flow. Of common interest are chapters on governing equations, laminar flows, boundary layers, instability, and turbulence. This book also presents topics of recent interest, such as deterministic chaos, and double-diffusive instability. n Gives equal treatment to topics in both engineering and geophysical fluid dynamics n Suitable as an intermediate or graduate course textbook for students in their senior year or above n Treats topics of recent interest such as deterministic chaos, double diffusive instability and soliton n Extensively illustrated n Contains fully worked examples in each chapter as well as end-of-chapter problems n An instructor's manual is available

Table of Contents

Preface	xvii
Author's Notes	xxi
Introduction
Fluid Mechanics	1	(1)
Units of Measurement	2	(1)
Solids, Liquids, and Gases	3	(1)
Continuum Hypothesis	4	(1)
Transport Phenomena	5	(3)
Surface Tension	8	(1)
Fluid Statics	9	(3)
Classical Thermodynamics	12	(4)
Perfect Gas	16	(2)
Static Equilibrium of a Compressible Medium	18	(6)
Exercises	22	(1)
Literature Cited	23	(1)
Supplemental Reading	23	(1)
Cartesian Tensors
Scalars and Vectors	24	(1)
Rotation of Axes: Formal Definition of a Vector	25	(3)
Multiplication of Matrices	28	(1)
Second Order Tensor	29	(2)
Contraction and Miltiplication	31	(1)
Force on a Surface	32	(3)
Kronecker Delta and Alternating Tensor	35	(1)
Dot Product	36	(1)
Cross Product	36	(1)
Operator ∇: Gradient, Divergence, and Curl	37	(2)
Symmetric and Antisymmetric Tensors	39	(1)
Eigenvalues and Eigenvectors of a Symmetric Tensor	40	(2)
Gauss's Theorem	42	(1)
Stokes's Theorem	43	(1)
Comma Notation	44	(1)
Boldface versus Indicial Notation	45	(2)
Exercises	45	(1)
Literature Cited	46	(1)
Supplemental Reading	46	(1)
Kinematics
Introduction	47	(1)
Lagrangian and Eulerian Specifications	48	(1)
Material Derivative	49	(2)
Streamline, Path Line, and Streak Line	51	(2)
Reference Frame and Streamline Pattern	53	(1)
Linear Strain Rate	54	(1)
Shear Strain Rate	55	(1)
Vorticity and Circulation	56	(2)
Relative Motion near a Point: Principal Axes	58	(3)
Kinematic Considerations of Parallel Shear Flows	61	(1)
Kinematic Considerations of Vortex Flows	62	(4)
One-, Two-, and Three-Dimensional Flows	66	(1)
The Stream Function	66	(3)
Polar Coordinates	69	(5)
Exercises	70	(3)
Supplemental Reading	73	(1)
Conservation Laws
Introduction	74	(1)
Time Derivatives of Volume Integrals	75	(2)
Conservation of Mass	77	(2)
Origin of Forces in Fluid	79	(2)
Stress at a Point	81	(2)
Conservation of Momentum	83	(1)
Momentum Principle for a Mixed Volume	84	(3)
Angular Momentum Principle for a Fixed Volume	87	(2)
Constitutive Equation for Newtonian Fluid	89	(4)
Navier-Stokes Equation	93	(1)
Rotating Frame	94	(5)
Mechanical Energy Equation	99	(4)
First Law of Thermodynamics: Thermal Energy Equation	103	(2)
Second Law of Thermodynamics: Entropy Production	105	(1)
Bernoulli Equation	106	(3)
Applications of Bernoulli's Equation	109	(3)
Boussinesq Approximation	112	(7)
Exercises	116	(1)
Literature Cited	117	(1)
Supplemental Reading	118	(1)
Vorticity Dynamics
Introduction	119	(1)
Vortex Lines and Vortex Tubes	120	(1)
Role of Viscosity in Rotational and Irrotational Vortices	121	(3)
Kelvin's Circulation Theorem	124	(5)
Vorticity Equation in a Nonrotating Frame	129	(1)
Vorticity Equation in a Rotating Frame	130	(5)
Interaction of Vortices	135	(3)
Vortex Sheet	138	(3)
Exercises	139	(1)
Literature Cited	140	(1)
Supplemental Reading	140	(1)
Irrotational Flow
Relevance of Irrotational Flow Theory	141	(2)
Velocity Potential: Laplace Equation	143	(2)
Application of Complex Variables	145	(2)
Flow at a Wall Angle	147	(2)
