- A Btu is defined as the amount of heat required to raise the temperature of one pound of water one degree Fahrenheit.
- We must account for heat loss from the water storage tank and the efficiency of the heating element.
- The gallon per minute flow rate can be converted to pounds for the specified time use, and then converted back to Btu.
Source: Consumer Product Safety Commission
The cost of the thermal energy required to heat water can be calculated if the flow rate and the required temperature rise are known.
To illustrate with a simple example, the water flow for various home appliances is estimated per the following:
- Faucets: 0.75 gallons (2.84 liters) to 2.5 gallons (9.46 liters) per minute
- Low-flow showerheads: 1.2 gallons (4.54 liters) to 2 gallons (7.57 liters) per minute
- Older standard showerheads: 2.5 gallons (9.46 liters) to 3.5 gallons (13.25 liters) per minute
- Clothes washers and dishwashers: 1 gallon (3.79 liters) to 2 gallons (7.57 liters) per minute
Incoming potable water temperature is assumed to be 50°F (10°C). For most uses, the water heater temperature setting is 120°F (49°C), but can be as high as 140°F (60°C). For an end use such as a shower, a typical temperature of 105°F (41°C) is achieved with a combination of hot and cold water. To determine how much of a temperature rise is needed, subtract the incoming water temperature from the desired output temperature. Note that this same methodology can be applied to process water requirements for commercial or industrial applications.
Calculating BTU Requirements
A BTU is defined as the amount of heat required to raise the temperature of one pound of water one degree Fahrenheit. Since a gallon of water weighs 8.34 pounds, the gallon per minute flow rate can be converted to pounds for the specified time use, and then converted back to BTU. As an example, the BTU use of a 15-minute shower with a 2.5 GPM showerhead can be calculated as follows:
The amount of heat required = Water Volume (lb) x Temperature rise (°F) x 1 Btu/lb°F
Water Volume (lb) = 2.5 gal/min x 15 min x 8.34 lb/gal = 313 lb
Temperature rise from 50°F to 105°F = 55°F (assuming an average shower temperature of 105°F)
The amount of heat required = 313 lb x 55°F = 17,215 BTU required to raise 313lb of 50°F water up to 105°F
If the gas water heater efficiency is 68%, then there would be 25,316 BTU (17,215/0.68) required from the heating source to supply the thermal energy for this 15-minute shower. At a cost of $1.10 per ccf (103,000 BTU), the water heating cost for this 15-minute shower is approximately $0.27.
Line losses are not considered in this calculation, but will add to the BTU requirements. Line losses can be significant for heated water that is transported through uninsulated piping where the end use application is a considerable distance from the water heater.
The same methodology can be applied to calculating BTU requirements for heating process water in industrial applications once the flow rate, water heater (or boiler) efficiency, and line losses are known.