# Pipe Flow

## A Practical and Comprehensive Guide

2. Edition May 2022

384 Pages, Hardcover*Wiley & Sons Ltd*

**978-1-119-75643-9**

Pipe Flow

Provides detailed coverage of hydraulic analysis of piping systems, revised and updated throughout

Pipe Flow: A Practical and Comprehensive Guide provides the information required to design and analyze piping systems for distribution systems, power plants, and other industrial operations. Divided into three parts, this authoritative resource describes the methodology for solving pipe flow problems, presents loss coefficient data for a wide range of piping components, and examines pressure drop, cavitation, flow-induced vibration, and other flow phenomena that affect the performance of piping systems. Throughout the book, sample problems and worked solutions illustrate the application of core concepts and techniques.

The second edition features revised and expanded information throughout, including an entirely new chapter that presents a mixing section flow model for accurately predicting jet pump performance. This edition includes additional examples, supplemental problems, and a new appendix of the speed of sound in water. With clear explanations, expert guidance, and precise hydraulic computations, this classic reference text remains required reading for anyone working to increase the quality and efficiency of modern piping systems.

* Discusses the fundamental physical properties of fluids and the nature of fluid flow

* Demonstrates the accurate prediction and management of pressure loss for a variety of piping components and piping systems

* Reviews theoretical research on fluid flow in piping and its components

* Presents important loss coefficient data with straightforward tables, diagrams, and equations

* Includes full references, further reading sections, and numerous example problems with solution

Pipe Flow: A Practical and Comprehensive Guide, Second Edition is an excellent textbook for engineering students, and an invaluable reference for professional engineers engaged in the design, operation, and troubleshooting of piping systems.

