Chapter 3
Mass Balance
Review Questions
Which of the following statements are true and which are false?
1. The mass balance is based on the law of conservation of mass.
2. Mass balance may refer to total mass balance or component mass balance.
3. Control volume is a region in space surrounded by a control surface
through which the fluid flows.
4. Only streams that cross the control surface take part in the mass balance.
5. At steady state, mass is accumulated in the control volume.
6. In a component mass balance, the component generation term has the same
sign as the output streams.
7. It is helpful to write a mass balance on a component that goes through the
process without any change.
8. Generation or depletion terms are included in a component mass balance if
the component undergoes chemical reaction.
9. The degrees of freedom of a system is equal to the difference between the
number of unknown variables and the number of independent equations.
10. In a properly specified problem of mass balance, the degrees of freedom
must not be equal to zero.
Examples
Example 3.1
How much dry sugar must be added in 100 kg of aqueous sugar solution in
order to increase its concentration from 20% to 50%?
S. Yanniotis, Solving Problems in Food Engineering.
Ó Springer 2008
11
12
3 Mass Balance
Solution
Step 1
Draw the process diagram:
100%
S1
100 kg
S2
MIXING
20%
S3
50%
Step 2
State your assumptions:
l
dry sugar is composed of 100% sugar.
Step 3
Write the total and component mass balances in the envelope around the
process:
i) Overall mass balance
100 þ S2 ¼ S3
(3:1)
ii) Soluble solids mass balance
0:20 100 þ S2 ¼ 0:50 S3
(3:2)
Solving eqns (3.1) and (3.2) simultaneously, find S2=60 kg and S3=160 kg.
Therefore 60 kg of dry sugar per 100 kg of feed must be added to increase its
concentration from 20% to 50%.
Example 3.2
Fresh orange juice with 12% soluble solids content is concentrated to 60% in a
multiple effect evaporator. To improve the quality of the final product the
concentrated juice is mixed with an amount of fresh juice (cut back) so that
the concentration of the mixture is 42%. Calculate how much water per hour
must be evaporated in the evaporator, how much fresh juice per hour must be
added back and how much final product will be produced if the inlet feed flow
rate is 10000 kg/h fresh juice. Assume steady state.