Sources and Sinks	149	(1)
Irrotational Vortex	149	(1)
Doublet	150	(2)
Flow past a Half Body	152	(1)
Flow past a Circular Cylinder without Circulation	153	(3)
Flow past a Circular Cylinder with Circulation	156	(3)
Forces on a Two-Dimensional Body	159	(3)
Source near a Wall: Method of Images	162	(1)
Conformal Mapping	163	(2)
Flow around an Elliptic Cylinder with Circulation	165	(1)
Uniqueness of Irrotational Flows	166	(2)
Numerical Solution of Plane Irrotational Flow	168	(5)
Axisymmetric Irrotational Flow	173	(2)
Stream Function and Velocity Potential for Axisymmetric Flow	175	(1)
Simple Examples of Axisymmetric Flows	176	(2)
Flow around a Streamlined Body of Revolution	178	(1)
Flow around an Arbitrary Body of Revolution	179	(1)
Concluding Remarks	180	(4)
Exercises	181	(2)
Literature Cited	183	(1)
Supplemental Reading	183	(1)
Gravity Waves
Introduction	184	(1)
The Wave Equation	185	(2)
Wave Parameters	187	(3)
Surface Gravity Waves	190	(4)
Some Features of Surface Gravity Waves	194	(6)
Approximations for Deep and Shallow Water	200	(5)
Influence of Surface Tension	205	(3)
Standing Waves	208	(1)
Group Velocity and Energy Flux	209	(3)
Group Velocity and Wave Dispersion	212	(4)
Nonlinear Steepening in a Nondispersive Medium	216	(2)
Hydraulic Jump	218	(3)
Finite Amplitude Waves of Unchanging Form in a Dispersive Medium	221	(2)
Stokes's Drift	223	(3)
Waves at a Density Interface between Infintely Deep Fluids	226	(3)
Waves in a Finite Layer Overlying an Infinitely Deep Fluid	229	(3)
Shallow Layer Overlying an Infinitely Deep Fluid	232	(2)
Equations of Motion for a Continuously Stratified Fluid	234	(2)
Internal Waves in a Continuously Stratified Fluid	236	(4)
Dispersion of Internal Waves in a Stratified Fluid	240	(2)
Energy Considerations of Internal Waves in a Stratified Fluid	242	(6)
Exercises	246	(1)
Literature Cited	247	(1)
Dynamic Similarity
Introduction	248	(1)
Nondimensional Parameters Determined from Differential Equations	249	(3)
Dimensional Matrix	252	(1)
Buckingham's Pi Theorem	253	(2)
Nondimensional Parameters and Dynamic Similarity	255	(2)
Comments on Model Testing	257	(2)
Significance of Common Nondimensional Parameters	259	(4)
Exercises	262	(1)
Laminar Flow
Introduction	263	(2)
Analogy between Heat and Vorticity Diffusion	265	(1)
Pressure Change Due to Dynamic Effects	265	(1)
Steady Flow between Parallel Plates	266	(4)
Steady Flow in a Pipe	270	(1)
Steady Flow between Concentric Cylinders	271	(3)
Impulsively Started Plate: Similarity Solutions	274	(6)
Diffusion of a Vortex Sheet	280	(2)
Decay of a Line Vortex	282	(2)
Flow Due to an Oscillating Plate	284	(3)
High and Low Reynolds Number Flows	287	(2)
Creeping Flow around a Sphere	289	(3)
Nonuniformity of Stokes's Solution and Oseen's Improvement	292	(4)
Final Remarks	296	(3)
Exercises	296	(2)
Literature Cited	298	(1)
Supplemental Reading	298	(1)
Boundary Layers and Related Topics
Introduction	299	(1)
Boundary Layer Approximation	300	(5)
Different Measures of Boundary Layer Thickness	305	(2)
Boundary Layer on a Flat Plate: Blasius Solution	307	(8)
Karman Momentum Integral	315	(2)
Effects of Pressure Gradient	317	(1)
Separation	318	(3)
Description of Flow past a Circular Cylinder	321	(6)
Description of Flow past a Sphere	327	(1)
Dynamics of Sports Balls	327	(6)
Two-Dimensional Jets	333	(3)
Perturbation Techniques	336	(4)
An Example of a Regular Perturbation Problem	340	(2)
An Example of a Singular Perturbation Problem	342	(8)
Exercises	347	(1)
Literature Cited	348	(1)
Supplemental Reading	348	(2)
Instability
Introduction	350	(1)
Method of Normal Modes	351	(1)
Thermal Instability: The Benard Problem	352	(11)
