As promised, revisiting this to give a more detailed answer to your question.
To calculate how much of a given concentrate (or higher brix starting product) you need, it's probably easiest to break the calculation into two in two parts, at least until you're familiar with what it's doing. The first stage calculates how many grams of soluble solids are required per L to achieve the target finished product Brix, and then second calculates how many grams of concentrate (or starting liquid/blend) are required to provide this quantity of soluble solids. Obviously these can be combined into one once you’re familiar with it, but splitting it like this helps understand what’s going on to start with.
Soluble solids required (g per L) = 1000 x [(Brix at single strength)/100] x (specific gravity at single strength) x (density of water at reference temperature used for specific gravity)
It’s fairly simple to understand what it’s about if we look at the individual terms:
- (Brix at single strength / 100) – if our Brix value is effectively how many grams of soluble solids there are per 100g of product, then dividing this by 100 gives us the quantity of soluble solids per g of product. Multiplying this by the factory of 1000 then gives us the g of soluble solids per kg.
- To turn this into a value per L we then need to multiply by the density, hence the inclusion of specific gravity, but that is a relative density so we then also need to include the conversion factor for water at the temperature reference point used.
For the specific gravity (SG) you’ll generally want to find this from a suitable reference table – a common option for this is the USDA’s Sucrose Conversion Tables (ref. 135-A-50), which is attached for reference.
Considering your specific question, we have a target “brix at single strength” of 14.0, and using the USDA table we can see that this corresponds to an SG of 1.05683.
Our reference density for water is 0.99715g/ml.
Putting these into the above formula we get:
Soluble solids required = 1000 x (14.0/100) x 1.05683 x 0.99715 = 147.5345g per L. This is effectively how much “stuff” we need in our finished juice / drink, so we can then move on to calculate how much of the concentrate base we need to achieve this.
Concentrate required (in grams) = (soluble solids required) x [100/(Brix of concentrate)]
Again we have a formula that makes sense if we look at the component terms.
The soluble solids required is the figure that we’ve just calculated above.
“Brix of concentrate” is the soluble solids per 100g in the concentrate/base we’re using, so if we multiply that by 10 we get the soluble solids per kg. What we actually need is grams, so we divide that by 1000, and thus get: 10 x (Brix of Concentrate) / 1000
Which simplifies down to: (Brix of Concentrate)/100
The formula above is therefore basically dividing the soluble solids figure we need, by the soluble solids per g in the concentrate, to calculate how many grams of concentrate are required.
Putting your figures into this we get:
Concentrate required = 147.5345 x (100/14.5) = 1017.4793g
To make 1L of product at 14.0 Brix you therefore need 1017.4793g of the 14.5 Brix product.
You can also calculate how much water you need, as you already have the figure for the SG as we looked it up for the first calculation. The density of the product is therefore 1.05683 x 0.99715 = 1.05382kg/L.
We know that we already have 1.0174793kg of material from the concentrate base, so the remainder (the "missing" figure is the difference) is the water component that we need to add.
Thus for 1000L of product you need:
1000 x 1.0174793 = 1017.4793kg of 14.5 Brix material
1000 x (1.05382 – 1.0174793) = 36.3kg water.