(a) Estimate the annual energy cost of domestic hot water heating for an office building occupied by 1,000 people. Each person uses on average 3 gallons per day of hot water. The water temperature at the bathroom sink is 120°F. Due to the length of the distribution system, an average of 20°F

Question

(a) Estimate the annual energy cost of domestic hot water heating for an office building occupied by 1,000 people. Each person uses on average 3 gallons per day of hot water. The water temperature at the bathroom sink is 120°F. Due to the length of the distribution system, an average of 20°F decrease in water temperature occurs before the hot water reaches the bathroom sink. The heater is an oil-fired boiler with an efficiency of 75 percent. The cost of fuel oil is $1.20/gal. Assume that the entering water temperature is 55°F and that the building is occupied 300 days per year.
(b) Determine the cost savings if the losses in hot water temperature in the distribution system are virtually eliminated by insulating the pipes.

Accepted Answer

(a) Using Eq. (15.1), the annual fuel use by the water heater can be estimated. First, the water mass can be determined

[latex]E_{w} =m_{w} c_{w,p} (T_{wi}- T_{w,o})/ η_{WH}[/latex] (15.1)

[latex]m_{w} = 3.0gal/pers/day *1000pers *300days/yr *8.33lbm/gal = 7.497*10^{6} lbm/yr[/latex]

Therefore, the fuel use required to heat the water from 55°F to 140°F (=120°F + 20°F) is:

[latex]FU = 7.497*10^{6} lbm/yr*1.0Btu/lbm⋅°F [(140−55)°F]/(0.75*138*10^{3}Btu/gal)z[/latex]

or

FU = 6,157gals/yr

Thus, the annual fuel energy cost for water heating is:

Cost =[6,157gals/yr]*$1.20/gal = $7,388/yr

When the temperature decrease across the piping system is reduced from 20°F to 10°F (so that the actual hot water temperature from the heater is reduced from 140°F to 130°F), a reduction in the annual cost of heating the water results and is estimated to be:

ΔCost =[1−(130−55)/(140−55)]*$7,388/yr = $869/yr

It should be noted that the losses through the distribution systems are generally referred to as parasite losses and can represent a significant fraction of the fuel use requirements for water heating.

An economic evaluation analysis should be conducted to determine the cost-effectiveness of insulating the piping system.

Question 15.3: (a) Estimate the annual energy cost of domestic hot water he...

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