The average hot water use per day was 44
gallons, in a study of 30 Canadian households.
The DOE test assumes 64 gallons. (Natural
Resources Canada PDF,
2008)
Households used 69.3
gallons of total water (hot+cold) per
capita in a large study. (AWWA PDF,
1999)
After installing water-saving toilets, washers, showerheads,
and faucets, total (hot+cold) household use dropped
39% from 175 g/d (gallons per day) to 107 g/d, and hot water
use dropped 10.8 g/d from 55
g/d to 44.2 g/d, a 20% reduction. (EPA
PDF,
2005)
The design spec for hot water use per person is 20-35
g/d. (Engineering
Toolbox)
By the way, you can get a thermostatic
shower valve to keep the water temperature constant even
when people flush toilets or turn on sinks in other parts of the
house.
Energy required to heat one gallon of water, and one tank of
water
Definitions & Conversion Factors
A Btu, or British thermal unit, is the amount of energy
needed to raise one pound of water from 60°F to 61°F at sea
level. (Wikipedia)
Heating a gallon of water by 1°F with no losses thus takes
8.33 lbs x 1 Btu/lb = 8.33
Btu's.
One therm is 100,000 btu's. So one Btu is 0.00001 therms.
(U.C.
Irvine)
Heating a gallon of water by 1°F with no losses thus takes
8.33 ÷ 100,000 = 0.00008.33
therms.
One kWh is 3413
Btu's, so one Btu is 1/3413 = 0.000293 kWh.
Heating a gallon of water by 1°F with no losses thus takes
8.33 Btu x 1/3413 kWh/Btu = 0.00244
kWh.
Temperature of groundwater. Varies from 35-77°F in
the U.S., and eyeballing a temperature
map, 47-67° seems like a good range, ad 57° seeming
like a good average.
Energy required to heat a 40-gallon tank of water
Groundwater 47°F, Heater set to 110°F: 63° rise x
8.33 Btu x 40 gallons = 20,992 Btus
Groundwater 47°F, Heater set to 120°F: 73° rise x
8.33 Btu x 40 gallons = 24,324 Btus
Groundwater 47°F, Heater set to 140°F: 93° rise x
8.33 Btu x 40 gallons = 30,988 Btus
Groundwater 57°F, Heater set to 110°F: 53° rise x
8.33 Btu x 40 gallons = 17,660 Btus
Groundwater 57°F, Heater set to 120°F: 63° rise (see
#1 above)
Groundwater 57°F, Heater set to 140°F: 83° rise x
8.33 Btu x 40 gallons = 27,656 Btus
Groundwater 67°F, Heater set to 110°F: 43° rise x
8.33 Btu x 40 gallons = 14,328 Btus
Groundwater 67°F, Heater set to 120°F: 53° rise (see
#4 above)
Groundwater 67°F, Heater set to 140°F: 73° rise (see
#2 above)
Above assumes 100% efficiency.
Cost to heat water a 40-gallon tank with gas
The federal standard for gas water heaters is only
55.6-59.4% efficiency (higher for smaller tanks), and actual
models are rarely much better, except for Energy Star models
which are at least 67% efficient. (DoE
2010, p. 9)
Gas price figured at $1.42/therm.
1 therm = 100,000 BTU, so cost is $1.42/therm x 1
therm/100,000 BTU = $0.0000142/BTU
43° rise: 14,328 Btus ÷ 67%
& 55.6% efficiency = 21,385 & 25,770 BTU, x
$0.0000142/BTU = $0.30 to
$0.37/tank
53° rise: 17,660 Btus ÷ 67%
& 55.6% efficiency = 26,358 & 31,763 BTU, x
$0.0000142/BTU = $0.37 to
$0.45/tank
63° rise: 20,992 Btus ÷ 67%
& 55.6% efficiency = 31,331 & 37,755 BTU, x
$0.0000142/BTU = $0.44 to
$0.54/tank
73° rise: 24,324 Btus ÷ 67%
& 55.6% efficiency = 36,304 & 43,748 BTU, x
$0.0000142/BTU = $0.52 to
$0.62/tank
83° rise: 27,656 Btus ÷ 67%
& 55.6% efficiency = 41,278 & 49,741 BTU, x
$0.0000142/BTU = $0.59 to
$0.71/tank
93° rise: 30,998 Btus ÷ 67%
& 55.6% efficiency = 46,266 & 55,752 BTU, x
$0.0000142/BTU = $0.66 to
$0.79/tank
Another source comes up with a similar figure: 0.40 therms
for the tank, based on 0.11 therms to heat 11 gallons of
water. (Multi-housing
Laundry Association)
MHLA also says it takes 3.3 therms to keep 11 gallons hot
for one month.
