Appendix A.

VALIDITY OF BEER-LAMBERT RELATIONSHIP

In November 1967, the SAE Diesel Smoke Measurement Task Force conducted a test program to establish the correlation between a number of diesel smoke measurement systems. A secondary goal of this task force was to establish the validity of the Beer-Lambert relationship for the transmission of light through various diameter plumes:
T = e ^–naQ1= e ^–K1

Where:

T = transmission.

n = number of particles per unit volume.

a = mean particle projected area.

Q = particle extinction coefficient.

l = length of light path.

e = base of natural logarithms.

The n, a, and Q variables are often referred to as the turbidity on attenuation coefficient (k); and are constant for a given soot density.

In the final published report, the SAE Task Force concluded that the Beer-Lambert relationship was usable for transmission predictions.

Figure 5 of the Task Force report (A.W. Carey Jr., ‘‘Steady-State Correlation of Diesel Smoke Meters.’’ Paper 690492 presented at SAE Mid-Year Meeting, Chicago, May 1969) is reproduced in this appendix as Figure A-1. The following is noted in the report:

‘‘Fig. 5 presents the results obtained when the stack size was varied. The effect of stack size as shown in Fig. 5 clearly demonstrates the powerful influence this variable has on the apparent opacity of the smoke column. It is entirely reasonable to expect that the greater optical path length through the smoke column issuing from the 6 inch diameter stack will produce greater extinction of the light than would that from a 3 inch stack. The effect is predicted quite accurately by the Beer-Lambert relationship, as evidenced by the Beer-Lambert prediction points which have been placed along the 6 inch diameter and 3 inch diameter correlation lines. These Beer-Lambert predictions are based on the observed opacity correlation obtained with the 4 inch diameter stack and accuracy of the prediction is excellent.’’

The results of this test are included in SAE J255.

Figure A-1—EFFECT OF STACK SIZE

Source

The provisions of this Appendix A adopted August 26, 1977, effective August 27, 1977, 7 Pa.B. 2432.