Pipe Flow: A Practical and Comprehensive GuideISBN: 9780470901021
312 pages
May 2012

Pipe Flow provides the information required to design and analyze the piping systems needed to support a broad range of industrial operations, distribution systems, and power plants. Throughout the book, the authors demonstrate how to accurately predict and manage pressure loss while working with a variety of piping systems and piping components.
The book draws together and reviews the growing body of experimental and theoretical research, including important loss coefficient data for a wide selection of piping components. Experimental test data and published formulas are examined, integrated and organized into broadly applicable equations. The results are also presented in straightforward tables and diagrams.
Sample problems and their solution are provided throughout the book, demonstrating how core concepts are applied in practice. In addition, references and further reading sections enable the readers to explore all the topics in greater depth.
With its clear explanations, Pipe Flow is recommended as a textbook for engineering students and as a reference for professional engineers who need to design, operate, and troubleshoot piping systems. The book employs the English gravitational system as well as the International System (or SI).
PREFACE xv
NOMENCLATURE xvii
Abbreviation and Definition xix
PART I METHODOLOGY 1
Prologue 1
1 FUNDAMENTALS 3
1.1 Systems of Units 3
1.2 Fluid Properties 4
1.2.1 Pressure 4
1.2.2 Density 5
1.2.3 Velocity 5
1.2.4 Energy 5
1.2.5 Viscosity 5
1.2.6 Temperature 5
1.2.7 Heat 6
1.3 Important Dimensionless Ratios 6
1.3.1 Reynolds Number 6
1.3.2 Relative Roughness 6
1.3.3 Loss Coeffi cient 7
1.3.4 Mach Number 7
1.3.5 Froude Number 7
1.3.6 Reduced Pressure 7
1.3.7 Reduced Temperature 7
1.4 Equations of State 7
1.4.1 Equation of State of Liquids 7
1.4.2 Equation of State of Gases 8
1.5 Fluid Velocity 8
1.6 Flow Regimes 8
References 12
Further Reading 12
2 CONSERVATION EQUATIONS 13
2.1 Conservation of Mass 13
2.2 Conservation of Momentum 13
2.3 The Momentum Flux Correction Factor 14
2.4 Conservation of Energy 16
2.4.1 Potential Energy 16
2.4.2 Pressure Energy 17
2.4.3 Kinetic Energy 17
2.4.4 Heat Energy 17
2.4.5 Mechanical Work Energy 18
2.5 General Energy Equation 18
2.6 Head Loss 18
2.7 The Kinetic Energy Correction Factor 19
2.8 Conventional Head Loss 20
2.9 Grade Lines 20
References 21
Further Reading 21
3 INCOMPRESSIBLE FLOW 23
3.1 Conventional Head Loss 23
3.2 Sources of Head Loss 23
3.2.1 Surface Friction Loss 24
3.2.1.1 Laminar Flow 24
3.2.1.2 Turbulent Flow 24
3.2.1.3 Reynolds Number 25
3.2.1.4 Friction Factors 25
3.2.2 Induced Turbulence 28
3.2.3 Summing Loss Coeffi cients 29
References 29
Further Reading 30
4 COMPRESSIBLE FLOW 31
4.1 Problem Solution Methods 31
4.2 Approximate Compressible Flow Using Incompressible Flow Equations 32
4.2.1 Using Inlet or Outlet Properties 32
4.2.2 Using Average of Inlet and Outlet Properties 33
4.2.2.1 Simple Average Properties 33