PREFACE TO THE SECOND EDITION

NOMENCLATURE

Abbreviation and Definition

PART I METHODOLOGY

Prologue

1 FUNDAMENTALS

1.1 Systems of Units

1.2 Fluid Properties

1.2.1 Pressure

1.2.2 Temperature

1.2.3 Density

1.2.4 Viscosity

1.2.5 Gas Constant

1.2.6 Velocity

1.2.7 Energy

1.2.8 Heat

1.2.9 Enthalpy

1.3 Important Dimensionless Ratios

1.3.1 Reynolds Number

1.3.2 Relative Roughness

1.3.3 Loss Coefficient

1.3.4 Mach Number

1.3.5 Froude Number

1.3.6 Reduced Pressure

1.3.7 Reduced Temperature

1.3.8 Ratio of Specific Heats

1.4 Equations of State

1.4.1 Equation of State of Liquids

1.4.2 Equation of State of Gases

1.4.3 Two-Phase Mixtures

1.5 Fluid Velocity

1.6 Flow Regimes

1.7 Similarity

1.7.1 The Principle of Similarity

1.7.2 Limitations

1.8 Kinematics of Fluid Flow

1.8.1 Path Lines and Streamlines

1.8.2 One-Dimensional Method of Flow Analysis

References

Further Reading

2 CONSERVATION EQUATIONS

2.1 Conservation of Mass

2.2 Conservation of Momentum

2.3 The Momentum Flux Correction Factor

2.4 Conservation of Energy

2.4.1 Potential Energy

2.4.2 Pressure Energy

2.4.3 Kinetic Energy

2.4.4 Heat Energy

2.4.5 Mechanical Work Energy

2.5 Generalized Energy Equation

2.6 Head Loss

2.7 The Kinetic Energy Correction Factor

2.8 Conventional Head Loss

2.9 Grade Lines

References

Further Reading

3 INCOMPRESSIBLE FLOW

3.1 Conventional Head Loss

3.2 Sources of Head Loss

3.2.1 Surface Friction Loss

3.2.1.1 Laminar Flow

3.2.1.2 Turbulent Flow

3.2.1.3 Reynolds Number

3.2.1.4 Friction Factor

3.2.2 Induced Turbulence

3.2.3 Summing Loss Coefficients

References

Further Reading

4 COMPRESSIBLE FLOW

4.1 Introduction

4.2 Problem Solution Methods

4.3 Approximate Compressible Flow Using Incompressible Flow Equations

4.3.1 Using Inlet or Outlet Properties

4.3.2 Using Average of Inlet and Outlet Properties

4.3.2.1 Simple Average Properties

4.3.2.2 Comprehensive Average Properties

4.3.3 Using Expansion Factors

4.4 Adiabatic Compressible Flow with Friction: Ideal Equations

4.4.1 Shapiro's Adiabatic Flow Equation

4.4.1.1 Solution when Static Pressure and Static Temperature Are Known

4.4.1.2 Solution when Static Pressure and Total Temperature Are Known

4.4.1.3 Solution when Total Pressure and Total Temperature Are Known

4.4.1.4 Solution when Total Pressure and Static Temperature Are Known

4.4.2 Turton's Adiabatic Flow Equation

4.3.3 Binder's Adiabatic Flow Equation

4.5 Isothermal Compressible Flow with Friction: Ideal Equation

4.6 Isentropic Flow: Treating Changes in Flow Area

4.7 Pressure Drop in Valves

4.8 Two-Phase Flow

4.9 Example Problems: Adiabatic Flow with Friction by Iteration

4.9.1 Solve for p2 and t2 - K, p1, t1 and W are Known

4.9.1.1 Solve Using Expansion Factors

4.9.1.2 Solve Using Shapiro's Equation

4.9.1.3 Solve Using Binder's Equation

4.9.1.4 Solve Using Turton's Equation

4.9.2 Solve for W and t2 - K, p1, t1 and p2 are Known

4.9.2.1 Solve Using Expansion Factors

4.9.2.2 Solve Using Shapiro's Equation

4.9.2.3 Solve Using Binder's Equation

4.9.2.4 Solve Using Turton's Equation

4.9.3 Observations

4.10 Example Problem: Natural Gas Pipeline

4.10.1 Ground Rules and Assumptions

4.10.2 Input Data

4.10.3 Initial Calculations

4.10.4 Solution

4.10.5 Comparison with Crane's Solutions

References

Further Reading

5 NETWORK ANALYSIS

5.1 Coupling Effects

5.2 Series Flow

5.3 Parallel Flow

5.4 Branching Flow

5.5 Example Problem: Ring Sparger

5.5.1 Ground Rules and Assumptions

5.5.2 Input Parameters

5.5.3 Initial Calculations

5.5.4 Network Flow Equations

5.5.4.1 Continuity Equations

5.5.4.2 Energy Equations

5.5.5 Solution

5.6 Example Problem: Core Spray System

5.6.1 New, Clean Steel Pipe

5.6.1.1 Ground Rules and Assumptions

5.6.1.2 Input Parameters

5.6.1.3 Initial Calculations

5.6.1.4 Adjusted Parameters

5.6.1.5 Network Flow Equations

5.6.1.6 Solution

5.6.2 Moderately Corroded Steel Pipe

5.6.2.1 Ground Rules and Assumptions

5.6.2.2 Input Parameters

5.6.2.3 Adjusted Parameters

