Hot Water Formulas and Calculations
09 Dec 07 | Solar Hot WaterThe 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
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Tags: design, SDHW, Solar Hot Water, solar thermal
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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.
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
Great resource. Keep up the good work.
[...] 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. [...]
[...] 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. [...]
This is actually one of the few blogs that I want to keep up with.
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.