Question
If fresh apple juice contains 10% solids, what would be the solid content of a concentrates that would yield single-strength juice after diluting one part of the concentrate with three parts of water? Assume that the densities are constant and are equal to the density of water.
Answers
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To solve this problem, we need to use the equation:
% solids in concentrate = (% solids in single-strength juice) x (volume reduction ratio)
Volume reduction ratio = 1 / (dilution factor)
Dilution factor = total volume of single-strength juice / volume of concentrate
For this problem, the % solids in single-strength juice is 10%, and the dilution factor is 1:3, since we are diluting one part of concentrate with three parts of water. Therefore:
Dilution factor = (1+3) / 1 = 4
Volume reduction ratio = 1 / 4 = 0.25
% solids in concentrate = 10% x 0.25 = 2.5%
Therefore, the solid content of the concentrate would be 2.5% to yield single-strength juice after diluting one part of the concentrate with three parts of water.
% solids in concentrate = (% solids in single-strength juice) x (volume reduction ratio)
Volume reduction ratio = 1 / (dilution factor)
Dilution factor = total volume of single-strength juice / volume of concentrate
For this problem, the % solids in single-strength juice is 10%, and the dilution factor is 1:3, since we are diluting one part of concentrate with three parts of water. Therefore:
Dilution factor = (1+3) / 1 = 4
Volume reduction ratio = 1 / 4 = 0.25
% solids in concentrate = 10% x 0.25 = 2.5%
Therefore, the solid content of the concentrate would be 2.5% to yield single-strength juice after diluting one part of the concentrate with three parts of water.