monroe l. weber-shirk s chool of civil and environmental engineering pipeline systems
TRANSCRIPT
Monroe L. Weber-Shirk
School of Civil and
Environmental Engineering
Pipeline systemsPipeline systems
Pipeline systemsPipeline systems
Pipe networks contain pipe loops or parallel
pipes can have multiple
and multiple paths for water to get between any two points
Manifolds and diffusers single source multiple sinks along a single pipe (the manifold)
Pipe networks contain pipe loops or parallel
pipes can have multiple
and multiple paths for water to get between any two points
Manifolds and diffusers single source multiple sinks along a single pipe (the manifold)
sourcessourcessinkssinks
ManifoldsManifolds
Examples sprinkler irrigation system wastewater discharge (multiport diffuser)
Design objectives distribute a given discharge through
multiple ports choose pipe size given constraints of head loss,
flow distribution, and cost
Examples sprinkler irrigation system wastewater discharge (multiport diffuser)
Design objectives distribute a given discharge through
multiple ports choose pipe size given constraints of head loss,
flow distribution, and cost
uniformlyuniformly
Multiport DiffuserMultiport Diffuser
Objectives Minimize detrimental
effects of the discharge on the environment
Maximize initial Meet regulatory
requirements
Objectives Minimize detrimental
effects of the discharge on the environment
Maximize initial Meet regulatory
requirements
Pollutants treated wastewater
Cooling water from power plant
Sites Rivers, Lakes,
Oceans
Pollutants treated wastewater
Cooling water from power plant
Sites Rivers, Lakes,
Oceans
dilutiondilution
BOD, N, P, metalsBOD, N, P, metals
HeatHeat
Multiport DiffuserMultiport Diffuserenergy grade lineenergy grade linehydraulic grade linehydraulic grade line
z = 0z = 0??
Representation of EGL and HGL for multiport diffuser. Does it make sense?What happens to HGL across the ports?
Representation of EGL and HGL for multiport diffuser. Does it make sense?What happens to HGL across the ports?
Remember Venturi
Multiport Diffuser:Flow CalculationsMultiport Diffuser:Flow Calculations
We will derive equations in terms of __________ ____ because pressure controls the port flow
Port flow based on ______ equation head loss through port (possibly including a riser)
Piezometric head change (H) across port flow expansion
Piezometric head change ( H) between ports Darcy-Weisbach and Swamee-Jain
We will derive equations in terms of __________ ____ because pressure controls the port flow
Port flow based on ______ equation head loss through port (possibly including a riser)
Piezometric head change (H) across port flow expansion
Piezometric head change ( H) between ports Darcy-Weisbach and Swamee-Jain
energyenergy
In diffuser
piezometric headpiezometric headpz
g+
Port typesPort types
Nozzle riser diffuser can be buried nozzle can give direction to discharge
Port cast in wall of diffuser pipe can’t be used if diffuser pipe is buried generally not recommended
Nozzle riser diffuser can be buried nozzle can give direction to discharge
Port cast in wall of diffuser pipe can’t be used if diffuser pipe is buried generally not recommended
The ProblemThe Problem
Given a desired discharge Calculate the head (pressure) required Calculate the flow from each port
Develop a strategy to solve this problem
Given a desired discharge Calculate the head (pressure) required Calculate the flow from each port
Develop a strategy to solve this problem
A Simple SolutionA Simple Solution
Constant pressure in the diffuser pipe Each port is like an orifice
Constant pressure in the diffuser pipe Each port is like an orifice
StrategyStrategy
The diffuser has many ports. If we can develop equations describing pressures and flows at one port we can then apply it to all of the ports.
We need equations describing Flow from a port as a function of pressure in the
diffuser Head loss (and pressure drop) in the diffuser Flow in the diffuser
The diffuser has many ports. If we can develop equations describing pressures and flows at one port we can then apply it to all of the ports.
We need equations describing Flow from a port as a function of pressure in the
diffuser Head loss (and pressure drop) in the diffuser Flow in the diffuser
Port FlowPort Flow
H
p
z H
p
z
Vr Vr
riserriser
portport
diffuser pipediffuser pipe
Vd Vd
Lp
pa
d hg
VH
g
VH
22
22
Lp
pa
d hg
VH
g
VH
22
22
L
p
p
paa
a hg
Vz
p
g
Vz
p 22
22
L
p
p
paa
a hg
Vz
p
g
Vz
p 22
22
Hd
Vp2
2ghL
Hd
Vp2
2ghL
piezometric headpiezometric head
z = 0 at water surfacez = 0 at water surface
aVaV
pVpV
p p
00pa VV pa VV
Control volume?
