APPENDIX 7-B. HOT WATER DRAW MODEL
 

TABLE OF CONTENTS
 

7-B.1 INTRODUCTION ................................................................................................. 7-B-1 

7-B.2 SEASONAL EFFECT ADJUSTMENTS.............................................................. 7-B-1 

7-B.3 CLOTHES WASHER AND DISHWASHER ADJUSTMENTS ......................... 7-B-2 

7-B.4 HOT WATER DRAW MODEL COEFFICIENTS AND VARIABLES.............. 7-B-2 

7-B.5 SAMPLE CALCULATION USING THE HOT WATER DRAW MODEL ....... 7-B-4 

7-B.6 REGIONAL AVERAGE DAILY HOT WATER USE VOLUMES .................... 7-B-6 

LIST OF TABLES 

Table 7-B.2.1 Summary of EPRI Analysis Results for Seasonal Coefficients................. 7-B-1
 

Table 7-B.2.2 Summary of Seasonal Values .................................................................... 7-B-1
 

Table 7-B.3.1 Impact of Clothes Washer and Dishwasher Adjustments.......................... 7-B-2
 

Table 7-B.4.1 Variable Definition and Value Derivations ............................................... 7-B-3
 

Table 7-B.4.2 Coefficient Definitions............................................................................... 7-B-4
 

Table 7-B.5.1 Sample Hot Water Draw Model Calculation for a 40-Gallon Water
 

Heater......................................................................................................... 7-B-5
 

LIST OF FIGURES 

Figure 7-B.5.1 Average Daily Hot Water Use for Sample Calculation............................. 7-B-5 

Figure 7-B.6.1 Regional Average Daily Hot Water Use for Gas-Fired Storage Water 

Heaters ....................................................................................................... 7-B-6 

Figure 7-B.6.2 Regional Average Daily Hot Water Use for Electric Storage Water 

Heaters ....................................................................................................... 7-B-6 

Figure 7-B.6.3 Regional Average Daily Hot Water Use for Oil-Fired Storage Water 

Heaters ....................................................................................................... 7-B-7 

Figure 7-B.6.4 Regional Average Daily Hot Water Use for Gas-Fired Instantaneous 

Water Heaters............................................................................................. 7-B-7
 

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APPENDIX 7-B. HOT WATER DRAW MODEL 

7-B.1 INTRODUCTION 

DOE developed a modified Hot Water Draw Model1 as an improvement on a previously 

existing model. The Hot Water Draw Model estimates the average daily volume of hot water 

used by various households by accounting for the key characteristics described below. 

DOE modified the Hot Water Draw Model to be able to calculate seasonal hot water use. 

DOE also adjusted the Hot Water Draw Model to account for changes in hot water use by clothes 

washers and dishwashers due to the updated Federal energy conservation standards for these 

products. 

7-B.2 SEASONAL EFFECT ADJUSTMENTS 

The seasonal coefficients for spring, summer, fall, and winter were derived using the 

linear regression results in the EPRI study found in appendix A of Modeling Patterns of Hot 

Water Use in Households.1 Table 7-B.2.1 provides the detailed seasonal coefficients by hour. To 

obtain the total values, number of hours was multiplied by the coefficients. 

Table 7-B.2.1 Summary of EPRI Analysis Results for Seasonal Coefficients 

hour # hours 

Weekday (I-P units) Weekend (I-P units) 

a10 a11 a12 a13 a10 a11 a12 a13 

(spring) (summer) (fall) (winter) (spring) (summer) (fall) (winter) 

11-6 7 0 0 0 0.1459 0.0907 0.1675 0 0.1696 

6-8 2 0 -3.593 0 0 0 -1.569 -0.6553 0 

8-11 3 0 0 -0.432 0.5654 1.2574 0 0 1.3516 

11-1 2 0 0 -0.4447 0.4012 0 -1.2638 0 1.4804 

1-5 4 0 0 0 0.683 0 -0.9405 0 1.1756 

5-7 2 0 -0.9736 0 0.9658 0 -1.4838 0 1.6384 

7-9 2 0 -2.1273 -0.8588 0 0.8262 -0.9764 0 0 

9-11 2 0 -0.8922 -0.9381 0 0 0 -0.3788 0 

Total 0 -15.1722 -5.7792 8.1835 6.0595 -13.1755 -2.0682 16.182 

To obtain the daily average values (see Table 7-B.2.2) the coefficients were weighted by 

the number of days in the week which are weekend and weekday. 

