hunter curve
TRANSCRIPT
Hunter’s Curve in the 21st Century
ACEEE Hot Water Forum
Steven Buchberger
November 4, 2013
What is Hunter’s Curve?
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Hunter’s Curve Predicts Peak Flow
Fixture Units
GPM
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Life in 1940
Population = 2.3B Gas = $0.2/gal5
Life in 2013
Population = 7.0B Gas = $4/gal6
Hour
Flo
w (
L/m
in) Friday, May 16
0 4 8 12 16 20 24
0
20
40
60
80
100
End User Demand (21 units)
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t
T
q
One Fixture is a Bernoulli Trial
p = t/T = Average duration of flow
Avg time btn consecutive uses8
t
T
q
Three Key Parameters…..
Fixture Characteristics
Human Behaviorp = t/T
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Many Fixtures Exist
1 2 3 n• • • k • • •
1
2
3
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Many Fixtures Exist
1 2 3 n• • • k • • •
1
2
3
11Overlapping pulses
Design Problem
“Assuming that there are n (identical ) fixtures in a system, each operated once in Tseconds on the average, and that each operation is of t seconds average duration, what is the probability that k fixtures will be found operating simultaneously at any arbitrarily chosen instant of observation”?
(Roy Hunter, 1940)
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Many Fixtures are Binomial
1 2 3 n• • • k • • •
Pr 1
0,1,...,
k n kexactly k busy fixtures np p
out of n total fixtures k
twhere p k n
T
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Binomial Distribution Example
p=0.20; n=7
Binomial Distribution for Flush Tanks
Number of Busy Fixtures
pro
bability
0 2 4 6 8
0
0.1
0.2
0.3
0.4
77
Pr 0.2 0.8 0,1,...,7k kexactly k
kbusy fixtures k
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p=0.20; n=7
Binomial Distribution for Flush Tanks
Number of Busy Fixtures
pro
bability
0 2 4 6 8
0
0.1
0.2
0.3
0.4
Design Condition is 99th Percentile
1% chance
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99% chance
Design Flow, One Fixture Group
n
Fixture Group A
0 10 20 30 40
0
10
20
30
40
Q(0.99)
p=t/T=0.2
(gpm)n=7; Q=16 gpm
0.99
47 4 16
gpmQ n m q fixtures gpm
fixture
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Design Flows, Two Fixture Groups
n
Fixture Group A
Fixture Group B
Q(0.99)
0 10 20 30 40
0
10
20
30
40
p=t/T=0.20
p=t/T=0.05(gpm)
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Common Currency One Curve
Fixture Units
GPM
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Hunter’s curve has withstood the test of time and is the basis for plumbing codes around the globe today.
Hunter’s curve went viral long before U-tube arrived; not surprising, it is clever, convenient, correct.
However, today Hunter’s curve is often faulted for giving overly conservative design….why?
Hunter’s Track Record
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[1] Simplicity is seductive. Hunter’s curve has been applied to many situations for which it was not intended.
[2] Times have changed. Water use fixtures (hot and cold) have become much more efficient since Hunter’s pioneering work.
Two Main Issues
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Hunter’s Curve in 1940
Fixture Units
GPM
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Hunter’s Curve in 2013
GPMLEED, NZE, HE fixtures = lower q
uncongested use = lower n, p
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National effort in US to update Hunter’s curve for peak water demands.
Driven by professional societies, not the US Gov’t (not Nat’l Bureau Standards).
Prevailing sentiment is to simply revise the fixture units in the code.
What would Roy Hunter do?
Old Habits Die Hard
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IAPMO Sub-Task Group Orders
“….work singularly to develop the probability model to predict peak residential demands based on the number of plumbing fixtures of different kinds installed in one system.”
