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Outline

Branched Systems

Looped Systems

Network Analysis

Hydraulic modeling

Branched System

Distribution networks are multi-path pipelines

One topological structure is branching

Branched System

Node Inflow = Outflow Energy is unique value

Links Head loss along line

Branched System

Head loss in each pipe

Common head at the node

Branched System

Continuity at the node

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

Looped System

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

Looped System

Nodes: Inflow = Outflow Energy Unique

Links Head loss along pipe Head loss in any loop is zero LOOP

Examples

Branched System

Loop System

Networks

Branched and looped systems are called networks

Multiple paths for water to flow in the system

Networks – Why Model?

What is the flow distribution if the demands are changed as shown?

0.1 cfs

0.4 cfs

Sketch and Label

Node-Arc Incidence Matrix

Energy Losses in Loop

Determine “sign” for loop equations from loop traverse direction and assumed flow directions.

Build a Computation Tool

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

NEXT TIME

Introduction to EPA-NET software for pipeline and network simulation