Need math expert for heating water for pool

[layla2052]

I'm wanting to know how much hot water it would take to change temp in 27000 gals by 3 degrees. We have an instant water heater we've considered using temporarily. Thing is, our pool is in shade most of the time (only in full sun about 4-5 hrs a day) so it doesn't get much opportunity to get real warm. It's been unseasonably cool here this summer as well so looking to explore our options without spending a fortune. Currently, the pool temp stays around 76-78 but has been up to 82 for a few days so would like to get it back at least there or better & keep it there for the rest of the season. Considering a solar cover to get help hold it there once attained. All opinions welcome.

 

[JohnT]

Way more than your heater can handle. More than 2000 gallons of water at 120F added to the pool to raise it 3 degrees.

 

[layla2052]

The instant on demand water heating system is what we have for the house & we have an outside spigot for it that we use for any purpose we need hot water outside. It runs on our natural gas & will run indefinitely but eventually would get costly, the gas cost, I mean. That's why we were wondering how many gallons of hot to make small temp change in the pool.

 

[chem geek]

You should get a clear solar cover since that will not only retain heat, but will let sunlight through to heat the pool during the day. That is by far the most economical way for you to raise the temperature of your pool even with only 4-5 hours per day of full sun.

1 British Thermal Unit (BTU) is the amount of energy needed to heat one pound of water by 1ºF. 27,000 gallons is around 225,000 pounds of water so would take 675,000 BTU's to heat up by 3 degrees. While residential swimming pool gas heaters range from roughly 125,000 to 400,000 BTU/hr and assuming 84% efficiency it would take 2 to 6.4 hours to heat the pool with gas heat.

Tankless water heaters are most commonly rated up to 199,900 BTU/hr maximum input and high-end 95% efficiency with a maximum flow rate of 7.5 to 9.8 GPM depending on model. So assuming you have one of these largest units and you used your pool water as input to it then it would take around 3-1/2 hours to heat the pool by 3ºF, assuming there were no heat losses from the pool. The heating at 9.8 GPM (81.634 pounds water per minute) from cold water to hot would be 39ºF.

If you are instead just talking about adding hot water to the pool, then you'd need to remove water from the pool to replace and mix. This would be less efficient than what I described above because most of the heat from the tankless water heater would be raising the cold tap water temperature rather that starting from your likely already warmer pool water temperature. As noted above, the temperature gain at maximum flow rate is 39ºF, but if your cold water is 60ºF then the hot water is only 100ºF. So to answer your question we'd have to know the temperature of your water from the hot water outlet and the flow rate at that temperature so we can tell you how long it will take. Again, most of the energy is completely wasted on heating water that is likely colder than your pool.

As John noted it would take
((27000 - x)*T) + x * 120 = 27000*(T+3)
27000*T - x*T + x*120 = 27000*T + 3*27000
x*(120-T) = 3*27000
x = 81000/(120-T) or the general formula (Gallons To Replace) = (Temp Rise)*(Gallons in Pool)/((Temp of Hot Water) - (Temp of Pool Initially))
so starting with 79ºF this is 1975 gallons while starting with 80ºF this is 2025 gallons of 120ºF water. At 5 GPM, this would take 6-2/3 hours.

 

[layla2052]

Thanks Chem geek! That's exactly what I needed to know. I like to know all the variables before making a good decision so I really appreciate it.