Fluid Mechanics – Fundamentals and Applications Solution Manual

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Yunus a. Cengel, John M. Cimbala

حل كتاب
Fluid Mechanics – Fundamentals and Applications Solution Manual
Fourth Edition
Yunus a. Cengel, John M. Cimbala
Contents
Preface Xv
Chapter O N E
Introduction and Basic
Concepts 1
1–1 Introduction 2
What is a Fluid? 2
Application Areas of Fluid Mechanics 4
1–2 a Brief History of Fluid Mechanics 6
1–3 the No-slip Condition 8
1–4 Classification of Fluid Flows 9
Viscous Versus Inviscid Regions of Flow 10
Internal Versus External Flow 10
Compressible Versus Incompressible Flow 10
Laminar Versus Turbulent Flow 11
Natural (or Unforced) Versus Forced Flow 11
Steady Versus Unsteady Flow 12
One-, Two-, and Three-dimensional Flows 13
Uniform Versus Nonuniform Flow 14
1–5 System and Control Volume 15
1–6 Importance of Dimensions and Units 16
Some Si and English Units 17
Dimensional Homogeneity 19
Unity Conversion Ratios 21
1–7 Modeling in Engineering 22
1–8 Problem-solving Technique 24
Step 1: Problem Statement 24
Step 2: Schematic 24
Step 3: Assumptions and Approximations 24
Step 4: Physical Laws 24
Step 5: Properties 25
Step 6: Calculations 25
Step 7: Reasoning, Verification, and Discussion 25
1–9 Engineering Software Packages 26
Equation Solvers 27
Cfd Software 28
1–10 Accuracy, Precision, and Significant Digits 28
Application Spotlight: What Nuclear Blasts and
Raindrops Have in Common 32
Summary 33
References and Suggested Reading 33
Problems 33
Chapter T W O
Properties of Fluids 37
2–1 Introduction 38
Continuum 38
2–2 Density and Specific Gravity 39
Density of Ideal Gases 40
2–3 Vapor Pressure and Cavitation 41
2–4 Energy and Specific Heats 43
2–5 Compressibility and Speed of Sound 45
Coefficient of Compressibility 45
Coefficient of Volume Expansion 46
Speed of Sound and Mach Number 49
2–6 Viscosity 51
2–7 Surface Tension and Capillary Effect 56
Capillary Effect 59
Summary 62
Application Spotlight: Cavitation 63
References and Suggested Reading 64
Problems 64
Chapter T H R E E
Pressure and Fluid Statics 77
3–1 Pressure 78
Pressure at a Point 79
Variation of Pressure With Depth 80
3–2 Pressure Measurement Devices 84
The Barometer 84
The Manometer 87
Other Pressure Measurement Devices 90
3–3 Introduction to Fluid Statics 91
3–4 Hydrostatic Forces on Submerged
Plane Surfaces 92
Special Case: Submerged Rectangular Plate 95
3–5 Hydrostatic Forces on Submerged Curved
Surfaces 97
3–6 Buoyancy and Stability 100
Stability of Immersed and Floating Bodies 104contents
Ix
3–7 Fluids in Rigid-body Motion 106
Special Case 1: Fluids at Rest 108
Special Case 2: Free Fall of a Fluid Body 108
Acceleration on a Straight Path 108
Rotation in a Cylindrical Container 110
Summary 114
References and Suggested Reading 115
Problems 115
Chapter F O U R
Fluid Kinematics 137
4–1 Lagrangian and Eulerian Descriptions 138
Acceleration Field 140
Material Derivative 143
4–2 Flow Patterns and Flow Visualization 145
Streamlines and Streamtubes 145
Pathlines 146
Streaklines 148
Timelines 150
Refractive Flow Visualization Techniques 151
Surface Flow Visualization Techniques 152
4–3 Plots of Fluid Flow Data 152
Profile Plots 153
Vector Plots 153
Contour Plots 154
4–4 Other Kinematic Descriptions 155
Types of Motion or Deformation of Fluid Elements 155
4–5 Vorticity and Rotationality 160
Comparison of Two Circular Flows 163
4–6 the Reynolds Transport Theorem 164
Alternate Derivation of the Reynolds Transport
Theorem 169
Relationship Between Material Derivative and Rtt 172
Summary 172
Application Spotlight: Fluidic Actuators 173
Application Spotlight: Smelling Food; the
Human Airway 174
References and Suggested Reading 175
Problems 175
Chapter F I V E
Bernoulli and Energy Equations 189
5–1 Introduction 190
Conservation of Mass 190
The Linear Momentum Equation 190
Conservation of Energy 190
5–2 Conservation of Mass 191
Mass and Volume Flow Rates 191
Conservation of Mass Principle 193
Moving or Deforming Control Volumes 195
Mass Balance for Steady-flow Processes 195
