Fluid Mechanics (Dover Books on Physics)

✍ Scribed by Robert A. Granger

• Publisher: Dover Publications
• Year: 1995
• Tongue: English
• Leaves: 931
• Edition: 1
• Category: Library

✦ Synopsis

"The mixture of prose, mathematics, and beautiful illustrations is particularly well chosen." — American Scientist
This monumental text by a noted authority in the field is specially designed to provide an orderly structured introduction to fluid mechanics, a field all too often seen by students as an amorphous mass of disparate equations instead of the coherent body of theory and application it should be. In addition, the book will help upgrade students' mathematical skills as they learn the fundamentals of fluid mechanics.
The text presents a unified method of analysis that poses fluid mechanics problems in precise mathematical language without becoming stiff or unnecessarily rigorous. This method involves three steps: First, the text carefully defines each problem so the student knows what is given and what is missing. Second, each chapter treats the physical aspects of the problems so the student can visualize how things work in the real world. Third, the text represents the physical model by appropriate mathematical symbols and operators, collects these into equations, and then solves them. The result is a superb learning and teaching process that covers everything the engineer needs to know — nature of fluids, hydrostatics, differential and integral equations, dimensional analysis, viscous flows, and other topics — while allowing students to see each element in its relation to the whole.
Each chapter contains numerous examples incorporating problem-solving techniques, demonstrations to illustrate topical material, study questions, boxed equations of significant results, appropriate references to supplementary materials and other study aids. Over 760 illustrations enhance the text. This volume will be an indispensable reference and resource for any student of fluid mechanics or practicing engineer.

✦ Table of Contents

Front Matter
Table of Contents
Prefaces
Preface to the Dover Edition
Preface to the First Edition
1. Format and Fundamentals
1.1 Introduction: A Survey of Fluid Mechanics
1.2 Format of This Text
1.2.1 The Subject of Fluid Mechanics
1.2.2 The Structure of Fluid Mechanics
1.3 Fundamental Quantities, Units
1.3.1 Le Systéme International, SI System
1.3.2 The USCS System
1.3.3 Two other Systems of Units
1.3.4 Secondary Dimensions
1.4 Fundamental Idealizations
1.5 Fundamental Coordinates
1.6 Fundamental Kinematic Field
1.6.1 Absolute Velocity
1.6.2 Relative Velocity
1.6.3 Absolute Acceleration Field
1.6.4 Relative Acceleration Field
1.7 Fundamental Descriptions: Lagrange versus Euler Description
1.7.1 Lagrangian Description
1.7.2 Eulerian Description
1.7.3 Substantive Derivative D/Dt: The Stokes Derivative
1.7.3.1 The Acceleration in the Eulerian Description
References
Study Questions
Problems
2. Description of Fluids
2.1 Introduction
2.2 What is a Fluid?
2.2.1 Concerning Water
2.3 Classification of Fluid Flows
2.3.1 Gases versus Liquids
2.3.2 Continuum versus Discrete Fluids
2.3.3 Perfect versus Real Fluids
2.3.4 Newtonian versus Non-Newtonian Fluids
2.3.5 Compressible and Incompressible Fluids
2.3.6 Steady and Unsteady Fluid Flows
2.3.7 One, Two, and Three-Dimensional Flows
2.3.8 Rotational versus Irrotational Flow
2.4 Properties of Fluids
2.4.1 Mass, M
2.4.2 Density, rho
2.4.3 Specific Weight, gamma
2.4.4 Specific Gravity, S
2.4.5 Pressure, p
2.4.6 Bulk Modulus of Elasticity, K
2.4.7 Absolute or Dynamic Viscosity, mu
2.4.8 Kinematic Viscosity, v
2.4.9 Surface Tension, sigma
2.4.10 Capillary Rise or Depression, h
References
Study Questions
Problems
3. Aerohydrostatics
3.1 Hydrostatics
3.1.1 Manometers
3.1.2 Barometer