4.2.2.2 Comprehensive Average Properties 34
4.2.3 Using Expansion Factors 34
4.3 Adiabatic Compressible Flow with Friction: Ideal Equation 37
4.3.1 Using Mach Number as a Parameter 37
4.3.1.1 Solution when Static Pressure and Static Temperature Are Known 38
4.3.1.2 Solution when Static Pressure and Total Temperature Are Known 39
4.3.1.3 Solution when Total Pressure and Total Temperature Are Known 40
4.3.1.4 Solution when Total Pressure and Static Temperature Are Known 40
4.3.1.5 Treating Changes in Area 40
4.3.2 Using Static Pressure and Temperature as Parameters 41
4.4 Isothermal Compressible Flow with Friction: Ideal Equation 42
4.5 Example Problem: Compressible Flow through Pipe 43
References 47
Further Reading 47
5 NETWORK ANALYSIS 49
5.1 Coupling Effects 49
5.2 Series Flow 50
5.3 Parallel Flow 50
5.4 Branching Flow 51
5.5 Example Problem: Ring Sparger 51
5.5.1 Ground Rules and Assumptions 52
5.5.2 Input Parameters 52
5.5.3 Initial Calculations 53
5.5.4 Network Equations 53
5.5.4.1 Continuity Equations 53
5.5.4.2 Energy Equations 53
5.5.5 Solution 54
5.6 Example Problem: Core Spray System 54
5.6.1 New, Clean Steel Pipe 55
5.6.1.1 Ground Rules and Assumptions 55
5.6.1.2 Input Parameters 56
5.6.1.3 Initial Calculations 57
5.6.1.4 Adjusted Parameters 57
5.6.1.5 Network Flow Equations 57
5.6.1.6 Solution 58
5.6.2 Moderately Corroded Steel Pipe 58
5.6.2.1 Ground Rules and Assumptions 58
5.6.2.2 Input Parameters 58
5.6.2.3 Adjusted Parameters 59
5.6.2.4 Network Flow Equations 59
5.6.2.5 Solution 59
References 60
Further Reading 60
6 TRANSIENT ANALYSIS 61
6.1 Methodology 61
6.2 Example Problem: Vessel Drain Times 62
6.2.1 Upright Cylindrical Vessel 62
6.2.2 Spherical Vessel 63
6.2.3 Upright Cylindrical Vessel with Elliptical Heads 64
6.3 Example Problem: Positive Displacement Pump 65
6.3.1 No Heat Transfer 65
6.3.2 Heat Transfer 66
6.4 Example Problem: TimeStep Integration 67
6.4.1 Upright Cylindrical Vessel Drain Problem 67
6.4.2 Direct Solution 67
6.4.3 TimeStep Solution 67
References 68
Further Reading 68
7 UNCERTAINTY 69
7.1 Error Sources 69
7.2 Pressure Drop Uncertainty 69
7.3 Flow Rate Uncertainty 71
7.4 Example Problem: Pressure Drop 71
7.4.1 Input Data 71
7.4.2 Solution 72
7.5 Example Problem: Flow Rate 72
7.5.1 Input Data 72
7.5.2 Solution 73
PART II LOSS COEFFICIENTS 75
Prologue 75
8 SURFACE FRICTION 77
8.1 Friction Factor 77
8.1.1 Laminar Flow Region 77
8.1.2 Critical Zone 77
8.1.3 Turbulent Flow Region 78
8.1.3.1 Smooth Pipes 78
8.1.3.2 Rough Pipes 78
8.2 The Colebrook–White Equation 78
8.3 The Moody Chart 79
8.4 Explicit Friction Factor Formulations 79
8.4.1 Moody’s Approximate Formula 79
8.4.2 Wood’s Approximate Formula 79
8.4.3 The Churchill 1973 and Swamee and Jain Formulas 79
8.4.4 Chen’s Formula 79
8.4.5 Shacham’s Formula 80
8.4.6 Barr’s Formula 80
8.4.7 Haaland’s Formulas 80
8.4.8 Manadilli’s Formula 80
8.4.9 Romeo’s Formula 80
8.4.10 Evaluation of Explicit Alternatives to the Colebrook–White Equation 80
8.5 AllRegime Friction Factor Formulas 81
8.5.1 Churchill’s 1977 Formula 81
