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(A) GAL.
FT.
(C) GRAMS — LITER ~_~
)GAL
(BC+ Bo)GAL. FT.
(D) GRAMS FT
/ _±_
Equation IV: D = (-A\C0TA~ (General) / A
C(T + (A B)f)
A
A \
~B)
B
Equation V: (A = O)
Equation VI : (A = Bc)
D = B
(Co C)
ln(T Bf)
D =
*•)(
-Af,
Fig. 2. Concentration of a constituent after passage of film. Constituent is depleted by chemical reaction and by carry-over.
constituents may be calculated from the equations listed in Fig. 3.
Calculation of Replenishment Rates and Formulas
Processing solutions that are maintained constantly at the concentration values of the original formula — or a "seasoned solution" formula — can be expected to produce film of unchanging photographic qualities. The ideal replenishment system will constantly counterbalance dilution and contamination effects of film, and thereby continuously restore constituents of the processing solutions to concentrations of the basic formula. A chemical removed from the solution by carry-over, overflow or chemical action must be supplied by the replenisher at the same rate at which it is lost; a chemical added to the solution as a result of film passage must be removed by replenishment action at
the rate at which it tends to build up. The equality which should exist between the replenishment rate and the exhaustion rate may be expressed mathematically. If the weight of chemical in a tank at any time is W, film footage is /, velocity of film passage is F, concentration of chemical in replenisher is Cr, and rate (in time) of addition of the replenisher solution is /?, then:
Q ft = y (32)
The term dW/df must now be evaluated. The rate of loss, and therefore the rate of replenishment, of a nonreactive constituent depends on concentration of the chemical and on rate of removal of the liquid from the tank. It was shown previously that the rate at which a nonreactive chemical is lost can be expressed by the following equation:
Goldwasser; Mathematical Replenishment Techniques
17