Please Check My OG Calculation

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AlexKay

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I'm making a blueberry Kolsch, and added concentrated blueberry juice mid-fermentation. I'm trying to figure out what the OG would be if I had added the concentrate right away. Here's my thinking:

Wort was SG 1.031. That's 7.8 Plato, meaning 78 g sugar/liter of water, which means 9 L of wort had ~700 g of sugar in it.

Blueberry concentrate was 68 Brix. I added 0.8 kg of it, which, at 1.35 SG, should be 0.6 L. 0.6 L @ 68 Brix should have ~410 g sugar.

Total 1110 g of sugar in 9.6 L is 11.5 P, which converts to an OG of 1.046.

Is this right? Is there an easier calculation?
 
I haven’t done the calculations in a long time, but I thought that you have to consider the volume increase in the final calculation to be really close. We need a mead guy to chime in, this is in their wheelhouse.
 
Both Plato and Brix scales are weight, not volume, based. They are both defined as the weight % of sucrose in solution with water, which is 100 * wt of sucrose / (wt of sucrose + wt of water)

9 L @ 1.031 (7.8°P} will weight 0.9982 kg/L * 9 * 1.031 = 9.26 kg and have 0.078 * 9.26 = 0.7225 kg of sugar. The density of water at 68°F (20°C) is 0.9982 kg/L. It maxes out at 1.000 kg/L at 4°C.

0.8 kg of concentrate @ 68°Brix will have 0.8 * 0.68 = 0.544 kg of sugar.

Total sugar is then 0.7225 + 0.544 = 1.2665 kg. Total liquid weight is 9.26 + 0.8 = 10.06 kg. So combined Plato/Brix is:

Plato/Brix = 100° * 1.2665 / 10.06 = 12.59°P​
12.59°P -> 1.051 SG

Brew on :mug:
 
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