Special Case: Incompressible Flow 196
5–3 Mechanical Energy and Efficiency 198
5–4 the Bernoulli Equation 203
Acceleration of a Fluid Particle 204
Derivation of the Bernoulli Equation 204
Force Balance Across Streamlines 206
Unsteady, Compressible Flow 207
Static, Dynamic, and Stagnation Pressures 207
Limitations on the Use of the Bernoulli Equation 208
Hydraulic Grade Line (Hgl) and Energy
Grade Line (Egl) 210
Applications of the Bernoulli Equation 212
5–5 General Energy Equation 219
Energy Transfer by Heat, Q 220
Energy Transfer by Work, W 220
5–6 Energy Analysis of Steady Flows 223
Special Case: Incompressible Flow With No Mechanical
Work Devices and Negligible Friction 226
Kinetic Energy Correction Factor, ?? 226
Summary 233
References and Suggested Reading 234
Problems 235
Chapter S I X
Momentum Analysis of Flow
Systems 249
6–1 Newton's Laws 250
6–2 Choosing a Control Volume 251
6–3 Forces Acting on a Control Volume 252
6–4 the Linear Momentum Equation 255
Special Cases 257
Momentum-flux Correction Factor, ? 257
Steady Flow 259
Flow With No External Forces 260
6–5 Review of Rotational Motion and Angular
Momentum 269
6–6 the Angular Momentum Equation 272
Special Cases 274
Flow With No External Moments 275
Radial-flow Devices 275x
Fluid Mechanics
Application Spotlight: Manta Ray
Swimming 280
Summary 282
References and Suggested Reading 282
Problems 283
Chapter S E V E N
Dimensional Analysis and
Modeling 297
7–1 Dimensions and Units 298
7–2 Dimensional Homogeneity 299
Nondimensionalization of Equations 300
7–3 Dimensional Analysis and Similarity 305
7–4 the Method of Repeating Variables and the
Buckingham Pi Theorem 309
Historical Spotlight: Persons Honored by
Nondimensional Parameters 317
7–5 Experimental Testing, Modeling, and Incomplete
Similarity 325
Setup of an Experiment and Correlation
Of Experimental Data 325
Incomplete Similarity 326
Wind Tunnel Testing 326
Flows With Free Surfaces 329
Application Spotlight: How a Fly Flies 332
Summary 333
References and Suggested Reading 333
Problems 333
Chapter E I G H T
Internal Flow 351
8–1 Introduction 352
8–2 Laminar and Turbulent Flows 353
Reynolds Number 354
8–3 the Entrance Region 355
Entry Lengths 356
8–4 Laminar Flow in Pipes 357
Pressure Drop and Head Loss 359
Effect of Gravity on Velocity and Flow Rate
In Laminar Flow 361
Laminar Flow in Noncircular Pipes 362
8–5 Turbulent Flow in Pipes 365
Turbulent Shear Stress 366
Turbulent Velocity Profile 368
The Moody Chart and Its Associated
Equations 370
Types of Fluid Flow Problems 372
8–6 Minor Losses 379
8–7 Piping Networks and Pump Selection 386
Series and Parallel Pipes 386
Piping Systems With Pumps and Turbines 388
8–8 Flow Rate and Velocity Measurement 396
Pitot and Pitot-static Probes 396
Obstruction Flowmeters: Orifice, Venturi,
And Nozzle Meters 398
Positive Displacement Flowmeters 401
Turbine Flowmeters 402
Variable-area Flowmeters (Rotameters) 403
Ultrasonic Flowmeters 404
Electromagnetic Flowmeters 406
Vortex Flowmeters 407
Thermal (Hot-wire and Hot-film)
Anemometers 408
Laser Doppler Velocimetry 410
Particle Image Velocimetry 411
Introduction to Biofluid Mechanics 414
Application Spotlight: Piv Applied to Cardiac
Flow 420
Application Spotlight: Multicolor Particle
Shadow Velocimetry/accelerometry 421
Summary 423
References and Suggested Reading 424
Problems 425
Chapter N I N E
Differential Analysis of Fluid
Flow 443
9–1 Introduction 444
9–2 Conservation of Mass—the Continuity
Equation 444
Derivation Using the Divergence Theorem 445
Derivation Using an Infinitesimal Control Volume 446
Alternative Form of the Continuity Equation 449
Continuity Equation in Cylindrical Coordinates 450
Special Cases of the Continuity Equation 450
9–3 the Stream Function 456
The Stream Function in Cartesian Coordinates 456
The Stream Function in Cylindrical Coordinates 463
The Compressible Stream Function 464contents
Xi
9–4 the Differential Linear Momentum Equation—
Cauchy's Equation 465
Derivation Using the Divergence Theorem 465
Derivation Using an Infinitesimal Control Volume 466
