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Concentrated orange juice contains 45 wt% solids and 55 wt% water. The concentrated juice is made by evaporating water from natural juice that contains 10 wt% solids. To improve the taste of the concentrated juice, a fraction of the fresh juice bypasses the evaporator and is mixed with a stream leaving the evaporator that has 60 wt% solids in order to form the desired 45 wt% solids product stream.

The flowchart below illustrates the process.

For a given mass flow rate of feed (stream 1), you need to determine the mass flow rates of all the other streams (numbered 2, 3, 4, 5, 6). For the purposes of calculation, assume that the feed stream consists of two species: liquid and solid, and use a basis of calculation of 1 kg/s feed flow rate.

4 1 3 5 6 Evaporator 2 2 Bypass Problem 1 Write out mass balance equations and do a degrees of freedom analysis. For this analysis, consider all the possible mass balances that may written to relate the unknown quantities. Carry out a degrees of freedom analysis on the entire process and each sub-system of the process (evaporator, split point, mix point). In [ ]: Problem 2 Solve the system of equations developed in Problem 1 using Sympy. In [ ]: Problem 3 Solve the system of equations developed in Problem 1 using the "Istsq" function contained in the linalg module of NumPy. In [ ]: Problem 4 Solve the system of equations developed in Problem 1 using the "solve" function contained in the linalg module of NumPy. To use the "solve" function, remember that the overall degrees of freedom must be zero (5 independent equations that can be solved for the 5 unknowns). In [ ]: 4 1 3 5 6 Evaporator 2 2 Bypass Problem 1 Write out mass balance equations and do a degrees of freedom analysis. For this analysis, consider all the possible mass balances that may written to relate the unknown quantities. Carry out a degrees of freedom analysis on the entire process and each sub-system of the process (evaporator, split point, mix point). In [ ]: Problem 2 Solve the system of equations developed in Problem 1 using Sympy. In [ ]: Problem 3 Solve the system of equations developed in Problem 1 using the "Istsq" function contained in the linalg module of NumPy. In [ ]: Problem 4 Solve the system of equations developed in Problem 1 using the "solve" function contained in the linalg module of NumPy. To use the "solve" function, remember that the overall degrees of freedom must be zero (5 independent equations that can be solved for the 5 unknowns). In [ ]