Environmental Engineering Reference
In-Depth Information
Control
volume
V
,
y
A
i
,
y
B
i
F
,
z
A
o
,
z
B
o
O
,
x
A
i
,
x
B
i
Figure 3.20
Control volume used to explain lever-arm rule.
O
x
B
i
F
z
B
o
B
V
y
B
i
A
y
A
i
z
A
o
x
A
i
COMPONENT
A
Figure 3.21
Graphical representation of mass balances for a two-liquid feed
stream on a right triangle diagram.
The mass balances for the system are represented graphically on a right triangular diagram
(Figure 3.21) [2].
Analytically, there are three independent mass balances for this system:
Overall:
V
+
O
=
F
Component
A
:
Vy
A
i
+
Ox
A
i
=
Fz
A
o
Component
B
:
Vy
B
i
+
Ox
B
i
=
Fz
B
o
.
Combining these equations, it can be shown that the concentrations of the mixed stream
F
are then:
Vy
A
i
+
Ox
A
i
z
A
o
=
(3.28)
V
+
O
Vy
B
i
+
Ox
B
i
z
B
o
=
.
(3.29)
V
+
O
The mass balances can be combined into two equations to eliminate
F
. The result proves
that the points
V
,
O
and
F
are colinear as pictured in Figure 3.21,
V
O
=
z
A
o
−
x
A
i
V
O
=
z
B
o
−
x
B
i
and
z
B
o
.
(3.30)
y
A
i
−
z
A
o
y
B
i
−
Search WWH ::
Custom Search