oEPA
United States
Environmental Protection
Agency
Industrial Environmental Research EPA-600'7-78-226
Laboratory November 1978
Research Triangle Park NC 2771 1
Cascade Impactor
Data Reduction with
SR-52 and TI-59
Programmable Calculators
Interagency
Energy/Environment
R&D Program Report
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
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The nine series are:
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4. Environmental Monitoring
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RESEARCH AND DEVELOPMENT series. Reports in this series result from the
effort funded under the 17-agency Federal Energy/Environment Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic
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essary environmental data and control technology. Investigations include analy-
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This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/7-78-226
November 1978
Cascade Impactor Data Reduction
with SR-52 and TI-59
Programmable Calculators
by
Leslie E. Sparks
Environmental Protection Agency
Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, North Carolina 27711
Program Element No. EHE624A
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, DC 20460
-------
ABSTRACT
This report is intended to provide useful tools for obtaining
particle size distributions and graded penetration data from Cascade
impactor measurements. The programs calculate impactor ?_: jdynamic cut
points, total mass collected by the impactor, cumulative mass fraction
less than for each stage, log-normal size distribution parameters for
the data, and graded penetration. These programs are written specif-
ically for the Texas Instruments SR-52 and TI-59 programmable calculators
and the PC-100A printer. A general discussion of the program, an example
problem, program listing, and user instructions are provided for each
program.
11
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CONTENTS
Abstract ii
Figures v
Tables vi
Nomenclature vii
Introduction 1
Notes on the Programs 2
SR-52 Program Set 3
General Discussion 3
Card 1 4
Card 2 5
Card 3 8
Card 4 8
Card 5 9
Card 6 10
Programming the Six Cards 11
Programming Card 1 11
Programming Card 4 11
Use of the Data Reduction Package 12
Example 1. Use of Data Reduction Package 12
TI-59 Program Set 23
General Discussion 23
Card 1 23
Example 2. Use of TI-59 Reduction Package 26
Example 3. Use of Programs to Convert Aerodynamic Diameter
to Physical Diameter 30
Example 4. Calculation of Viscosity of Gas Mixtures 34
Cards 2, 3, and 4 (Calculation of Penetration as a Function of
Particle Diameter with TI-59) 37
Example 5 39
Comparison of Graded Efficiency Calculated from Curve Fit
and Spline Fit 47
Recommendations for Running Impactors 50
References 52
-------
CONTENTS (Cont'd)
Appendix A. User Instructions and Program Listing for SR-52
Data Reduction Programs
Appendix B. User Instructions and Program Listing for TI-59
Impactor Data Reduction Package
Appendix C. User Instructions and Program Listing for TI-59
Program to Convert Aerodynamic Diameter to
Physical Diameter
Appendix D. User Instructions and Program Listing for Program
to Estimate Viscosity of Mixtures
Appendix E. User Instructions and Program Listing for Spline
Fit Program
Appendix F. User Instructions and Program Listing for Calculation
of Penetration as a Function of Particle Diamete^
for TI-59
A-l
B-l
C-l
D-l
E-l
F-l
IV
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FIGURES
Number Page
1 Inlet cascade impactor data for example l--use of
SR-52 data reduction programs 17
2 Outlet cascade impactor data for example l--use of
SR-52 data reduction programs 19
3 Penetration as a function of particle diameter printer
output for example l--use of SR-52 data reduction
programs 21
4 Contents of R4Q through R52 for MRI impactor 25
5 Output from example 3--use of TI-59 data reduction
package 28
6 Printer output for example 3--use of programs to
convert d. to d 33
7 Printer output for example 4--use of program to
estimate viscosity 36
8 Printer output for example 5--use of TI-59 program
to calculate penetration as a function of particle
diameter 44
Appendix A
Impactor data reduction program listing card 1 A-4
Impactor data reduction program listing card 2 A-6
Impactor data reduction program listing card 3 A-8
Impactor data reduction program listing card 4 A-9
Impactor data reduction program listing card 5 A-ll
Log-normal penetration program listing A-14
Appendix B
Program listing TI-59 cascade impactor data reduction--
card 1 B-3
Appendix C
Program listing program to convert aerodynamic
diameter to physical diameter C-3
Appendix D
Program listing viscosity program D-3
-------
FIGURES (cont'd)
Number Pa^e.