5.6.2.4 Network Flow Equations

5.6.2.5 Solution

5.7 Example Problem: Steam Line Pressure Drop

5.7.1 Ground Rules and Assumptions

5.7.2 Input Data

5.7.3 Initial Calculations

5.7.4 Loss Coefficient Calculations

5.7.5 Individual Loss Coefficients

5.7.2 Series Loss Coefficients

5.7.3 Steam Dome to Steam Drum Pressure Drop

5.7.4 Steam Drum to Stop Valves Pressure Drop

5.7.5 Predicted Pressure at Stop Valves

References

Further Reading

6 TRANSIENT ANALYSIS

6.1 Methodology

6.2 Example Problem: Vessel Drain Times

6.2.1 Upright Cylindrical Vessel with Flat Heads

6.2.2 Spherical Vessel

6.2.3 Upright Cylindrical Vessel with Elliptical Heads

6.3 Example Problem: Positive Displacement Pump

6.3.1 No Heat Transfer

6.3.2 Heat Transfer

6.4 Example Problem: Time Step Integration

6.4.1 Upright Cylindrical Vessel Drain

6.4.1.1 Direct Solution

6.4.1.2 Time-Step Solution

References

Further Reading

7 UNCERTAINTY

7.1 Error Sources

7.2 Pressure Drop Uncertainty

7.3 Flow Rate Uncertainty

7.4 Example Problem: Pressure Drop

7.3.1 Input Data

7.3.2 Solution

7.5 Example Problem: Flow Rate

7.5.1 Input Data

7.5.2 Solution

PART II LOSS COEFFICIENTS

Prologue

8 SURFACE FRICTION

8.1 Friction Factor

8.1.1 Laminar Flow Region

8.1.2 Critical Zone

8.1.3 Turbulent Flow Region

8.1.3.1 Smooth Pipes

8.1.3.2 Rough Pipes

8.2 The Colebrook-White Equation

8.3 The Moody Chart

8.4 Explicit Friction Factor Formulations

8.4.1 Moody's Approximate Formula

8.4.2 Wood's Approximate Formula

8.4.3 The Churchill 1973 and Swamee and Jain Formulas

8.4.4 Chen's Formula

8.4.5 Shacham's Formula

8.4.6 Barr's Formula

8.4.7 Haaland's Formula

8.4.8 Manadilli's Formula

8.4.9 Romeo's Formula

8.4.10 Evaluation of Explicit Alternatives to the Colebrook-White Equation

8.5 All-Regime Friction Factor Formulas

8.5.1 Churchill's 1977 Formula

8.5.2 Modification to Churchill's 1977 Formula

8.4 Absolute Roughness of Flow Surfaces

8.7 Age and Usage of Pipe

8.7.1 Corrosion and Encrustation

8.7.2 The Relationship between Absolute Roughness and Friction Factor

8.7.3 Inherent Margin

8.8 Noncircular Passages

8.9 Machined Surfaces

References

Further Reading

9 ENTRANCES

9.1 Sharp-Edged Entrance

9.1.1 Flush Mounted

9.1.2 Mounted at a Distance

9.1.3 Mounted at an Angle

9.2 Rounded Entrance

9.3 Beveled Entrance

9.4 Entrance through an Orifice

9.4.1 Sharp-Edged Orifice

9.4.2 Round-Edged Orifice

9.4.2 Thick-Edged Orifice

9.4.4 Beveled Orifice

References

Further Reading

10 CONTRACTIONS

10.1 Flow Model

10.2 Sharp-Edged Contraction

10.3 Rounded Contraction

10.4 Conical Contraction

10.4.1 Surface Friction Loss

10.4.2 Local Loss

10.5 Beveled Contraction

10.6 Smooth Contraction

10.7 Pipe Reducer - Contracting

References

Further Reading

11 EXPANSIONS

11.1 Sudden Expansion

11.2 Straight Conical Diffuser

11.3 Multi-Stage Conical Diffusers

11.3.1 Stepped Conical Diffuser

11.3.2 Two-Stage Conical Diffuser

11.4 Curved Wall Diffuser

11.5 Pipe Reducer - Expanding

References

Further Reading

12 EXITS

12.1 Discharge from a Straight Pipe

12.2 Discharge from a Conical Diffuser

12.3 Discharge from an Orifice

12.3.1 Sharp-Edged

12.3.2 Round-Edged

12.3.3 Thick-Edged

12.3.4 Bevel-Edged

12.4 Discharge from a Smooth Nozzle

13 ORIFICES

13.1 Generalized Flow Model

13.2 Sharp-Edged Orifice

13.2.1 In a Straight Pipe

13.2.2 In a Transition Section

13.2.3 In a Wall

13.3 Round-Edged Orifice

13.3.1 In a Straight Pipe

13.3.2 In a Transition Section

13.3.3 In a Wall

13.4 Bevel-Edged Orifice

13.4.1 In a Straight Pipe

13.4.2 In a Transition Section

13.4.3 In a Wall

13.5 Thick-Edged Orifice

13.5.1 In a Straight Pipe

13.5.2 In a Transition Section

13.5.3 In a Wall

13.6 Multi-hole Orifices

13.7 Non-circular Orifices

References

Further Reading

14 FLOW METERS

14.1 Flow Nozzle

14.2 Venturi Tube

14.3 Nozzle/Venturi

References

Further Reading

15 BENDS

15.1 Overview

15.2 Bend Losses

15.2.1 Smooth-Walled Bends

15.2.2 Welded Elbows and Pipe Bends

15.3 Coils

15.3.1 Constant Pitch Helix

