Transcript Pipe Networks - Cornell University

Pipe Networks
Monroe L. Weber-Shirk
School of Civil and
Environmental Engineering
Closed Conduit Flow:
Review
Energy equation
 Head loss

major losses
 minor losses

EGL and HGL
 Non circular conduits
 Pipeline systems

pipe networks
 measurements
 manifolds and diffusers


Pumps
Pipeline systems:
Pipe networks
Water distribution systems for municipalities
 Multiple sources and multiple sinks connected
with an interconnected network of pipes.
 Computer solutions!

KYpipes
 WaterCAD
 CyberNET

Water Distribution System
Assumption


Each point in the
system can only
have one _______
pressure
The pressure change
from 1 to 2 by path a
must equal the
pressure change
from 1 to 2 by path b
a
1
2
b
V12
p2 V22

 z1  
 z 2  hL
 2g
 2g
p1
p2


p1


V12
a
2g
 z1 
V22
a
2g
 z 2  hL
a
Water Distribution System
Assumption
V12
a
2g
 z1 
V22
a
2g
 z 2  hL 
a
V12
b
2g
 z1 
a
2g

V22
a
2g
hL  hL
a
b
 hL 
a
V12
b
2g

V22
b
2g
 hL
b
2g
 z 2  hL
b
a
1
Pressure change by path a
V12
V22
b
2
b
zero
Or sum of head loss around loop is _____.
(Need a sign convention)
Pipe diameters are constant
 Model withdrawals as occurring at nodes so
V is constant

Pipes in Parallel
 Find
discharge given pressure at A and B
 ______&
energy
 add
 Find
flows
____
S-J equation
Qtotal A
Q1
Q2
B
head loss given the total flow
a discharge Q1’ through pipe 1
 solve for head loss using the assumed discharge
 using the calculated head loss to find Q2’
 assume that the actual flow is divided in the same
_________
proportion as the assumed flow
 assume
Networks of Pipes
conservation at
 Mass
____ __________
all nodes
 The proper relationship
between head loss and
discharge must be maintained
for each pipe
 Darcy-Weisbach
0.32
A
0.28 m3/s
?
equation
Swamee-Jain
 Exponential friction formula
m3/s
a
 _____________
1
2
Hazen-Williams
 _____________
b
Network Analysis
Find the flows in the loop given the inflows
and outflows.
The pipes are all 25 cm cast iron (e=0.26 mm).
0.32 m3/s
A
B
C
D
0.28 m3/s
100 m
0.10 m3/s
200 m
0.14 m3/s
Network Analysis
 Assign
a flow to each pipe link
 Flow into each junction must equal flow out
of the junction
arbitrary
0.32 m3/s
0.32
0.00
0.10 m3/s
0.28 m3/s
B
A
0.04
C
D
0.10
0.14 m3/s
Network Analysis
 Calculate the
 8 fL  2
h f   5 2 Q
gD  
head loss in each pipe
f=0.02 for Re>200000
A
1
B
h f  0.222m
2
h f  3.39m
C
h f  0.00m
4
4
h
fi
 31.53m
i1
0.28 m3/s
2
4
0.10 m3/s
1
3
h f = kQ Q Sign convention +CW
k1,k3=339
 8(0.02)(200) 
  339
k1  
k2,k4=169
 (9.8)(0.25)5  2 


0.32 m3/s
h f  34.7m
3
D
0.14 m3/s
Network Analysis
The head loss around the loop isn’t zero
 Need to change the flow around the loop

clockwise flow is too great (head loss is
the ___________
positive)
 reduce the clockwise flow to reduce the head loss


Solution techniques
Hardy Cross loop-balancing (___________
_________)
optimizes correction
 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

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 “solver” to set the sum of the head loss to 0 by changing Q
the column Q0+ Q contains the correct flows
∆Q
pipe
P1
P2
P3
P4
0.000
f
0.02
0.02
0.02
0.02
L
200
100
200
100
D
0.25
0.25
0.25
0.25
k
Q0 Q0+∆Q
339 0.32 0.320
169 0.04 0.040
339 -0.1 -0.100
169
0 0.000
Sum Head Loss
hf
34.69
0.27
-3.39
0.00
31.575
Solution to Loop Problem
Q0+ Q
0.218
0.062
0.202
0.102
0.32 m3/s
1
A
0.218
4
2
0.102
0.10
m3/s
C
0.28 m3/s
B
0.062
0.202
3
D
0.14 m3/s
Better solution is software with a GUI showing the pipe network.
Pressure Network Analysis
Software: WaterCAD™
reservoir
pipe
0.32 m3/s
junction
1
A
0.218
4
2
0.102
0.10
m3/s
C
0.28 m3/s
B
0.062
0.202
3
D
0.14 m3/s
Network Elements

Controls
Check valve (CV)
 Pressure relief valve
 Pressure reducing valve (PRV)
 Pressure sustaining valve (PSV)
 Flow control valve (FCV)

Pumps
 Reservoirs
 Tanks

Check Valve
 Valve
only allows flow in one direction
 The valve automatically closes when flow
begins to reverse
open
closed
Pressure Relief Valve
pipeline
closed
open
relief flow
Low pipeline pressure
High pipeline pressure
Valve will begin to open when pressure in
exceeds a set pressure
the pipeline ________
(determined by force on the spring).
Pressure Regulating Valve
sets maximum pressure downstream
closed
High downstream pressure
open
Low downstream pressure
Valve will begin to open when the pressure
less
downstream
___________ is _________
than the setpoint
pressure (determined by the force of the spring).
Pressure Sustaining Valve
sets minimum pressure upstream
closed
Low upstream pressure
open
High upstream pressure
Valve will begin to open when the pressure
upstream is _________
greater than the setpoint pressure
________
(determined by the force of the spring).
Flow control valve (FCV)
 Limits
the ____
___
flow rate
through the valve to a
specified value, in a
specified direction
 Commonly used to limit
the maximum flow to a
value that will not
adversely affect the
provider’s system
Reservoirs
constant water
modeled as ________
level sources
 Can supply any demand!
 Are
Tanks
Obey conservation
of mass
 Have a finite size
 Water level moves
up and down and
thus pressures
_______ in
system change!
 Need to define
tank geometry

Pumps
Require a Pump
Curve (discharge
vs. head)
 Initial setting
 Controls for
extended time
analysis

Water Distribution System
Reservoir - used to model a clear well
 Pump to lift water to elevated storage tank


turns on and off based on water level in tank
Tank feeds distribution grid
 Demands applied at junctions
