reaction mechanism - In the production of vinegar, where does water come from?

In the production of vinegar, where does the water come from?

I have heard that vinegar production involves these two reactions..

$$\ce{C2H6O {(ethanol)} + NAD+ -> C2H4O {(acetaldehyde)} + NADH + H+}$$

and

$$\ce{C2H4O {(acetaldehyde)} + NAD+ + H2O -> C2H4O2 {(acetic acid)} + NADH + H+}$$

But I don't see where water comes from as an input into the second reaction. Like if it's added manually or if it's produced by something else.

Note- there was an additional part of the question which i've since removed.. some of that is addressed https://biology.stackexchange.com/questions/56995/do-acetic-acid-bacteria-use-the-electron-transport-chain-when-converting-ethanol