Does drain plumbing come down inside the wall? Washer is there, so some plubming is in the area. Any chance a condensate drain for an AC, like in the attic, is routed down through that wall, maybe to a basement sump pit?
If the WH had a leak, 2 drops a min, it wouldn't be long before water showed up on the floor.
Gas or Electric? If it's gas, try using a flashlight and looking down the flue hole when it is heating water. You might see mist, indicating a leak in the flue.
A few years ago I began to notice occasional water on top of the water heater. Sometimes it would be there, sometimes not. I checked all of the pipes and fittings and they were always dry, even when there was water on top of the tank. It turned out that just below the top of the tank, a hole had rusting through the flue and mist would blow out whenever the tank was heating water. They mist would rise with the flue gases, make contact with the "inverted funnel" at the base of the external flue and drip back down onto the top of the water heater. If not noticed soon afterwards, it would evaporate.
Perhaps your flue is leaking someplace where you can't see it, and the condensation is dripping someplace, again, where you can't see it.
Only thing I see there that's a bit unusual are the water stains on the sheetrock near the bottom. Is that from something you know about from the past? Any evidence it's wet now, ie that something is leaking inside the wall? The area around the bottom of the WH is all dry and it has a pan.
What makes you so sure that the water isn't coming from the pipe? It sure looks like it from the pic. First thing to figure out is where that pipe goes and what it does. The most likely candidate is that it;s from the TPR valve on the WH. So.....I took a look back at the pics you posted of the WH. And you can't see a TPR. It sure looks like the idiots put it in with the TPR facing into the corner, where you may not even be able to get at it. There is a copper pipe that comes out from the right of the WH, and that must be connected to the TPR valve. Is that copper pipe connected to the PVC that emerges from the outside? It must go somewhere that it could release water if the WH pressure or temp gets too high. Typically they just end above a basement floor or get routed outside. Where is that outside pipe in relation to the WH when we're looking at in inside the garage?
If it's not from the WH, then any chance that PVC is a central AC condensate drain line??
I don't think there's enough water to be a condensate line.
Most likely you called it right as a TPR drip. Really bad installation to hide the TPR and have no shutoff valves anywhere.
But there's another possibility. He says the washer and dryer are just on the other side of that wall, the one to the right seems likely. Washer hoses go bad often, he should check that too.
What makes you say that? In the pic, there is a decent size puddle and you can only see the part that's in the pic, no idea where it ends or runs off to. Also, no idea how much the AC is running or not running.
The only part there that doesn't make sense is the pipe outside is PVC and the pipe at the WH is copper. Then could have transitioned it, but usually you wouldn't.
It could still be the TPR, which might not be connected to that pipe at all. As trader says, it would be unusual to transition copper to PVC, though not impossible.
Or the TPR might be connected to that pipe, and then something else must be leaking.
That's an exterior wall, are you in a climate where something could freeze and burst? Did you check wash machine hoses and drain?
If it were me, I'd open the interior wall before I'd open the outer wall. It's much easier to repair and match an interior wall than an exterior wall, especially one with a textured finish. Even if I had to move a washer, dryer, even the water heater, I'd still start inside.
Besides, once you find the leak, an interior wall repair can wait. A hole in the exterior, not so much.
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