Part a
Basis - 100 kg of corn steep liquor
Let mass of corn steep liquor = C kg
Mass of beet molasses = B kg
Mass of water inlet = W kg
Mass of product stream exit = P kg
Part b
Overall balance
C + B + W = P
100 + B + W = P
Dextrose balance
C*wcD + B*wbD + W*wwD = P*wpD
100*0.025 + B*0.01 + W*0 = P*0.02
2.5 + 0.01B = 0.02P............ eq1
Sucrose balance
C*wcSu + B*wbSu + W*wwSu = P*wpSu
100*0 + B*0.50 + W*0 = P*0.126
0.50B = 0.126P
B = 0.252 P
from eq1
2.5 + 0.01(0.252P) = 0.02P
2.5 + 0.00252P = 0.02P
2.5 = (0.02 - 0.00252)P
P = 143 kg
B = 0.252*143 = 36 kg
W = P - B - 100
= 143 - 36 - 100
= 7 kg
Solid balance
C*wcS + B*wbS + W*wwS = P*wpS
100*0.475 + 36*0.31 + 7*0 = 143*wpS
58.66 = 143*wpS
wpS = 0.41 = 41%
wpW = 44.4%
Dextrose % in product = wpD = 2%
Sucrose % in product = wpSu = 12.6%
Solid % in product = wpS = 41%
Water % in product = wpW = 44.4%
Now we can check our calculations
Water balance
100*0.50 + 36*0.18 + 7*1 = 143*wpW
63.48 = 143*wpW
wpW = 0.444 = 44.4%
It means we are correct in our math above.
Part c
Mass flow of water / mass flow of corn steep liquor
W/C = 7/100 = 0.07
% water, the rest of the liquor stream is solids. Beet molasses contains 50 wt% sucrose,...
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