Riser Head LossRiser Head Loss
gV
Kh relel 2
2
gV
Kh relel 2
2
hriserf
Lr
Dr
Vr2
2g hriserf
Lr
Dr
Vr2
2g
VrDr2 VpDp
2
VrDr2 VpDp
2
Vr
2 Vp2 Dp
Dr
4
Vr
2 Vp2 Dp
Dr
4
continuitycontinuity Vp Vp
hL hentrance hriser helbowhcontraction hL hentrance hriser helbowhcontraction
hL Ken f
Lr
Dr
Kel
Vr
2
2g Kc
Vp2
2g hL Ken f
Lr
Dr
Kel
Vr
2
2g Kc
Vp2
2g
g
VK
D
DK
D
LfKh p
c
r
pel
r
renL
2
24
g
VK
D
DK
D
LfKh p
c
r
pel
r
renL
2
24
hc Kc
Vp2
2g hc Kc
Vp2
2g
g
VKh renen
2
2
g
VKh renen
2
2
p p
Riser Head Loss CoefficientRiser Head Loss Coefficient
Hd Kr
Vp2
2g
r
dp
K
gHV
2
(riser loss coefficient)Note that the riser coefficient is a function of ________ number.
(riser loss coefficient)Note that the riser coefficient is a function of ________ number.
Port velocity (or flow) given piezometric head in diffuser and a riser loss coefficient
Port velocity (or flow) given piezometric head in diffuser and a riser loss coefficient
r
dpp
K
gHDQ
2
4
2
Hd
Vp2
2ghL
g
VK
D
DK
D
LfKH p
c
r
pel
r
rend
21
24
Kr 1 Ken f
Lr
Dr
Kel
Dp
Dr
4
Kc
ReynoldsReynolds
Orifice equation!
Head Loss across PortHead Loss across Port
_________ applied over entire cross section
_________ applied over entire cross section
___________ transferred over smaller area
___________ transferred over smaller area
Flow ____________ Same equation applies
as derived previously The velocities
upstream and downstream from the port are determined from continuity
Flow ____________ Same equation applies
as derived previously The velocities
upstream and downstream from the port are determined from continuity
( )2
1
2i
i iL
V Vh
g+-
=( )2
1
2i
i iL
V Vh
g+-
=
1 2
separationseparation
Vi Vi+1
PressurePressure MomentumMomentum
expansionexpansion
HGL in Diffuser across PortHGL in Diffuser across Port
Head loss occurs between section 1 and section 2 some distance downstream (~5 times the diameter of the diffuser)
We will treat this head loss as if it all occurred immediately after the port
Although there is head loss past the port the pressure (HGL) will __________ (proof coming up)
Head loss occurs between section 1 and section 2 some distance downstream (~5 times the diameter of the diffuser)
We will treat this head loss as if it all occurred immediately after the port
Although there is head loss past the port the pressure (HGL) will __________ (proof coming up)
hLi
Vi Vi1 2
2g hLi
Vi Vi1 2
2g
H from pressure recovery
H from pressure recovery
EGLEGL
HGLHGL
1 2
ViVi Vi+1Vi+1
increaseincrease
HGL in Diffuser across PortHGL in Diffuser across Port
ii Lii
ii hg
V
g
VHHH
22
2
1
2
1expansion ii Lii
ii hg
V
g
VHHH
22
2
1
2
1expansion
gVVV
H iii 11expansion i
gVVV
H iii 11expansion i
________ equation using definition of piezometric head
________ equation using definition of piezometric head
pressure increase across abrupt expansionpressure increase across abrupt expansion
g
VV
g
V
g
VH iiii
222
2
1
2
1
2
expansioni
g
VV
g
V
g
VH iiii
222
2
1
2
1
2
expansioni
hLi
Vi Vi1 2
2g hLi
Vi Vi1 2
2g
Li
ii
i hgV
HgV
H 22
2
11
2
Li
ii
i hgV
HgV
H 22
2
11
2
energyenergy
1 ii VV 1 ii VV
HGL in Diffuser across PortHGL in Diffuser across Port
Vi Vi1
Qpi
Ad Vi Vi1
Qpi
Ad
gVVV
H iii
i
11expansion
gVVV
H iii
i
11expansion
d
pi
gA
QVH i
i
1
expansion
d
pi
gA
QVH i
i
1
expansion
Vi1 Vi
Qpi
Ad Vi1 Vi
Qpi
Ad
continuitycontinuityHow can we find velocity downstream of port i? ___________How can we find velocity downstream of port i? ___________
1 ipi QQQi 1 ipi QQQi
Now we have the velocity downstream of the next portNow we have the velocity downstream of the next port
And we can calculate the increase in HGL across the port
