Aqueducts - Cornell Engineering

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Aqueducts - Cornell Engineering
Aqueducts
Monroe L. Weber-Shirk
School of Civil and
Environmental Engineering
Where Are We?
We estimated the land area needed to supply
water to NYC
How large a pipe is needed to carry the
water to NYC?
We will look at the construction of the Catskill
Aqueduct
We will figure out how large a pipe is needed to
carry the water from the Delaware system
Aqueducts
How does NYC get the water from upstate
reservoirs down to the city?
Pressurized Tunnels
Deep pressurized, bedrock tunnel
water flows under pressure just like in the pipes in
your apartment
Grade Tunnels
Not pressurized
water surface is in the tunnel
water flow is similar to water flow in a stream
Supply Aqueducts and Tunnels
Catskill Aqueduct (1915)
Shandaken Tunnel (1928)
Delaware Aqueduct (1944)
Neversink Tunnel (1950)
East Delaware Tunnel (1954)
West Delaware Tunnel (1967)
Types of Aqueducts
On Hydraulic Grade
 Following natural surface
Below Hydraulic Grade

 open channel
 cut-and-cover
wooden pipe
 reinforced concrete pipe
 steel pipe
 plastic pipe

 Above natural surface
 embankment
 viaduct
 Below natural surface
 grade tunnel
Following or above
natural surface

Below natural surface

pressure tunnel
Profile of Catskill Aqueduct
Small Scale profile of Catskill Aqueduct, Ashokan
Reservoir to Silver Lake Reservoir. (White p. 46)
Cross-section of Cut-and-Cover
Cut and Cover
Aqueduct
Construction of cover embankment. Rock was usually excavated to a 6 on 1 slope. Minimum
thickness of concrete along sides 20 ins., but usually thicker owing to disintegrated condition of
surface rocks. (White p. 50)
Delaware Aqueduct
10 km
Flow Profile for Delaware
Aqueduct
Rondout Reservoir
(EL. 256 m)
Sea Level
70.5 km
West Branch Reservoir
(EL. 153.4 m)
Valves to control flow?
(Designed for 39 m3/s)
Hudson River crossing
(El. -183 m)
Size of the Delaware Aqueduct
How big does the tunnel have to be?
What variables do you think are important?
Simplified Delaware Aqueduct
Rondout Reservoir
(EL. 102.6 m wrt West Branch)
West Branch Reservoir
L
70.5 km
hf
Hydraulic Grade Line:
level to which water will rise
slope of HGL 
hf
L
(Designed for 890 mgd
or 39 m3/s)
Darcy-Weisbach Formula
viscous resistance to
Energy loss due to _______
flow
L æV 2 ö
gh f = f ç ÷
Dè 2 ø
hf  f
LV2
D 2g
f = friction factor [dimensionless]
L = length of pipe [L]
D = diameter of pipe [L]
g = acceleration due to gravity [L/T2]
V = average velocity of water in pipe [L/T]
hf = loss of head [L]
Darcy-Weisbach Equation
(Function of Flow)
hf  f
LV2
Darcy-Weisbach
D 2g
hf  f
8 LQ 2
 g D
2
V
5

2
8
LQ

D f


2
  g hf 
4Q
D 2
0.2
Solve for D
Darcy-Weisbach Equation:
What About f?

2
8
LQ

D f


2
  g hf 
0.2
 f is a function of (V*D/ν) ______________
Reynolds number
 f is a function of pipe ___________
roughness
 Take Fluid Mechanics (and Hydraulic Engineering)
to learn how to use this equation...
Frictional Losses in Straight Pipes
Where
is
Capillary
tube
ortemperature?
24
ft diameter
tunnel
Where
do you
specify
the fluid?
0.1
Moody Diagram
0.05
0.04
0.03
f
friction factor
0.02
0.015
0.01
0.008
0.006
0.004
laminar
0.002
0.001
0.0008
0.0004
0.0002
0.0112
0.0001
0.00005
0.01
1E+03
smooth
1E+04
1E+05
R
1E+06
1E+07
1E+08

D
Swamee-Jain pipe size equation


2
1.25  LQ 

D  0.66 



gh
f 


  1.007x10 6 m 2 /s
Q  39 m /s
g  9.8 m/s
2
1E+03
1E+04
1E+05
R
1E+06
1E+07
1E+08
smooth
0.00005
0.0001
 ?








Moody + Darcy Weisbach =Swamee-Jain
0.01
0.0002
0.0004
0.0008
0.001
rotcaf noitcirf
h f  102.6 m

9.4  L
 Q

 gh f
5.2 0.04
Yes!
Do the units work? _________
3
L  70,500 m
4.75
f
0.002
laminar
0.004
0.006
0.008
0.01
0.015
0.02
0.03
0.04
0.05
D

hf  f
LV2
D 2g
4.75



2
LQ
  Q 9.4  L
D  0.66 1.25 




 gh f 
 gh f





5.2 0.04




Pipe Roughness
pipe material
glass, drawn brass, copper
commercial steel or wrought iron
asphalted cast iron
galvanized iron
cast iron
concrete
rivet steel
corrugated metal
pipe roughness  (mm)
0.0015
0.045
Watch these units!
0.12
0.15
0.26
0.18-0.6
0.9-9.0
45.0
Delaware Tunnel Diameter


