Open Time*
The amount of time the adhesive should be left to set, before it is covered.
If you're gluing two sticks together, with an adhesive with 30 seconds open time. You should apply the glue to one stick, then wait at least 30 seconds before affixing the second stick.
The amount of time the adhesive can be left before it is covered.
If you're gluing two sticks together, with an adhesive with 30 seconds open time. You should apply the glue to one stick, and affix the second stick before 30 seconds has elapsed.
Working Time
The amount of time from when the adhesive has set, to the time it will no longer bond.
Again gluing two sticks together, this time with an adhesive with a 5 minute working time. Once you apply the glue to the first stick, you have to affix and position the second stick in less than 5 minutes. If you don't affix the sticks within this time, the adhesive will not bond (or at least is not guaranteed to bond).
Set Time
The amount of time the adhesive needs to form a good bond.
Back to the sticks, this time with an adhesive with a 10 minute set time. Now that the sticks are affixed, you'll have to wait 10 minutes before they are adequately stuck together.
Pot Life
The amount of time an adhesive can remain viable after being mixed.
If you're gluing the sticks using a 2 part epoxy, with a pot life of 2 hours. Once you mix the epoxy, you have 2 hours to use it before it becomes useless.
Notes
*Some manufacturers use open time, and working time interchangeably. Open time should only be assumed to be different than working time, when working with adhesives that need to activate or set before being usable.
After doing more research, it appears there really isn't a set vocabulary used throughout the industry. Your best bet would be to contact the manufacturer, and ask them what they mean.
Beware that if in a use that is subject to plumbing code, your 3D printed item almost certainly will be a code violation.
The probable best bet (and I'm not guaranteeing success) would be a "Multipurpose plastic pipe glue" - go to the plumbing section, find the PVC pipe cement, don't buy that - look for the somewhat smaller stock of pipe cement that claims to work on PVC, ABS, and perhaps a few other variants of plastics - try that. Use PVC pipe cleaner and primer on the PVC side of the joint. Make some test joints and try to tear them apart after they have had a day or two to cure.
If, as I vaguely gather, PLA is essentially the most common form of hot glue, then judicious and careful use of a hot glue gun would be the other option that might work.
Best Answer
I would think a marine grade epoxy should do the trick for you. It would definitely be waterproof and it's made to hold up under the stresses of a moving boat, and to hold up to salt water which is much harsher than the fresh water in your rain barrel