And we can calculate the increase in HGL across the port
HGL between PortsHGL between Ports
HGL is parallel to EGL so H = E between diffusers
E = -hf and is due to friction loss (major losses)
HGL is parallel to EGL so H = E between diffusers
E = -hf and is due to friction loss (major losses)
2
9.0Re
74.5
7.3log
25.0
D
f
2
9.0Re
74.5
7.3log
25.0
D
f
Re
VD
ReVD
hf fLD
V2
2g hf f
LD
V2
2g
Multiport Diffuser: SolutionMultiport Diffuser: Solution The diffuser number, spacing, and jet velocity would be
determined in part by the mixing required in the ambient water (Environmental Fluid Mechanics)
Available head and total flow would be determined by the water source hydraulics
A criteria may also be established for uniformity of flow from the ports
Alternate design criteria may dictate different solution methods
The diffuser number, spacing, and jet velocity would be determined in part by the mixing required in the ambient water (Environmental Fluid Mechanics)
Available head and total flow would be determined by the water source hydraulics
A criteria may also be established for uniformity of flow from the ports
Alternate design criteria may dictate different solution methods
Multiport Diffuser: SolutionMultiport Diffuser: Solution Given total discharge, pipe
diameter, port size... Calculate the piezometric
head (measured from the water surface) required to give the necessary discharge in the first port loss coefficient for port head required to get
desired flow from port
Given total discharge, pipe diameter, port size...
Calculate the piezometric head (measured from the water surface) required to give the necessary discharge in the first port loss coefficient for port head required to get
desired flow from port
r
dpp
K
gHDQ
2
4
2
r
dpp
K
gHDQ
2
4
2
Hd
Kr
2g
4Qp
Dp2
2
Hd
Kr
2g
4Qp
Dp2
2
Kr 1 Ken f
Lr
Dr
Kel
Dp
Dr
4
Kc Kr 1 Ken f
Lr
Dr
Kel
Dp
Dr
4
Kc
Multiport Diffuser: SolutionMultiport Diffuser: Solution
Starting with the first port and proceeding to the last port ... Calculate the discharge from port i Calculate velocity change in
diffuser past port i Calculate the piezometric head
increase across port i Calculate the piezometric head
decrease between ports i and i+1 Calculate the piezometric head at
port i+1
Starting with the first port and proceeding to the last port ... Calculate the discharge from port i Calculate velocity change in
diffuser past port i Calculate the piezometric head
increase across port i Calculate the piezometric head
decrease between ports i and i+1 Calculate the piezometric head at
port i+1
d
pi
gA
QVH i
i
1expansion
d
pi
gA
QVH i
i
1expansion
Vi1 Vi
Qpi
Ad Vi1 Vi
Qpi
Ad
Hpipe f
LDd
Vi12
2g Hpipe f
LDd
Vi12
2g
iiii pipedd HHHH expansion1 iiii pipedd HHHH expansion1
r
dpp
K
gHDQ i
i
2
4
2
r
dpp
K
gHDQ i
i
2
4
2
Multiport Diffuser: SolutionMultiport Diffuser: Solution
ViVi
r
dpp
K
gHDQ i
i
2
4
2
r
dpp
K
gHDQ i
i
2
4
2
Vi1 Vi
Qpi
Ad Vi1 Vi
Qpi
Ad
HGLHGL1
5
g
V
D
LfH i
d
pipe
2
21g
V
D
LfH i
d
pipe
2
21
3
2
4
(_________ in pressure)(_________ in pressure)
(__________ in pressure)(__________ in pressure)
idH
idH
d
pi
gA
QVH i
i
1expansion
d
pi
gA
QVH i
i
1expansion
iiii pipedd HHHH expansion1 iiii pipedd HHHH expansion1
Known from previous stepKnown from previous step
increaseincrease
decreasedecrease
Multiport Diffuser: SolutionMultiport Diffuser: Solution
Calculate the total discharge from the ports Compare with design discharge Adjust the _________ ____ at first port to give design
discharge (use goal seeking, solver, or trial and error on spreadsheet). Alternately, set velocity past last port = 0 by changing piezometric head at first port.
