Pumps, Turbines, and Pipe Networks, part 3

Pipe-Pump Networks

• Large scale systems (e.g. water supply) almost always have complex networks, with pumps, pipes, reservoirs, tanks, valves, outlets, etc.

• A nonlinear system that may vary in time• Simple networks can be examined by

hand, complex networks require other methods

General Network Principles1. Increase in storage = flow in – flow out

a. Tanks, reservoirs change storageb. Filled pipes do not change storagec. Flow into junction = flow out of junction

2. Total change in head around a closed loop = 0a. Need to keep track of signsb. Often ignore losses at junctionsc. Usually ignore velocity head in large networks

3. Total change in head in unclosed loop is the sum of all its parts

a. Usually ignore velocity head

Hardy-Cross Method for Pipe Networks

• Iterative method to find flow rates in different parts of a pipe network, given system properties– Junction equations– Head loss equations– Looks at flow clockwise and counterclockwise

around loops– Initial guess, iterate– Often assume constant friction factor

Example Network

1

2

3

1 m3/s in0.5 m3/s out

0.5 m3/s out

f=0.02, L=150m, D=0.3m

f=0.02, L=100mD=0.3m

f=0.03, L=500m, D=0.2m

Pipe Network Program EPANET2

• Public Domain program to compute flow through pipe-pump networks– Steady, time-varying demand– Water quality features (will not use)– Easy to use, with pull-down menus– Used in practice both as stand-alone program

and hidden beneath other layers• To be used in HW4• Loaded on computers in Stinson-Remick

Example for EPANET2

• Simple Pump-Pipe system– Reservoir to pump to pipe to second reservoir– Water demand at one node

• Create all portions of system• Modify Properties to what we want• Run Analysis• Examine Properties• Be Careful – easy to have hidden properties that

are not what you want

Summary for Pumps/Pipes

• Important Points– Conservation of Mass– Conservation of Momentum– Bernoulli’s Equation– Dimensional Analysis

• Relatively simple concepts that lead to useful and general results

What Have We Learned?• Pumps and turbines

– How these vary with physical parameters– Power, Discharge, Head – how these vary– Types and uses

• Pump-pipe systems– Interaction between pumping systems and

pipe networks– Determining characteristics and finding

appropriate pumps, pipes– Cavitation– Complex networks and iterative solutions