### Hydraulics of pipeline systems

## Monday, November 16, 2009

TABLE OF CONTENTS

1. Introduction

2. Review of Fundamentals

2.1 The fundamental principles

2.1.1. The basic equations

2.1.2. Energy and Hydraulic Grade Lines

2.2 Head loss formulas

2.2.1. Pipe friction

2.2.2. Darcy-Weisbach equation

2.2.3. Empirical equations

2.2.4. Exponential formula

2.2.5. Local and minor losses

2.3 Pump theory and characteristics

2.4 Steady flow analyses

2.4.1. Series pipe flow

2.4.2. Series pipe flow with pump(s)

2.4.3. Parallel pipe flow, equivalent pipes

2.4.4. Three reservoir problem

2.5 Problems

3. Manifold Flow

3.1 Introduction

3.2 Analysis of manifold flow

3.2.1. No friction

3.2.2. Barrel friction only

3.2.3. Barrel friction with junction losses

3.3 A hydraulic design procedure

3.4 Problems

4. Pipe Network Analysis

4.1 Introduction

4.1.1. Defining an appropriate pipe system

4.1.2. Basic relations between network elements

4.2 Equation systems for steady flow in networks

4.2.1. System of Q-equations

4.2.2. System of H-equations

4.2.3. System of ?Q-equations

4.3 Pressure reduction and back pressure valves

4.3.1. Q-equations for networks with PRV's/BPV's

4.3.2. H-equations for networks with PRV's/BPV's

4.3.3. ?Q-equations for networks with PRV's/BPV's

4.4 Solving the network equations

4.4.1. Newton method for large systems of equations

4.4.2. Solving the three equation systems via Newton

4.4.3. Computer solutions to networks

4.4.4. Including pressure reducing valves

4.4.5. Systematic solution of the Q-equations

4.4.6. Systematic solution of the H-equations

4.4.7. Systematic solution of the ?Q-equations

4.5 Concluding remarks

4.6 Problems

5. Design of Pipe Networks

5.1 Introduction

5.1.1. Solving for pipe diameters

5.1.2. Solution based on the Darcy-Weisbach equation

5.1.3. Solution based on the Hazen-Williams equation

5.1.4. Branched pipe networks

5.2 Large branched systems of pipes

5.2.1. Network layout

5.2.2. Coefficient matrix

5.2.3. Standard Linear Algebra

5.3 Looped network design criteria

5.4 Designing special components

5.5 Developing a solution for any variables

5.5.1. Logic and use of NETWEQS1

5.5.2. Data to describe the pipe system

5.5.3. Combinations that can not be unknowns

5.6 Higher order representations of pump curves

5.6.1. Within range polynomial interpolation

5.6.2. Spline function interpolation

5.7 Sensitivity analysis

5.8 Problems

6. Extended Time Simulations and Economical Design

6.1 Introduction

6.2 Extended time simulations

6.3 Elements of engineering economics

6.3.1. Economics applied to water systems

6.3.2. Least cost

6.4 Economic network design

6.4.1. One principal supply source

6.4.2. Design guidelines for complex networks

6.5 Problems

7. Introduction to Transient Flow

7.1 Causes of transients

7.2 Quasi-steady flow

7.3 True transients

7.3.1. The Euler equation

7.3.2. Rigid-column flow in constant-diameter pipes

7.3.3. Water hammer

7.4 Problems

8. Elastic Theory of Hydraulic Transients (Water Hammer)

8.1 The equation for pressure head change ?H

8.2 Wave speed for thin-walled pipes

8.2.1. Net mass inflow

8.2.2. Change in liquid volume due to compressibility

8.2.3. Change in pipe volume due to elasticity

8.3 Wave speeds in other types of conduits

8.3.1. Thick-walled pipes

8.3.2. Circular tunnels

8.3.3. Reinforced concrete pipe

8.4 Effect of air entrainment on wave speed

8.5 Differential equations of unsteady flow

8.5.1. Conservation of mass

8.5.2. Interpretation of the differential equations

8.6 Problems

9. Solution by the Method of Characteristics

9.1 Method of characteristics, approximate governing equations

9.1.1. Development of the characteristic equations

9.1.2. The finite difference representation

9.1.3. Setting up the numerical procedure

9.1.4. Computerizing the numerical procedure

9.1.5. Elementary computer programs

9.2 Complete method of characteristics

9.2.1. The complete equations

9.2.2. The numerical solution

9.2.3. The ?s- ?t grid

9.3 Some parameter effects on solution results

9.3.1. The effect of friction

9.3.2. The effect of the size of N

9.3.3. The effect of pipe slope

9.3.4. Numerical instability and accuracy

9.4 Problems

10. Pipe System Transients

10.1 Series pipes

10.1.1. Internal boundary conditions

10.1.2. Selection of ?t

10.1.3. The computer program

10.2 Branching pipes

10.2.1. Three-pipe junctions

10.2.2. Four-pipe junctions

10.3 Interior major losses

10.4 Real valves

10.4.1. Valve in the interior of a pipeline

10.4.2. Valve at downstream end of pipe at reservoir

10.4.3. Expressing KL as a function of time

10.4.4. Linear interpolation

10.4.5. Parabolic interpolation

10.4.6. Transient valve closure effects on pressures

10.5 Pressure-reducing valves

10.5.1. Quick-response pressure reducing valves

10.5.2. Slower acting pressure-reducing or pressure-sustaining valves

10.6 Wave transmission and reflection at pipe junctions

10.6.1. Series pipe junctions

10.6.2. Tee junctions

10.6.3. Dead-end pipes

10.7 Column separation and released air

10.7.1. Column separation and released air

10.7.2. Analysis with column separation and released air

10.8 Problems

11. Pumps in Pipe Systems

11.1 Pump power failure rundown

11.1.1. Setting up the equations for booster pumps

11.1.2. Finding the change in speed

11.1.3. Solving the equations

11.1.4. Setting up the equations for source pumps

11.2 Pump startup

11.3 Problems

12. Network Transients

12.1 Introduction

12.2 Rigid-column unsteady flow in networks

12.2.1. The governing equations

12.2.2. Three-pipe problem

12.3 A general method for rigid-column unsteady flow in pipe networks

12.3.1. The method

12.3.2. An example

12.4 Several pumps supplying a pipe line

12.5 Air chambers, surge tanks and standpipes

12.6 A fully transient network analysis

12.6.1. The initial steady state solution

12.6.2. TRANSNET

12.7 Problems

13. Transient Control Devices and Procedures

13.1 Transient problems in pipe systems

13.1.1. Valve movement

13.1.2. Check valves

13.1.3. Air in lines

13.1.4. Pump startup

13.1.5. Pump power failure

13.2 Transient control

13.2.1. Controlled valve movement

13.2.2. Check valves

13.2.3. Surge relief valves

13.2.4. Air venting procedures

13.2.5. Surge tanks

13.2.6. Air chambers

13.2.7. Other techniques for surge control

13.3 Problems

14. References

Appendices

A. Numerical Methods

A.1 Introduction

A.2 Linear algebra

A.2.1. Gaussian elimination

A.2.2. Use of the linear algebra solver SOLVEQ

A.3 Numerical integration

A.3.1. Trapezoidal rule

A.3.2. Simpson's rule

A.4 Solutions to ordinary differential equations

A.4.1. Introduction

A.4.2. Runge-Kutta method

A.4.3. Use of the ODE solver ODESDOL

B. Pump characteristic curves

C. Valve loss coefficients

C.1 Globe and angle valves

C.2 Butterfly valves

C.3 Ball valves

D. Answers to selected problems

Total 533 pages 5 mb

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