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Measuring SG after late DME addition

M

Mets17

Had a question I was hoping someone could point me in the right direction for....

I attempted a pumpkin ale this past weekend, using a combo of all grain and fresh, cooked pie pumpkin.  If it matters, I brewed this concoction using a Brew Magic brewing system that my partner and I picked up used about a year ago.

My recipe assumed a post-boil volume of 5.5 gallons, and according to BeerSmith, my post-boil SG should have been around 1.057, without taking into account any additional conversion from the pumpkin (I've been told by others that your mileage may vary as to what, if any, added sugar you get when using vegetable adjuncts).

Due to a mis-calibration of the sight tube, while the post-boil volume appeared to be 5.5 gallons, the actual post-boil volume was only 4.25 gallons.  And making matters worse, my efficiency, for whatever reason, must have also sucked, because my post-boil OG was only 1.051, even *with* the much lower projected volume.   

So I quickly boiled up whatever light DME I had in the house (just under 1.5 pounds) in about a gallon and a half of water, and boiled it down to one gallon, then pitched it into the not-yet-fermenting-wort.  However, in my frazzled state to fix the volume problem, I neglected to take another hydrometer reading, so I don't know what the adjusted SG was prior to pitching the yeast.

What I am wondering is if there is a mathematical calculation that can help determine what the SG would have been after pitching the additional DME wort in to the 4.25 of original wort from my mash?  IOW, what could I expect the SG to be by adding 1 gallon of wort at roughly 1.064 to 4.25 gallons of 1.051 wort?
 
I recently disvovered that beersmith has a function for just this.

Choose Dilution Tool under "Tools".

It states that if you dilute 4.25 gallons of 1.051 wort with one gallon of 1.064 wort you end up with 5.25 gallons of 1.053 wort.

 
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