It may be necessary to adjust diffuser or port diameter. It will likely be possible to decrease the size of the
diffuser pipe as the flow decreases. This may also help increase the discharge uniformity of the ports.
Calculate the total discharge from the ports Compare with design discharge Adjust the _________ ____ at first port to give design
discharge (use goal seeking, solver, or trial and error on spreadsheet). Alternately, set velocity past last port = 0 by changing piezometric head at first port.
It may be necessary to adjust diffuser or port diameter. It will likely be possible to decrease the size of the
diffuser pipe as the flow decreases. This may also help increase the discharge uniformity of the ports.
piezometric headpiezometric head
Multiport Diffuser: SolutionMultiport Diffuser: Solution
total flow (Q) 2.5port velocity (Vp) 3port diameter (Dp) 0.230port area (Ap) 0.04number of ports 20port flow (Qp) 0.13terminal piezometric head (H) 0.8distance between ports (L) 4pipe roughness () 0diffuser diameter (Dd) 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 20 40 60 80distance along diffuser (m)
(m)
EGL
HGL
SI units
Multiport Diffuser: SolutionMultiport Diffuser: Solution
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 20 40 60 80distance along diffuser (m)
(m)
EGL
HGLtotal flow (Q) 2.5port velocity (Vp) 3port diameter (Dp) 0.230port area (Ap) 0.04number of ports 20port flow (Qp) 0.13terminal piezometric head (H) 1.2distance between ports (L) 4pipe roughness () 0diffuser diameter (Dd) 0.63
SI units
Design GuidelinesDesign Guidelines The port discharge velocity should be _______ to achieve
good mixing with the ambient water. The sum of all port areas must be less than the diffuser pipe
area. The best area ratio (port area/diffuser area) is usually between 1/3 and 2/3.
The effects of pipe friction and pressure recovery will tend to cancel when Ld is the total length of the diffuser pipe and the friction factor, f, is
obtained by iteration since it is a function of the pipe diameter. If the diffuser area obtained using this method is less than 1.5 x
port area then this design criteria can not be used.
The port discharge velocity should be _______ to achieve good mixing with the ambient water.
The sum of all port areas must be less than the diffuser pipe area. The best area ratio (port area/diffuser area) is usually between 1/3 and 2/3.
The effects of pipe friction and pressure recovery will tend to cancel when Ld is the total length of the diffuser pipe and the friction factor, f, is
obtained by iteration since it is a function of the pipe diameter. If the diffuser area obtained using this method is less than 1.5 x
port area then this design criteria can not be used.
3
dd
fLD
3
dd
fLD
~3 m/s~3 m/s
Multiport Diffuser:Thought ExperimentsMultiport Diffuser:
Thought Experiments What happens to the uniformity of flow rates from the
ports as the size of the diffuser pipe decreases? (Assume the pressure in the feeder pipe is varied to maintain constant flow while the port size remains the same.) ______________
What happens to the uniformity of flow rates from the ports as the size of the ports decreases? ______________
If the goal is uniform flow distribution why not use very small ports? ____________________
Which port will have the highest flow rate? _____________
What happens to the uniformity of flow rates from the ports as the size of the diffuser pipe decreases? (Assume the pressure in the feeder pipe is varied to maintain constant flow while the port size remains the same.) ______________
What happens to the uniformity of flow rates from the ports as the size of the ports decreases? ______________
If the goal is uniform flow distribution why not use very small ports? ____________________
Which port will have the highest flow rate? _____________
First or last!
Energy requirements
More Uniform
Less Uniform
Diffuser HomeworkDiffuser Homework
Hometown WWTP
300 m 95 m
20 ports20 ports
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