Alternative Form of Cauchy's Equation 469
Derivation Using Newton's Second Law 469
9–5 the Navier–stokes Equation 470
Introduction 470
Newtonian Versus Non-newtonian Fluids 471
Derivation of the Navier–stokes Equation
For Incompressible, Isothermal Flow 472
Continuity and Navier–stokes Equations
In Cartesian Coordinates 474
Continuity and Navier–stokes Equations
In Cylindrical Coordinates 475
9–6 Differential Analysis of Fluid Flow
Problems 476
Calculation of the Pressure Field
For a Known Velocity Field 476
Exact Solutions of the Continuity
And Navier–stokes Equations 481
Differential Analysis of Biofluid Mechanics Flows 499
Summary 502
References and Suggested Reading 502
Application Spotlight: the No-slip Boundary
Condition 503
Problems 504
Chapter T E N
Approximate Solutions of the
Navier–stokes Equation 519
10–1 Introduction 520
10–2 Nondimensionalized Equations of Motion 521
10–3 the Creeping Flow Approximation 524
Drag on a Sphere in Creeping Flow 527
10–4 Approximation for Inviscid Regions of Flow 529
Derivation of the Bernoulli Equation in Inviscid Regions
Of Flow 530
10–5 the Irrotational Flow Approximation 533
Continuity Equation 533
Momentum Equation 535
Derivation of the Bernoulli Equation in Irrotational
Regions of Flow 535
Two-dimensional Irrotational Regions of Flow 538
Superposition in Irrotational Regions of Flow 542
Elementary Planar Irrotational Flows 542
Irrotational Flows Formed by Superposition 549
10–6 the Boundary Layer Approximation 558
The Boundary Layer Equations 563
The Boundary Layer Procedure 568
Displacement Thickness 572
Momentum Thickness 575
Turbulent Flat Plate Boundary Layer 576
Boundary Layers With Pressure Gradients 582
The Momentum Integral Technique for Boundary Layers 587
Summary 595
References and Suggested Reading 596
Application Spotlight: Droplet Formation 597
Problems 598
Chapter E L E V E N
External Flow: Drag and Lift 611
11–1 Introduction 612
11–2 Drag and Lift 614
11–3 Friction and Pressure Drag 618
Reducing Drag by Streamlining 619
Flow Separation 620
11–4 Drag Coefficients of Common Geometries 621
Biological Systems and Drag 622
Drag Coefficients of Vehicles 625
Superposition 627
11–5 Parallel Flow Over Flat Plates 629
Friction Coefficient 631
11–6 Flow Over Cylinders and Spheres 633
Effect of Surface Roughness 636
11–7 Lift 638
Finite-span Wings and Induced Drag 642
Lift Generated by Spinning 643
Flying in Nature! 647
Summary 650
Application Spotlight: Drag Reduction 652
References and Suggested Reading 653
Problems 653
Chapter T W E L V E
Compressible Flow 667
12–1 Stagnation Properties 668
12–2 One-dimensional Isentropic Flow 671
Variation of Fluid Velocity With Flow Area 673
Property Relations for Isentropic Flow of Ideal Gases 675xii
Fluid Mechanics
12–3 Isentropic Flow Through Nozzles 677
Converging Nozzles 678
Converging–diverging Nozzles 682
12–4 Shock Waves and Expansion
Waves 685
Normal Shocks 686
Oblique Shocks 691
Prandtl–meyer Expansion Waves 696
12–5 Duct Flow With Heat Transfer and Negligible
Friction (Rayleigh Flow) 701
Property Relations for Rayleigh Flow 706
Choked Rayleigh Flow 708
12–6 Adiabatic Duct Flow With Friction
(Fanno Flow) 710
Property Relations for Fanno Flow 713
Choked Fanno Flow 716
Application Spotlight: Shock-wave/
Boundary-layer Interactions 720
Summary 721
References and Suggested Reading 722
Problems 722
Chapter T H I R T E E N
Open-channel Flow 733
13–1 Classification of Open-channel Flows 734
Uniform and Varied Flows 734
Laminar and Turbulent Flows in Channels 735
13–2 Froude Number and Wave Speed 737
Speed of Surface Waves 739
13–3 Specific Energy 741
13–4 Conservation of Mass and Energy
Equations 744
13–5 Uniform Flow in Channels 745
Critical Uniform Flow 747
Superposition Method for Nonuniform
Perimeters 748
13–6 Best Hydraulic Cross Sections 751
Rectangular Channels 753
Trapezoidal Channels 753
13–7 Gradually Varied Flow 755
Liquid Surface Profiles in Open Channels, Y(X) 757
Some Representative Surface Profiles 760
Numerical Solution of Surface Profile 762
