How long to raise pool temperature

[raguayo]

I've been out of school for about 19 years and would like to solve a diff. eqn.
If someone can point me toward the right equation that would be great. I will look for it as well and will try to solve the problem as well. If someone else finds info, I can use it to verify my findings. Thanks

Trying to heat my kids' above ground pool by using black polytubing used in gardening.

I am using a 1/3hp motor to pump water from the pool through the tuning and then return it to the pool. It's not even that cold but I need to have stuff to do to keep myself out of trouble : )

the pool itself is about 1500 gallons at 75.38 deg F

the heated water flows back in at 78.62 deg F at a rate of 473 gallons per hour.

ps. i had a different system used lower rate and higher temp diff that raised temp about 8 degrees in about 8 hours

 

[edgepflow]

You can basically solve an equation of the form:

m C dTpool / dt = UA (T_hot water - Tpool)

for the temperature of the pool, Tpool
m = mass of pool water = density of water X Volume
C = specific heat of water
U = overall heat transfer coefficient
T_hot water = average hot water temperature

 

[raguayo]

thanks for the info and the reply.
I do remember equations of the form

dT/dt = k (TH-TL)

basically the rate of T temp change with respect to time is proportional to high temp - low temp. Do you know if this takes into account if same water is pumped back in, or if it is replacing lost water?

Again this is just for fun, don't take too much time.

Thanks.

I will look at your previous response in detail tomorrow.

 

[edgepflow]

This model is for a fixed mass in the pool. It has been some time since I did cases of replacing fluid. I remember ending up with some recursive equations. I would try the fixed mass first.

BTW, I have also been out of school about the same length of time. But fortunately I do this stuff at work somewhat frequently and also for fun. I just try to keep my pea brain primed with this kind of stuff.

 

[egg84]

Please answer this for since I really cannot do the equation. If my pool temperature is currently 80 degrees and I am using a heat exchanger to raise the temperature ( pump runs at 900 gallon per hour) at what temperature do I need my heat exchanger to run at to effective raise the pool temperature

 

[raguayo]

Thanks edgepflow;


I will check out the solution I come up with and let you know what I get.



egg84: I am not familiar with working with heat exchangers, and did not realize you can set them at different temperatures. If I had to guess (and it's only a guess) getting the pool to the desired temperature as quickly as possible would be the most energy effficient way to do it so that you are not competing againts the heat loss to the environment for as long.

good luck.

 

[Naty1]

You don't need a formula, you can take measurements and get an exact answer...you have all the information.

"the pool itself is about 1500 gallons at 75.38 deg F

the heated water flows back in at 78.62 deg F at a rate of 473 gallons per hour."


So you are heating 473 gallons of water 78.6-75.4 or about 3.2 degrees in an hour...

You'll circulate all the water in about 1500/473 or about 3.2 hours...and some will be heated a bit more than the 3.2 degrees because it is passed twice...but as the water warms it will pick up a bit less heat from the heat exchanger...

So your current arrangement should heat your water about 3 degrees in three hours...seems like the same rate of heating your had before...about a degree per hour...

what is the question?

 

[raguayo]

Thanks, I understand that.

I have a data logger, temperature probes and a bucket and a stop watch. Empirical values are great and useful, but checking to see if predicted values are observed is a lot more fun and rewarding. I did figure its about three hours to replace the entire mass, but it's continuous, not discreet.

And again it's just for fun. I will not make any money, I may lose money on black poly tubing. LOL

Thanks.

Ps. If i get decent results from my equations, I will try to use variable coefficients for "k" and try to calibrate for angle of incidence of sunlight. : )