OK,
curiosity got the better of me so I've done a very basis calculation.
I do it in metric because its easier for me, but feel free to poke holes or redo it in Imperial units
The thing that is probably saving you here is the PE....
Thermal conductivity PE is quoted on many locations as circa 0.4 W/m/K ( compared to steel which is 45), PE thickness at SDR 11 is 32mm for a 355 mm OD pipe
Plugging your values into a heat loss calculator - I used
gets you about 400W/m (might be a bit less if you assume PE ID is OD in this calculator)
You've got 5750m so overall your water/pipe is losing 2.3 MW of heat along its length
Your water contents in a 14" pipe with 32mm PE wall is 384,000kg
Heat capacity of water is 4000 J/kg/C.
So total heat capacity in the pipeline per C is 1.53 x 10^9 J
Your water is in the pipeline for 2600 seconds so in total the heat loss during that time is 5.6 x 10^9 J. So you will lose between 3 to 4 C from one end to the other.
ON the same basis ( OK the heat loss will go down a bit as the temperature falls but the delta doesn't change too much) the time for a static water to cool from the now 6C is it at the end to zero is 66 minutes - basically an hour.
Do the maths yourself to make sure.
It does seem about right once you factor in 32mm of PE "insulation".
Make sure your incoming water is at or more than 10C... You don't have a lot to play with here, and keep the flow going or drain / clear it within an hour.
LI
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