Question

Engineers Sophia and Giles are modifying a process to make concentrated apple cider starting from a slurry - a slurry is a mixture of solids in a liquid that can normally be pumped. A slurry made with apples having a mass fraction of 0.462 and the balance water is fed to a juicer at a rate of 31.7 kg/min. Seventy percent of the apples entering the juicer leave as part of the solid waste stream (containing apples and water). The primary product from the juicer is cider (33.7 wt% apples and 66.3 wt% water). The cider is sent to an evaporator where concentrate - apple concentration increases to 49.9 wt% - is produced along with a stream of pure water that is recycled. The pure water stream leaving the evaporator is mixed with fresh water entering the process. The combined water stream mixes with pristine apples entering the process to create the slurry. Determine the following three unknowns.

Mass fraction of apple in the solid waste

Total flow rate of the concentrate in kg/min

Flow rate of pure water entering the overall system in kg/min

Answer 1