8.5.2 Modifi cations to Churchill’s 1977 Formula 81
8.6 Surface Roughness 82
8.6.1 New, Clean Pipe 82
8.6.2 The Relationship between Absolute Roughness and Friction Factor 82
8.6.3 Inherent Margin 84
8.6.4 Loss of Flow Area 84
8.6.5 Machined Surfaces 84
8.7 Noncircular Passages 85
References 87
Further Reading 87
9 ENTRANCES 89
9.1 SharpEdged Entrance 89
9.1.1 Flush Mounted 89
9.1.2 Mounted at a Distance 90
9.1.3 Mounted at an Angle 90
9.2 Rounded Entrance 91
9.3 Beveled Entrance 91
9.4 Entrance through an Orifice 92
9.4.1 SharpEdged Orifice 92
9.4.2 RoundEdged Orifice 93
9.4.3 ThickEdged Orifice 93
9.4.4 Beveled Orifice 93
References 99
Further Reading 99
10 CONTRACTIONS 101
10.1 Flow Model 101
10.2 SharpEdged Contraction 102
10.3 Rounded Contraction 103
10.4 Conical Contraction 104
10.4.1 Surface Friction Loss 105
10.4.2 Local Loss 105
10.5 Beveled Contraction 106
10.6 Smooth Contraction 107
10.7 Pipe Reducer: Contracting 107
References 112
Further Reading 112
11 EXPANSIONS 113
11.1 Sudden Expansion 113
11.2 Straight Conical Diffuser 114
11.3 Multistage Conical Diffusers 117
11.3.1 Stepped Conical Diffuser 117
11.3.2 TwoStage Conical Diffuser 118
11.4 Curved Wall Diffuser 120
11.5 Pipe Reducer: Expanding 121
References 128
Further Reading 128
12 EXITS 131
12.1 Discharge from a Straight Pipe 131
12.2 Discharge from a Conical Diffuser 132
12.3 Discharge from an Orifi ce 132
12.3.1 SharpEdged Orifi ce 132
12.3.2 RoundEdged Orifi ce 133
12.3.3 ThickEdged Orifi ce 133
12.3.4 BevelEdged Orifi ce 133
12.4 Discharge from a Smooth Nozzle 134
13 ORIFICES 139
13.1 Generalized Flow Model 139
13.2 SharpEdged Orifi ce 140
13.2.1 In a Straight Pipe 140
13.2.2 In a Transition Section 141
13.2.3 In a Wall 141
13.3 RoundEdged Orifi ce 142
13.3.1 In a Straight Pipe 143
13.3.2 In a Transition Section 143
13.3.3 In a Wall 144
13.4 BevelEdged Orifice 145
13.4.1 In a Straight Pipe 145
13.4.2 In a Transition Section 145
13.4.3 In a Wall 146
13.5 ThickEdged Orifice 146
13.5.1 In a Straight Pipe 146
13.5.2 In a Transition Section 148
13.5.3 In a Wall 148
13.6 Multihole Orifices 149
13.7 Noncircular Orifices 149
References 154
Further Reading 154
14 FLOW METERS 157
14.1 Flow Nozzle 157
14.2 Venturi Tube 158
14.3 Nozzle/Venturi 159
References 161
Further Reading 161
15 BENDS 163
15.1 Elbows and Pipe Bends 163
15.2 Coils 166
15.2.1 Constant Pitch Helix 167
15.2.2 Constant Pitch Spiral 167
15.3 Miter Bends 168
15.4 Coupled Bends 169
15.5 Bend Economy 169
References 174
Further Reading 174
16 TEES 177
16.1 Diverging Tees 178
16.1.1 Flow through Run 178
16.1.2 Flow through Branch 179
16.1.3 Flow from Branch 182
16.2 Converging Tees 182
16.2.1 Flow through Run 182
16.2.2 Flow through Branch 184
16.2.3 Flow into Branch 185
References 200
Further Reading 200
17 PIPE JOINTS 201
17.1 Weld Protrusion 201
17.2 Backing Rings 202
17.3 Misalignment 203
17.3.1 Misaligned Pipe Joint 203
17.3.2 Misaligned Gasket 203
18 VALVES 205
18.1 Multiturn Valves 205
18.1.1 Diaphragm Valve 205
18.1.2 Gate Valve 206
18.1.3 Globe Valve 206
