# Wort Dilution

### Help Support Homebrew Talk:

#### Nil

##### Well-Known Member
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 &#8594; 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.

Thanks, Nil

#### Bosh

##### Well-Known Member
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.

Nil

#### Pkrd

##### Supporting Member
HBT Supporter
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 &#8594; 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

OP
N

#### Nil

##### Well-Known Member
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.