3.1.3 U-Tube Manometer
3.1.4 Inclined Manometer
3.2 Uniform Acceleration
3.3 Aerostatics
3.3.1 Halley's Law
3.3.2 Logarithmic Law
3.4 Forces on Planar Bodies
3.4.1 Force on a Planar Body in a Horizontal Plane
3.4.2 Pressure Force on Inclined Planar Surfaces
3.5 Hydrostatic Forces on Curved Bodies
3.5.1 Horizontal and Vertical Components of a Pressure Force
3.6 Buoyant Forces on Submerged Bodies
3.7 Initial Stability of Floating and Submerged Ships
3.7.1 Relative Location of Reference Points
3.7.2 Initial Stability of a Surface Ship
3.7.3 Initial Stability for the Submerged Submarine
3.7.4 Methods of Improving Initial Stability
Study Questions
Problems
4. Differential Forms of Fluid Behavior
4.1 Introduction
4.2 General Property Balance
4.3 The Differential Form of the Conservation of Mass
4.4 The Differential Form of the Conservation of Linear Momentum
4.4.1 The Physics of the Problem
4.4.2 The Composition of Velocity
4.4.3 The Strain Rate Dyadic S
4.4.4 Geometric Interpretation of the Velocity Components
4.4.5 The Stress Dyadic, P
4.4.6 The Surface Forces, F_s
4.4.7 Vorticity, zeta
4.4.8 Cauchy's Equation of Motion
4.4.9 The Navier-Stokes Equations
4.4.10 The Gromeka-Lamb Form of the Navier-Stokes Equation
4.4.10.1 Beltrami Flow
4.4.11 Boundary Conditions
4.4.11.1 Kinematic Boundary Condition
4.4.11.2 Stress Boundary Condition
4.5 The Differential Form of the Conservation of Energy
4.5.1 Boundary Conditions for the Energy Equation
4.6 Air as an Incompressible and/or Inviscid Fluid
References
Study Questions
Problems
5. Integrated Forms of Fluid Behavior
5.1 Introduction
5.2 The Integral Form of the Conservation of Mass
5.2.1 Incompressible Flow Form of the Continuity Equation
5.3 The Integral Form of the Conservation of Linear Momentum
5.3.1 Linear Momentum Equation for Inertial Control Volume
5.3.1.1 Simplified Steady State Forms
5.3.1.2 One-Dimensional Steady Flow Case
5.3.1.3 Free Jet Reaction
5.3.1.4 Free Jet Reaction with Moving Wall
5.3.1.5 Airfoil Forces in Plane Flow
5.3.2 Integral Form of the Linear Momentum Equation for a Noninertial Control Volume
5.3.2.1 Moving Vanes in Steady Nonaccelerating Flows
5.4 The Integral Form of the Conservation of Angular Momentum
5.4.1 Case 1: V_r = 0. Rigid Body Motion
5.4.2 Case 2: Inertial Frame of Reference
5.4.2.1 Moment of Momentum Equations Applied to Pumps and Turbines
5.4.2.2 An Application: Centrifugal Pumps and Their Characteristics
5.4.2.3 Pump Performance Analysis
5.4.2.4 Some Limiting Factors in Pump Operation
5.4.2.5 Combination of Pump and System
5.5 The Integral Form of the Conservation of Energy
5.5.1 Rate of Heat Transfer, _i Q_e
5.5.2 Fluid Power, _i W_e
5.5.2.1 Work due to Shear Stresses, W_st
5.5.2.2 Work due to Normal Stresses, W_sp
5.5.3 Integral Form of the Energy Equation
5.5.3.1 Steady State Form
5.5.3.2 One-Dimensional Form
5.5.4 The Steady Flow Energy Equation versus Bernoulli's Equation
5.5.5 Energy Grade Lines
Study Questions
Problems
6. Recapitulation
6.1 Summary
6.2 Special Forms of the Governing Equations
6.3 Problem-Solving Technique
6.4 Examples of Problem-Solving Technique
7. Dimensional Analysis and Similitude
7.1 Introduction
7.2 Dimensional Analysis
7.2.1 The Principle of Dimensional Homogeneity
7.3 Buckingham Pi Theorem
7.3.1 Applications of the Buckingham Pi Theorem
7.4 The Rayleigh Method
7.4.1 A Critique of the Two Methods
7.5 Dimensionless Parameters
7.5.1 Dimensionless Navier-Stokes Equation
7.5.2 Scaling Rules
7.5.3 Reynolds Number, R_L
7.5.4 Froude Number, F_r
7.5.5 Mach Number M and Cauchy Number C
7.5.6 Weber Number, W
7.5.7 Euler Number E, and the Pressure Coefficient C_p
7.6 Similitude
7.7 Similarity Solutions and Transformations
7.8 Geometric and Dynamic Similitude
7.9 Modeling
7.9.1 Reynolds Number Modeling
7.9.2 Froude Number Modeling