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Aquacraft Data Sets
• 2011 California Single Family Home Water Use Efficiency Study (n=750)
• 2011 Albuquerque Retrofit Study
o Pre-retrofit (n=240)
o Post-retrofit (n=29)
• 2010 EPA Standard New Homes (n=302)
• 2010 EPA High Efficiency New Homes (n=25)
[1,346 homes ….. >15,000 home days]
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Data Base Queries
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2
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5
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home unique ID
range of home IDs
Aquacraft data set(s)
age of home
retrofit status of home (Y/N)
geographic location of home
fixture performance (NLF, LF, ULF )
fixture group
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Data Base Queries
1
2
3
4
5
6
7
8
home unique ID
range of home IDs
Aquacraft data set(s)
age of home
retrofit status of home (Y/N)
geographic location of home
fixture performance (NLF, LF, ULF )
fixture group
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10
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12
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14
15
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indoor water use
outdoor water use
weekday water use
weekend water use
AM or PM use
hot or cold water use *
per capita daily water use
total annual household water use
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Data Base Queries
1
2
3
4
5
6
7
8
home unique ID
range of home IDs
Aquacraft data set(s)
age of home
retrofit status of home (Y/N)
geographic location of home
fixture performance (NLF, LF, ULF )
fixture group
9
10
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12
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14
15
16
indoor water use
outdoor water use
weekday water use
weekend water use
AM or PM use
hot or cold water use
per capita daily water use
total annual household water use
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21
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home square footage
yard square footage
number of bedrooms
number of bathrooms
number of occupants
age of occupants
water meter size
? _____________
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Six Types of Residential Fixtures
[1] Toilets (3 efficiency levels)
[2] Showers
[3] Bathtubs
[4] Faucets (all sinks)
[5] Dishwasher (energy star ratings)
[6] Clothes Washer (energy star ratings)
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Three Characteristics of Fixtures
[1] Pulse Intensity (q)
[2] Pulse Duration (t)
[3] Pulse Frequency (T)
t
q
T
Water Pulse Characteristics
Fixture Group
No of Fixtures
Typical MinimumWater Pulse
Average (Nominal) Water Pulse
Typical MaximumWater Pulse
Standard Deviation Water Pulse
Sample Size
Terms and Units Water Pulse
n q t v=qt q t v=qt q t v=qt q t v N q t v
FG 1 100 1.00 1.50 1.50 1.50 2.00 3.00 2.00 2.50 5.00 0.25 0.25 1.00 774
FG 2 100 1.50 3.50 5.25 3.00 8.00 24.00 3.50 10.00 35.00 0.50 1.50 6.00 191 gpm min gal
FG 4 50 1.00 0.50 0.50 1.00 0.50 0.50 1.00 0.50 0.50 0.00 0.00 0.00 1040.3
Average (Nominal) Water Pulse
q t v=qt1.50 2.00 3.003.00 8.00 24.001.00 0.50 0.50
(gpm) (min) (gal)
Fixture Group
FG 1FG 2FG 4
(example, N=50 homes)
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Peak Flow (99th percentile)
Fixture Group
FG 1, n=100FG 2, n=100FG 4, n=50
7 am 8 am0.026 0.0410.103 0.051
0.028 0.019
Probability of Fixture Use
p=t/T
(example, N=50 homes)
Hour ending 7 amFixtures Flow (gpm)
mean var mean var2.6 2.5 3.9 5.7
10.3 9.2 30.9 83.21.4 1.4 1.4 1.4
14.3 13.1 36.2 90.3
58.3 gpmQ(0.99)=
per Wistort 199432
Normal approximation (Wistort, 1994)
Computer simulation: SIMDEUM or PRPsym
Full enumeration of CDF (WDSA 2012)
Merge w/ Bldg Information Modeling (BIM)
“There’s an app for that!”
Tantalizing Possibilities
+ =+ +33
Phones to Faucets Analogy
“Arrival Rates”
Poisson Model Erlang 1918
“Time Between Uses”
Binomial Model Hunter 1940
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Shutterstock.com
End User Examples - 1
Schools
Hospitals
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Shutterstock.com
End User Examples - 2
Opera Houses
Bus/Rail Stations
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Shutterstock.com
End User Examples – 3…
Hotels, CBD
Sports Stadiums
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