1. CE 3372 WATER SYSTEMS DESIGN LECTURE 004

2. OUTLINE Branched Systems Looped Systems Network Analysis Hydraulic modeling

3. BRANCHED SYSTEM Distribution networks are multi-path pipelines One topological structure is branching

4. BRANCHED SYSTEM Node  Inflow = Outflow  Energy is unique value Links  Head loss along line

5. BRANCHED SYSTEM Head loss in each pipe Common head at the node

6. BRANCHED SYSTEM Continuity at the node

7. BRANCHED SYSTEM 4 Equations, 4 unknowns Non-linear so solve by  Newton-Raphson/Quasi-Linearization Quadratic in unknown, so usually can find solution in just a few iterations

8. LOOPED SYSTEM Looped system is extension of branching where one or more pipes rejoin at a different node.

9. LOOPED SYSTEM Nodes:  Inflow = Outflow  Energy Unique Links  Head loss along pipe  Head loss in any loop is zero LOOP

10. EXAMPLES Branched System Loop System

11. NETWORKS Branched and looped systems are called networks Multiple paths for water to flow in the system

12. Networks – Why Model? What is the flow distribution if the demands are changed as shown? 0.1 cfs 0.4 cfs

13. SKETCH AND LABEL

14. NODE-ARC INCIDENCE MATRIX

15. ENERGY LOSSES IN LOOP Determine “sign” for loop equations from loop traverse direction and assumed flow directions.

16. BUILD A COMPUTATION TOOL

17. WHAT IF? Once the tool is built, then “what-if” questions can be posed.  What is the flow distribution if the demands are changed as shown? 0.1 cfs 0.4 cfs

18. NEXT TIME Introduction to EPA-NET software for pipeline and network simulation