Table 7-B.2.2 Summary of Seasonal Values 

Seasonal Coefficient Average Value Standard Deviation 

Spring 1.731286 0.52 

Summer -14.6017 4.35 

Fall -4.71891 1.41 

Winter 10.46879 3.12 

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7-B.3 CLOTHES WASHER AND DISHWASHER ADJUSTMENTS
 

The Hot Water Draw Model incorporates the parameters for clothes washer and 

dishwasher hot water use. These parameters reflect assumptions about clothes washer and 

dishwasher water use as they existed in the 1990s. Since that time, there has been a considerable 

change to clothes washer and dishwasher technology that has resulted in lower hot water use. In 

particular, updated Federal energy conservation standards for clothes washers that became 

effective in 20072 and for dishwashers that will become effective in 20103 have a significant 

impact on clothes washer and dishwasher hot water use. 

The baseline water use for clothes washers in the 1990s was 39.2 gallons/cycle and the 

water use calculated based on the 2007 standard is 21.0 gallons/cycle.2 The baseline water use 

for dishwashers in the 1990s was 8.2 gallons/cycle and the water use calculated based on the 

2010 standard is 6.5 gallons/cycle.4 Therefore, DOE updated the draw model to account for the 

reduced hot water use by adjusting the dishwasher and clothes washer water use variables to 

account for the new standards. The results are shown in Table 7-B.3.1. For example, the impact 

on gas-fired storage water heaters was a reduction of the average daily water use by 10.7 percent. 

Table 7-B.3.1 Impact of Clothes Washer and Dishwasher Adjustments 

Product Classes Average Hot 

Water Use 

(not Adjusted) 

Average 

Hot Water 

Use 

(Adjusted) 

Change in 

Hot Water 

Use 

Percent 

Change 

gal Gal gal % 

Gas-fired (Storage) Water Heater 50.7 45.3 -5.4 -10.7 

Electric Water Heater 47.5 43.1 -4.4 -9.3 

Oil-fired Water Heater 48.2 43.0 -5.2 -10.8 

Gas (Instantaneous) Water Heater 51.3 46.4 -4.9 -9.6 

7-B.4 HOT WATER DRAW MODEL COEFFICIENTS AND VARIABLES 

The Hot Water Draw Model uses an equation that is expressed as follows: 

vol = {sea _ coef + ( per _ coef * per ) + (age 1_ coef * age 1) + age 2 _ ceof * age 2 +

[age 34 _ coef *(age 3 + age 4) + (T tank _ coef *T tank ) + (Tanksz _ coef *Tanksz ) +

(T in _ coef *T in air ) + (T _ coef + T air ) + (hom e _ coef * at hom e) −

[(0.692 * per +1.335* per ) * dw _ adj −[(1.1688* per + 4.7737 * per ) * cw _ adj ]}*
 

(senior _ mf _ coef * senior _ mf ) *(no _ pay _ coef * no _ pay ) 

Table 7-B.4.1 lists the variables used in the equation as well as the definition and 

derivation of the value for each RECS household 

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Table 7-B.4.1 Variable Definition and Value Derivations
 

Variable Definition Value Derivation 

per total number of persons in 

household 

=NHSLDMEM* 

age1 number of preschool children, age 

0-5 yrs 

=PRESCHOOLCHILDREN** 

age2 number of school age children, age 

6-13 yrs 

=SCHOOLCHILDREN** 

age3 number of adults, age 14-64 yrs =ADULTS** 

age4 number of adults, age 65 yrs and 

over 

=SENIORS** 

Ttank water heater thermostat setting, oF Uniform distribution from contractor 

survey (See Ch. 7) 

