Recirculation pump calculation.

[Qmavam]

Because I lack so much data his is almost impossible to calculate, but I'd like some best guestimates.
I'm trying figure the cost difference between wasting 4.2 gallons of water that will need to be replaced and reheated, paid for and paid again to dispose down the sewer, vs heating and recirculating water.
I have calculated that 3 showers a day, wasting 1.4 gallons each time before we get hot water, for a total of 4.2 gallons. The cost to heat the water plus the cost of the water and the cost of the sewer is $0.25 per day.
Now the question is how much water do I need to recirculate each day to keep the water hot at the bathrooms. (i.e. how much extra water will I need to reheat each day because of the water that cools in the pipes before recirculation.? I expect to run the pump 15 hrs a day, but it will only flow water when the faucet has cooled to 90*F
The two bathrooms are at the opposite end from the water heater. That's 40 ft of 1/2" copper pipe in/under a concrete slab in Fl. that fills and
cools before recirculating. That calculates to 0.9 gallons of water to heat each time the water cools to 89*F. I could heat about 7 or 8 gallons of water for the cost of the wasted 4.2 gallons of water used without the recirculating pump.
How many times do you think the valve cycles in a 15 hour day? The cost benefit gets better when I start adding in the use from the kitchen sink, but I don't have a number for how often we wait for hot water and how much water flows while waiting.
This all seemed to be for my clarification and edification, but if you have any incite about this, please post.
BTW, my electricity cost is about 17cents per kWh and my water with sewer cost is 2.4 cents a gallon.
Qmavam.

 

[Jeff H Young]

I cant help with the math . but why do you need hot water for 15 hours showering only as you say? . put a manual switch or a motion sensor in bathroom and a 99 degree sensor why heat water 15 hours a day if you arent in bathroom I see no point in circulaing the water?

 

[Sponsor]

 

[Qmavam]

Because of the kitchen sink! My first thought about the hot water situation started with the kitchen sink, and having to wait so long to get hot water. I was first contemplating installing a 2.5 gallon water heater under the sink, but because of room considerations I dropped that and then got on to the recirculating pump idea. Now I'm trying to decide if I want it to work on just the kitchen sink or to both bathrooms.
As to the motion sensor or manual switch, I agree it is time these things get automated. I think a thermistor to measure the undersink water temp and a radio transmitter to tell a receiver at the pump to turn on the pump, would be the best answer. And add a timer to shut it off any hours your not home or asleep.
Qmavam