Simple Expression for Estimating the Switch Peak Voltage ...
Estimating Peak Water Demands in Buildings with … › media › 5304 ›...
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Estimating Peak Water Demands in Buildings with Efficient Fixtures
STEVEN BUCHBERGER
INTERNATIONAL EMERGING TECHNOLOGY SYMPOSIUMMAY 10, 2016
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Outline[1] Background/Motivation[2] Water Use Database[3] Water Use Parameters[4] Water Use Model
[5] Application
[6] Conclusion
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[1] BACKGROUND / MOTIVATION
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Hunter’s Curve
Today, Hunter’s curve is often faulted for giving overly conservative designs….Why?
4Fixture Units
GPM
High efficiency fixtures = lower q
Uncongested use = lower p
1940
2016
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Changing Times
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Modified Hunter’s Curve(s)
6http://www.armstronginternational.com/files/products/wheaters/pdf/sizing%20chart.pdf
Different curve for different end users
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Daniel Cole, Chair , IAPMO, Mokena, IL 60448Jason Hewitt, CB Engineers, San Francisco, CA 94103
Timothy Wolfe, TRC Worldwide Engineering MEP, LLC, Indianapolis, IN 46240Toritseju Omaghomi, College of Engineering, University of Cincinnati, Cincinnati , OH 45221Steven Buchberger, College of Engineering, University of Cincinnati, Cincinnati, OH 45221
Task Group Sponsors and Members
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IAPMO Task Group Orders
“….will work singularly to develop the probability model to predict peak demands based on the number of plumbing fixtures of different kinds installed in one system.”
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(Bring Hunter into 21st Century)
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Project Activities
Acquire Data
Analyze Data
Develop Model
Peer Review & Publication of
Report
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[2] WATER USE DATABASE
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Database: Location of HomesSurvey 1996‐2011
1,038 households
2,800 residents
11,350 monitoring days
MS Access DB
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Database: Summary of Measured Data
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Water Use Event Duration Volume
Percen
tage
Bathtub
Clothes washer
Dishwasher
Faucet
Shower
Toilet
Others
Leak
Six unique fixtures
862,900 events*
1,591,700 gallons*
889,700 minutes*
*excluding leaks
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‐Evaporative Cooler
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Database: Details of Water Use at FixtureNUMBER OF “HITS” VOLUME OF WATER USE
Bathtub5.2%
Clothes washer25.0%
Dishwasher1.9%
Faucet20.2%
Shower21.9%
Toilet25.8%
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Bathtub0.5%
Clothes washer3.2%
Dishwasher1.5%
Faucet73.5%
Shower2.5%
Toilet18.8%
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Database: Residential Fixture ClassificationFixture* Ultra‐Efficient Efficient Inefficient
Clothes washer (gallons/load)
< 20 20 – 30 > 30
Dishwasher(gallons/cycle)
< 1.8 1.8 – 3.0 > 3.0
Shower(gallons/minute)
< 2.2 2.2 – 2.5 > 2.5
Toilet(gallons/flush)
< 1.8 1.8 – 2.2 > 2.2
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*Bathtubs and faucets were excluded
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[3] WATER USE PARAMETERS
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Key Fixture Characteristics
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Fixture Flow Rateq:
Fixture Countn:1 2 3 . . . x . . . . n
1 ‐
2 ‐
3 ‐ Fixture Probability of Usep:itp
T= ∑
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Computed Fixture Flow Rate; q
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( )( )
Volumeof each pulse gallonsq
Duration of each pulse minutes= ∑∑
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Summary of “Efficient” Fixture Flow Rate
18“Efficient” = Ultra‐efficient and Efficient Fixtures
0123456789
10
Bathtub Clothes Washer Toilet Shower Faucet Dishwasher
Flow
rate (gpm
)
MeanOutliersRecommended
C.W.