Appendix E
Spline fit card 1 E-3
Spline fit card 2 E-8
Appendix F
Program listing Pt(d) program for TI-59 F-3
TABLES
Number Page
1 Values of stage constants for MRI and University
of Washington impactors 6
2 Values of constants for inverse normal function 9
3 Steps for using SR-52 data reduction package 13
4 Comparison of graded penetration calculated
using log-normal fit, quadratic log-normal fit
and spline fit on actual impactor data 48
5 Comparison of graded penetration calculated
with spline and log-normal fits with actual
graded penetrations from ESP model 49
VI
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Constants for rational approximation of inverse normal function
NOMENCLATURE
A - Used to calculate Cunningham correction factor
A - Least-squares curve fit parameter in y = A + Bx
B - Least-squares curve fit parameter in y = A + Bx
C - Cunningham correction factor
Ci - Stage constant for i impactor stage
C0
Cl
C2
C3
C4
C5
D. - Diameter of holes for i impactor stage, cm
d - Particle diameter, ym
d - Physical impactor cut point, ym
- Aerodynamic impactor cut point, ymA
d,, - Mass mean diameter, ym
9
f. - Cumulative mass fraction less than total mass for i
impactor stage
fr(d) - Inlet cumulative size distribution
fQ(d) - Outlet cumulative size distribution
K50, - Inertia! impaction parameter for 50% collection efficiency on
the i impactor stage
M. - Weight of particulate collected by i impactor stage, mg
Mj - Total weight of particulate collected by impactor, mg
N. - Number of holes on the i impactor stage
P - Pressure, cm Hg
Pt(d) - Penetration of particles with diameter d
vii
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NOMENCLATURE (Cont'd)
Pt(d)|N - Penetration of particles with diameter d calculated using
linear log-normal fit
Pt(d)|N2 - Penetration of particles with diameter d calculated using
quadratic log-normal fit
K(d)M - Penetration of particles with diameter d from electrostatic
precipitator model
Pt(d) - Penetration of particles with diameter d calculated using spline
3 fit
Q - Gas flow rate through impactor, 1/m
R. . - Storage register ij
2
r - Correlation coefficient
S(x.) - Spline fit function evaluated at xi
S'(x.j) - d [S(x)]/dx evaluated at xi
S"(x.j) - d2[S(x)]/dx2 evaluated at xi
S'"(x1) - d3[S(x)]/dx3 evaluated at xn-
T - Temperature, °C
t - Dummy variable used in inverse normal function calculation
t - Dummy variable used in spline fit program
Vi - Jet velocity for ith stage, m/s
Wj - Inlet mass concentration, g/m
WQ - Outlet mass concentration, g/m
X - Inverse normal function
x - General variable
x - Average value of x
y - General variable
y - Average value of y
Z - Dummy variable
vm
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NOMENCLATURE (Cont'd)
M - Gas viscosity, poise
X - Gas mean free path
AQ - Gas mean free path at 23°C
p - Particle density, g/cc
a - Geometric standard deviation
OT - Inlet geometric standard deviation
a - Outlet geometric standard deviation
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INTRODUCTION
Cascade impactors are the major instrument for obtaining information
on the instack particle size distribution before and after air pollution
control equipment. Data reduction is tedious, time consuming, and
generally requires access to a computer. Thus, there may be a long
delay in obtaining reduced data after the measurements are made. Such
delays can be especially troublesome in the field.
Recent advances in calculator technology make it possible to do
much of the data reduction without a computer. Thus, reduced data can
be available shortly after the measurements are made. The ability to
examine reduced data shortly after the measurements are made is especially
important in field tests. Trends and problems can be found while still
in the field and corrective action can be taken to improve data taken
later.
