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Introduction to Fluid Mechanics by Philip J. Pritchard and John C. Leylegian

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' Fox and McDonald’s Introduction to Fluid Mechanics Eighth Edition written by Philip J. Pritchard , Manhattan College. With special contributions from: John C. Leylegian , Manhattan College. This book is intended to help undergraduate engineering students learn the fundamentals of fluid mechanics. It was developed for use in a first course on fluid mechanics, either one or two semesters/terms. While the principles of this course has been well established for many years, fluid mechanics education has envolved and improved.

Fox and McDonald’s Introduction to Fluid Mechanics Eighth Edition written by Philip J. Pritchard cover the following topics.

• 1 INTRODUCTION
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

• 2 FUNDAMENTAL CONCEPTS
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
References 46
Problems 46

• 3 FLUID STATICS
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

• 4 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME
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

• 5 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION
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
*5.5 Introduction to Computational Fluid Dynamics 208
The Need for CFD 208
Applications of CFD 209
Some Basic CFDNumerical 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

• 6 INCOMPRESSIBLE INVISCID FLOW
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
*6.6 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

• 7 DIMENSIONAL ANALYSIS AND SIMILITUDE
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
7.7 Summary and Useful Equations 318
References 319
Problems 320

• 8 INTERNAL INCOMPRESSIBLE VISCOUS FLOW
8.1 Introduction 330
Laminar versus Turbulent Flow 330
The Entrance Region 331
PART A. FULLY DEVELOPED LAMINAR FLOW 332
8.2 Fully Developed Laminar Flow between Infinite Parallel Plates 332
Both Plates Stationary 332
Upper Plate Moving with Constant Speed, U 338
8.3 Fully Developed Laminar Flow in a Pipe 344
PART B. FLOW IN PIPES AND DUCTS 348
8.4 Shear Stress Distribution in Fully Developed Pipe Flow 349
8.5 Turbulent Velocity Profiles in Fully Developed Pipe Flow 351
8.6 Energy Considerations in Pipe Flow 353
Kinetic Energy Coefficient 355
8.7 Calculation of Head Loss 357
Major Losses: Friction Factor 357
Minor Losses 361
Pumps, Fans, and Blowers in Fluid Systems 367
Noncircular Ducts 368
8.8 Solution of Pipe Flow Problems 369
Single-Path Systems 370
*Multiple-Path Systems 383
PART C. FLOW MEASUREMENT 387
8.9 Direct Methods 387
8.10 Restriction Flow Meters for Internal Flows 387
The Orifice Plate 391
The Flow Nozzle 391
The Venturi 393
The Laminar Flow Element 394
8.11 Linear Flow Meters 397
8.12 Traversing Methods 399
8.13 Summary and Useful Equations 400
References 402
Problems 403

• 9 EXTERNAL INCOMPRESSIBLE VISCOUS FLOW
PART A. BOUNDARY LAYERS 423
9.1 The Boundary-Layer Concept 423
9.2 Boundary-Layer Thicknesses 425
9.3 Laminar Flat-Plate Boundary Layer: Exact Solution (on the Web) W-19
9.4 Momentum Integral Equation 428
9.5 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient 433
Laminar Flow 434
Turbulent Flow 439
Summary of Results for Boundary-Layer Flow with Zero Pressure Gradient 441
9.6 Pressure Gradients in Boundary-Layer Flow 442
PART B. FLUID FLOW ABOUT IMMERSED BODIES 445
9.7 Drag 445
Pure Friction Drag: Flow over a Flat Plate Parallel to the Flow 446
Pure Pressure Drag: Flow over a Flat Plate Normal to the Flow 450
Friction and Pressure Drag: Flow over a Sphere and Cylinder 450
Streamlining 456
9.8 Lift 459
9.9 Summary and Useful Equations 474
References 477
Problems 478

• 10 FLUID MACHINERY
10.1 Introduction and Classification of Fluid Machines 494
Machines for Doing Work on a Fluid 494
Machines for Extracting Work (Power) from a Fluid 496
Scope of Coverage 498
10.2 Turbomachinery Analysis 499
The Angular-Momentum Principle: The Euler Turbomachine Equation 499
Velocity Diagrams 501
Performance: Hydraulic Power 504
Dimensional Analysis and Specific Speed 505
10.3 Pumps, Fans, and Blowers 510
Application of Euler Turbomachine Equation to Centrifugal Pumps 510
Application of the Euler Equation to Axial Flow Pumps and Fans 512
Performance Characteristics 516
Similarity Rules 522
Cavitation and Net Positive Suction Head 526
Pump Selection: Applications to Fluid Systems 529
Blowers and Fans 541
10.4 Positive Displacement Pumps 548
10.5 Hydraulic Turbines 552
Hydraulic Turbine Theory 552
Performance Characteristics for Hydraulic Turbines 554
Sizing Hydraulic Turbines for Fluid Systems 558
10.6 Propellers and Wind-Power Machines 562
Propellers 563
Wind-Power Machines 571
10.7 Compressible Flow Turbomachines 581
Application of the Energy Equation to a Compressible Flow Machine 581
Compressors 582
Compressible-Flow Turbines 586
10.8 Summary and Useful Equations 586
References 589
Problems 591

