**Success!**

**Error!**

**Information !**

### Rights Contact Login For More Details

### More About This Title Pipe Flow

- English

### English

*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).

- English

### English

**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.

- English

### English

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: Time-Step Integration 67

6.4.1 Upright Cylindrical Vessel Drain Problem 67

6.4.2 Direct Solution 67

6.4.3 Time-Step 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 All-Regime 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 Sharp-Edged 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 Sharp-Edged Orifice 92

9.4.2 Round-Edged Orifice 93

9.4.3 Thick-Edged Orifice 93

9.4.4 Beveled Orifice 93

References 99

Further Reading 99

**10 CONTRACTIONS 101**

10.1 Flow Model 101

10.2 Sharp-Edged 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 Two-Stage 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 Sharp-Edged Orifi ce 132

12.3.2 Round-Edged Orifi ce 133

12.3.3 Thick-Edged Orifi ce 133

12.3.4 Bevel-Edged Orifi ce 133

12.4 Discharge from a Smooth Nozzle 134

13 ORIFICES 139

13.1 Generalized Flow Model 139

13.2 Sharp-Edged 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 Round-Edged 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 Bevel-Edged 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 Thick-Edged 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 Quarter-Turn Valves 207

18.2.1 Ball Valve 208

18.2.2 Butterfl y Valve 208

18.2.3 Plug Valve 208

18.3 Self-Actuated 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 FLOW-INDUCED 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

- English

### English

“This book should be valuable as a text for engineering students and as a reference for engineers who design, operate, and troubleshoot piping systems.” (*Chemical Engineering Progress*, 1 August 2012)