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1. Introduction to Momentum Transfer 1
1.1 Fluids and the Continuum 1
1.2 Properties at a Point 2
1.3 Point-to-Point Variation of Properties in a Fluid 5
1.4 Units 8
1.5 Compressibility 10
1.6 Surface Tension 11
2. Fluid Statics 16
2.1 Pressure Variation in a Static Fluid 16
2.2 Uniform Rectilinear Acceleration 19
2.3 Forces on Submerged Surfaces 20
2.4 Buoyancy 23
2.5 Closure 25
3. Description of a Fluid in Motion 29
3.1 Fundamental Physical Laws 29
3.2 Fluid-Flow Fields: Lagrangian and Eulerian Representations 29
3.3 Steady and Unsteady Flows 30
3.4 Streamlines 31
3.5 Systems and Control Volumes 32
4. Conservation of Mass: Control-Volume Approach 34
4.1 Integral Relation 34
4.2 Specific Forms of the Integral Expression 35
4.3 Closure 40
5. Newton’s Second Law of Motion: Control-Volume Approach 44
5.1 Integral Relation for Linear Momentum 44
5.2 Applications of the Integral Expression for Linear Momentum 47
5.3 Integral Relation for Moment of Momentum 53
5.4 Applications to Pumps and Turbines 55
5.5 Closure 59
6. Conservation of Energy: Control-Volume Approach 65
6.1 Integral Relation for the Conservation of Energy 65
6.2 Applications of the Integral Expression 71
6.3 The Bernoulli Equation 74
6.4 Closure 79
7. Shear Stress in Laminar Flow 85
7.1 Newton’s Viscosity Relation 85
7.2 Non-Newtonian Fluids 86
7.3 Viscosity 88
7.4 Shear Stress in Multidimensional Laminar Flows of a Newtonian Fluid 93
7.5 Closure 97
8. Analysis of a Differential Fluid Element in Laminar Flow 99
8.1 Fully Developed Laminar Flow in a Circular Conduit of Constant Cross Section 99
8.2 Laminar Flow of a Newtonian Fluid Down an Inclined-Plane Surface 102
8.3 Closure 104
9. Differential Equations of Fluid Flow 107
9.1 The Differential Continuity Equation 107
9.2 Navier–Stokes Equations 110
9.3 Bernoulli’s Equation 118
9.4 Spherical Coordinate Forms of the Navier–Stokes Equations 119
9.5 Closure 121
10. Inviscid Fluid Flow 124
10.1 Fluid Rotation at a Point 124
10.2 The Stream Function 127
10.3 Inviscid, Irrotational Flow about an Infinite Cylinder 129
10.4 Irrotational Flow, the Velocity Potential 131
10.5 Total Head in Irrotational Flow 134
10.6 Utilization of Potential Flow 135
10.7 Potential Flow Analysis—Simple Plane Flow Cases 136
10.8 Potential Flow Analysis—Superposition 137
10.9 Closure 139
11. Dimensional Analysis and Similitude 141
11.1 Dimensions 141
11.2 Dimensional Analysis of Governing Differential Equations 142
11.3 The Buckingham Method 144
11.4 Geometric, Kinematic, and Dynamic Similarity 147
11.5 Model Theory 148
11.6 Closure 150
12. Viscous Flow 154
12.1 Reynolds’s Experiment 154
12.2 Drag 155
12.3 The Boundary-Layer Concept 160
12.4 The Boundary-Layer Equations 161
12.5 Blasius’s Solution for the Laminar Boundary Layer on a Flat Plate 163
12.6 Flow with a Pressure Gradient 167
12.7 von Kármán Momentum Integral Analysis 169
12.8 Description of Turbulence 172
12.9 Turbulent Shearing Stresses 174
12.10 The Mixing-Length Hypothesis 175
12.11 Velocity Distribution from the Mixing-Length Theory 177
12.12 The Universal Velocity Distribution 178
12.13 Further Empirical Relations for Turbulent Flow 179
12.14 The Turbulent Boundary Layer on a Flat Plate 180
