There is nothing more annoying then not being able to get the joint up to temp then having to chase all of that water out of the pipe.
Or here is a better one you think all of the water is out of the pipe and then when you start heating water "finds it way" to your joint and starts releasing steam.
Stupid steam if I am not insterested in making distilled water
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Can't pipes ever be level so all the water will just pour out?
What I do to verify if its dry for soldering is put my compressed air gun into the pipe and spray if it mists keep purging.
The bread just gives me nightmares of it getting stuck in an elbow or something I would never do that.
Someone should make something that attaches to your wet vac so that you could just suck the water out or to your air compressor so that it can be pushed out a faucet or something.
That tool is pretty cool wish I knew about it when I replaced all of my rusted tight 1940s shutoffs in my house. They were so cheap they didn't even install a shutoff on the hot line to the water heater. Anyone whos been showered when the cold backflows through the hot line when someone opens both faucets knows what I mean
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Cmosack as for your question there is no easy solution to this you will have to estimate where you think the towel clog is and start cutting pipes then turn the water on a bit and see if it flows. Once the clog is removed join the cut pipes with a sweat coupling.