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How to calculate btu output of each ft of copper pipe or stainless steal pipe for a heat exchanger
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mottywalter
Member Posts: 4
HI if someone can help with the calc. of btu output of copper pipe & stainless steal pipe i am trying to make a heat exchanger for a pool with a coil running inside boiler water the pool need to be heated to 104 deg. boiler water awt is 170 image
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Odd shape, Looks like your going to dip it in the pool. Under some stairs maybe??
Heat transfer is going to vary with velocity of pool water flow over it. Without a pool water pump/fan pushing water over it , it'll be natural convection. Warmed pool water will slowly move past it due to buoyancy of warmer water. Lower heat transfer rate than forced convection (pump/fan moving water past it)
But with strainless pipe in pipe for faster forced convection heard high speed chlorinated pool water eats a hole in stainless in ~ 3 days. ( SS 316 ?? thermo well for temp gauge in 2 inch plastic pipe)
Gota look, but think stainless has ~3x or so less thermal conductivity vs copper. But in this case I suspect if natural convection (NC) then those NC limitations will dominate overall heat transfer rate.
How large is the pool? Run some numbers on needed BTU/hr, the numbers may surprise you even for a 1ft deep x 8ft dia blow up pool.1 
You're missing all the numbers, not that I have the answers but that isn't going to work, the pool is a giant heat sink.0

This will help but you need to know the pool construction (wall) is it in the ground? 55*F, how many gallons, how many degrees above the average (55?) you want to raise it and then find the btu required, not to mention air loss, is it inside outside? generally pool heaters run 250,000btu/hr and up.
https://www.deppmann.com/blog/mondaymorningminutes/swimmingpoolwaterheaterscalculatingload/0 
Initial water heat up will require more power than maintaining temp.
Just to throw some numbers out there on a very hot day I laid out 900 ft of garden hose on hot pavement to raise 50 deg city water to ~ 100 degs to fill a 1 ft deep x 8 ft blow up pool. Had to flow water slowly to get warm water out, maybe 1/2 ?? GPM. Took about 45 hours to sort of fill pool.
Thought about modifying a 20k BTU window AC to heat the water. Ran the numbers and turns out it would have taken at least 23 x as long to heat the water. So maybe ~ 50k BTU/hr for 45 hours to fill a SMALL kiddie pool, and it didn't stay warm that long.
In end I added a large old car aluminum radiator and window box fan to preheat the 50 deg water with 90 deg summer air. Only helped ~ 10 degs, rad was too small . Maybe next time I'll use a junk condenser unit from a central AC for the preheater, faster air and longer tubing. Might put it in the HOT attic too.0 
Contact John "JohnNY" Cataneo, NYC Master Plumber, Lic 1784
Consulting & Troubleshooting
Heating in NYC or NJ.
Classes1 
Copper in a chlorinated pool?
Titinium heat exchangers are available for just that purpose0 
Might be able to use that air table for natural convection and ratio it for water. But have to ratio it for specific heat of water and viscosity/density of water ( need to look in an engineering heat transfer book for details) . Or just look in an engineering book for forced convection and assume a very slow flow rate maybe 3/4 ft/sec
I'ld expect there to be LOT more heat loss with water VS air. But bottom line think you'll need to pump water over tubing to get a reasonably high BTU/hr transfer rate.0 
Never got back with specifics
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no they make specific engineering for pools and it's not the temp difference it's the water mass, it's denser and a pool could be a few hundred gallons to thousands and thousands plus the construction and if it's inground or above or indoors or or orLeonard said:Might be able to use that air table for natural convection and ratio it for water. But have to ratio it for specific heat of water and viscosity/density of water ( need to look in an engineering heat transfer book for details) . Or just look in an engineering book for forced convection and assume a very slow flow rate maybe 3/4 ft/sec
I'ld expect there to be LOT more heat loss with water VS air. But bottom line think you'll need to pump water over tubing to get a reasonably high BTU/hr transfer rate.0 
Found these, one has formulas, the other gives an idea of the btu's required, an olympic sized pool for example would require @ 7 million btus/hr just for average temps, I did a rough calc for giggles and using water weight per gallons and btu average calc it came out higher, not sure why.
https://www.bryanboilers.com/pdfs/EP/WPIndirectPoolHeaters/1078.pdf
https://www.bryanboilers.com/pdfs/EP/WPIndirectPoolHeaters/Form640.pdf0 
Not such an easy calculation as the output changes as delta t and water temperature in the pool changes. Having water flowing across it will help output quite a bit.
Why not connect a btu meter and drop it in the pool for real time data?
Karl and Moses in Brooklyn, NY built a bunch of those for some pools, they ran some calcs and may have actual data by nowBob "hot rod" Rohr
trainer for Caleffi NA
Living the hydronic dream0 


@mottywalter
It sounds like you are working on a Mikvah.
See if you can get a hold of Kal and Moses.
https://forum.heatinghelp.com/discussion/comment/1304813#Comment_1304813"If you can't explain it simply, you don't understand it well enough"
Albert Einstein0 
yes i am doing mikvas (pools ) already for years but i want to get the real numbers of how much sq ft of copper pipe need to be in the pool to deliver the heat !! i think the way to collect this is how we all probably know width x length x height x = cu ft x (gal )7.48 x (LB ) 8.33 X temp. rise 55 this will give us the numbers of btu needed in 1 hour than you can divided i how many hours you want to bring up the temp to the desire temp ! once you know that ! you will have to calc. of how many sq ft . of heat transmitter you will need to transfer the heat in 1 hour !! so lets do an example the pool is 10 x10 x 4 = 400 x 7.48 x 8.33 x 55 = 1,370,784 divided in 6 hours = 228,464.13 so we will need to know sq ft heat transmitter !! so if someone can help me with calc. please reply i atached here some files that might be a help0

