SG Dilution Formula

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SG Dilution Formula

Postby jayhawk » Fri Oct 18, 2002 8:27 am

Does anyone have a formula for diluting wort to achieve a new SG. For example, if I had 20L (5imp gal) of 1.070, how much water would I have to add to achieve 1.050? If anyone has a general formula for this, please let me know.
Chris
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Ah, gravity.....

Postby Gravity Thrills » Fri Oct 18, 2002 9:39 am

Chris,

SG dilution is easy if you remember that it is determined as Points/Pound/Gallon. You can use the Recipe Calculator as a test, but here's the deal, using an imaginary 1 gallon brew:

If your gallon of wort is at your stated targetOG of 1.070, you could add another gallon of appropriately pre-treated water and bring the OG to exactly half of what you started at, 1.035. The reason is that instead of having X total extract points/Y lbs of grain/1 gallon of water, you now have X total extract points/Y lbs of grain/2 gallons of water. That is, you diluted your concentration of dissolved extract exactly by half.

For your particular situation - going from 1.070 to 1.050 - here's the approach. First, lose the integer part of the OGs, so we are dealing with 070 (=70) and 050 (=50). The desktop calculator on my mac tells me that 50 is 71.4% of 70. So, figure out what the new volume of diluted wort should be that will give you a .714 x original extract concentration. in your case, 2 gallons will do it since the resulting 7 gallon wort volume divided by the initial 5 gallon volume gives a new concentration of 71.4% of the orignal. Your algebra may be as bad as mine, but like I said work through it on the recipe calculator to convince yourself.

The upside of this is, of course, a big ol' batch of beer. The downside is that, unless your undiluted wort is also substantially over-hopped, dilution to a new target OG may give you the body and alcohol level you want but it will also greatly diminish your hopping rates. To dilute or not to dilute - the decisions that try men's souls!

There have been a couple interesting BYO articles on high gravity brewing that talk about making a double-strength, double-hopped wort to be diluted by half AFTER fermentation to normal strength. As many brewers know, this is the approach Miller takes with many of its products. It saves money for Miller because they can brew the same amount of beer using only half the fermentation space.

Hope some of this helps.

Nunc Bibendum Est
(now it's time to drink)
Jim
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hops and a correction

Postby jayhawk » Fri Oct 18, 2002 10:40 am

Thanks for the help, Thrills. Just one thing, it should be 5 gallons (initial vol) divided by 7 gallons(total vol) equal 0.714.
I am a little confused as to what you mean by reduced hopping rates. Lets say I boiled 25L of wort for a 25L batch because I forgot to account for boil off (this actually happened). Because I am able to achieve a rigorous boil, I boil off 6L for total of 19l. If I add 6l of water to the fermenter, will that affect bitterness. Or are you referring to high gravity brewing where extra hopping would be necessary to account for the dilution near the end of the whole process. (Is this making any sense, or am I just rambling?)
The reason I was faced with this predicament was due to a late night brew session. Things got ugly; stuck mash, then I misread my kettle volume dipstick and ended up with 19L instead of 25L. I ended up just throwing in what I thought was 6L in to the fermenter to make up the difference. High gravity brewing is something I may look in to if more people keep asking me to make them beer, but I have many things I want to experiment with first.
Git brewin
Chris
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I thought there'd be no math!

Postby Gravity Thrills » Fri Oct 18, 2002 11:28 am

Yeah, you're right -- 5/(5+2), not the other way around. Like I said, me and algebra never saw eye to eye :-)

And your addition of make-up water in this instance should be fine and hop levels should be close to what you intended (there is less hop utilization in a more concentrated wort, but 6L difference shouldn't be a huge problem. Where hopping would be an issue is if you hopped according to the 19L final wort volume and then decided that you wanted a lower SG. Similarly, if a beer doesn't ferment out and you want to moderate the cloying sweetness by dilution before packaging, you'll dilute the unfermented sugars but also cut the alcohol and the bitterness to something less than you were shooting for.

Nunc Bibendum Est
(now it's time to drink)
Jim
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Averaging Is the Answer

Postby BillyBock » Fri Oct 18, 2002 7:48 pm

Chris: Your answer involves some basic algebra. This is actually an averaging problem. To put the problem in words:

You have 5 gals of wort, SG=1.070, to which you want to add x gals of water, SG=1.000. You want to therefore end up with 5+x gals of wort at SG=1.050. Mathematically, it looks like this:

(5)(1.070) + X(1.000) = (5+X)(1.050)
5.35 + X = (5+X)(1.050)
5.35 + X = 5.25 + 1.050X
0.1 + X = 1.050X
0.1 = 0.050X
X = 2

Therefore, you need to add 2 gals of water. This will work for any dilution you want to do. Even you wish to dilute wort with wort, substitute the appropriate gravities in the equation. Let me know if you have any questions.

v/r
Bill
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thanks

Postby jayhawk » Sat Oct 19, 2002 6:29 pm

Hey, this method is great. Thanks a lot.
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makes it look easy

Postby Gravity Thrills » Sat Oct 19, 2002 7:32 pm

Yep, that's the algebra I was fumbling for. At least my 2 gallons was right - I would have been on Jayhawks bad list if I led him to overdilute a real winner.

You were probably good at those SAT word problems too, weren't you :-)

Nunc Bibendum Est
(now it's time for a drink)
Jim
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LOL

Postby BillyBock » Sun Oct 20, 2002 5:50 am

Hey, Jim: Well I always enjoyed math--brewing gives me a perfect excuse to use it (when of course I don't have ProMash handy) :-)

v/r
Bill
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