62621099-02-Pipe-Networks

8/3/2019 62621099-02-Pipe-Networks

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Monroe L. Weber-Shirk School of Civil andEnvironmental Engineering

Pipe NetworksPipe Networks

Pipeline systemsTransmission lines

Pipe networks

MeasurementsManifolds and diffusers

Pumps

Transients

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Pipeline systems:

Pipe networks

Water distribution systems for municipalities

Multiple sources and multiple sinks connected

with an interconnected network of pipes.

Computer solutions!

KYpipes

WaterCADCyberNET

EPANET http://www.epa.gov/ORD/NRMRL/wswrd/epanet.html

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Water Distribution System

Assumption

Each point in thesystem can onlyhave one _______

The pressure changefrom 1 to 2 by path a

must equal the pressure changefrom 1 to 2 by path b

a

p1

K V

1

2

2 g z

1! p

2

K V

2

2

2 g z

2 h L

K

p1

K !

V 1a

2

2 g z1

V 2 a

2

2 g z2 h La

b

1 2 pressure

Same for path b!

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h La

! h Lb

a

b

1 2Pressure change by path a

Water Distribution System

Assumption

Pipe diameters are constant or K.E. is small

Model withdrawals as occurring at nodes so

V is constant between nodes

Or sum of head loss around loop is _____.zero

(Need a sign convention)

V

1a

2

2 g z

1V

2a

2

2 g z

2 h La

!V

1b

2

2 g z

1V

2 b

2

2 g z

2 h Lb

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Pipes in Parallel

A B

Q1

Qtotal

energy

proportion

Find discharge given pressure at A and B

______& ____ equation

add flows

Find head loss given the total flow

assume a discharge Q1¶ through pipe 1

solve for head loss using the assumed dischargeusing the calculated head loss to find Q2¶

assume that the actual flow is divided in the same

_________ as the assumed flow

Q2

S-J

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Networks of Pipes

____ __________ at all nodes

The relationship between head

loss and discharge must be

maintained for each pipe

Darcy-Weisbach equation

_____________

Exponential friction formula

_____________

A

0.32 m3/s 0.28 m3/s

?

b

a

1 2

Mass conservation

Swamee-Jain

Hazen-Williams

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Network Analysis

Find the flows in the loop given the inflowsand outflows.The pipes are all 25 cm cast iron (I=0.26 mm).

A B

C D0.10 m3/s

0.32 m3/s 0.28 m3/s

0.14 m3/s200 m

100 m

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Network Analysis

Assign a flow to each pipe link

Flow into each junction must equal flow out

of the junction

A B

C D0.10 m3/s

0.32 m3/s 0.28 m3/s

0.14 m3/s

0.320.00

0.10

0.04

arbitrary

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Network Analysis

Calculate the head loss in each pipe

f=0.02 for Re>200000

h f !8 fL

gD5

T 2

¨

ª

© ¸

º

¹Q 2

f h kQ Q=

339

)25.0

)(8.

9(

)200)(02.0(8

251

!¹¹

º

¸

©©

ª

¨!

T

k k1,k3=339k2,k4=169

A B

C D0.10 m3/s

0.32 m3/s 0.28 m3/s

0.14 m3/s

1

4 2

3

f 1! 34.7m

h f 2

! 0.222m

h f 3! 3.39

mh f

4

! 0.00m

h f i

i!1

4

§ ! 31.53m

Sign convention +CW

5

s

m

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Network Analysis

The head loss around the loop isn¶t zero

Need to change the flow around the loop

the ___________ flow is too great (head loss is

positive)

reduce the clockwise flow to reduce the head loss

Solution techniques

Hardy Cross loop-balancing (___________ _________)

Use a numeric solver (Solver in Excel) to find a change

in flow that will give zero head loss around the loop

Use Network Analysis software (EPANET)

clockwise

optimizes correction

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Numeric Solver

Set up a spreadsheet as shown below.