There are two sets of calculator programs in this report--one set
for the Texas Instruments SR-52 calculator and a second set for the
Texas Instruments TI-59 calculator. The programs in each set perform
the following calculations:
1. Calculate aerodynamic cut points for each impactor stage.
2. Calculate total mass collected by the impactor.
3. Calculate the cumulative mass fraction less than
for each stage.
4. Calculate the log-normal size distribution that best
fits the data.
5. Calculate penetration as a function of particle
diameter (graded penetration).
The methods used for the first four calculations are the same for
both sets of programs. Graded penetration is calculated from the log-
normal fit results in the SR-52 program set and from a spline fit to the
impactor data in the TI-59 program set. A brief comparison of these two
1
-------
methods for calculating graded penetration is included. Two additional
TI-59 programs are also providedone to convert aerodynamic diameter to
physical diameter and one to estimate the viscosity of mixtures of
gases.
NOTES ON THE PROGRAMS
In the user instructions and examples, a convention of underline
letters or numbers has been adopted to dencte the key or keys on the SR-
52 or TI-59 keyboard which should be pressed to conduct the operation
discussed. For example: in the instruction Press A_, the underline
indicates that the A button on the keyboard should be pressed. Storage
registers are indicated by R... For example: ROI refers to (/'rage
register 01.
The programs all make extensive use of the indirect recall and
indirect store features of the SR-52 and TI 59. Thus, it is essential
that the counter for the indirect recall and indirect store registers be
set at the proper initial value and advanced at the required times.
Anyone who wishes to modify the programs should remember that the programs
as written depend on indirect recall and indirect store instructions.
Two of the SR-52 programs store data in registers that normally are
used to store program instructions. This use of the program registers
can cause problems with program execution if the magnetic cards containing
the programs are read improperly.
Magnetic cards are read into the SR-52 calculator by:
Step Procedure Press
1 Enter side A 2nd rst 2nd read
2 Enter side B 2nd read
Instructions for reading magnetic cards into the TI-59 calculator
are given in the appropriate user instructions.
2
-------
The programs as written are for the Meteoroloy Research, Inc. (MRI)
Cascade Impactor. The programs can be modified for use with other
impactors provided:
1. Calibration data for the impactor are available.
2. Number of useful stages - 7 (including filter).
SR-52 PROGRAM SET
GENERAL DISCUSSION
The SR-52 program set is contained on six magnetic cards that must
be executed in the following order: Cards 1, 2, 3, 4, 5 for inlet data;
Cards 1, 2, 3, 4, 5 for outlet data; and then Card 6 for combined inlet
and outlet data.
Card 1 is used to calculate and store the aerodynamic cut diameter,
d.5Q, for each impactor stage. Impactor flow rate and impactor temperature
are entered before the calculation.
Card 2 is used to calculate and store the total mass collected by
the impactor, My, and the cumulative mass fraction less than total mass
collected by each stage, f.. Mass collected by each stage, M., is
entered and printed before the calculation is performed.
Card 3 is used to print MT, d/\5Q> and fi.
Card 4 is used to transform the f^ so that a log-normal fit to the
data can be calculated using Card 5.
Card 5 is used to calculate a least-squares best fit to the data
transformed by Card 4. The log-normal parameters, mass geometric mean
diameter, d , and geometric standard deviation, a, are printed along
with the least-squares fit parameters, A and B for y = A + Bx, and the
p
correlation coefficient, r .
-------
Card 6 is used to calculate and print the graded penetration for
two log-normal particle size distributions. Inlet mass concentration,
Wy, outlet mass concentration, WQ, inlet geometric standard deviation,
OT, outlet geometric standard deviation, OQ, inlet mass mean diameter,
d j, and outlet mass mean diameter, d , are entered before the calcula-
tion is performed.
