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

3

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

Changing Times

5

Modified Hunter’s Curve(s)

6http://www.armstronginternational.com/files/products/wheaters/pdf/sizing%20chart.pdf

Different curve for different end users

7

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 

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)

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

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%

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

[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= ∑

Computed Fixture Flow Rate; q

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( )( )

Volumeof each pulse gallonsq

Duration of each pulse minutes= ∑∑

Summary of “Efficient” Fixture Flow Rate 

18“Efficient” = Ultra‐efficient  and Efficient Fixtures

0123456789

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Bathtub Clothes Washer Toilet Shower Faucet Dishwasher

Flow

 rate (gpm

)

MeanOutliersRecommended

C.W. 

Hourly Fixture Use (Volume)

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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

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)

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)

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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)

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

=⋅ ⋅

−−−−

∑

Probability of Fixture Use at Individual Homes

Considered only efficient fixtures24

10 0.171 1 60

minutespfixture day minutes

= =⋅ ⋅

ii

tp

n D T=

⋅ ⋅

∑

Probability of Fixture Use – Group of Homes

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Number of residents

Number of bathrooms

Number of bedrooms

Positive Correlation

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

Design Fixture Probability Values

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p = 0.010

p = 0.005p = 0.025

p = 0.050

[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

−⎛ ⎞ ⎛ ⎞= −⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

“Frequency Factor” Approach

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( )0.99 0.99Q Mean z Standard Deviation= +

99th Percentile

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)

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= =

= + −∑ ∑

[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

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

Modified Hunter’s Curve(s)

39http://www.armstronginternational.com/files/products/wheaters/pdf/sizing%20chart.pdf

Different curve for different end users

Universal Dimensionless Design Curve

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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?

[6] CONCLUSION

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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.

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Single Family Homes

Questions?

Steven.Buchberger@uc.edu

University of Cincinnati

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Demand Sensitivity to p and q values

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Distribution of p values for home with 2 residents

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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)

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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