A question for physicists

[Tom NJ]

We have a warm spell coming and so I want to heat my in-ground pool up as quickly as possible. My heat pump for the pool says its maximum efficiency is at a flow rate of 48 gallons/minute. When I set my variable speed pump to deliver 48 GPM the water temperature entering the pool is 92.4°F (33.6°C or 307°K).

Alternatively, I can set my pump to deliver the heated water faster but slightly cooler, i.e. 67 GPM with the water entering the pool at 91.0°C (32.8°C or 306°K). So I’d like to know which setting will heat my pool faster.

The other variables such as pool volume, pool water temperature, air temperature, wind speed, and sun shine are all constants and should not factor into this calculation. And the cost of operating the pump is also not an issue, only how fast I can heat the pool.

So I guess my question amount to this: Which would have more total energy, a vessel containing 48 gallons of water at 92.4F, or a vessel of water containing 67 gallons of water at 91.0F?

 

[mk378]

BTU production is the temperature rise between the input and output of the heater times the flow rate (in lb/hour which of course is directly proportional to gallon/minute). When those BTUs mix with the large volume of water in the pool, the rate of rise of the pool overall is BTU/hr from the heater divided by pounds of water in the pool.

A heat pump will move more BTU when the difference in temperature between the cold side and the hot side is smaller. This suggests using a high flow rate to remove heat from the hot side better (since you have no control over the cold side). Also all the work done by the pump ultimately also increases the temperature of the water, so running the pump faster will heat the pool faster. This is a less efficient use of electricity than the heat pump but you said you don't care about that. As you said, the manufacturer's recommendation of 48 gpm is based on efficiency-- balancing the heat pump benefiting from low delta T versus higher pump energy usage as flow increases.

 

[Pablo]

So there is no supplemental resistance heater? Seems like just a few short bursts would aid the situation without severe bill impacts

And I would say ultimately the higher volume bit lower temp water holds more energy

 

[fsdork]

Taking a stab from some quick online research - someone with a PhD in thermodynamics will probably tear this apart.

Assuming an intake temperature (not provided) of 70°F:

67 gallons @ 91.0°F
67 gal = 254 L
Delta-t = 21.0°F
Energy required to reach 91.0°F = 12390586 J

48 gallons @ 92.4°F
48 gal = 182 L
Delta-t = 22.4F
Energy required to reach 92.4°F= 9470180 J

Ratio = 0.7643

Therefore, the warmer, lower volume output absorbed roughly 24% less energy than the cooler, higher volume output.

 

[Elkins45]

Maximum thermal efficiency would happen if you could pass so much water over the heating element that it would bleed off all the heat it was producing and stay at the same temp it was before you turned it on. As long as the water is leaving at a higher temperature than it entered then higher flow rates give more heat transfer.

 

[Tom NJ]

Thanks everyone! So it seems the consensus is that the higher flow rate will heat the pool faster, so I increased the pump speed. Given the cold nights and cool days it took three days, but I got the water up to 89°F today (heater took it to 87° and the sun beating on the dark blue automatic pool cover added another 2°). Had a nice swim today and will again the next two days before the air temperature drops to the low 50s. That will be it for the season.

 

[Foreman04]

Must ask. Are you taking a bath or going swimming?

 

[bbhero]

Thanks everyone! So it seems the consensus is that the higher flow rate will heat the pool faster, so I increased the pump speed. Given the cold nights and cool days it took three days, but I got the water up to 89°F today (heater took it to 87° and the sun beating on the dark blue automatic pool cover added another 2°). Had a nice swim today and will again the next two days before the air temperature drops to the low 50s. That will be it for the season.

Tom I would have suggested having huge bonfire and having large rocks put in that large bonfire… Then put the large rocks in your pool… That would have been my suggestion.

 

[MolaKule]

Thanks everyone! So it seems the consensus is that the higher flow rate will heat the pool faster, so I increased the pump speed. Given the cold nights and cool days it took three days, but I got the water up to 89°F today (heater took it to 87° and the sun beating on the dark blue automatic pool cover added another 2°). Had a nice swim today and will again the next two days before the air temperature drops to the low 50s. That will be it for the season.

My suggestion would be to invite as many BITOG members as possible into your pool and allow their 100W per person power dissipation (due to metabolism) raise the temperature.

Of course feeding them might bankrupt you.

 

[Skippy722]

My suggestion would be to invite as many BITOG members as possible into your pool and allow their 100W per person power dissipation (due to metabolism) raise the temperature.

Of course feeding them might bankrupt you.

I’ve got 4 sons who love swimming… they will absolutely bankrupt your food budget however, and my 3rd child will somehow manage to set the water on fire. Don’t ask me how, all I know is he is mischievous and smart enough to figure it out.

 

[Tom NJ]

Must ask. Are you taking a bath or going swimming?

87° to 89° is refreshing when the air temperature is only 72°. The pool water has gotten as high as 92° on hot summer days - now that is more like a bath. When I really want hot I jump in my hot tub at 103°!

 

[Tom NJ]

Tom I would have suggested having huge bonfire and having large rocks put in that large bonfire… Then put the large rocks in your pool… That would have been my suggestion.

That would have worked, but then how do you get the large rocks out?

 

[oil pan 4]

That's just mechanical engineering.
Input temperature would help and need to know volume of water.
I hot wired a natural gas pool heater at an air bnb we rented, figured it was doing about 100,000btu per hour based on gas meter spinnings.

 

[bbhero]

That would have worked, but then how do you get the large rocks out?

You hire one of the World’s Strongest man contest to haul them out of there…

 

[userfriendly]

That would have worked, but then how do you get the large rocks out?

Large rocks weigh less when they are in water.