15.3.2 Constant Pitch Spiral

15.4 Miter Bends

15.5 Coupled Bends

15.5 Bend Economy

References

Further Reading

16 TEES

16.1 Overview

16.1,1 Previous Endeavors

16.1.2 Observations

16.2 Diverging Tees

16.2.1 Diverging Flow through Run

16.2.2 Diverging Flow through Branch

16.2.3 Diverging Flow from Branch

16.3 Converging Tees

16.3.1 Converging Flow through Run

16.3.2 Converging Flow through Branch

16.3.3 Converging Flow into Branch

16.4 Full Flow through Run

References

Further Reading

17 PIPE JOINTS

17.1 Weld Protrusion

17.2 Backing Rings

17.3 Misalignment

17.3.1 Misaligned Pipe Joint

17.3.2 Misaligned Gasket

18 VALVES

18.1 Multi-Turn Valves

18.1.1 Diaphragm Valve

18.1.2 Gate Valve

18.1.3 Globe Valve

18.1.4 Pinch Valve

18.1.5 Needle Valve

18.2 Quarter-Turn Valves

18.2.1 Ball Valve

18.2.2 Butterfly Valve

18.2.3 Plug Valve

18.3 Self-Actuated Valves

18.3.1 Check Valve

18.3.2 Pressure Relief Valve

18.4 Control Valves

18.5 Valve Loss Coefficients

References

Further Reading

19 THREADED FITTINGS

19.1 Reducers-Contracting

19.2 Reducers-Expanding

19.3 Elbows

19.4 Tees

19.5 Couplings

References

Further Reading

PART III FLOW PHENOMENA

Prologue

20 CAVITATION

20.1 The Nature of Cavitation

20.2 Pipeline Design

20.3 Net Positive Suction Head

20.4 Example Problem: Core Spray Pump NPSH

20.4.1 New, Clean Steel Pipe

20.4.1.1 Input Parameters

20.4.1.2 Solution

20.4.1.3 Results

20.4.2 Moderately Corroded Steel Pipe

20.4.2.1 Input Parameters

20.4.2.2 Solution

20.4.2.3 Results

20.5 Example Problem: Pipe Entrance Cavitation

20.5.1 Input Parameters

20.5.2 Calculations and Results

References

Further Reading

21 FLOW INDUCED VIBRATION

21.1 Steady Internal Flow

21.2 Steady External Flow

21.3 Water Hammer

21.4 Column Separation

References

Further Reading

22 TEMPERATURE RISE

22.1 Head Loss

22.2 Pump Temperature Rise

22.3 Example Problem: Reactor Heat Balance

22.4 Example Problem: Vessel Heat-Up

22.5 Example Problem: Pumping System Temperature

References

23 FLOW TO RUN FULL

23.1 Open Flow

23.2 Full Flow

23.3 Submerged Flow

23.4 Example Problem: Reactor Application

Further Reading

24 JET PUMP PERFORMANCE

24.1 Performance Characteristics

24.2 Mixing Section Model

24.2.1 Momentum Balance

24.2.2 Drive Flow Mixing Coefficient

24.2.3 Suction Flow Mixing Coefficient

24.2.4 Discharge Flow Density

24.3.5 Discharge Flow Viscosity

24.3 Flow Losses

24.3.1 Surface Friction

24.3.2 Component Losses

24.4 Hydraulic Performance Flow Paths

24.4.1 Drive Flow Path

24.4.2 Suction Flow Path

24.5 Flow Model Validation

24.6 Example Problem: Water-Water Jet Pump Performance

24.6.1 Flow Conditions

24.6.2 Jet Pump Geometry

24.6.3 Preliminary Calculations

24.6.4 Loss Coefficients

24.6.5 Predicted Performance

24.7 Studies

24.7.1 Surface Roughness Differences

24.7.2 Drive Nozzle to Throat Area Ratio

24.7.3 Density Differences

24.7.4 Viscosity Differences

24.7.5 Straight Line and Parabolic Performance Depictions

24.8 Epilogue

References

Further Reading

APPENDIX A PHYSICAL PROPERTIES OF WATER AT 1 ATMOSPHERE

APPENDIX B PIPE SIZE DATA

B.1 Commercial Pipe Data

APPENDIX C PHYSICAL CONSTANTS AND UNIT CONVERSIONS

C.1 Important Physical Constants

C.2 Unit Conversions

APPENDIX D COMPRESSIBILITY FACTOR EQUATIONS

D.1 The Redlich-Kwong Equation

D.2 The Lee-Kesler Equation

D.3 Important Constants for Selected Gases

APPENDIX E ADIABATIC COMPRESSIBLE FLOW WITH FRICTION USING MACH NUMBER AS A PARAMETER

E.1 Solution when Static Pressure and Static Temperature are Known

E.2 Solution when Static Pressure and Total Temperature are Known

E.3 Solution when Total Pressure and Total Temperature are Known

E.4 Solution when Total Pressure and Static Temperature are Known

References

APPENDIX F VELOCITY PROFILE EQUATIONS

F.1 Benedict Velocity Profile Derivation

F.2 Street, Watters & Vennard Velocity Profile Derivation

References

APPENDIX G SPEED OF SOUND IN WATER

APPENDIX H JET PUMP PERFORMANCE PROGRAM

INDEX