Modified Parti-glye Split batch

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Brewslikeaking

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I want to make 2 iPas like so:
Make a 7.5gallon batch of a DIPA (eg. A target of 8%abv). I want to split off 5 gallons of this to be a double ipa. As for the remaining 2.5gallons of wort - I wish to add 2.5gallons of water to bring it up to 5gallons and make a session ipa with it. My question is this; what can I expect the OG to be from the 2nd batch and how do I calculate it?
 
c1*v1= c2*v2
8% * 2.5 gal = c2 * 5 gal , solve for new concentration.
20 %(gal) = c2 * 5gal , simplify both sides
20 %(gal) / 5gal = c2 * 5gal / 5gal, divide both sides by new vol.
c2 = 4%

Works for any change of volume, boil-off or dilution. You can substitute abv for gravity, plato, or any solution concentration.

****Shortcut****
If you double the volume, you halve the concentration.
2.5 gal @ 8% = 5 gal @ 4%
 

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