Ok so my batch size is supposed to be 5 gal. But for some reason I only put in 4 gal in primary. Am I screwed for this beer or can I add 1 gal. Of water in secondary?
If you are past the first 12 hours in the fermenter, you should not add straight water. If you want to add it, you need to boil it for 10 minutes to remove any oxygen that is dissolved in it, and then of course, cool it.
You could just accept a 4 gallon batch. It will be stronger, and have more flavor.
You can probably get away with it if you added it now.
If it were me, I'd quickly boil a gallon, cool it quick in the sink, and add it in an hour or so.
If you add straight water now, you will worry if you screwed it up. It will probably be OK, but might not be.
Oxidizing beer results in poor storage life, and the beer going stale quickly. Might taste great fresh, but after a few weeks/months may start to taste stale.
Take it from someone who has tried this before. Don't add water to beer that has been fermenting. You'll wind up with 2 cases of worthless bottled garbage.
Please just ride it out and settle for less beer of higher quality.
Your beer will be higher gravity. You can add a gallon at bottling time with your priming sugar. Deathbrewer has brewed strong, small batches before and diluted later, so I see no reason you couldn't.
I always end up a lot lower than anticipated. I aim for 5 gallon batches (which, if I am not mistaken, means 5 gallons of finished beer in the bottle), and always end up with less than 4. This last one I just bottle should have been around 50 bottles and I only got 38. I'm hitting all my numbers and everything is just the way it should be. Good beer, better buzz. Don't worry. Just let it be and it will turn out fine.