• 11 FLOW IN OPEN CHANNELS
11.1 Basic Concepts and Definitions 603
Simplifying Assumptions 604
Channel Geometry 605
Speed of Surface Waves and the Froude Number 606
11.2 Energy Equation for Open-Channel Flows 610
Specific Energy 613
Critical Depth: Minimum Specific Energy 616
11.3 Localized Effect of Area Change (Frictionless Flow) 619
Flow over a Bump 620
11.4 The Hydraulic Jump 625
Depth Increase Across a Hydraulic Jump 627
Head Loss Across a Hydraulic Jump 628
The Manning Equation for Uniform Flow 633
Energy Equation for Uniform Flow 639
Optimum Channel Cross Section 640
11.6 Flow with Gradually Varying Depth 641
Calculation of Surface Profiles 643
11.7 Discharge Measurement Using Weirs 646
Suppressed Rectangular Weir 646
Contracted Rectangular Weirs 647
Triangular Weir 648
11.8 Summary and Useful Equations 650
References 652
Problems 653

• 12 INTRODUCTION TO COMPRESSIBLE FLOW
12.1 Review of Thermodynamics 659
12.2 Propagation of Sound Waves 665
Speed of Sound 665
Types of Flow—The Mach Cone 670
12.3 Reference State: Local Isentropic Stagnation Properties 673
Local Isentropic Stagnation Properties for the Flow of an Ideal Gas 674
12.4 Critical Conditions 681
12.5 Summary and Useful Equations 681
References 683
Problems 683

• 13 COMPRESSIBLE FLOW
13.1 Basic Equations for One-Dimensional Compressible Flow 691
13.2 Isentropic Flow of an Ideal Gas: Area Variation 694
Subsonic Flow, M , 1 697
Supersonic Flow, M . 1 697
Sonic Flow, M 5 1 698
Reference Stagnation and Critical Conditions for Isentropic Flow of an Ideal Gas 699
Isentropic Flow in a Converging Nozzle 704
Isentropic Flow in a Converging-Diverging Nozzle 709
13.3 Normal Shocks 715
Basic Equations for a Normal Shock 716
Fanno and Rayleigh Interpretation of Normal Shock 718
Normal-Shock Flow Functions for One-Dimensional Flow of an Ideal Gas 719
13.4 Supersonic Channel Flow with Shocks 724
Flow in a Converging-Diverging Nozzle 724
Supersonic Diffuser (on the Web) W-24
Supersonic Wind Tunnel Operation (on the Web) W-25
Supersonic Flow with Friction in a Constant-Area Channel (on the Web) W-26
Supersonic Flow with Heat Addition in a Constant-Area Channel (on the Web) W-26
13.5 Flow in a Constant-Area Duct with Friction 727
Basic Equations for Adiabatic Flow 727
Adiabatic Flow: The Fanno Line 728
Fanno-Line Flow Functions for One-Dimensional Flow of an Ideal Gas 732
Isothermal Flow (on the Web) W-29
13.6 Frictionless Flow in a Constant-Area Duct with Heat Exchange 740
Basic Equations for Flow with Heat Exchange 740
The Rayleigh Line 741
Rayleigh-Line Flow Functions for One-Dimensional Flow of an Ideal Gas 746
13.7 Oblique Shocks and Expansion Waves 750
Oblique Shocks 750
Isentropic Expansion Waves 759
13.8 Summary and Useful Equations 768
References 771
Problems 772

• APPENDIX
A FLUID PROPERTY DATA 785
B EQUATIONS OF MOTION IN CYLINDRICAL COORDINATES 798
C VIDEOS FOR FLUID MECHANICS 800
D SELECTED PERFORMANCE CURVES FOR PUMPS AND FANS 803
E FLOW FUNCTIONS FOR COMPUTATION OF COMPRESSIBLE FLOW 818
F ANALYSIS OF EXPERIMENTAL UNCERTAINTY 829
G SI UNITS, PREFIXES, AND CONVERSION FACTORS 836
H A BRIEF REVIEW OF MICROSOFT EXCEL (ON THE WEB) W-33

• Index

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