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Hourly Fixture Use (Volume)
19
Clothes washer10
Dishwasher20
Faucet18
Shower07
Toilet07
Bathtub19
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Daily Volum
e (gallons)
Hour of Day
Average hourly volume of water use at a fixture per home per day
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Single Home 12 Day Water Use Profile
20
0
50
100
150
200
250
300
350
400
00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Volume (gallons)
Hour of Day
Clothes washerDishwasherFaucetShowerToiletTotal Volume
Peak Hour
(10S761)
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Fixture peak hour of water use (by Volume)
Bathtub; 19
Clothes washer; 10Dishwasher; 20
Faucet; 18
Shower; 07
Toilet; 07
05
101520253035404550
00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Volume (gallons)
Hour of Day
Average hourly volume of water consumed at each fixture
Multiple Homes Water Use Profile (by Volume)
21
Home #1;10S761
Home #2; 10S764
Home #3; Cal_Fed‐15151
0
5
10
15
20
25
30
00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Average da
ily volum
e (gallons)
Hour of Day
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2 homes
151 homes
57 homes
0
5
10
15
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Percen
tage (%
)
Hour of Day
Distribution of Peak Hour of Water Use(N = 1,038 Homes)
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Probability of Fixture Use at Individual HomesFocused on only efficient fixtures
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( )
ii
thi
tp
n D Tt Duration of i water use eventn Number of fixturesD Number of observation daysT 60 minutes 1hour observation window
=⋅ ⋅
−−−−
∑
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Probability of Fixture Use at Individual Homes
Considered only efficient fixtures24
10 0.171 1 60
minutespfixture day minutes
= =⋅ ⋅
ii
tp
n D T=
⋅ ⋅
∑
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Probability of Fixture Use – Group of Homes
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Number of residents
Number of bathrooms
Number of bedrooms
Positive Correlation
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Probability of Toilet Use
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I – Group weighted average
Conservative Value
N = 62
N = 209
N = 82
N = 29
N = 83
N = 8
N = 8
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Design Fixture Probability Values
27
p = 0.010
p = 0.005p = 0.025
p = 0.050
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[4] (PEAK) WATER USE MODEL
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Binomial Model
29Hunter did this
exactly busyPr (1 )
out of fixturesx n xx n
p pn x
−⎛ ⎞ ⎛ ⎞= −⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
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“Frequency Factor” Approach
30
( )0.99 0.99Q Mean z Standard Deviation= +
99th Percentile
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Normal Approximation
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( ) ( ) 20.99 0.99
1 11
K K
k k k k k k kk k
Q n p q z n p p q= =
= + −∑ ∑
( )0.99 0.99q qQ zμ σ= + per Wistort (1995)
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Binomial Distribution (small building)
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Zero Truncated Binomial Distribution
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Modified Wistort’s Model
Note:is probability of stagnation in a home (i.e. no water use)
Addresses water demand in single family homes with high P0
Transitions back to Wistort’s model as P0 approaches 0
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( ) ( ) ( )2
20.99 0.99 0 0
1 1 10
1 1 11
K K K
k k k k k k k k k kk k k
Q n p q z P n p p q P n p qP = = =
⎡ ⎤⎡ ⎤ ⎛ ⎞⎢ ⎥= + − − − ⎜ ⎟⎢ ⎥− ⎢ ⎥⎣ ⎦ ⎝ ⎠⎣ ⎦∑ ∑ ∑
( )01
1 kk
nkP p= −∏
( ) ( ) 20.99 0.99
1 1
1K K
k k k k k k kk k
Q n p q z n p p q= =
= + −∑ ∑
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[5] APPLICATION
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HypotheticalResidential Building Pipe Layout
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Peak Flow Calculations
Section UPC FU
UPC Method(gpm)
MWMethod(gpm)
1 25.5 18.0 11.8
2 10.5 8.5 6.9
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Example: 2.5 bath single family home
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Sizing Pipes
Section UPC Method Pipe Size* MW
Method Pipe Size*
1 18.0 gpm 1” 11.8 gpm 3/4"
2 8.5 gpm 3/4" 6.9 gpm 3/4"
38* Maximum flow rate at 8 f/s
Example: 2.5 bath single family home
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Modified Hunter’s Curve(s)
39http://www.armstronginternational.com/files/products/wheaters/pdf/sizing%20chart.pdf
Different curve for different end users
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Universal Dimensionless Design Curve
40
Hunter Number, H
Dim
ensi
onle
ss D
eman
d 99th Percentile
0 5 10 15 20 25 30 35 40 45 500
10
20
30
40
50
60
70
Glimpse of the Future?
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[6] CONCLUSION
41
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ConclusionIntroduced a new model to estimate peak water
demand in single and multi‐family dwellings. Replaced fixture units with fixture counts.Runs on a spreadsheet. Recommended fixture p and q values.Results are more sensitive to q than to p.Can be applied to a wide spectrum of buildings.
42
Single Family Homes
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Demand Sensitivity to p and q values
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Distribution of p values for home with 2 residents
45
4
109
67
177 4 0 0 0 1
0
20
40
60
80
100
120
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045
Freq
uency
Probability
(N = 209)
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Summary Probability of Fixture of UseEach fixture has a unique water use profile.Probability of fixture use depends on frequency
and duration of use.Probability of fixture use increased as the number
of residents increased.
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