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re: how far can hot water be piped.
23 apr 1999
henry wrote:
>can anyone give us heat flow figures for good insulation materials?
sure. styrofoam has a us r-value of 5 per inch, ie a 5 f temperature
difference can push 1 btu/h of heat through a square foot 1" thick.
>the broad question is, 'what fraction of heat might be lost when water
>is piped for ten miles or so at an initial temperature of 100 degc. is
>it likely to be 10% or 70%.
ten miles seems like a lot. could we buy a cheap 6 kw water-cooled honda
generator with a heat output of 30 kw (102k btu/h) on 1/2/2000 and heat
our house and a neighbor's 500 feet away? the generator might start
automatically and make the meter run backwards when the temperature of
a water storage tank dropped. suppose the neighbor needs 50k btu/h peak.
sending 175 f water that cools to 125 in the neighbor's house means moving
1000 pounds of water per hour, ie about 2.1 gpm, doable with a garden hose.
suppose we enclosed 2 hoses in a buried styrofoam box like this:
2" 1" 2"
---------------------- ---
| | | |
| | | |
--- | . | . | . | 2"
| | | |
| . |----| . | ---
| | | |
| . | hh | . | hh is the hot hose.
4" | | | | 2"
| . | ch | . | ch is the cold hose.
| |----| | ---
| . | | . |
| | | | [use courier font.]
--- | . | . | . | 2"
| | | |
---------------------- ---
| 3" |
the bottom sandwich might be glued, and the top might be fastened with
deck screws. the extra space in the 1x2" hole in the center might be
filled with polystyrene beads. the hoses should keep them dry. since
warm air rises, i'd put the cold hose below the hot one to avoid making
a heat exchanger with input and output temperatures close to each other
that carried little net heat.
one simple overestimate of the thermal conductance of this little utility
corridor is the exterior surface divided by the r-value, ie 22"/12"x1'/r10
= 0.183 btu/h-f per linear foot. but it's less than that, since the exterior
surface is larger than the average area through which the heat flows. we
might refine that estimate by using the dotted line path above, which has a
14" perimeter, which makes the conductance 14"/12"x1'/r10 = 0.117 btu/h-f
per linear foot.
a further refinement might divide the walls into 4 half-inch thick nested
shoeboxes. the inner one has an average perimeter of 8 inches, and the next
3 have 12, 16, and 20" average perimeters. each shoebox wall has an r-value
of 2.5, so the series resistance is 2.5(1/8+1/12+1/16+1/20)x12 = 9.625, and
the overall conductance is 1/9.625 = 0.104 btu/h-f per linear foot.
if we conservatively assume the inside cavity is 175 f top to bottom and
for the whole length of the hose, and not so conservatively guess that the
ground around the box is 55 f, the heat loss during transmission is about
(175-55)0.104x500' = 6200 btu/h, or 12.5% of the transmitted heat.
nick
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