SOLUTION MANUAL FOR
Fox and McDonald's Introduction to Fluid Mechanics
by Robert W. Fox, Alan T. McDonald ( 10th Edition)
, www.TheSolutionManual.com
CHAPTER 1 INTRODUCTION /1
1.1 Note To Students /3
1.2 Scope Of Fluid Mechanics /4
1.3 Definition Of A Fluid /4
1.4 Basic Equations /5
1.5 Methods Of Analysis /6
System And Control Volume /7
Differential Versus Integral Approach /8
Methods Of Description /9
1.6 Dimensions And Units /11
Systems Of Dimensions /11
Systems Of Units /11
Preferred Systems Of Units /13
Dimensional Consistency And “Engineering” Equations /14
1.7 Analysis Of Experimental Error /15
1.8 Summary /16
Problems /17
CHAPTER 2 FUNDAMENTAL CONCEPTS /20
2.1 Fluid As A Continuum /21
2.2 Velocity Field /23
One-, Two-, And Three-Dimensional Flows /24
Timelines, Pathlines, Streaklines, And Streamlines /25
2.3 Stress Field /29
2.4 Viscosity /31
Newtonian Fluid /32
Non-Newtonian Fluids /34
2.5 Surface Tension /36
2.6 Description And Classification Of Fluid Motions /38
Viscous And Inviscid Flows /38
Laminar And Turbulent Flows /41
Compressible And Incompressible Flows /42
Internal And External Flows /43
2.7 Summary And Useful Equations /44
V
, www.TheSolutionManual.com
Vi Contents
References /46
Problems /46
CHAPTER 3 FLUID STATICS /55
3.1 The Basic Equation Of Fluid Statics /56
3.2 The Standard Atmosphere /60
3.3 Pressure Variation In A Static Fluid /61
Incompressible Liquids: Manometers /61
Gases /66
3.4 Hydraulic Systems /69
3.5 Hydrostatic Force On Submerged Surfaces /69
Hydrostatic Force On A Plane Submerged Surface /69
Hydrostatic Force On A Curved Submerged Surface /76
*3.6 Buoyancy And Stability /80
3.7 Fluids In Rigid-Body Motion (On The Web) /W-1
3.8 Summary And Useful Equations /83
References /84
Problems /84
CHAPTER 4 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME /96
4.1 Basic Laws For A System /98
Conservation Of Mass /98
Newton’s Second Law /98
The Angular-Momentum Principle /99
The First Law Of Thermodynamics /99
The Second Law Of Thermodynamics /99
4.2 Relation Of System Derivatives To The Control Volume Formulation /100
Derivation /101
Physical Interpretation /103
4.3 Conservation Of Mass /104
Special Cases /105
4.4 Momentum Equation For Inertial Control Volume /110
*Differential Control Volume Analysis /122
Control Volume Moving With Constant Velocity /126
4.5 Momentum Equation For Control Volume With Rectilinear Acceleration /128
4.6 Momentum Equation For Control Volume With Arbitrary Acceleration (On The Web) /W-6
*4.7 The Angular-Momentum Principle /135
Equation For Fixed Control Volume /135
Equation For Rotating Control Volume (On The Web) /W-11
4.8 The First Law Of Thermodynamics /139
Rate Of Work Done By A Control Volume /140
Control Volume Equation /142
4.9 The Second Law Of Thermodynamics /146
4.10 Summary And Useful Equations /147
Problems /149
CHAPTER 5 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION /171
5.1 Conservation Of Mass /172
Rectangular Coordinate System /173
Cylindrical Coordinate System /177
*5.2 Stream Function For Two-Dimensional Incompressible Flow /180
5.3 Motion Of A Fluid Particle (Kinematics) /184
Fluid Translation: Acceleration Of A Fluid Particle In A Velocity Field /185
Fluid Rotation /190
Fluid Deformation /194
5.4 Momentum Equation /197
Forces Acting On A Fluid Particle /198
Differential Momentum Equation /199
Newtonian Fluid: Navier—Stokes Equations /199
, www.TheSolutionManual.com
Contents Vii
*5.5 Introduction To Computational Fluid Dynamics /208
The Need For CFD /208
Applications Of CFD /209
Some Basic CFD/Numerical Methods Using A Spreadsheet /210
The Strategy Of CFD /215
Discretization Using The Finite-Difference Method /216
Assembly Of Discrete System And Application Of Boundary Conditions /217
Solution Of Discrete System /218
Grid Convergence /219