7.10 Drag
7.11 Lift
7.12 Vorticity Effect in Lift and Drag
References
Study Questions
Problems
8. Flow Visualization
8.1 Introduction
8.2 Equation of a Streamline
8.3 Stream Function, psi
8.3.1 Cauchy-Riemann Conditions
8.3.2 Orthogonality of phi and psi
8.4 Visualization Techniques
8.4.1 Methods for Visualizing Flows of Liquids and Gases
8.4.1.1 Dyes
8.4.1.2 Smoke
8.4.1.3 Tufts
8.4.1.4 Small Particles
8.4.1.5 Optical Set-Ups
References
Study Questions
Problems
9. Viscous Fluid Flows
9.1 Introduction
9.2 Rectilinear Flow between Parallel Plates
9.2.1 Temperature Distributions for Couette and Poiseuille Flows
9.2.1.1 Couette Flow Temperature Distribution
9.2.1.2 Poiseuille Flow Temperature Distribution
9.3 Suddenly Accelerated Flat Plate in a Viscous Fluid
9.4 Rotational Viscous Flows
9.4.1 Equations of Motion
9.4.2 Some Exact Solutions
9.4.2.1 Oseen's Solution
9.4.2.2 A Decaying Vortex
References
Study Questions
Problems
10. Laminar Pipe Flow
10.1 Introduction
10.2 Description of the Physical Phenomenon
10.3 Equations of Motion for Laminar Flow in a Pipe
10.4 The Moody Diagram
10.4.1 Other Ways to Use the Moody Diagram
10.5 Minor Losses
10.5.1 Fittings and Obstructions
10.5.1.1 Loss Coefficient k for a Few Valves
10.5.2 Elbows, Tees, and Such
10.5.3 Sudden Contractions
10.5.4 Sudden Expansion
10.5.5 Gradual Expansion
10.6 Energy Equation for Real Fluid Flow in a Pipe
10.7 Examples of Pipe Flow
10.7.1 The Siphon
10.7.2 Pipes in Series
10.7.3 Flow in Parallel Pipes
References
Study Questions
Problems
11. Turbulent Pipe Flow
11.1 Introduction
11.2 Detecting Turbulence
11.3 On the Origin of Turbulence
11.3.1 The Role of Vorticity in the Origin of Turbulence
11.4 Definitions of Various Velocity Terms
11.4.1 The Equations of Motion for Turbulent Flow
11.5 Zero-Equation Model for Fully Turbulent Flow
11.5.1 The Mixing Length Hypothesis MLH
11.5.2 Experimental Determination of Mixing Length
11.5.3 Advantages and Disadvantages of the MLH
11.6 Fully Turbulent Flow in a Pipe
References
Study Questions
Problems
12. Potential Flow
12.1 Introduction
12.2 Laplace's Equation
12.2.1 Methods of Solving Laplace's Equation
12.3 The Complex Potential, Omega
12.4 The Complex Velocity, dOmega/dz
12.4.1 Stagnation Points
12.4.2 The Speed
12.5 Complex Potential for Fundamental Flows
12.5.1 Uniform Flow
12.5.2 Sources and Sinks
12.5.3 Vortex Motions
12.5.3.1 Circulation, Gamma
12.5.3.2 Complex Potential for an lrrotational Vortex
12.5.4 Doublet
12.6 Conservation of Circulation
12.7 Equation of the Body
12.8 Blasius' Theorem for Forces
12.9 Various Complex Potentials Omegaz and Corresponding Physical Flows
12.10 Combined Flows
12.10.1 Principle of Superposition
12.10.2 Flow about a Half-Body
12.10.3 Uniform Flow Past a Source and a Sink
12.10.4 Uniform Flow Past a Doublet: Flow Past a Cylinder
12.10.5 Uniform Flow Past a Cylinder with Circulation
12.11 Lift and Drag
12.11.1 The Phenomenon of Lift
12.11.2 The Phenomenon of Drag
12.11.3 Some Illustrative Projects on Lift and Drag
12.11.3.1 Purpose
12.12 Method of Images or a Way to Create Straight Boundaries
12.13 Potential and Stream Functions in Real Fluids
12.13.1 Compressible Fluids
12.13.2 Viscous Flows
12.13.3 Rotational Flows Being Ideal
12.14 Comparison of Potential Theory with Experiment
References
Study Questions
Problems
13. Open-Channel Flow
13.1 Introduction
13.2 Steady Open-Channel Flow
13.2.1 Flow Classification
13.2.2 Uniform Open-Channel Flow
13.2.2.1 Evaluating the Chézy Coefficient C
13.2.2.2 Evaluating the Channel Geometry
13.2.2.3 The Most Efficient Channel Profile
13.2.3 Specific Energy
13.2.3.1 Specific Energy and Critical Depth for Free-Surface Flow in a Uniform Flat Bed Channel
13.3 Surge Waves and the Hydraulic Jump
13.3.1 Open-Channel Flow Past a Broad-Crested Weir
13.3.2 The Hydraulic Jump