2
LQ

D  0.66 1.25 



 gh f 

viscosity
Q
L
hf
roughness
g
D
4.75

9.4  L
 Q

 gh f
1.01E-06 m2/s
39
70500
102.6
0.0006
9.8
4.12
m3/s




5.2 0.04




Which term
dominates?
m
m
m
m/s2
m
The actual diameter!
Swamee-Jain Head Loss
Equation
Calculate head loss given a new flow…
hf  f
f 
8 LQ
Energy loss measured as lost potential energy
Darcy-Weisbach equation
 2 g D5
0.25
  
log

R
2
VD

5.74 
 0.9 

 3.7 D R 
2
Swamee-Jain equation for f
Reynolds number
Tunnel Explorations
 How long does it take water to get from Rondout
to West Branch (70.5 km)? D 4.12m
A
 D2
4
 13.33m
2
Q 39 m3 /s
V 
2.93m / s
2
A 13.33 m
 What is the Reynolds number?
VD
R

L 70,500m
t 
6.7hr
V 2.93m / s
n = 1x10- 6 m2 / s
2.93m / sfa
4.12mf
a

12 10
6
1 106 m2 / s
 What happens to head loss in the tunnel if the flow
rate is decreased?
8 LQ 2
2
hf  f 2

Q
 g D5
Where does excess PE go?
Solve the tunnel size using
Moody?
0.05
0.04
f
0.03
friction factor
0.02
0.015
0.01
0.008
0.006
0.004
laminar

D
e 0.0006m
=
= 0.00015
D
4.12m
0.002
0.001
0.0008
f = 0.0112
0.0004
0.0002
0.0001
0.00005
0.01
smooth
0.05
0.04
f
0.03
1E+04
1E+05
R
1E+06
1E+07
1E+08
0.02
0.015
friction factor
1E+03
0.01
0.008
0.006
0.004
laminar
0.002
0.001
0.0008
0.0004
0.0002
R = 12 ´ 10

2
8
LQ

D f


2

g
h
f 

6
0.2
0.0001
0.00005
0.01
1E+03
smooth
1E+04
1E+05
R
1E+06
1E+07
1E+08

D
Summary
Catskill and Delaware water is transported
to NYC without use of pumps
We can calculate the size of a tunnel based
on the required flow rate
The diameter of the tunnel, surface
roughness, length, and elevation drop
determine the maximum flow rate
What is a mgd?
Million Gallons per Day
 1,000,000 gallons  3.7854 L  1 day 



  43.8L/s

 1 gallon  86,400 sec 
day




Swamee-Jain Excel Equation


2
1.25  LQ 

D  0.66 



 gh f 

4.75

9.4  L
 Q

 gh f




5.2 0.04




=0.66*('roughness'^1.25*('L'*'Q'*'Q'/g/'hf')^4.75
+'viscosity'*'Q'^9.4*('L'/g/'hf')^5.2)^0.04
Construction of
Cut-and-cover
Aqueduct
Shows steel form and
carriage; also locomotive
crane used to place
concrete, move outside
forms, and assist in
excavation. (White p.
220)
Electric
carriage for
moving
interior forms
Carriage and upper jacks
are motor driven. Side
jacks and turntable hand
driven. (White p. 221)
Traveling Aqueduct
Building Plant
Traveling crushing concrete, mixing, and form-moving plant
completing last section of aqueduct adjoining shaft 1 of contract 12.
This plant built 7500 feet of aqueduct in two seasons. (White p. 223)
Cut-and-cover Arch
This section was
cast between steel
forms with steel plate in
expansion joints at 60-ft
intervals. Steel plates 6” x
3/8” were places in both
invert and arch joints to act
as water stops. (White p.
236)
Steel Forms and Locomotive Crane
Continuous method was here used, forms being used “telescoping.”
60- to 75-foot section concreted daily. (White p. 374)
Cut-and-cover
Aqueduct on
Curve
Arch cast with aid of
steel forms built
wedge-shaped in 5foot lengths to 200
feet radius. Section
17 feet high by 17
feet 6 inches wide.
(White p. 237)
Peak Tunnel
(Grade Tunnel)
Ready for
Concrete Lining
Footing courses are in
place. Center track for
hauling material to upper
portion of contract 11.
Tunnel is 3450 feet long
on tangent.(White p. 243)
Completed Pressure Tunnel Lining
Note smooth finish and close joints at invert and springing line.
Concrete surface very dry. (White p. 331)
Hunters Brook
Steel Pipe
Siphon
Laying of steel pipe on
concrete pedestal blocks.
Later pipe was filled with
water, covered with
concrete and earth and
lined with 2 ins. of mortar.
(White p. 467)
Hudson River Crossing
Section/Homework Comments
How can you meter the alum into your
filtration plant? (remember the peristaltic
pump limitations)
What range of alum dosage should you be
able to provide?
What happened to the stream flow below
the reservoir in 1978?
Stream flow below reservoir
Mean Daily Streamflow
1000
Flow Rate (m3/s)
100
10
1
0.1
1/1/1990
1/1/1988
1/1/1986
1/1/1984
1/1/1982
1/1/1980
1/1/1978
1/1/1976
1/1/1974
1/1/1972
1/1/1970
1/1/1968
1/1/1966
1/1/1964
1/1/1962
1/1/1960
1/1/1958
1/1/1956
1/1/1954
1/1/1952
1/1/1950
1/1/1948
1/1/1946
1/1/1944
1/1/1942
0.01
Date Which season are the higher controlled flows in?
Why does low flow rate appear to have regular pattern?
What causes flows over 10 m3/s?
Note frequency of flows over 10 m3/s
Why did low flow rate increase in 1978?
How do you explain occasional low flows after 1978?

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