The popularity of orange juice, especially as a breakfast drink, makes this beverage an important

factor in the economy of orange$-$growing regions. Most marketed juice is concentrated and frozen

and then reconstituted before consumption, and some is "not$-$from$-$concentrate." Although

concentrated juices are less popular in the United States than they were at one time, they still have

a major segment of the market for orange juice.

The approaches to concentrating orange juice include evaporation, freeze concentration, and. Here

we examine the evaporation process by focusing only on two constituents in the juice: solids and

water. Fresh orange juice $($Feed$)$ contains approximately $10wt\%$ solids and frozen concentrate

contains approximately $42wt\%$ solids. The frozen concentrate is obtained by evaporating water

from the fresh juice to produce a mixture that is approximately $65wt\%$ 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 to produce a final concentrate that is approximately

$42wt\%$ solids.

a$.$ Draw reverse osmosis and label a flowchart of this process

b$.$ Calculate the amount of product $(42\%$ concentrate$)$ produced per $100kg$ fresh juice fed to

the process and the fraction of the feed that bypasses the evaporator