|Fig. 1: Drain water heat recovery system. (Courtesy of the U.S. Department of Energy)|
Energy consumption is a large topic in the modern world of science. With increasing costs and knowledge of adverse effects on the environment, new ways to create and conserve energy have been beneficial to our world. However, few methods have been implemented in households.
According to an analysis of the state of Washington, individuals use about gallons of hot water per day, which is about V = 100 liters.  Water enters a water heater at about Tc = 20°C, and hot water appliances use water at about Th = 40°C.  A certain amount of heat, Q, must be added to the water in order to increase its temperature by 20°C. This heat is determined by the expression 
where ρ = 1 kg/L and Cp = 4.2 kJ/(kg °K). Calculating this expression we find that each person uses about 8400 kJ per day.
The drain water of all hot water appliances goes through a heat exchanger. The point of a heat exchanger is to extract heat out of one fluid and put it into another without the two coming in contact. In this case, we do not want the dirty drain water to come into contact with the pure and cold water, but we want to pull heat out of the drain water to preheat the clean water. The warm drain water passes through a pipe that is coiled around the pipe carrying the incoming cold water. Heat is transferred from the drain water to the pipe by convection, conducted through the pipe material, and dissipated into the clean water through convection again. Knowing the fact that the heat exchanger is able to extract about 50% of the drain water heat, we can find the amount of energy we save with preheating the heat.  Only about 15% of the heat of water exiting the water heater is dissipated before entering the drain. 
If 15 percent of the water is dissipated before it enters the drain, and 50% of the heat is dissipated after flowing through the heat exchanger, the temperature of the incoming cold water is
Again Q = 8400 kJ, ρ = 1 kg/L, Th = 40°C, and Cp = 4.2 kJ/(kg °K). The temperature of the cold water is now 31.5°C with the drain heat exchanger. With this new temperature the energy usage per person to heat water is now 3570 kJ.
The drain heat exchanger can save a large amount of energy. Using the assumptions of this report, 4830 kJ can be saved with a heat exchanger capturing some of the waste heat of the drain water. Pay offs of this caliber should not be ignored. Residents using this technology will use much less energy, saving money and the environment.
© Nick Davidson. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 "2011Buildings Energy Data Book," U.S. Office of Energy Efficiency and Renewable Energy, March 2012, Fig. 8.2.4.
 F. Meggers and H. Leibundgut, "The Potential of Wastewater Heat and Exergy: Decentralized High-Temperature Recovery With a Heat Pump," Energ. Buildings 43, 879 (2011).
 A. McNabola and K. Shields, "Efficient Drian Water Heat Recovery in Horizontal Domestic Shower Drains" Appl. Energ. 59, 44 (2013).