# Daily Hot Water Use - Legacy system

### Daily Hot Water Use

The Home Energy Saver web site uses the following equation[1] to estimate average daily hot water use in gallons per day (Lutz, et al. 1996). This equation was modified and improved from Lutz et al's version by subtracting out the constant assumed hot water use of clothes washers and dishwashers (the variables cloth and dish in Equation 4), and adding two variables (cwGals and dwGals) that allow users to individually specify their clothes washer and dishwasher hot water use (e.g. specifying loads washed at certain temperatures). These two variables (cwGals and dwGals) are used to allocate the water heater energy consumption into three portions; clothes washer, dishwasher and other. The energy consumed by the water heater for the clothes washer and dishwasher portions is reported with the Major Appliance energy in the final report. The calculation of hot water use by the clothes washer is described here and the calculation of hot water use by the dishwasher is described here.

Equation 4

where

Usewh = hot water consumption (gallons/day)

occupants = number of persons in household (sum age1-4)

age1 = number of people aged 0-5 yrs

age2 = number of people aged 6-13 yrs

age3 = number of people aged 14-64 yrs

age4 = number of people aged 65- yrs

Ttank= water heater thermostat setpoint (°F)

tank_size = rated volume of water heater (gallons)

Tin = inlet water temperature (°F)

average_temp = average annual outdoor air temperature (°F)

adult_at_home = 1 if TRUE, 0 if FALSE, adult at home during day

dish = dishwasher hot water use embedded in original Lutz et al. equation (Lutz, et al. 1996, Equation 12)

cloth = clothes washer hot water use embedded in original Lutz et al. equation (Lutz, et al. 1996, Equation 8)

cwGals = calculated gallons of hot water used by clothes washer based on user inputs, see Clothes Washer Energy Consumption [replaces more generic estimation method (cloth)] (gallons/day)

dwGals = calculated gallons of hot water used by dishwasher based on user inputs, see Dishwasher Energy Consumption [replaces more generic estimation method (dish)] (gallons/day)

The original model set pay to 1.3625 if residents do not pay for energy to make hot water (to reflect less water-conserving behavior), but since HES does not have an option for multi-family or solar, pay is currently fixed at 1.

senior = 0.379 if only seniors live in household and it is a multifamily residence, otherwise senior = 1

[1] The original development of the water heating analytical method was sponsored by the U.S. Department of Energy, Office of Building Technology, State, and Community Programs as part of their appliance standards analysis program (US DOE 2000c).