The popularity of orange juice, especially as a breakfast drink, makes it an imp

Question

The popularity of orange juice, especially as a breakfast drink, makes it an important factor in the economy of orange-growing regions. Marketed juice has either gone through a process in which it was concentrated, or it may be a not-from-concentrate juice. Frozen concentrated juice is reconstituted before consumption. Although concentrated juices are less popular in the United States than at one time, they still have a major segment of the market. The approaches to concentrating orange juice include evaporation, freeze concentration, and reverse osmosis. Here we examine the evaporation process by focusing only on two constituents in the juice: solids and water. Fresh orange juice contains approximately 10.0 wt% solids (sugar, citric acid and other indigenous ingredients) and frozen concentrate contains approximately 39.0 wt% solids. The frozen concentrate is obtained by evaporating water from the fresh juice to produce a mixture that is approximately 61.0 wt% solids. However, so that the flavor of the concentrate will closely approximate that of fresh juice, the concentrate from the evaporator is blended with fresh orange juice (and other minor additives) to produce a final concentrate that is approximately 39.0 wt% solids. Assume a basis of 400 kg of fresh juice fed to the process. What is the mass of final concentrate produced?

Explanation / Answer

Initial weight of fresh orange juice: 400 Kg

Total amount of solids present: 40 Kg out of 400Kg juice, i.e 10% wt/v

If we remove 83.6075 Kg of water from 100 Kg the remaining amount (16.3925 Kg) will be solids and water. Of which 10 Kg will be solids and 6.3925 Kg will be water. This accounts to = 10/16.3925 x 100 = 61% of solids and 6.3925/16.3925 x 100 = 39% of water.

That means from 400 Kg of orange juice (83.6075 x 4 = ) 334.43 Kg of water is removed and then the remaining concentrate is 65.57 Kg which is 61% in solids (40 Kg) and 39% water (25.57 Kg). This was further reconstituted with fresh orange juice to get 39% solids and 61% water as given below.

If for 100 Kg of concentrate 56.45 Kg of fresh juice (10% wt in fresh juice is ignored) is added then the total weight of juice concentrate and fresh juice will be 156.45 Kg.

Of this water will be (156.45 – 61 = ) 95.45 Kg, that will be 95.45/156.45 x 100 = 61% water and 61/156.45 x 100 = 39% juice concentrate.

If for 100 Kg of concentrate one need to add 56.45 Kg of fresh juice to get reconstituted juice of 39%.

Then for 65.57 kg of concentrate how much one need to add = 65.57 x 56.45 / 100 = 37.01 Kg of fresh juice need to add. This will bring the total concentrate weight to 65.57 + 37.01 = 102.58 Kg.

So from 400 Kg of 10% fresh juice one will get reconstituted juice of 39% about 102.58 Kg.   

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