The usual way to think about waste water heat recovery is a classical drain water heat recovery device with a vertical copper drain that transfer the heat to cold water. These device are efficient if your family take showers, but not if they take bath...unless you have an additional storage tank, wich can be expensive. So I spent some time to think about an efficient, safe, cheap and easy wat to recover heat from hot water in a bath. You just let the bath water goes to room temperature before you flush it! That's a keep it simple stupid idea, but I'm far from being the first who think about that. But there is a big issue with that idea: relative humidity. Letting bath hot water for an hour or two will significantly increase the relative humidity in your bathroom...a very good recipe for mold. You might think about a bathroom fan to reduce that humidity, but that solution is a "Go back to start, do not pass go" idea since you'll also remove heat along with it. So, I finally found an alternative solution for those who have a HRV. You put an exhaust opening in the bathroom (let's say a 4 inch opening to get sufficient CFM). You'll remove the humidity and if your HRV is efficient, you'll recover most of the heat. I know it's a seasonal solution for cold climates, but it's better than to lose nearly 100% of it. It will cause some condensation in the heat exchanger, but as far as you have a drain that collect and drain that condensation, it's not a big problem. Regarding the shower, the best single solution is the "traditional" heat recovery drain, but replace your showerhead with a very low debit showerhead (let's say 1.5 GMP) will be more cost efficient and you can leave the hot water in the bath until it get to room temperature instead of draining it. Does this idea make sense? Any other suggestion? Thank you!

What happens when there are three children in a row needing baths? Do you need to wait for each one to lose the heat?

Other suggestion: Is more energy used for one shower (2 gpm, 6 minutes, 106F), or one bath (44 gal, 102F)?

Good question indeed! The only other option that I've thinked about is to replace parts of PVC bath and main vertical drain pipe with copper pipes, but even if copper is an effective heat conductor, I'm not sure about the % heat recovery that I would get even with a total of 15 feet of pipes (10 feet 1,5 inch and 5 feet 3 inches). I guess 25%....at best! I don't think it's worth the cost and trouble...

Regarding your other suggestion, it is indeed a very simple one! But not an easy one... I would have to convince my wife! ;-)

I guess 25%....at best!

Mmmmmmm....doubtful. Water has 10X the heat capacity of copper. You might have 15 lbs of copper there and 300 lbs of water (20X). That's more like 1/2 of 1%, and the next cold water that goes down the drain will take it away.

I would think that assumption is reasonable because with a little bit less than 5 feet of 3" vertical drain line you get approximately 50% heat recovery when there is a cold water copper line around it (colder than air, so more heat exchange). I'm not a specialist, but I would be surprised to get a 1% or so heat recovery rate. I checked the temperature with the actual pvc drain and at the beginning I got 36 degrees Celcius and at the end it was at approximately at 35, so actually that's already more than 1%. And PVC is a far less heat conductive material than copper.

60 gallons per bath @ 8 lbs per gallon with a 10 degree temp drop across your heat exchanger would give you about 4800 btus recoverable (but not necessarily usable) per bath. If gas cost $1.50 therm and your water heater was about 60% efficient, you'd save a theoretical maximum of about $3.60 per month, if you take one bath a day. Your actual benefit would be much less than that in my opinion because even if you could design a heat exchanger that could pull 10 degrees per pass out of that water and still drain the bathtub at an acceptable rate, it would still have to store the preheated water for later and would have stand by losses back through the drain pipe. A single pass heat exchanger, which is the most likely design, would be really pressed to get a 10 degree drop out of the bath water with only a 30 degree or so temp difference between the warm bath water and the cold incoming water.

Bumping from a 60% efficient to a 90% efficient water heating source would save you more money because you would save on the entire amount of heat input to the bath water, not just the portion of the residual heat you could recover from the now warm, not hot bath water when you were done with it.

In short, don't waste your time.

50% heat recovery when there is a cold water copper line around it

That's because there is a surplus of cold water available to remove the heat.

Float a piece of flexible foam (neoprene?) or drape plastic sheet in the bathtub and the humidity issue goes away. Put a pinhole leak in the drain plug and the bathtub will be empty about 24 hours later.

Of course there are fewer btus saved in letting 100F water drop to 70F vs having 100F water preheat incoming 50F water.