Dealing With Nonlinearity /220
Direct And Iterative Solvers /221
Iterative Convergence /222
Concluding Remarks /223
5.6 Summary And Useful Equations /224
References /226
Problems /226
CHAPTER 6 INCOMPRESSIBLE INVISCID FLOW /235
6.1 Momentum Equation For Frictionless Flow: Euler’s Equation /237
6.2 Euler’s Equations In Streamline Coordinates /238
6.3 Bernoulli Equation—Integration Of Euler’s Equation Along A Streamline For Steady Flow /241
*Derivation Using Streamline Coordinates /241
*Derivation Using Rectangular Coordinates /242
Static, Stagnation, And Dynamic Pressures /244
Applications /247
Cautions On Use Of The Bernoulli Equation /252
6.4 The Bernoulli Equation Interpreted As An Energy Equation /253
6.5 Energy Grade Line And Hydraulic Grade Line /257
*6.6 Unsteady Bernoulli Equation: Integration Of Euler’s Equation Along A Streamline
(On The Web) /W-16
*6.7 Irrotational Flow /259
Bernoulli Equation Applied To Irrotational Flow /260
Velocity Potential /261
Stream Function And Velocity Potential For Two-Dimensional, Irrotational, Incompressible
Flow: Laplace’s Equation /262
Elementary Plane Flows /264
Superposition Of Elementary Plane Flows /267
6.8 Summary And Useful Equations /276
References /279
Problems /279
CHAPTER 7 DIMENSIONAL ANALYSIS AND SIMILITUDE /290
7.1 Nondimensionalizing The Basic Differential Equations /292
7.2 Nature Of Dimensional Analysis /294
7.3 Buckingham Pi Theorem /296
7.4 Determining The Π Groups /297
7.5 Significant Dimensionless Groups In Fluid Mechanics /303
7.6 Flow Similarity And Model Studies /305
Incomplete Similarity /308
Scaling With Multiple Dependent Parameters /314
Comments On Model Testing /317
7.7 Summary And Useful Equations /318
References /319
Problems /320
CHAPTER 8 INTERNAL INCOMPRESSIBLE VISCOUS FLOW /328
8.1Introduction /330
Laminar Versus Turbulent Flow /330
The Entrance Region /331
PART A. FULLY DEVELOPED LAMINAR FLOW /332
Fox and McDonald's Introduction to Fluid Mechanics
by Robert W. Fox, Alan T. McDonald ( 10th Edition)
, www.TheSolutionManual.com
CHAPTER 1 INTRODUCTION /1
1.1 Note To Students /3
1.2 Scope Of Fluid Mechanics /4
1.3 Definition Of A Fluid /4
1.4 Basic Equations /5
1.5 Methods Of Analysis /6
System And Control Volume /7
Differential Versus Integral Approach /8
Methods Of Description /9
1.6 Dimensions And Units /11
Systems Of Dimensions /11
Systems Of Units /11
Preferred Systems Of Units /13
Dimensional Consistency And “Engineering” Equations /14
1.7 Analysis Of Experimental Error /15
1.8 Summary /16
Problems /17
CHAPTER 2 FUNDAMENTAL CONCEPTS /20
2.1 Fluid As A Continuum /21
2.2 Velocity Field /23
One-, Two-, And Three-Dimensional Flows /24
Timelines, Pathlines, Streaklines, And Streamlines /25
2.3 Stress Field /29
2.4 Viscosity /31
Newtonian Fluid /32
Non-Newtonian Fluids /34
2.5 Surface Tension /36
2.6 Description And Classification Of Fluid Motions /38
Viscous And Inviscid Flows /38
Laminar And Turbulent Flows /41
Compressible And Incompressible Flows /42
Internal And External Flows /43
2.7 Summary And Useful Equations /44
V
, www.TheSolutionManual.com
Vi Contents
References /46
Problems /46
CHAPTER 3 FLUID STATICS /55
3.1 The Basic Equation Of Fluid Statics /56
3.2 The Standard Atmosphere /60
3.3 Pressure Variation In A Static Fluid /61
Incompressible Liquids: Manometers /61
Gases /66
3.4 Hydraulic Systems /69
3.5 Hydrostatic Force On Submerged Surfaces /69
Hydrostatic Force On A Plane Submerged Surface /69
Hydrostatic Force On A Curved Submerged Surface /76
*3.6 Buoyancy And Stability /80
3.7 Fluids In Rigid-Body Motion (On The Web) /W-1
3.8 Summary And Useful Equations /83
References /84
Problems /84
CHAPTER 4 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME /96
4.1 Basic Laws For A System /98
Conservation Of Mass /98
Newton’s Second Law /98
