2.17.8: Making orange juice concentrate. Maximus and Theodora are optimizing a steady state processing making orange juice concentrate. A stream of oranges (0) and a stream of water (W, H₂O)

enter a juicing machine. The exit stream from the juicing machine contains 55.8 kg/hr orange juice (OJ, MW = 108), 21.3 kg/hr pulp solids (PS), and 43.5 kg/hr water. The exit stream from the juicing machine enters a filter. The filter removes all of the pulp solids and 20.2% of the water entering the filter as one exiting stream. The other stream exiting the filter contains water and orange juice. The water/orange juice mixture is finally sent to an evaporator to produce a concentrate stream (80.1 wt% orange juice and the balance water) and a stream of pure water. The pure water is recycled, mixed with a fresh stream of pure water, and fed into the juicing machine. Determine the following three unknowns. Mole fraction of orange juice in the concentrate stream =Ex: 0.309 Mass flow rate of water entering the evaporator =Ex: 30.9 kg/hr Mass flow rate of water entering the overall system =Ex: 16.8 kg/hr