ChrisR said:
Thermodynamics isn't involved, and the conductivity is sufficiently constant in the temperature range being considered not to affect the result. Allow half a centimeter per meter.
OK ChrisR, thats a crude method to estimate expansion.
the rate of thermal expansion only gives a simple expansion vs temp change ratio, it says nothing about what energy over what period of time would be required to create that temperature change!
as for thermodynamics not being involved, well thermodynamics is just a the branch of physics designed to help think about thermal systems, Id say your application (just use co-effiecent of thermal expansion and assume 70-90 degrees) doesn't use much knowledge of thermodynamics, thats a failing not an advantage.
Id say Ive got an open system, with heat, work and matter flowing across the system boundary (waste into the stack mostly)
I think expansion is likely to be less than you estimate due to due to:
1. the inherant resistance to heat increase/insulating property of the material will prevent heat change and therefore expansion.
2 likely rate of flow and thermal gradient, the pipe will never be totally full of matter at 70 degrees C for any period of time and will typically be used for only 2-3 minutes at a time maximum.
3. loss of energy to the first 2 thirds of my system from the source, before we even get to an expansion critical area.
My guestimate says I could run hot water from now until forever down the waste and the walled section is unlikely to ever get to 50 degrees C.
As I said I'm not likely to want to run the numbers fully on this because (despite your suggestions that this would be a simple problem to prove/solve) I'm pretty sure its a non trivial task, my idea is to suck it and see as they say, place the pipe, run hot water for half an hour chucking in the odd kettle and washing machine run and have a nose at how much expansion I actually get, I'll let you know what I see...