18.1.4 Pinch Valve 207
18.1.5 Needle Valve 207
18.2 QuarterTurn Valves 207
18.2.1 Ball Valve 208
18.2.2 Butterfl y Valve 208
18.2.3 Plug Valve 208
18.3 SelfActuated Valves 209
18.3.1 Check Valve 209
18.3.2 Relief Valve 210
18.4 Control Valves 210
18.5 Valve Loss Coefficients 211
References 211
Further Reading 212
19 THREADED FITTINGS 213
19.1 Reducers: Contracting 213
19.2 Reducers: Expanding 213
19.3 Elbows 214
19.4 Tees 214
19.5 Couplings 214
19.6 Valves 215
Reference 215
PART III FLOW PHENOMENA 217
Prologue 217
20 CAVITATION 219
20.1 The Nature of Cavitation 219
20.2 Pipeline Design 220
20.3 Net Positive Suction Head 220
20.4 Example Problem: Core Spray Pump 221
20.4.1 New, Clean Steel Pipe 222
20.4.1.1 Input Parameters 222
20.4.1.2 Solution 222
20.4.1.3 Results 222
20.4.2 Moderately Corroded Steel Pipe 222
20.4.2.1 Input Parameters 223
20.4.2.2 Solution 223
20.4.2.3 Results 224
Reference 224
Further Reading 224
21 FLOWINDUCED VIBRATION 225
21.1 Steady Internal Flow 225
21.2 Steady External Flow 225
21.3 Water Hammer 226
21.4 Column Separation 227
References 228
Further Reading 228
22 TEMPERATURE RISE 231
22.1 Reactor Heat Balance 232
22.2 Vessel Heat Up 232
22.3 Pumping System Temperature 232
References 233
23 FLOW TO RUN FULL 235
23.1 Open Flow 235
23.2 Full Flow 237
23.3 Submerged Flow 237
23.4 Reactor Application 239
Further Reading 240
APPENDIX A PHYSICAL PROPERTIES OF WATER AT 1 ATMOSPHERE 241
APPENDIX B PIPE SIZE DATA 245
B.1 Commercial Pipe Data 246
APPENDIX C PHYSICAL CONSTANTS AND UNIT CONVERSIONS 253
C.1 Important Physical Constants 253
C.2 Unit Conversions 254
APPENDIX D COMPRESSIBILITY FACTOR EQUATIONS 263
D.1 The Redlich–Kwong Equation 263
D.2 The Lee–Kesler Equation 264
D.3 Important Constants for Selected Gases 266
APPENDIX E ADIABATIC COMPRESSIBLE FLOW WITH FRICTION, USING MACH NUMBER AS A PARAMETER 269
E.1 Solution when Static Pressure and Static Temperature Are Known 269
E.2 Solution when Static Pressure and Total Temperature Are Known 272
E.3 Solution when Total Pressure and Total Temperature Are Known 272
E.4 Solution when Total Pressure and Static Temperature Are Known 273
References 274
APPENDIX F VELOCITY PROFILE EQUATIONS 275
F.1 Benedict Velocity Profile Derivation 275
F.2 Street, Watters, and Vennard Velocity Profile Derivation 277
References 278
INDEX 279
Donald C. Rennels has been working in the Nuclear Energy Division of GE since 1971. His work has included developing network flow models of reactor vessel internals and various nuclear steam supply systems as well as preparing technical design procedures. In his time at GE, he has won six General Manager Awards.
Hobart M. Hudson has been working in the Test Division of Aerojet since 1977. As a senior engineering specialist, he performed analyses of existing rocket test equipment and designed new equipment. As a mechanical engineering consultant, he has worked on various rocket test system designs and analyses, including the Mars Lander Engine.
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