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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

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Reader's Comments

  1. Oil Future | January 1st, 2008 at 3:47 pm

    Hello webmaster…I Googled for oil heater, but found your page about er Formulas and Calculations | Sun Volt Solar Blog…and have to say thanks. nice read.

  2. Matt Stewart | April 6th, 2008 at 3:26 pm

    Thankyou for a very informative article and everything we can do to cut back will help.
    I am also working at getting off the grid and I am installing
    a water4gas hydrogen generator on my truck that will increase the mileage and cut back on emissions.
    My main goal is to be as self reliant as possible by using
    solar, wind, and water for everything as it becomes possible.
    Thanks again
    mattrock

  3. Reeves | April 8th, 2008 at 1:38 pm

    Great resource. Keep up the good work.

  4. Formulas for Solar Hot Water Systems | Sun Volt Solar Blog | April 9th, 2008 at 10:50 am

    [...] of thumb, here is how to calculate the actual energy required for any SDHW system. First, use the Hot Water Formulas and Calculations to determine how much hot water will be used. That use needs to be converted to a unit of energy. [...]

  5. air specific heat btu lb | June 11th, 2008 at 1:46 pm

    [...] it holds up well in most cases. As far as solar hot water system design, I and others recommehttp://www.sun-volt.com/blog/2007/12/09/hot-water-formulas-and-calculations/Drying and Storage of Grains and Oilseeds - Google Books Resultby Donald B. Brooker, Fred W. [...]

  6. Mike | June 13th, 2008 at 7:13 pm

    This is actually one of the few blogs that I want to keep up with.

  7. Vince | September 4th, 2008 at 1:38 pm

    For example, if there are 8 people in a household, and according to the equation for calculating hot water use by household clothes washer (cw_use = 1.1688^per+4.7737^per gal/day) = 1.1688^8 + 4.7737^8 = 269,679 gallons per day!!!! This does not look right at all.



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