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Hot Water Formulas and Calculations

09 Dec 07 | Solar Hot Water

The general use calculation for hot water heating system design is about 80 gallons of hot water for a family of four. That is a very rough estimate, however, it holds up well in most cases. As far as solar hot water system design, I (and others) recommend installing systems this size on most residential housing units. It is not all that much more expensive than a 60 gallon system, which is the next size down.

Even if less than four people live in that particular house, solar domestic hot water (SDHW) systems have service lives of 25-35 years or more. Chances are good that the property will transfer ownership in that time, possibly to a larger family.

Several years ago, the US Department of energy put a great deal of effort into defining an equation which would more precisely calculate hot water use. Their work is below:

Daily Hot Water Use

Use the following equation to estimate average daily hot water use in gallons per day.

vol = ( -1.78 + 0.9744 x per + 6.3933 x age1 + 10.5178 x age2 + 15.3052 x (age3+age4) -0.1277 x thermostat + 0.1437 x tanksz - 0.1794 x wtmp + 0.5155 x atmp + 10.2191 x athome - (1-dw) x dw_use - (1-cw) x cw_use ) x IF(senior_only,0.379,1) x IF(NOT(pay),1.3625,1)
variable units (or equation) description
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
per = sum(age1,age2,age3,age4) total number of people in household
tstat °F water heater thermostat setpoint
tanksz gals rated volume of water heater
wtmp °F inlet water temperature
atmp °F average annual outdoor air temperature
athome = 1 if TRUE, 0 if FALSE adult at home during day
pay = 1 if TRUE, 0 if FALSE residents pay for energy to make hot water
senior_only = 1 if TRUE, 0 if FALSE only seniors live in household and it is a multifamily residence<
dw = 1 if TRUE, 0 if FALSE dishwasher present in home
cw = 1 if TRUE, 0 if FALSE clothes washer present in home
dw_use =0.692^per+1.335^per gal/day hot water use by household dishwasher
cw_use =1.1688^per+4.7737^per gal/day hot water use by household clothes washer
(if use hot or warm water for clothes washing)

Daily Water Heater Energy Use

To estimate average daily hot water energy consumption in BTUs per day, use the following equation.

variable units (or constants) description
vol gals/day average daily hot water use.
RE   recovery efficiency of water heater
UA BTU/hr-°F standy heat loss coefficient of water heater (if not available see section below)
Pon BTU/hr rated input power of water heater
Ttank °F tank thermostat set point
Tinlet °F inlet water temperature
Tamb °F air temperature around water heater
dens 8.293752 lb/gal density of water
Cp 1.000743 BTU/lb-°F specific heat of water

Annual Water Heater Energy Use

To estimate average annual hot water energy consumption by type of fuel, use the following equations.

fuel type equation (with units) description
electricity = 365 * Qin / 3412.76 kWh/yr annual water heater electricity use
natural gas = 365 * Qin / 100,000 therm/yr annual water heater natural gas use
propane = 365 * Qin / 91,500 gal/yr annual water heater propane use
fuel oil = 365 * Qin / 138,690 gal/yr annual water heater fuel oil use
 
variable units description

Standby Heat Loss Coefficient

To calculate UA, if necessary, use the following equation.
UA has units of BTU/hr-°F. EF, RE and Pon come from water heater product data.
This calculation is based on the DOE Energy Factor test procedure for water heaters.

variable units description
EF =   Energy Factor
RE =   Recovery Efficiency
Pon = BTU/hr rated input power
Qout = 41093.7 BTU/day Energy content of water drawn from water heater during 24 hour test.

Source:
1996 Lutz, J. D., Liu, X., McMahon, J. E., Dunham, C., & McGrue, Q. T. “Modeling Residential Hot Water Use Patterns” No. LBL-37805. Lawrence Berkeley National Laboratory. November 1996
About Hot Water Heating Module

Related posts:

  1. Formulas for Solar Hot Water Systems
  2. Solar Domestic Hot Water for my house
  3. Solar Domestic Hot Water Systems
  4. Does solar hot water work in cold climates?
  5. Shortage of Solar Hot Water Collectors

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09 Dec 07 | Solar Hot Water | Comments (7)