Occasionally, a soft drink company's technical officer is asked to calculate how much juice concentrate should be added to a This calculation often stymies soft beverage in order to attain a prescribed legal minimum juice drink technologists not acquainted content in the drink. The reverse also happens, where the person with juice technology. is asked if the juice content in an existing juice-containing beverage is what it says it is on the label of the product.
As I mentioned in the previous section, soft drink technical personnel (other than in companies where juices are the core business), are often not too familiar with the finer peculiarities and esoteric nature of fruit juice technology. If the person asked to do such a calculation has never done this before, he or she is usually stymied at first but then reacts logically enough to say something along these lines:
I was told that the juice is six-times concentrated, so I must add a sixth of the target juice percentage in the form of concentrate to a certain volume of beverage, and thus, the required target juice percentage will be achieved.
This might work, but it is very likely that he or she will significantly overshoot the minimum specified percentage level, and as such all is legally in order. However, fruit juice is a relatively costly item and a lot of money could be going down the drain. Also, overshooting the target could affect some of the quality parameters of the beverage, e.g., Brix, acidity, cloud intensity, and general overall taste.
In this section, I propose to show the reader that this calculation, though seemingly complex, is actually very simple when mastered. The first item to clarify and establish in this calculation is that the percentage juice in a beverage is usually required by food laws to be expressed (e.g., on the label) on a volume-for-volume basis. Thus, in a 6% juice beverage, one expects there to be 6 ml of juice in every 100 ml of beverage. The second basic item is that these 6 ml of juice must be on the single-strength basis of the particular juice involved.
Having established these two basic prerequisites for correct calculation methodology, we can now proceed. I will employ this 6% juice numerical example to demonstrate the calculation and use what by now is the well-known lemon juice concentrate Lemon 30 Brix, as the juice involved. It will be referred to as lemon concentrate.
Given:
Lemon concentrate:
Brix corrected for acidity = 34.00°B D20 (from tables) = 1.14530
Lemon juice, single strength:
Brix corrected for acidity = 7.50°B D20 (from tables) = 1.02685
Required:
Calculate the volume of lemon concentrate required in 1000 liters of final beverage to obtain 6% vol/vol single-strength lemon juice in the beverage.
Calculation:
Step 1: 1000 liters of final beverage must contain 6% vol/vol of single-strength lemon juice. Therefore:
Step 2: Calculate total dissolved solids in 60 liters of single-strength lemon juice:
(2) Weight of 60 liters of single-strength lemon juice = 60 x (D20 single-strength lemon juice)
(3) Total dissolved juice solids in 61.611 kg single-strength lemon juice = 61.611 x (Brix single-strength lemon juice)
= 61.611 x 7.50°B (expressed as percent) = 61.611 x 0.075 = 4.62083 kg
This is the amount of lemon juice solids that the 1000 liters of beverage must contain in order for the beverage to have the equivalent 6% vol/vol single-strength lemon juice. These solids will be supplied from the lemon concentrate that will be added to the beverage formulation.
Step 3: Calculate weight (W) of lemon concentrate that will contain 4.62083 kg dissolved solids. By definition of Brix:
Lemon Concentrate dissolved solids _ Brix Lemon Concentrate Weight (W) Lemon Concentrate (expressed as percent)
Therefore, (4)
4.62083
Therefore, (5)
4.62083
0.34
This is the weight of lemon concentrate that will contain 4.62083 kg lemon juice dissolved solids.
Step 4: Calculate the volume V (in liters) of 13.59066 kg lemon concentrate. (7)
13.59066
(D20 Lemon Concentrate) 13.59066
1.14530 V = 11.86646 liters
Result:
V = 11.86646 liters of lemon concentrate and will contain 4.62083 kg lemon juice dissolved solids. This volume of lemon concentrate will represent 6% vol/vol single-strength lemon juice in 1000 liters of final beverage. The value can be conveniently rounded off to 11.866 liters.
This then is one way to calculate how much juice concentrate is required to achieve a specified percentage of single-strength juice in a beverage. This method was presented in order to enable the reader to understand the rationale of the steps involved and the interplay of Brix, density, dissolved solids, etc., that result in the final volume figure of concentrate.
All of these calculations can be represented in a single math formula applicable to any juice, at any target percentage in a beverage:
where
Vfjc= the volume (in liters) of fruit juice concentrate required to achieve the target percentage of single-strength juice in the beverage;
P = the target percent single-strength juice for the beverage (in decimal form);
Vb = the volume of the beverage in liters;
Dssj = the D20 of the single-strength juice (from Brix/density tables);
Bssj = the Brix of the single-strength juice (in decimal form);
Bfjc= the Brix of the fruit juice concentrate (in decimal form); and
Dfjc = the D20 of the fruit juice concentrate (from Brix/density tables).
Note: A point to take note of is that the Brix and percentage values should always be used in decimal format, e.g., 7.50°B as 0.075 and 6% as 0.06. This will save having always to divide by 100 and will put the decimals in their right places in the calculated results.
This formula can be mathematically rearranged to calculate the reverse, i.e., if the volume of fruit concentrate in a formulation is known, by isolating for P, the percentage single-strength juice in the beverage can be calculated.
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