Is there an equation or relation to describe how much sugar is to be added to water to obtain a liquid with a specific gravity?
In This question, for example, it is mentioned that "1 lb in 1 gallon is 1.046" - but is there a known scale? Or is extrapolating from this the only way?
Bonus points for metric units, double points for referenced answer!
To add up on Denny's answer, the density of a solution of sugar and water is (quasi)linear in the range we use in homebrewing (e.g. between 1 and 1.2). (see graph below [0] where concentration in wt% is equivalent to degree Plato)
Using this graph, you could make a sugar solution with known density by adding sugar into water. E.g. a 5°Plato (5 wt%) solution would roughly be 5g of sugar in 95g of water.
Sugar has about 45 ppg. That's gravity points per pound per gallon. So, one lb. of sugar in one gal. of water will give you a specific gravity of about 1.045. That is the known scale. 2 lb. in 1 gal. gives you 1.090, etc.
I needed to find more info about this bc I use the International Metric System and I wanted to know how to get this data using a formula or something so i started to research a lot...
*I was studying about SG and is really called Relative Density bc it's relative to the thing you are using to solubilize or "the solvent" which in this case is water* - So after this said i'm going to continue
The Relative Density is: Solution Density(1.xxx) / Water Density (at 20ºC is about .9982)
The relative density tell us about how is the density of a solution taking account that one is denser than other, easy right? well a lot of literature there complicates this shid a lot
The density of water is .9982 gr/cm3 and pure sucrose is 1.59 gr/cm3, so you will never surpass the 1.59 in your SG if this is made of pure sucrose. Relative Density tell us what is the relation between 2 different densities
So i'm making some math and correct me if i'm wrong:
Density: mass/vol Density of a solution water + pure sucrose = (mass water + mass sucrose)/(vol water + vol sucrose) Example of a calculation based on pounds/galon
(3778.2 gr + 454 gr)/(3785 cm3 + 285.53 cm3)= 1.0395... Relative density: 1.0397/.9982 = 1.0415
So let me ask, ¿¿¿where do people is getting that a pound (454gr) of pure sucrose in a gal (3.785 lt) is 1.045???
I've been checking my calculations with pages like this and im getting pretty close with this formula than the one it's used by everyone
https://onlinelibrary.wiley.com/doi/pdf/10.1002/9780471790990.oth1
https://www.homebrewtalk.com/threads/1-kg-water-8-g-sugar-1-003-gravity.357672/
*Take in account that starch density is 1.5 gr/cm3 so maybe there is something going on between transformed starches and not 100%transformed by the enzymes
The only way to get the 1.045 SG that everyone uses is that the sugar had 1.67 gr/cm3