Double-Diffusive Instability	363	(5)
Centrifugal Instability: Taylor Problem	368	(5)
Kelvin-Helmholtz Instability	373	(8)
Instability of Continuously Stratified Parallel Flows	381	(6)
Squire's Theorem and Orr-Sommerfeld Equation	387	(4)
Inviscid Stability of Parallel Flows	391	(4)
Some Results of Parallel Viscous Flows	395	(6)
Experimental Verification of Boundary Layer Instability	401	(1)
Comments on Nonlinear Effects	402	(1)
Transition	403	(2)
Deterministic Chaos	405	(11)
Exercises	413	(2)
Literature Cited	415	(1)
Turbulence
Introduction	416	(2)
Historical Notes	418	(2)
Averages	420	(3)
Correlations and Spectra	423	(3)
Averaged Equations of Motion	426	(7)
Kinetic Energy Budget of Mean Flow	433	(2)
Kinetic Energy Budget of Turbulent Flow	435	(3)
Turbulence Production and Cascade	438	(3)
Spectrum of Turbulence in Inertial Subrange	441	(2)
Wall-Free Shear Flow	443	(5)
Wall-Bounded Shear Flow	448	(7)
Eddy Viscosity and Mixing Length	455	(3)
Coherent Structures in a Wall Layer	458	(2)
Turbulence in a Stratified Medium	460	(6)
Taylor's Theory of Turbulent Dispersion	466	(8)
Exercises	471	(2)
Literature Cited	473	(1)
Geophysical Fluid Dynamics
Introduction	474	(2)
Vertical Variation of Density in Atmosphere and Ocean	476	(2)
Equations of Motion	478	(3)
Approximate Equations for a Thin Layer on a Rotating Sphere	481	(3)
Geostrophic Flow	484	(5)
Ekman Layer at a Free Surface	489	(3)
Ekman Layer on a Rigid Surface	492	(4)
Shallow Water Equations	496	(2)
Normal Modes in a Continuously Stratified Layer	498	(6)
High and Low Frequency Regimes in Shallow Water Equations	504	(2)
Gravity Waves with Rotation	506	(3)
Kelvin Wave	509	(4)
Potential Vorticity Conservation in Shallow Water Theory	513	(4)
Internal Waves	517	(9)
Rossby Wave	526	(6)
Barotropic Instability	532	(1)
Baroclinic Instability	533	(8)
Geostrophic Turbulence	541	(6)
Exercises	545	(1)
Literature Cited	546	(1)
Aerodynamics
Introduction	547	(1)
The Aircraft and Its Controls	548	(2)
Airfoil Geometry	550	(1)
Forces on an Airfoil	551	(1)
Kutta Condition	552	(2)
Generation of Circulation	554	(2)
Conformal Transformation for Generating Airfoil Shape	556	(4)
Lift of Zhukhovski Airfoil	560	(2)
Wing of Finite Span	562	(2)
Lifting Line Theory of Prandtl and Lanchester	564	(4)
Results for Elliptic Circulation Distribution	568	(3)
Lift and Drag Characteristics of Airfoils	571	(2)
Propulsive Mechanisms of Fish and Birds	573	(2)
Sailing against the Wind	575	(4)
Exercises	576	(1)
Literature Cited	577	(1)
Supplemental Reading	578	(1)
Compressible Flow
Introduction	579	(4)
Speed of Sound	583	(2)
Basic Equations for One-Dimensional Flow	585	(3)
Stagnation and Sonic Properties	588	(2)
Area-Velocity Relations in One-Dimensional Insentropic Flow	590	(7)
Normal Shock Wave	597	(4)
Operation of Nozzles at Different Back Pressures	601	(5)
Mach Cone	606	(2)
Oblique Shock Wave	608	(5)
Expansion and Compression in Supersonic Flow	613	(1)
Thin Airfoil Theory in Supersonic Flow	614	(4)
Exercises	616	(1)
Literature Cited	617	(1)
Supplemental Reading	617	(1)
Appendix A Some Properties of Common Fluids
A1. Useful Conversion Factors	618	(1)
A2. Properties of Pure Water at Atmospheric Pressure	619	(1)
A3. Properties of Dry Air at Atmospheric Pressure	619	(1)
A4. Properties of Standard Atmosphere	620	(1)
Appendix B Curvilinear Coordinates
B1. Cylindrical Polar Coordinates	621	(2)
B2. Plane Polar Coordinates	623	(1)
B3. Spherical Polar Coordinates	624	(2)
Appendix C Founders of Modern Fluid Dynamics
Ludwig Prandtl (1875-1953)	626	(1)
Geoffrey Ingram Taylor (1886-1975)	627	(1)
Supplemental Reading	628	(1)
Index	629