Wort Dilution

[Nil]

So… here is my theoretical situation:

I want to dilute a wort with and OG: 1.047 to 1.040 in order to have a final ABV 5%. I don’t know how to determine in advance the volume of water needed to hit the desired gravity points. So…

Got 100 mL of a wort with an OG: 1.081 and added 30 ml of water. The gravity now was 1.060. Kept adding water as follows:

Volume (mL) Gravity
---------------- ----------
30…………………………..1.060
40…………………………..1.055
50…………………………..1.050
70…………………………..1.044
90…………………………..1.038
110…………………………1.035
130…………………………1.031
150…………………………1.028
170…………………………1.026
200…………………………1.023
230…………………………1.020
260…………………………1.018
300…………………………1.016

Found that the correlation is logarithmic.
Log (Vol) = -22.203xOG + 25.014

Going back to my problem, with an OG: 1.047,

Vol = 10^(-22.203x1.047 + 25.014) = 58.5 mL

For 1.040,

Vol = 10^(-22.203x1.040 + 25.014) = 83.7 mL

The difference between the two is 83.7 mL – 58.5 mL = 25. 2 mL.
This suggests that I need to add 25.2 mL of water/100 mL wort (at OG: 1.047) to get the desired gravity points (40).

Since my knockout volume is 5.5 gallons, there are 5.5 x 3785 = 20,817.5 mL, which, divided by 100 mL, gives me 208.175.

Therefore,

208.175 x 25.2 mL = 5,246.01 mL/3785 = 1.386 gallon = 1.4 gallons of water.
If my calculations are correct, this means that I can setup a mash with a target FG: 1.060 and a knockout volume of 7 gallons. To reduce 1.060 → 1.040, I would need to add 3.75 gallons of water (53.6 mL/100 mL wort) to have a total final volume of 10.75 gallons.

This may be a very nice way to control FG and thus have a more consistent ABV between batches.

Please let me know your thoughts.

Thanks, Nil

 

[Bosh]

Only problem is it can screw with IBUs since you can't just make a 200 IBU beer and dilute it down to 100 IBUs.

 

[Pkrd]

If my calculations are correct, this means that I can setup a mash with a target FG: 1.060 and a knockout volume of 7 gallons. To reduce 1.060 → 1.040, I would need to add 3.75 gallons of water (53.6 mL/100 mL wort) to have a total final volume of 10.75 gallons.

You're close, it's pretty simple...

V1 * (G1-1) = V2 * (G2-1)

V2=(V1 * (G1-1))/(G2-1)

V1=7
G1=1.060
V2=10.5
G2=1.040

 

[Nil]

Bosh, it is true what you said about the IBU, as the relationship is not directly proportional. One may add the amount of hops for (to say) 10.5 gallons to a volume of 7 gallons with a scrap factor for 5 - 10%. The extra hops would help to manage the utilization reduction due to higher sugar concentration. This most likely deliver an acceptable bitterness profile after dilution.