The Angular-Momentum Principle /99
The First Law Of Thermodynamics /99
The Second Law Of Thermodynamics /99
4.2 Relation Of System Derivatives To The Control Volume Formulation /100
Derivation /101
Physical Interpretation /103
4.3 Conservation Of Mass /104
Special Cases /105
4.4 Momentum Equation For Inertial Control Volume /110
*Differential Control Volume Analysis /122
Control Volume Moving With Constant Velocity /126
4.5 Momentum Equation For Control Volume With Rectilinear Acceleration /128
4.6 Momentum Equation For Control Volume With Arbitrary Acceleration (On The Web) /W-6
*4.7 The Angular-Momentum Principle /135
Equation For Fixed Control Volume /135
Equation For Rotating Control Volume (On The Web) /W-11
4.8 The First Law Of Thermodynamics /139
Rate Of Work Done By A Control Volume /140
Control Volume Equation /142
4.9 The Second Law Of Thermodynamics /146
4.10 Summary And Useful Equations /147
Problems /149
CHAPTER 5 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION /171
5.1 Conservation Of Mass /172
Rectangular Coordinate System /173
Cylindrical Coordinate System /177
*5.2 Stream Function For Two-Dimensional Incompressible Flow /180
5.3 Motion Of A Fluid Particle (Kinematics) /184
Fluid Translation: Acceleration Of A Fluid Particle In A Velocity Field /185
Fluid Rotation /190
Fluid Deformation /194
5.4 Momentum Equation /197
Forces Acting On A Fluid Particle /198
Differential Momentum Equation /199
Newtonian Fluid: Navier—Stokes Equations /199
, www.TheSolutionManual.com
Contents Vii
*5.5 Introduction To Computational Fluid Dynamics /208
The Need For CFD /208
Applications Of CFD /209
Some Basic CFD/Numerical Methods Using A Spreadsheet /210
The Strategy Of CFD /215
Discretization Using The Finite-Difference Method /216
Assembly Of Discrete System And Application Of Boundary Conditions /217
Solution Of Discrete System /218
Grid Convergence /219
Dealing With Nonlinearity /220
Direct And Iterative Solvers /221
Iterative Convergence /222
Concluding Remarks /223
5.6 Summary And Useful Equations /224
References /226
Problems /226
CHAPTER 6 INCOMPRESSIBLE INVISCID FLOW /235
6.1 Momentum Equation For Frictionless Flow: Euler’s Equation /237
6.2 Euler’s Equations In Streamline Coordinates /238
6.3 Bernoulli Equation—Integration Of Euler’s Equation Along A Streamline For Steady Flow /241
*Derivation Using Streamline Coordinates /241
*Derivation Using Rectangular Coordinates /242
Static, Stagnation, And Dynamic Pressures /244
Applications /247
Cautions On Use Of The Bernoulli Equation /252
6.4 The Bernoulli Equation Interpreted As An Energy Equation /253
6.5 Energy Grade Line And Hydraulic Grade Line /257
*6.6 Unsteady Bernoulli Equation: Integration Of Euler’s Equation Along A Streamline
(On The Web) /W-16
*6.7 Irrotational Flow /259
Bernoulli Equation Applied To Irrotational Flow /260
Velocity Potential /261
Stream Function And Velocity Potential For Two-Dimensional, Irrotational, Incompressible
Flow: Laplace’s Equation /262
Elementary Plane Flows /264
Superposition Of Elementary Plane Flows /267
6.8 Summary And Useful Equations /276
References /279
Problems /279
CHAPTER 7 DIMENSIONAL ANALYSIS AND SIMILITUDE /290
7.1 Nondimensionalizing The Basic Differential Equations /292
7.2 Nature Of Dimensional Analysis /294
7.3 Buckingham Pi Theorem /296
7.4 Determining The Π Groups /297
7.5 Significant Dimensionless Groups In Fluid Mechanics /303
7.6 Flow Similarity And Model Studies /305
Incomplete Similarity /308
Scaling With Multiple Dependent Parameters /314
Comments On Model Testing /317
7.7 Summary And Useful Equations /318
References /319
Problems /320
CHAPTER 8 INTERNAL INCOMPRESSIBLE VISCOUS FLOW /328
8.1Introduction /330
Laminar Versus Turbulent Flow /330
The Entrance Region /331
PART A. FULLY DEVELOPED LAMINAR FLOW /332
