Hydraulics of pipeline systems

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 ؤQ-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. ؤQ-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 ؤQ-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 ؤH 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 ؤs- ؤt 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 ؤt 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