Pipe Networks - Cornell University
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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
i1
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