Document 7313011
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Transcript Document 7313011
Pipeline systems
Monroe L. Weber-Shirk
School of Civil and
Environmental Engineering
Pipeline systems
Pipe
networks
contain
pipe loops or parallel
pipes
can have multiple sources
and sinks
multiple paths for water to get between any two points
Manifolds
single
and diffusers
source
multiple sinks along a single pipe (the manifold)
Manifolds
Examples
sprinkler
irrigation system
wastewater discharge (multiport diffuser)
Design
objectives
distribute
a given discharge uniformly through
multiple ports
choose pipe size given constraints of head loss,
flow distribution, and cost
Multiport Diffuser
Objectives
Minimize
detrimental
effects of the discharge
on the environment
Maximize initial dilution
Meet regulatory
requirements
Pollutants
treated
wastewater
BOD, N, P, metals
Cooling
water from
power plant
Heat
Sites
Rivers,
Oceans
Lakes,
Multiport Diffuser
energy grade line
hydraulic grade line
z=0
?
Remember Venturi
Representation of EGL and HGL for
multiport diffuser. Does it make sense?
What happens to HGL across the ports?
Multiport Diffuser:
Flow Calculations
piezometric ____
head
We will derive equations in terms of __________
p
because pressure controls the port flow
+z
g
Port flow
energy equation
based on ______
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
In diffuser
Port 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
The 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 Solution
Constant
pressure in the diffuser pipe
Each port is like an orifice
Strategy
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 Flow
z = 0 at water surface
V p2
Va2 p p
za
zp
hL
2g
2g
pa
H
p
z
piezometric head
p
riser
Va V p
Hd
2
a
V
0V 2
Hp
2g
Hd
Vp2
2g
port
Vp
p
2g
hL
Vr
hL
Va
Vd
diffuser pipe
Control volume?
Riser Head Loss
hL hentrance hriser helbow hcontraction
V
Lr
V
hL K en f
K el Kc
Dr
2g
2g
2
r
Vr Dr2 V p Dp2
continuity
4
D p
V V
Dr
4
V2
L
D
r
p
p
hL K en f
K el
Kc
D
2g
D
r
r
2
r
2
p
hc Kc
2
p
V p2
2g
Vr2
hel K el
2g
Vp
p
hriser
Lr Vr2
f
Dr 2g
hen K en
Vr2
2g
Riser Head Loss Coefficient
Hd
Vp2
2g
1
hL
V2
L
D
K f r K p K p
Hd
el
c
en
2g
D
D
r
r
4
Lr
Dp
(riser loss coefficient)
K r 1 K en f
K el Kc
Dr
Dr
Note that the riser
coefficient is a function
Vp2
Reynolds number.
H d Kr
of ________
2g
D p2 2 gH d Port velocity (or flow) given
2 gH d
Qp
piezometric head in diffuser
Vp
4
K r and a riser loss coefficient
Kr
4
Orifice equation!
Head Loss across Port
expansion
Flow ____________
Same equation applies
as derived previously
The velocities
upstream and
downstream from the
port are determined
from continuity
separation
Vi
Pressure
_________
applied over
entire cross
section
Vi+1
1
Momentum
___________
transferred
over smaller
area
2
hLi =
(Vi - Vi + 1 )
2g
2
HGL in Diffuser across Port
Vi Vi 1
hL
2g
2
EGL
i
HGL
H from
pressure
recovery
Vi
Vi+1
1
2
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
increase
(HGL) will __________
(proof coming up)
HGL in Diffuser across Port
Vi 2
Vi 21
Hi
H i 1
hL
2g
2g
energy equation using
________
definition of piezometric head
2
H expansion
i
2
i 1
Vi V
H i 1 H i
hL
2g 2g
i
Vi Vi 1
2
hL
i
2g
Vi 2 Vi 21 Vi Vi 1
2g 2g
2g
2
H expansion
H expansion
i
i
Vi 1 Vi Vi 1 pressure increase across abrupt expansion
Vi Vi 1
g
HGL in Diffuser across Port
H expansion
i
Vi 1 Vi Vi 1
g
How can we find velocity downstream
continuity
of port i? ___________
Qi Qp Qi 1
i
Vi Vi1
Qp
Vi 1 Vi
Qp
H expansion
i
i
Ad
Now we have the velocity
downstream of the next port
i
Ad
Vi 1Q p
gAd
i
And we can calculate the increase
in HGL across the port
HGL between Ports
parallel to EGL so H = E
between diffusers
E = -hf and is due to friction loss (major
losses)
HGL is
Re
VD
f
0.25
5.74
log
0.9
3.7 D Re
2
L V2
hf f
D 2g
Multiport 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
Multiport Diffuser: Solution
Given total discharge, pipe
4
diameter, port size...
