"Published in Suisun City, California, USA"
Fresh juice contains 15% solids and 85% water by weight and is to be concentrated to contain 40% solids by weight. In single-evaporation system, it is found that volatile constituents of juice escape with water leaving the concentrated juice with a flat taste. In order to overcome this problem, part of the fresh juice bypasses the evaporator. The operation is shown in the figure below
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| Photo by Math Principles in Everyday Life |
Calculate:
(a) The fraction of juice that bypasses the evaporator.
(b) The amount of concentrated juice produced (containing 40% solids) per 100 kg of fresh juice fed to the process.
Solution:
The given word problem is about evaporation of fresh juice to concentrated juice with bypassed fresh juice to be added to concentrated juice which involves the principles of Stoichiometry. The total amount of a substance in the reactants or incoming ingredients must be equal to the total amount of a substance in the final products. In short, the Law of Conservation of Mass must be followed all the time. To illustrate the given problem, it is better to label further the flow diagram as follows
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| Photo by Math Principles in Everyday Life |
Basis: 100 kg of Fresh Juice
Let x = be the amount of Fresh Juice fed to evaporator
y = be the amount of Fresh Juice bypasses the evaporator
z = be the amount of juice leaving the evaporator
p = be the amount of Concentrated Juice obtained
Overall Material Balance before Evaporator:
Overall Material Balance after Evaporator:
Material Balance of Solids over Evaporator:
Material Balance of Solids after Evaporator:
but
then the above equation becomes
Substitute the values of x and y to the first equation, we have
The value of x will be equal to
The value of y will be equal to
The value of p will be equal to
Therefore,
The amount of Concentrated Juice (40% solids) produced per 100 kg of Fresh Juice is 37.498 kg.