13–8 Rapidly Varied Flow and the Hydraulic
Jump 765
13–9 Flow Control and Measurement 769
Underflow Gates 770
Overflow Gates 772
Application Spotlight: Bridge Scour 779
Summary 780
References and Suggested Reading 781
Problems 781
Chapter F O U R T E E N
Turbomachinery 793
14–1 Classifications and Terminology 794
14–2 Pumps 796
Pump Performance Curves and Matching
A Pump to a Piping System 797
Pump Cavitation and Net Positive Suction Head 803
Pumps in Series and Parallel 806
Positive-displacement Pumps 809
Dynamic Pumps 812
Centrifugal Pumps 812
Axial Pumps 822
14–3 Pump Scaling Laws 830
Dimensional Analysis 830
Pump Specific Speed 833
Affinity Laws 835
14–4 Turbines 839
Positive-displacement Turbines 840
Dynamic Turbines 840
Impulse Turbines 841
Reaction Turbines 843
Gas and Steam Turbines 853
Wind Turbines 853
14–5 Turbine Scaling Laws 861
Dimensionless Turbine Parameters 861
Turbine Specific Speed 864
Application Spotlight: Rotary Fuel Atomizers 867
Summary 868
References and Suggested Reading 869
Problems 869
Chapter F I F T E E N
Introduction to Computational
Fluid Dynamics 885
15–1 Introduction and Fundamentals 886
Motivation 886
Equations of Motion 886
Solution Procedure 887
Additional Equations of Motion 889contents
Xiii
Grid Generation and Grid Independence 889
Boundary Conditions 894
Practice Makes Perfect 899
15–2 Laminar Cfd Calculations 899
Pipe Flow Entrance Region at Re = 500 899
Flow Around a Circular Cylinder at Re = 150 903
15–3 Turbulent Cfd Calculations 908
Flow Around a Circular Cylinder at Re = 10,000 911
Flow Around a Circular Cylinder at Re = 107 913
Design of the Stator for a Vane-axial Flow Fan 913
15–4 Cfd With Heat Transfer 921
Temperature Rise Through a Cross-flow Heat
Exchanger 921
Cooling of an Array of Integrated Circuit Chips 923
15–5 Compressible Flow Cfd Calculations 928
Compressible Flow Through a Converging–diverging
Nozzle 929
Oblique Shocks Over a Wedge 933
Cfd Methods for Two-phase Flows 934
15–6 Open-channel Flow Cfd Calculations 936
Flow Over a Bump on the Bottom of a Channel 936
Flow Through a Sluice Gate (Hydraulic Jump) 937
Summary 938
Application Spotlight: a Virtual Stomach 939
References and Suggested Reading 940
Problems 940
A P P E N D I X 1
Property Tables and Charts
(Si Units) 947
Table a–1 Molar Mass, Gas Constant, and
Ideal-gas Specific Heats of Some
Substances 948
Table a–2 Boiling and Freezing Point
Properties 949
Table a–3 Properties of Saturated Water 950
Table a–4 Properties of Saturated
Refrigerant-134a 951
Table a–5 Properties of Saturated Ammonia 952
Table a–6 Properties of Saturated Propane 953
Table a–7 Properties of Liquids 954
Table a–8 Properties of Liquid Metals 955
Table a–9 Properties of Air at 1 Atm Pressure 956
Table a–10 Properties of Gases at 1 Atm
Pressure 957
Table a–11 Properties of the Atmosphere at High
Altitude 959
Figure a–12 the Moody Chart for the Friction
Factor for Fully Developed Flow in
Circular Pipes 960
Table a–13 One-dimensional Isentropic
Compressible Flow Functions for an
Ideal Gas With K = 1.4 961
Table a–14 One-dimensional Normal Shock
Functions for an Ideal Gas With
K = 1.4 962
Table a–15 Rayleigh Flow Functions for an Ideal
Gas With K = 1.4 963
Table a–16 Fanno Flow Functions for an Ideal Gas
With K = 1.4 964
A P P E N D I X 2
Property Tables and Charts
(English Units) 965
Table a–1e Molar Mass, Gas Constant, and
Ideal-gas Specific Heats of Some
Substances 966
Table a–2e Boiling and Freezing Point
Properties 967
Table a–3e Properties of Saturated Water 968
Table a–4e Properties of Saturated
Refrigerant-134a 969
Table a–5e Properties of Saturated Ammonia 970
Table a–6e Properties of Saturated Propane 971
Table a–7e Properties of Liquids 972
Table a–8e Properties of Liquid Metals 973
Table a–9e Properties of Air at 1 Atm
Pressure 974
Table a–10e Properties of Gases at 1 Atm
Pressure 975
Table a–11e Properties of the Atmosphere at High
Altitude 977
Glossary 979
Index 993
Conversion Factors 1019
Nomenclature 1021
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