The programs on each card are discussed in detail in the next sections,
Card 1
3
Card 1 is used to enter the impactor flow rate, Q, in either ft /min
or 1/min and the impactor temperature, T, in either °F or °C. The program
on the card then calculates d,,- in pmA* for each stage. The d,,. are
stored in the calculator for use by other programs.
dA50i is given by
where y = the viscosity of the gas in poise
D, = the diameter of the holes on the ith stage in cm
J.L.
N.J = number of holes on the i stage
Q = gas flow rate in 1/m
K50i = inert1'al impaction parameter for 50% collection
efficiency on the i stage
Kcn< = d2^. Cp V,/9u D, X 108
S50i ' u 50i Op Vyy ui
d50i = Pnysical cut diameter, pm
C = Cunningham correction factor
p = particle density
j_ L
V.j = jet velocity for i"1 stage, m/s
*The convention to denote aerodynamic diameters by ymA will be used
throughout this report.
-------
The gas viscosity used in the program is for air and is estimated by
y = 1.68 X 10"4 + 2.292 X 10"7 X (1.8 T + 32) (2)
where yis in poise and T is in °C.
The value for K5Q. should be based on experimentally determined
-i
used.
Equation 1 can be rewritten as
calibration curves. If such curves are not available K,-Q. = 0.2 can be
dA50i = / C^/CQ X 10'S) (3)
o_U
where C. = stage constant for the i stage,
= 0.135 TiDiK. (4)
C. must be calculated at the time the calculator is first programmed and
is stored in registers Rg, - Rgy. When a program with C. stored in
these registers is recorded on a magnetic card, the C- are recorded on
the card and become a permanent part of the program.
C. for the MRI and University of Washington cascade impactors are
shown in Table 1.
To use the program with an impactor other than the MRI impactor,
store the appropriate stage constants in Rg, through Rg7-
Card 2
J.L
Card 2 is used to enter the mass collected on the i stage, M.,
and to calculate NL and f.. The M. are entered in order of i = 1 to i
N where i = 1 is the stage with the largest d. and i = N is the
filter.
-------
Table 1. VALUES OF STAGE CONSTANTS FOR MRI AND
UNIVERSITY OF WASHINGTON IMPACTORS
Stage
1
2
3
4
5
6
7
MRI
Ci
5.4069 X 10"2
6.8611 X 10"2
2.1484 X 10"2
3.8666 X 10"3
1.0147 X 10"3
3.5065 X 10"4
2.2899 X 10"4
University of Washington
Ci
7.4123 X 10"2
9.3954 X 10"2
1.3376 X 10"2
1.7759 X 10"3
1.8378 X 10"3
4.2206 X 10"4
1.0104 X 10"4
Store in
R91
R92
R93
R94
R
95
R96
R97
MRI stage constants for stages 4, 5, 6, and 7 are based on EPA/IERL-RTP/
Participate Technology Branch impactor calibration data. University of
Washington stage constants and MRI stage constants for stages 1, 2, and 3
are based on Southern Research Institute calibration data.
-------
The total mass collected is given by
MT = z" Mi
i = 1
The cumulative fraction less than the total collected on the i
stage, f^, is given by
i j = i - 1
V{ j = o jjl (6)
where j = 0 is the filter.
The f- are stored in the calculator for later use.
The cut points for the first two stages of the MRI impactor overlap.
The masses collected by these two stages should be manually added together.
The sum M-j + M2 is then entered into the calculator and is automatically
attributed to the second stage in the data reduction program. The first
two stages of the University of Washington impactor also overlap and
must be handled in the same way as the first two stages of the MRI
impactor.
The fact that the mass collected on the first two stages are added
together means that there are seven masses entered. These seven M^ are
used to calculate six cumulative fraction less than values which are
stored for later use. The number of cumulative fraction less than
values that can be stored is limited to six. If the impactor being used
has more than six useful stages plus filter, the mass collected by the
extra stages can be lumped with that of the top stage. For example, if
there are seven useful stages 1, 2, 3, 4, 5, 6, 7, plus filter; the mass
collected by stage 1 can be added to that collected by stage 2.