Tanksz water heater nominal tank size, gal Derived using WHEATSIZ and 

methodology described in Ch. 7 

Tin water heater inlet water 

temperature, oF 

Calculated (See Ch.7) 

Tair outdoor air temperature, o

F Derived using HD65 and CD65 

variables, using the methodology 

described in appendix 7-D 

athome presence of adults at home during 

day 

=ATHOME* 

dw_adj adjustment factor to account for 

the differences due to the current 

energy conservation standard for 

dishwasher and for the cases of 

households with no dishwasher 

= IF DISHWASH*=1 then .207 

IF DISHWASH*≠1 then 1 

cw_adj adjustment factor to account for 

the differences due to the current 

energy conservation standard for 

cloth washers and for the cases of 

households with no cloth washers 

= IF CWASHER*=1 then .464 

IF CWASHER*≠1 then 1 

senior_mf senior-only household in a multifamily building = IF TYPEHUQ*=4 or 5 AND 

NHSLDMEM*=YEAR4*, then 1; 

= IF TYPEHUQ*≠4 or 5 OR 

NHSLDMEM*≠YEAR4*, then 0 

no_pay household does not pay for hot 

water 

= IF (PGASHTWA, LPGPAY, 

PELHOTWA, or FOPAY)*=1 then 0 

= IF (PGASHTWA, LPGPAY, 

PELHOTWA, or FOPAY)*≠1 then 1 

* RECS 2005 variable. See appendix 7-A for definitions. 

** Values derived from RECS 2005 variables. 

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Table 7-B.4.2 lists the coefficients used in the equation as well as the definition and 

normal distribution parameters for each RECS household 

Table 7-B.4.2 Coefficient Definitions 

Coefficient Definition Normal Distribution 

Parameters 

Average 

Value 

Standard 

Deviation 

sea_coef coefficient for seasonal effects See Table D.2.2 

per_coef coefficient for total number of persons in household 0.974 0.09 

age1_coef coefficient for age1 6.393 0.71 

age2_coef coefficient for age2 10.518 0.63 

age34_coef coefficient for age3 + age4 15.305 0.67 

home_coef coefficient for athome 10.219 1.44 

Tanksz_coef coefficient for tank size 0.144 0.03 

Ttank_coef coefficient for water heater setpoint -0.128 0.02 

Tinlet_coef coefficient for water heater inlet temperature -0.179 0.05 

Tair_coef coefficient for average outdoor temperature 0.512 0.06 

senior_mf_coef coefficient for senior-only household in a multifamily building 1.00 0.2 

no_pay_coef coefficient for household does not pay for hot water 1.00 0.2 

7-B.5 SAMPLE CALCULATION USING THE HOT WATER DRAW MODEL 

Table 7-B.5.1 and Figure 7-B.5.1 provide a sample calculation and results for a 40-gallon 

water heater and common values for the hot water draw model variables. 

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Table 7-B.5.1 Sample Hot Water Draw Model Calculation for a 40-Gallon Water 

Heater 

Variable Values Coefficients Gallons Spring Summer Fall Winter Spring Summer Fall Winter Spring Summer Fall

Winter 

Sea_coef 1.73 -14.60 -4.72 10.46 1.7 -14.6 -4.7 10.5 

per 3 0.974 2.9 

age1 0 6.393 0 

age2 1 10.518 10.5 

age3 2 15.305 30.6 

age4 0 15.305 0 

Ttank 120 o

F -0.128 -15.4 

Tanksz 40 gal 0.144 5.8 

Tin 56.0 68.7 64.2 51.2 -0.179 -10.0 -12.3 -11.5 -9.2 

Tair 55.3 74.1 57.9 37.5 0.512 28.3 37.9 29.7 19.2 

athome 1 10.219 10.2 

dw_adj 1 -.207 *(0.692 * per + 1.335 *√per) -0.9 

cw_adj 1 -.464*(1.1688*per +4.7737 *√per) -5.4 

senior_mf 0 1 1 

no_pay 0 1 1 

Total Gallons per Day 58.3 49.4 51.8 58.8 

48 

50 

52 

54 

56 

58 

60 

1 2 3 4 5 6 7 8 9 10 11 12 

Month 

Daily Hot Water Use (gallons / day) 