12.15 Factors Affecting the Transition from Laminar to Turbulent Flow 182
12.16 Closure 183
13. Flow in Closed Conduits 186
13.1 Dimensional Analysis of Conduit Flow 186
13.2 Friction Factors for Fully Developed Laminar, Turbulent, and Transition Flow in Circular Conduits 188
13.3 Friction Factor and Head-Loss Determination for Pipe Flow 191
13.4 Pipe-Flow Analysis 195
13.5 Friction Factors for Flow in the Entrance to a Circular Conduit 198
13.6 Closure 201
14. Fluid Machinery 204
14.1 Centrifugal Pumps 205
14.2 Scaling Laws for Pumps and Fans 213
14.3 Axial- and Mixed-Flow Pump Configurations 216
14.4 Turbines 216
14.5 Closure 217
15. Fundamentals of Heat Transfer 220
15.1 Conduction 220
15.2 Thermal Conductivity 221
15.3 Convection 226
15.4 Radiation 228
15.5 Combined Mechanisms of Heat Transfer 228
15.6 Closure 232
16. Differential Equations of Heat Transfer 236
16.1 The General Differential Equation for Energy Transfer 236
16.2 Special Forms of the Differential Energy Equation 239
16.3 Commonly Encountered Boundary Conditions 240
16.4 Closure 244
17. Steady-State Conduction 247
17.1 One-Dimensional Conduction 247
17.2 One-Dimensional Conduction with Internal Generation of Energy 253
17.3 Heat Transfer from Extended Surfaces 256
17.4 Two- and Three-Dimensional Systems 263
17.5 Closure 269
18. Unsteady-State Conduction 277
18.1 Analytical Solutions 277
18.2 Temperature-Time Charts for Simple Geometric Shapes 286
18.3 Numerical Methods for Transient Conduction Analysis 288
18.4 An Integral Method for One-Dimensional Unsteady Conduction 291
18.5 Closure 295
19. Convective Heat Transfer 301
19.1 Fundamental Considerations in Convective Heat Transfer 301
19.2 Significant Parameters in Convective Heat Transfer 302
19.3 Dimensional Analysis of Convective Energy Transfer 303
19.4 Exact Analysis of the Laminar Boundary Layer 306
19.5 Approximate Integral Analysis of the Thermal Boundary Layer 310
19.6 Energy- and Momentum-Transfer Analogies 312
19.7 Turbulent Flow Considerations 314
19.8 Closure 320
20. Convective Heat-Transfer Correlations 324
20.1 Natural Convection 324
20.2 Forced Convection for Internal Flow 332
20.3 Forced Convection for External Flow 338
20.4 Closure 345
21. Boiling and Condensation 352
21.1 Boiling 352
21.2 Condensation 357
21.3 Closure 363
22. Heat-Transfer Equipment 365
22.1 Types of Heat Exchangers 365
22.2 Single-Pass Heat-Exchanger Analysis: The Log-Mean Temperature Difference 368
22.3 Crossflow and Shell-and-Tube Heat-Exchanger Analysis 372
22.4 The Number-of-Transfer-Units (NTU) Method of Heat-Exchanger Analysis and Design 376
22.5 Additional Considerations in Heat-Exchanger Design 383
22.6 Closure 385
23. Radiation Heat Transfer 390
23.1 Nature of Radiation 390
23.2 Thermal Radiation 391
23.3 The Intensity of Radiation 393
23.4 Planck’s Law of Radiation 394
23.5 Stefan–Boltzmann Law 398
23.6 Emissivity and Absorptivity of Solid Surfaces 400
23.7 Radiant Heat Transfer Between Black Bodies 405
23.8 Radiant Exchange in Black Enclosures 412
23.9 Radiant Exchange with Reradiating Surfaces Present 413
23.10 Radiant Heat Transfer Between Gray Surfaces 414
23.11 Radiation from Gases 421
23.12 The Radiation Heat-Transfer Coefficient 423
23.13 Closure 426
24. Fundamentals of Mass Transfer 431
24.1 Molecular Mass Transfer 432
