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(A) GAL.
(D)
>RAMS
(C) GRAMS -_-__ LITER
-(T+ (A-B) f )6AL.
.(B
n)GAL. FT.
Equation VII: D = (A) \C0T A ~ B C(T + (A B)f)A '
(General) Equation VIII :
C
(^
D
r
(
D
A ^ A B ^ +
fc if
\ A
^B)
#)(
-")
T \A
B
~ Cot '
= 0)
_ n
\ a~^/\r + ( \ */ V r v
Equation (C Co)
A B)f) IX: (A = B)
D = A( C
-Af T
r. — *
*ln
_ /"» _L
T ln(^ Bf) Dt_ T
Fig. 3. Concentration of a constituent after passage of film. Constituent is added to solution by film and is depleted by carry-over.
dW _ -WE
df "= T + (A J?y
(33)
and then substituting C0 for the term W
in which A is the volume of liquid carried into the tank per foot of film, B is the volume of solution carried out of the tank per foot, and T is the initial volume. In continuous replenishment, only an infinitesimal change of concentration or volume should occur before the replenisher restores the solution to its original condition. The value of
W
— therefore centers about
1 • -| (A — B)f
C0) and consequently:
CrR = BC0V
(34)
It is also possible to derive Eq. (34) by starting with the differential equation:
The constant 5, representing the total amount of solution lost from the tank as one foot of film passes through, includes the solution carried out by the film (Be) as well as the solution overflowing from the tank (B0). The rate of overflow is determined not only by the carry-over at the entrance (A) and the exit (Be) but also by the rate of addition of the replenisher solution (R). As long as the solution in the tank is maintained at the same level, the rates of admission and removal of liquid are equal, and the following equality may therefore be expressed:
dW
WE
=0
R
AV = BV = (Bc
(35)
where R indicates volume of replenisher
January 1954 Journal of the SMPTE VoL 62