Figure 7-B.5.1	 Average Daily Hot Water Use for Sample 

Calculation 

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7-B.6 REGIONAL AVERAGE DAILY HOT WATER USE VOLUMES
 

Figures 7-B.6.1 to 7-B.6.4 show the range of average daily hot water use volumes for 

each product class and region. For oil-fired storage water heaters, data was only available for the 

listed regions. 

Gas-Fired Storage Water Heaters, Average Daily Hot Water Draw 

Median; Box 25%-75%; Whisker: 5%-95% 

0 

20 

40 

60 

80 

100 

120 

1 2 3 4 5 6 7 8 9 10 11 12 13 

Region 

Gallons 

median 

Average 

Figure 7-B.6.1 Regional Average Daily Hot Water Use for GasFired Storage Water Heaters 

Electric Storage Water Heaters, Average Daily Hot Water Draw 

Median; Box 25%-75%; Whisker: 5%-95% 

0 

20 

40 

60 

80 

100 

120 

1 2 3 4 5 6 7 8 9 10 11 12 13 

Region 

Gallons 

median 

Average 

Figure 7-B.6.2	 Regional Average Daily Hot Water Use for Electric 

Storage Water Heaters 

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Oil Storage Water Heaters, Average Daily Hot Water Draw 

Median; Box 25%-75%; Whisker: 5%-95% 

0 

20 

40 

60 

80 

100 

120 

1 2 5 10 

Region 

Gallons 

median 

Average 

Figure 7-B.6.3 Regional Average Daily Hot Water Use for Oil-


Fired Storage Water Heaters
 

Gas-Fired Instantaneous Water Heaters, Average Daily Hot Water Draw 

Median; Box 25%-75%; Whisker: 5%-95% 

0 

20 

40 

60 

80 

100 

120 

140 

160 

1 2 3 4 5 6 7 8 9 10 11 12 13 

Region 

Gallons 

median 

Average 

Figure 7-B.6.4 Regional Average Daily Hot Water Use for GasFired Instantaneous Water Heaters 

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REFERENCES
 

1.	 Lutz, J. D., X. Liu, J. E. McMahon, C. Dunham-Whitehead, L. J. Shown, and Q. T. 

McGrue, Modeling Patterns of Hot Water Use in Households, 1996. Lawrence Berkeley 

National Laboratory. Berkeley, CA. Report No. LBNL-37805 Rev. 

2.	 U.S. Department of Energy-Office of Building Research and Standards, Final Rule 

Technical Support Document (TSD): Energy Efficiency Standards for Consumer 

Products: Clothes Washers, 2000. U.S. Department of Energy. Washington, DC. Report 

No. LBNL-47462. 

<http://www.eren.doe.gov/buildings/codes_standards/reports/cwtsd/index.html> 

3.	 United States Cong. House. 110th Congress, H. R. 6 Energy Independence and Security 

Act of 2007. 2007. http://frwebgate.access.gpo.gov/cgibin/getdoc.cgi?dbname=110_cong_bills&docid=f:h6enr.txt.pdf 

4.	 U.S. Department of Energy - Energy Efficiency & Renewable Energy, Technical Support 

Document: Energy Efficiency Program for Consumer Products and Commercial and 

Industrial Equipment, Residential Dishwashers, Dehumidifiers, and Cooking Products, 

and Commercial Clothes Washers, 2007. Washington, DC. 

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