Environmental Engineering Reference
In-Depth Information
D
F 1
Control
volume for
macroscopic
balance
B
Figure 3.3 Control volume for macroscopic balance.
A macroscopic balance is used when global information is sufficient, i.e., no infor-
mation at each point within the control volume is required. This type is used when the
concentration profiles within the C.V. are not of interest, but the values associated with
the masses and component concentrations that enter and leave the C.V. are of interest.
This balance is sometimes described as an integral balance since any effects of position
within the C.V. are averaged and only global values are evaluated. The system is treated
as a “black box.” In Figure 3.3 the composition and flowrate of streams F 1 , D and B are of
interest.
A microscopic (or differential) balance is used when information at each point within
the control volume is needed. Each term of the balance equation is then a rate (rate of input,
rate of generation, etc.). This type of balance is based on one or more differential equations
that are solved to obtain the concentration profiles. The control volume in Figure 3.4 could
be used if one were interested in the concentration profile across the membrane at each
axial position of the membrane.
3.3
Degrees of freedom analysis
An important criterion in the solution of separation problems is determining that there
is sufficient information to solve the problem. For any problem, there will be a cer-
tain number of independent variables ( V ) and a number of independent equations ( E ).
The degrees of freedom ( DF ) or the number of independent variables that one needs to
specify is
DF
=
V
E
.
(3.2)
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