Cost to heat water a 40-gallon tank with electricity
A typical electric water heater is 90.4-95% efficient. (DoE
2008, p. 2)
Conversion factor: 0.000293 kWh/Btu x $0.14/kWh =
$0.00004102/BTU
43° rise: 14,328 Btus ÷ 95%
& 90.4% efficiency = 15,082 & 15,850 BTU, x
$0.00004102/BTU = $0.62 to
$0.65/tank
53° rise: 17,660 Btus ÷ 95%
& 90.4% efficiency = 18,589 & 19,535 BTU, x
$0.00004102/BTU = $0.76 to
$0.80/tank
63° rise: 20,992 Btus ÷ 95%
& 90.4% efficiency = 22,097 & 23,221 BTU, x
$0.00004102/BTU = $0.91 to
$0.95/tank
73° rise: 24,324 Btus ÷ 95%
& 90.4% efficiency = 25,604 & 26,907 BTU, x
$0.00004102/BTU = $1.05 to
$1.10/tank
83° rise: 27,656 Btus ÷ 95%
& 90.4% efficiency = 29,112 & 30,603 BTU, x
$0.00004102/BTU = $1.19 to
$1.25/tank
93° rise: 30,998 Btus ÷ 95%
& 90.4% efficiency = 32,629 & 34,290 BTU, x
$0.00004102/BTU = $1.34 to
$1.41/tank
WaterHeaterTimer.org
gets 6.84 kWh for a 70°F rise; for the 63° rise I
calculated, that would be 6.16 kWh, so our figures are
within the ballpark of each other's.
Yearly energy requirements
The DoE test procedure assumes an inlet water
temperature of 58°F, a set point of 135°F, and daily hot water
demand of 64.3 gallons. Annual consumption is figured in
therms as 41,045 Btu/EF x 365/100,000, or 149.8 therms at 100%
efficiency. A 2008 EPA
report showed yearly energy use figures as follows:
2195 kWh for a 50-gallon air-based heat pump with a 2.00
energy factor
4435 kWh for an electric tankless with a 0.99 energy
factor
4622 kWh for a 50-gallon electric tank with a 0.95 energy
factor
242 therms/yr. for a 50-gallon gas tank with a 0.62 energy
factor
183 therms/yr. for a gas tankless with a 0.82 energy
factor
Miscellaneous
Average runtime for a water heater is 3 hours/day
according to WaterHeaterTimer.org.
Electric tank wattage
A typical 50-gallon electric tank runs at 4500 watts.
At 3.412 BTUs per watt, 4500 watts = 15,354 BTU.
At 92% efficiency, that's 14,126 BTU.
From above, heating a gallon of water by 1°F takes 8.33 BTU.
Heating from 68°F to 104°F would by a 36°F rise, or 36 x 8.33 =
300 BTU to heat 1 gallon of water.
With 14,126 BTU, we could heat 14,126 BTU ÷ 300 BTU/gallon = 47
gallons.
So, our typical 4500-watt electric heater can make 47 gallons of
hot water per hour — about a full tank.
Like others, I've wondered why specs often read "Top element:
4500 watts, Bottom element: 4500 watts, Total
wattage: 4500 watts". Is only one element used at a time,
and if so, why? I found an answer on Yahoo
Answers: "On a hot water tank there is only one of
the elements on at a time. The incoming cold water is taken to
the bottom of the tank through a pipe inside the tank. When the
lower thermostat senses the cold water the lower element turns
on. As you draw hot water from the top of the tank the cooler
water from the bottom will rise. When the top thermostat senses
the cool water it shuts off the bottom element and turns on the
top element. When this water is heated to the tank set- point it
shuts off and the lower element turns on to heat the rest of the
water. When the total tank temperature is at the set point all
elements turn off. By using this type of procedure there is
always hot water at the top of the tank for use."
Also, 9000 watts with both elements running
simultaneously would require a massive electrical circuit, and
it's not necessary, since as we see from the calculations above,
4500 watts at a time can heat a whole tank in pretty short order
anyway.
Solar water heaters
While solar electricity
takes a while to recoup its installation cost, solar water
heating works a lot better, and is easier to install
and maintain. A system starts at around $4500 for a family
of four, but rebates and tax credits can lower the cost
substantially. You're looking at a payback time of maybe
12 years. Mr. Electricity's family enjoys solar hot water,
and no longer being tethered to the gas company. See my
page on solar water heating.