Okay so I did the heat exchanger calculation on your shower drain. I'll set it up so you can change the numbers to fit what your set up is.
Cp for water: (75.4x10^-3)(KJ/mol C)
Gallons of water per shower: 40 Gal
# of showers per day: 1
Temperature of in coming water: 65 F
Temp of shower drain water: 95 F
Cost of electricity: $0.147/Kwh
Cost of Heat Exchanger: $300 - $500
Cost of instillation: DIY
First lets convert the water temp from F to C:
(95F-32)/1.8 = 35 C
(65F-32)/1.8 = 16.3 C
The difference of our temp is
16.7 C
Now lets convert Gallons of water to mols
the density of water is:1000Kg/m^3
(1000Kg/m^3)(1000g/Kg)(1mol/18g)(1m^3/264.17Gal) = 210.3mol/Gal
40Gal(210.3mol/Gal) =
8412 mols of water per shower
The energy balance:
Delta H = Cp(Delta Temp C)(mols of water) = Q
Q is the amount of energy transfered from the hot water to the cold water (assuming the amount of water in = out and that the amount of cold/hot water is the same, with the hot water coming out at the temp of the cold water and the cold water coming out at the temp of the hot water, 100% heat transfer)
Q = (75.4x10^-3)(KJ/mol C)(16.7 C)(8412 mol) = 10592.22 KJ
Let convert the KJ to Kw*h
10592.22KJ(1000J/1KJ)(2.778x10^-7/1J) =
2.94 Kwh saved
Money saved per day
(2.94Kwh)($0.147/Kwh) = $0.43 per day
(365days/year)($0.43/day) =
$156.95 saved per year
Remember I only take one shower a day, you might have more people in the house or take more than one shower per day.
How long does this take to pay for it self?
(Cost of heat exchanger + instillation)/($0.43/day)=(# of days to pay off)
$300/(0.43) = 697 days = 1.9 years
$500/(0.43) = 1162 days = 3.2 years
I found this website where I got the heat exchange numbers from:
http://www.toolbase.org/Technology-I...-heat-recovery
I personally think you could make your own system cheaper, but even if you had someone else do this for you it is generally good idea to do anything with a less than 3 year pay back period.
if you use gas here is the Kwh to Btu conversion:
2.778x10^-7 Kwh = 9.486x10^-4 Btu