How do I calculate BTU? (for a water heater project)

[OTAKUjbski]

The last time I dealt with any physics was 6 years ago in college, so forgive my apparent ignorance:

The Situation.

I have a swimming pool pump outside near the house's air conditioner unit (heat exchanger I think it's called). Well, the freon is coming out of the house in copper pipes to release heat and be cooled, and the swimming pool water is just begging to be heated.

I foresee a match made in heaven.
​

The Idea.

What I want to do is build a type of radiator to marry the hot freon with the cold water. If all goes well, this'll increase the efficiency of my air conditioning unit and save me lots of $$$ on a heating system for my pool.

I'll be using a large, PVC tank (similar to the one already on the pool pump system) to house the pool water I'm heating. The cool water will come into the bottom and exit near the top. Coiled inside of the tank will be the hot freon-filled copper pipes.​

The Problem.

• How big does this thing need to be?
  
  
• How do I calculate the BTU this thing is going to be capable of generating (to determine if this is even worth it)?
  
  
• Is there a better way to go about transferring the heat from the hot freon-filled copper pipes into the water?

According to http://www.fsec.ucf.edu/en/" and other Internet articles, it appears I'll need something like 100,000 BTU to raise the temperature of the pool 3 degrees F. So, I think that's my minimum goal.​

The Numbers.

PVC pipe housing the pool water

3" inside diameter
~40 PSI
75 - 83 degrees F
unknown water flow rate

Copper pipe with hot freon

0.5" inside diameter
110 - 120 degrees F
unknown pressure and flow rate

Water tank

I haven't built the system yet, so this is the major variable I'm trying to determine ... how big, and how much copper does this thing need to have in it?​

Thanks in advance to anybody who can help me with this problem.

 

[russ_watters]

Heat transfer problems like this are extrordinarily difficult to figure out mathematically. They are generally done experimentally. So you'll just have to pick some somewhat arbitrary conditions. Don't fret, though - the key factor isn't really the physical size of the heat exchanger, it's the flow rate. Physical size mainly affects how easy/difficult it is to pump your required flow rate. If, however, you find that you aren't pulling enough heat off the air conditioner, you can always just increase the flow rate of the water. I guess I'd probably make the coil of copper somewhere around the size of a roll of paper towels (maybe double-it up, too: two coils, one inside the other).

An air conditioner puts out a cooling capacity measured in Tons. A ton is 12,000 BTU (per hour). A BTU will raise the temperature of a pound of water 1 degree F. If 12,000 BTU is removed from your house, it must be dissipated at the condenser outside. Also dissipated is a portion of the compressor and fan energy. Let's say 75%. A typical residential air conditioner runs at about 1.5kW of electrical energy per ton of cooling. 1.5 kW is 5100 BTU, so that means the total energy dissipated at the condenser is 17,100 BTU per ton of cooling, give or take.

Now, typical heat exchangers go for a delta-T of 10 F, so if you have 17,100 BTU per hour, that's 3.4 gpm. So you'll need 3.4 gpm per ton of cooling going to your house. And remember, if you oversize the pump, it doesn't really matter because that's just more heat going into the water. You only lose perhaps 20% of it.

I've often toyed with the idea of using my air conditioner to preheat my hot water, but if the demands don't line up, it doesn't help much. Water heaters require a large energy input, but for a short time. For a pool water heater, where you don't care if the temperature fluctuates a little and you know you'll take days (weeks?) to heat up the water anyway, it isn't a major concern. If your pool is 30'x40'x5', that's 30,000 gallons, so it'll take 8 days to get a 10F temperature rise if you have 3 tons of cooling in your house and the air conditioner is running 1/4 of the time.

Disclaimer: I won't take any responsibility for what you're doing to your air conditioner here. I don't know how it will affect performance and reliability. I wouldn't think you would damage it if you take the refrigerant through the heatex after the compressor and before the condenser, but I don't really know. Low refrigerant pressure could be an issue. If it does become an issue, you could always reduce the heat transfer by reducing the flow rate.

 

[mgb_phys]

The system is generally known as a "heat pump" there are a few companies selling systems and a lot of web pages for DIY systems.
They are becoming popular in Europe with higher energy costs - generally the outside reservoir is a large pipe network buried in the ground and using ground water as the thermal mass - swimming pools are a little less common over here!