Question about OG/FG readings

Hey everyone, I'm definitely new to brewing (just started fermenting my second 5-gal batch), and I have a question. My first brew was a Hefeweizen, and I tried to primary in a 5-gallon PET carboy....that ended with krausen and beer all over me and my bathroom floor. When I brewed my second batch, I had about 4 gallons of wort, so instead of topping it off immediately to 5 gallons, I decided to wait 24 hours or so after pitching to let the fermentation settle down. I took an original gravity reading of the 4 gallons without thinking about it (I knew 1.061 seemed high...), but I was wondering how I can determine the actual OG if I had added the 1 gallon of water. I'm a chemical engineering student, so I know that you can't just weight the specific gravities, but if the wort is an ideal solution, you can weight the specific volumes...has anyone run into this before, or should I just stop worrying about it so much and buy a 6 gallon primary for next time?

 

61 points in 4 gallons which is 61*4 = 244

244/5 = 48.8 or 1.049 (rounded up)

 

And yeah, buy a 6.5 gallon bucket.

 

basic averaging. water has a gravity of 1.000

4 gallons @ 1.061 + 1 gallon @ 1.000 == 5 gallons @ 1.049

 

Thanks! I'll assume that's good enough of an estimate, haha.

 

+1 indeed.

 

yeah, i know how to average, but in my separations class, we learned that you can't just average densities without introducing significant error...you have to weight the specific volumes and adjust for unideal conditions in volume additivity...

maybe that's only relevant in industrial chemical processes?

 

Probably.

Basic averaging pans out just fine in our low-tech organic chemistry labs.

 

I don't think that really applies here. It's not all that different from adding water to water, so the additive volume is just the result of adding the two volumes together or is so close that it is insignificant.