13.4 Flows Past Sharp-Crested Weirs
13.5 Linear Theory of Simple Harmonic Long-Crested Waves of Small Amplitude
References
Study Questions
Problems
14. Boundary Layer Flows
14.1 Introduction
14.1.1 Reynolds' Experiment
14.2 The Boundary Layer Concept
14.3 Prandtl's Boundary Layer Equations
14.4 Blasius Solution for Laminar Boundary Layer Flow over a Flat Plate
14.5 Boundary Layer Thicknesses of Displacement and Momentum
14.6 Prandtl's Boundary Layer Theory from the Viewpoint of a Mathematician
14.6.1 Separation
14.6.2 On Prandtl's Boundary Layer Equations
14.7 Integral Momentum Principles
14.7.1 Momentum Principle for Boundary Layer Analysis
14.7.2 Method of Solution of the von Kármán-Pohlhausen Integral Momentum Equation
14.7.3 Laminar Boundary Layer Analysis on a Flat Plate
14.8 Mechanics of Boundary Layer Transition
14.8.1 The Nonlinear Region
14.8.1.1 Region of Instability to Small Wavy Disturbances
14.8.1.2 Region of Three-Dimensional Wave Amplification
14.8.1.3 Peak-Valley Development with Streamwise-Vortex System
14.8.1.4 Vorticity Concentration and Shear Layer Development
14.8.1.5 Breakdown
14.8.1.6 Turbulent-Spot Development
14.8.2 Salient Aspects of Transition
14.8.2.1 Transition in Pipe Flows
14.8.2.2 Transition in Flows over Bodies
14.8.3 Instability versus Transition
14.8.3.1 Determining the Position of the Instability Point for a Body
14.9 Turbulent Boundary Layers
14.9.1 The Inner Layer, 0 Less-Than or Equal to y/delta Less-Than or Equal to 0.2
14.9.1.1 Linear Sublayer, 0 Less-Than or Equal to uy/v Less-Than or Equal to 3
14.9.1.2 Buffer Layer, 3 < uy/v < 40
14.9.1.3 Logarithmic Law Region, 40 < uy/v < 0.2 delta u/v
14.9.2 The Outer Layer, 0.2 Less-Than or Equal to y/delta Less-Than or Equal to 1.0
14.9.2.1 The Viscous Superlayer
14.9.3 Fully Turbulent Boundary Layer Flow
14.10 Drag
14.10.1 Drag Coefficient of Automobiles
14.10.2 Effect of Thickness on the Drag of Symmetrical Bodies
14.10.3 The Effect of Shape on Drag
14.10.4 Effect of Roughness on the Drag of Airfoil Shapes
14.10.5 Aspects of Design for Minimum Drag
14.10.6 Applications
14.10.6.1 Drag on a Cylinder
14.10.6.2 Drag on a Sphere
References
Study Questions
Problems
15. One-Dimensional Compressible Flow
15.1 Introduction
15.2 The Description of a Perfect Gas
15.3 The Second Law of Thermodynamics
15.4 Equations of a Process
15.5 The Compressible Flow Energy Equation
15.6 Problem Solution Technique in Applying the Energy Equation
15.6.1 Application of the I.F. Energy Equation for Compressible Flow
15.6.1.1 Nozzles and Diffusers
15.6.1.2 Compressors, Turbines, and Fans
15.6.1.3 Throttle
15.6.1.4 One-Dimensional Isentropic Pipe Flow
15.7 Normal Shock Waves
15.7.1 Mach Number Relationships for a Normal Shock
15.7.2 Mach Number Relationships for Stagnation Conditions in Isentropic Nozzles
15.7.3 Mass Rate through an Isentropic Nozzle
15.7.4 Location of a Normal Shock in a Nozzle
15.7.5 The Prandtl Relation
15.7.6 Thickness of the Normal Shock
15.8 Isothermal Gas Flow in a Pipe
15.9 Other Types of Shock Waves
15.10 Drag Coefficient C_D for Compressible Flow
15.10.1 Subsonic Compressible Drag Coefficients
15.10.2 Transonic and Supersonic Drag Coefficients
15.11 Closure
References
Study Questions
Problems
Answers to Selected Odd-Numbered Problems
Dedication
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Z
Appendices
Appendix A: Complex Variables
A.1 Complex Numbers
A.2 de Moivre's Theorem
A.3 Some Useful Definitions
A.4 Regular Function
A.5 Singular Points
A.6 Taylor Series
A.7 Laurent Series
A.8 Cauchy-Goursat Theorem
A.9 Cauchy's Integral Formula
A.10 Residue
A.11 Residue Theorem
Appendix B: Vectors
B.1 Vector Products
B.2 Differentiation with Respect to a Scalar
B.3 Formulas of Partial Differentiation
B.4 Formulas of Integration
Appendix C: Gas Tables