the numbers in bold were entered, the other cells are

calculations

initially (Q is 0

use ³solver´ to set the sum of the head loss to 0 by changing (Q

the column Q0+ (Q contains the correct flows

¨Q 0 000

i e f Q0 0 ¨Q hf

P1 0.02 200 0.25 339 0.32 0 3 0 34.69

P2 0.02 100 0.25 169 0.04 0.040 0. 7

P3 0.02 200 0.25 339 -0.1 -0.100 -3.39

P4 0.02 100 0.25 169 0

0.000 0

.00

31.575Sum Head Loss

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Solution to Loop Problem

A B

C D0.10 m3/s

0.32 m3/s 0.28 m3/s

0.14 m3/s

0.218

0.102

0.202

0.062

1

4 2

3

Q0+ (Q

Better solution is software with a GUI showing the pipe network.

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Network Elements

Controls

Check valve (CV)

Pressure relief valvePressure reducing valve (PRV)

Pressure sustaining valve (PSV)

Flow control valve (FCV)

Pumps: need a relationship between flow and headReservoirs: infinite source, elevation is not

affected by demand

Tanks: specific geometry, mass conservation

applies

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Check Valve

Valve only allows flow in one direction

The valve automatically closes when flow

begins to reverse

closedopen

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Pressure Relief Valve

Valve will begin to open when pressure in the pipeline ________ a set pressure(determined by force on the spring).

pipelineclosed

relief flow

open

exceeds

Low pipeline pressure High pipeline pressure

Where high pressure could cause an explosion (boilers, water heaters, «)

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Pressure Regulating Valve

Valve will begin to open when the pressure ___________ is _________ than the setpoint pressure (determined by the force of the spring).

sets maximum pressure downstream

closed open

lessdownstream

High downstream pressure Low downstream pressure

Similar function to pressure break tank

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Pressure Sustaining Valve

Valve will begin to open when the pressure ________ is _________ than the setpoint pressure(determined by the force of the spring).

sets minimum pressure upstream

closed open

upstream greater

Low upstream pressure High upstream pressure

Similar to pressure relief valve

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Flow control valve (FCV)

Limits the ____ ___ through the valve to a

specified value, in aspecified direction

Commonly used to limitthe maximum flow to avalue that will notadversely affect the provider¶s system

flow rate

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Pressure Break TanksPressure Break Tanks

In the developing world small water supplies in

mountainous regions can develop too much

pressure for the PVC pipe.They don¶t want to use PRVs because they are too

expensive and are prone to failure.

Pressure break tanks have an inlet, an outlet, and

an overflow.

Is there a better solution?

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Network Analysis Extended Network Analysis Extended

The previous approach works for a simple

loop, but it doesn¶t easily extend to a whole

network of loops

Need a matrix method

Initial guess for flows

Adjust all flows to reduce the error in pressures

__________________________

_______________________________

Simultaneous equations

Appendix D of EPANET manual

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Pressure Network Analysis

Software: EPANET

A B

C D0.10 m3/s

0.32 m

3

/s0.28 m3/s

0.14 m3/s

0.218

0.102

0.202

0.062

1

4 2

3

junctionpipereservoir

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EPANET network solutionEPANET network solution

2n

i j ij ij ij H H h rQ mQ

0ij i

j

Q D§

AH = F

ii ij j

A p!

§ij ij

A p!

1

1

2ij n

ij ij

pnr Q m Q

h f !8 fL

gD5

T 2

¨

ª

© ¸

º

¹Q 2

5 2

8 f Lr

gD T

¨ ¸! © ¹

ª º

2n !

5 2

1

82

ij

ij

p fL

Q

gDT

¨ ¸© ¹

ª º

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i ij i ij if f

j j f

F y p¨ ¸

! © ¹ª º§ § §

2

sgnn

ij ij ij ij ij y p r m Q Q!

ij ij ij ij i jQ Q y p H H « »! ½

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62621099-02-Pipe-Networks