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re: questions about heat movement in water
29 may 2003
tom wrote:
>problem
>thermal stratification of heat within a swimming pool
>cold on the bottom, warm on the top.
a dark bottom could help. or just enjoy the difference,
like a cloudy lake in the sun.
>temperature difference perhaps 10 degrees
>
>solution?
with natural heat diffusion (ie no mixing or warm water bouyancy effect),
page 89 of the 1998 schaum's outline on heat transfer says: if the pool
has a uniform temp ti and the surface temp at x = 0 is suddenly changed to
ts for all time t>0, (t(x,t)-ts)/(ti-ts) = erf(x/sqr(4at)), where erf() is
the gaussian error function. page 352 says 68 f water has thermal diffusivity
a = 0.00554 ft^2/h, and erf(0.5) is about 0.5, and (t(x,t)-ts)/(ti-ts) = 0.5
= 6.7x/sqr(t), or t = 180x^2, so it would take 180 hours for a layer of ti
= 60 f water 1' below the ts = 70 f surface to warm to 65 f. well, longer
than that, since warm water rises. how much longer?
>run a small pv pump to take water off of the top and
>run a hose to the deep end that's 8 feet deep... if
>the warm water is pumped to the bottom of the deep end,
>the heat would rise slowly, thereby, retaining heat
>a little longer than "normal"...
>
>how slowly and at what rate the heat would "rise" the 8 feet?
if the pump is 1 gpm and the pool contains 5000 gallons of 60 f water
and 5000 gallons of 70 f water, with no external heat gain or loss,
how long do we have to pump to make the temp diff only 1 f?
tc(0) = 60 --> 64.5 f th(0) = 70 --> 65.5 f
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| 1/(1x8x60) f-h/btu / |
|---------------www-----------. .------|
| close at |
--- 40k btu/f t = 0 --- 40k btu/f
--- ---
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- -
nick
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