Answer:
A) 22.22 kg
B) 0.1364
Explanation:
When we perform a degree of freedom (DOF) analysis on the bypass subsystem, we will have 2 unknown masses which are; (m1, m2).l with degree of freedom as 1.
Secondly, when we perform a degree of freedom analysis on the overall system, we will have 2 unknown masses namely (m3, m5) with degree of freedom as 0.
Thirdly, when we perform a degree of freedom analysis on the evaporator, we will have 3 unknown masses namely (m1, m3, m4) with Degree of freedom as 1.
Lastky,when we perform a degree of freedom analysis on mixing point, we will have 3 unknown masses namely, (m2, m4, m5) with degree of freedom as 1.
We are given;
Fresh orange = 10.0 wt% solids
Frozen juice concentrate = 45.0wt% solids
Mixture produced = 67.0 wt% solids
Final concentrate = 45.0 wt% solids
Now, making use of the overall solids balance, we have;
0.1 × 100 = 0.45(m5)
m5 = (0.1 × 100)/0.45
m5 = 22.22 kg
Making use of overall mass balance, we have;
100 kg = m3 + m5
m3 = 100 - 22.22
m3 = 77.78 kg
Now, making use of the Mixing point mass balance, we have;
m4 + m2 = m5
So; m4 + m2 = 22.22 - - - (eq 1)
Also, making use of the Mixing point solids balance, we have;
0.67m4 + 0.1m2 = 0.45m5
0.67m4 + 0.1m2 = 9.999 - - - (eq 2)
Solving eq 1 and eq 2 simultaneously, we have;
m2 = 13.64 kg
m4 = 8.58 kg
Final concentrate is m5 = 22.22 kg
Now, fraction = m2/100 = 13.64/100 = 0.1364