Not a heating guy , but a BSME. Sounds like your trying to use the copper tubing without forced water flow over it. That is called natural convection. It's a bit harder to engineering wise calcluate that VS forced convection ( fan moving a fluid over the coils) , because you have to calculate what the (external ) water velocity over coils is. Likely easier to estimate it assuming forced convection and ASSUME a very low external flow velocity , maybe 3/4 ft/min.
There are tables in heat transfer engineering books for simple cases like single horizontal pipe. Your case with multiple vertically stacked pipes is a bit more complicated . And further complicated by the "staircase" triangular look of the assembly.
Numerical software solution FEA (finite element analysis) can do it , but you don't want to get into that. It's lot of work even for engineers..0 
Exactly what Leonard mentioned, very hard to calculate in static water. FEA is your best option, but I doubt someone would do that for freeBob "hot rod" Rohr
trainer for Caleffi NA
Living the hydronic dream0 
And the software is NOT cheap, (at least in the 80's) . Fundamentally it uses same numerical techniques as FEA I've used for stress/vibration analysis. There is also a learning curve to it that's not short.
Unless you can find some tables of previous work I'ld say estimate it with slow forced convection, throw in a large factor of safty (23 X) and see what happens, can always throttle it back. As a back up I'ld be prepared to flow water over heat exchanger to increase heat transfer rate. Or put a "chimney" (box) around exchanger to increase water velocity by chimney effect.
Or visit an existing installation and see what they did and ask how well it works. and what they would do differently. Benefit by their mistakes.
In an apt I once lived in windows got old and drafty. One cold windy night room started getting cool. Baseboards were copper finned tubing and they were HOT. So I rigged up some cardboard and a window box fan to blow air over fins. Place got nice and toasty in ~5 minutes. Basically I changed it from slow natural convection to fast forced convection. (Landlord supplied the heat)
Same effect applies here, doesn't really matter if the heat transfer FLUID is liquid, vapor, air, water , or oil , effect is the same. Only the numbers are different. Increase flow velocity over tubes and it increases heat transfer rate. The limiting case will be getting heated pool water away from tube fast enough so cool pool water can get to it to be heated.0 
There is a way to relatively easily MEASURE and get the BTU/foot numbers your looking for. Would have to measure at each level of your pipe array as upper pipes would have less heat flow rate ( since pool water is warmed by pipes below it). Or set up an experimental tank (bathtub maybe).
They have a heat flow measuring film sensor. It's a special piece plastic film, maybe inch or so square to measure heat flow rate (btu/hr). It's has a temp sensing pattern on both sides. Basically it's thickness and thermal conductivity is known, so if you measure temp of both sides you automatically know heat flow rate thru it. It is thin so unlikely to disturb you existing heat transfer rate by adding it. Think the film sensor is made by same company that sells mechanical glue on stain gauges, they are very similar design. https://en.wikipedia.org/wiki/Heat_flux_sensor (See 2nd pic, window sensor, size of a postage stamp)
Sounds like that will give you the better numbers your looking for your next design. Do remember that as pool warms up , delta T between pool and heater water drops , so heat flow rate will too. IT's one of those messy calculations where to get heating time have to integrate or sum up bunch of small time increments of heat flow.

Gave this a little thought this morning, came up with a ratioing sanity check. Even though it is a bit apples and oranges.
Web says a mikvas is ~ 180 gallons, that 's 4.5 times size of a 40 gallon electric water tank heater. I'll just assume surface of tank's SMALL electric element doesn't boil. So that's a wall temp of no more than 212 deg F.
Even though your copper pipe exchanger wall temp will likely only be 160 degs it has much more surface area than the electric element. So I'ld say it's likely your massive copper pipe exchanger will work, even with only natural convection cooling. But you likely already knew that since you've installed them.
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The only pool heater I have been near is a Raypack.
1,570,000 BTUH. I just talked to the muni pool people today.
(This is 68 miles from me).
They said it takes 14 to 15 hours to fill the pool with 225,000 gallons of water.
Then takes about 2 days of constant burner to get the 5153 degree water up to 8085 degrees.
The book calls for 40 to 85 GPM in the loop and 85 GPM thru the heater circuit. FWIW0 
If you still want to analyze the heat exchanger I'll analyze it in sections. One horizontal pipe at a time, and sum the results.
ASSUME forced convection and a slow velocity of pool water.
I ASSUME you have pipes installed in pool in same orientation they are standing in picture. Calculate increase in temp of a "chunk" of pool water from each horizontal pipe. Use that increased temp as input to calculate the above single pipe numbers. Also recalculate temp of cooled pipe water for next stage ( horizontal pipe).
A speadsheet should be a convenient way to to calculate the numbers and allow them to be automatically inputs to next pipe section for it's calculations.
Likely will have eddy vortexes mixing cool pool water with the heated water , so might be able to assume above pipe doesn't have full temp of heated pool water from below.
This can increase heat flux since cooler pool water, or can hurt since less chimney effect. Competing effects, have to see which one dominates. In engineering world without FEA I'ld model it with spread sheet then build a prototype and test it to see which effects dominate.
BTW Engineering heat transfer books do have calculations for single pipe natural convection.0 
this system works but maybe we can make it smaller. The hot tub size is about 8*10*4 W/L/H mines the stairs. Pipe size used is 3/4 L 3 coils feed/return going into a 1" L copper tend to leak after 5 to 12 year its indoor on ground calculator is a taco007 per satup after heat up the bottom is cold top hot until its mixed do to placement of thermostat once its hot it stays hot for a long time0
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