D
Lr
p
Kc
K
1
K
f
K
en
el
Calculate the piezometric r
Dr
Dr
head (measured from the
water surface) required to
2
D
2 gH d
give the necessary discharge
p
Qp
in the first port
4
Kr
loss coefficient for port
head required to get
2
desired flow from port
K 4Q
Hd
p
2
p
2g D
r
Multiport 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
Qp
i
D p2
2 gH d
4
Kr
Vi 1 Vi
Qp
i
Ad
H expansion
i
H pipe
i
Vi 1Q p
i
gAd
2
L Vi1
f
D d 2g
H di 1 H di H expansion i H pipei
Multiport Diffuser: Solution
1
HGL
Qp
i
4
D p2
2 gH d
4
Kr
L Vi 21
H pipe f
Dd 2 g
i
decrease in pressure)
(_________
3
Vi 1Q p
H expansion
gAd
i
i
increase in pressure)
(__________
Vi
H di
Known from previous step
2
Qp
Vi 1 Vi
Ad
5 H d H d H expansion H pipe
i
i 1
i
i
i
Multiport Diffuser: Solution
Calculate the total discharge from the ports
Compare with design discharge
piezometric ____
head at first port to give design
Adjust the _________
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.
Multiport Diffuser: Solution
SI units
EGL
HGL
1.2
1
(m)
total flow (Q)
2.5
port velocity (Vp)
3
port d iam eter (Dp)
0.230
port area (Ap)
0.04
nu m ber of ports
20
port flow (Qp)
0.13
term inal piezom etric head (H )
0.8
d istance betw een ports (L)
4
pipe rou ghness (e)
0
d iffu ser d iam eter (Dd )
1
1.4
0.8
0.6
0.4
0.2
0
0
20
40
60
distance along diffuser (m)
80
Multiport Diffuser: Solution
SI units
EGL
HGL
4.5
4
3.5
3
(m)
total flow (Q)
2.5
port velocity (Vp)
3
port d iam eter (Dp)
0.230
port area (Ap)
0.04
nu m ber of ports
20
port flow (Qp)
0.13
term inal piezom etric head (H )
1.2
d istance betw een ports (L)
4
pipe rou ghness (e)
0
d iffu ser d iam eter (Dd )
0.63
5
2.5
2
1.5
1
0.5
0
0
20
40
60
distance along diffuser (m)
80
Design Guidelines
~3 m/s to achieve
The port discharge velocity should be _______
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
fLd
D
d
to cancel when
3
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.
Multiport 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
Less Uniform
remains the same.) ______________
What happens to the uniformity of flow rates from
the ports as the size of the ports decreases?
______________
More Uniform
If the goal is uniform flow distribution why not
Energy requirements
use very small ports? ____________________
Which port will have the highest flow rate?
_____________
First or last!
Diffuser Homework
20 ports
Hometown WWTP
300 m
95 m
Wastewater Diffuser in Cayuga
Lake
Installation of Wastewater outfall diffuser in Cayuga Lake