24.2 The Diffusion Coefficient 441
24.3 Convective Mass Transfer 461
24.4 Closure 462
25. Differential Equations of Mass Transfer 467
25.1 The Differential Equation for Mass Transfer 467
25.2 Special Forms of the Differential Mass-Transfer Equation 470
25.3 Commonly Encountered Boundary Conditions 472
25.4 Steps for Modeling Processes Involving Molecular Diffusion 475
25.5 Closure 484
26. Steady-State Molecular Diffusion 489
26.1 One-Dimensional Mass Transfer Independent of Chemical Reaction 489
26.2 One-Dimensional Systems Associated with Chemical Reaction 500
26.3 Two- and Three-Dimensional Systems 510
26.4 Simultaneous Momentum, Heat, and Mass Transfer 513
26.5 Closure 520
27. Unsteady-State Molecular Diffusion 533
27.1 Unsteady-State Diffusion and Fick’s Second Law 533
27.2 Transient Diffusion in a Semi-Infinite Medium 534
27.3 Transient Diffusion in a Finite-Dimensional Medium under Conditions of Negligible Surface Resistance 538
27.4 Concentration-Time Charts for Simple Geometric Shapes 546
27.5 Closure 550
28. Convective Mass Transfer 556
28.1 Fundamental Considerations in Convective Mass Transfer 556
28.2 Significant Parameters in Convective Mass Transfer 559
28.3 Dimensional Analysis of Convective Mass Transfer 562
28.4 Exact Analysis of the Laminar Concentration Boundary Layer 564
28.5 Approximate Analysis of the Concentration Boundary Layer 572
28.6 Mass-, Energy-, and Momentum-Transfer Analogies 577
28.7 Models for Convective Mass-Transfer Coefficients 584
28.8 Closure 586
29. Convective Mass Transfer Between Phases 592
29.1 Equilibrium 592
29.2 Two-Resistance Theory 595
29.3 Closure 610
30. Convective Mass-Transfer Correlations 617
30.1 Mass Transfer to Plates, Spheres, and Cylinders 618
30.2 Mass Transfer Involving Flow Through Pipes 626
30.3 Mass Transfer in Wetted-Wall Columns 627
30.4 Mass Transfer in Packed and Fluidized Beds 630
30.5 Gas–Liquid Mass Transfer in Bubble Columns and Stirred Tanks 631
30.6 Capacity Coefficients for Packed Towers 634
30.7 Steps for Modeling Mass-Transfer Processes Involving Convection 635
30.8 Closure 644
31. Mass-Transfer Equipment 655
31.1 Types of Mass-Transfer Equipment 655
31.2 Gas–Liquid Mass-Transfer Operations in Well-Mixed Tanks 657
31.3 Mass Balances for Continuous-Contact Towers: Operating-Line Equations 662
31.4 Enthalpy Balances for Continuous-Contacts Towers 670
31.5 Mass-Transfer Capacity Coefficients 671
31.6 Continuous-Contact Equipment Analysis 672
31.7 Closure 686
Nomenclature 693
Appendixes
A. Transformations of the Operators ∇ and ∇^{2} to Cylindrical Coordinates 700
B. Summary of Differential Vector Operations in Various Coordinate Systems 703
C. Symmetry of the Stress Tensor 706
D. The Viscous Contribution to the Normal Stress 707
E. The Navier–Stokes Equations for Constant p and μ in Cartesian, Cylindrical, and Spherical Coordinates 709
F. Charts for Solution of Unsteady Transport Problems 711
G. Properties of the Standard Atmosphere 724
H. Physical Properties of Solids 727
I. Physical Properties of Gases and Liquids 730
J. Mass-Transfer Diffusion Coefficients in Binary Systems 743
K. Lennard–Jones Constants 746
L. The Error Function 749
M. Standard Pipe Sizes 750
N. Standard Tubing Gages 752
Index 754
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