-------
Card 3
Card 3 recalls MT, f 1 , and dA5Qi from memory and prints them in the
following order: MT> dA5Q1 , f 1 , ---- dA506' V
Card 4*
The f. are transformed to normal coordinates by use of the inverse
normal integral, X, based on the cumulative mass fraction f..
f(X) - /Vt2/2 dt (7)
- M /~2iF
where
f (- ») =0
f ( 0 ) =0.5
f (+ » ) = 1.0
Hastings gives a rational approximation that can be used to
calculate X
Q + £ + £ £
X = t + [ - - - - ~- J + error of order e (8)
C3t
0.00045
where t = /In U-4-) for f <1 (9)
y ]-f f >0.5
The calculator program accounts for all f. since
X (f. = m) = X (fi = 1 - m) for m < 0.5 by symmetry. (10)
For example X (f^. = 0.4) = - X (f^ = 0.6)
The constants CQ through C5 are stored in registers R92 through
Rg7. The values of CQ through C5 are given in Table 2.
*Much of the original work for the program on Card 4 is due to
H. F. Barbarika of Air Pollution Technology, Inc.
-------
Table 2. VALUES OF CONSTANTS FOR INVERSE NORMAL FUNCTION
CQ = 2.515517 stored in Rg2
C-| = 0.802853 stored in Rg3
C2 = 0.010328 stored in Rg4
C3 = 1.432788 stored in Rg5
0.189269 stored in
Rg6
C5 = 0.001308 stored in Rg7
The first time the program is read onto a magnetic card with CQ through
C5 stored in Rg2 through Rgy, the constants become a permanent part of
the program.
Card 5
Card 5 is used to determine the log-normal size distribution parameters
for the data entered previously. The log-normal parameters, d^ and a,
are determined by constructing a least-squares straight line through the
data transformed on Card 4. The fitted line is of the form
y = A + Bx (11)
The constants A and B are determined by
A = y - Bx (12)
B = S(xy) - 7 £x (13)
£(x2) -
where N = the number of data points
- (£x)2/N
x = £x/N is the average value of x and
y = Zy/N is the average value of y
-------
The log-normal parameters are given by
d = exp (- A/B) (14)
a = exp (1/B) (15)
2
The correlation coefficient r for the curve fit is given by
L(/) - (sy)VN
2
A, B, r , dfl , and a are all printed.
"9
Card 6
Card 6 calculates and prints penetration as a function of particle
diameter (the graded penetration) for two log-normal size distributions.
The penetration of particles of diameter d, Pt(d), is defined as
=
Wj LdfI(d)/ddJ
where W = mass concentration at outlet
Wj = mass concentration at inlet
fQ(d) = outlet cumulative size distributio
fj(d) = inlet cumulative size distribution
For a log-normal distribution:
exp [ 1 dd (18)
2 In a
Pt(d) becomes
Pt(d) = WQ Inaj exp (z£ - Z^)/2 (19)
I o
where Z = Ind - Ind
The program solves equation (19) for the range d = 0.1 to 20 ym and prints
d, Pt(d), and l-Pt(d) (the efficiency) in 0.1 Mm steps for 0.1 - d < 1 and
10
-------
in 1 ym steps for 1 - d - 20. The printed results are not reliable when
d is outside the range of the impactor data.
The log-normal penetrations calculated by this program are a good
representation of the data when the product of the inlet and outlet
correlation coefficients, r -n x r out> exceeds 0.985. When the r2 product
is less than 0.985 the calculated penetrations are still useful for
determining trends.
PROGRAMMING THE SIX CARDS
Programming the cards is straightforward except for Cards 1 and 4.
Data registers that normally store program instructions are used to
store constants used in the calculations for Cards 1 and 4. Special
care must be taken to ensure that the constants are stored in the proper
registers before the magnetic cards are recorded.
Programming Card 1
Turn the calculator on. Press LRN to put the calculator in the
learn mode. Enter the Impactor dA5Q program as listed in the program
listing. After the last instruction is entered, press LRN to return the
calculator to calculate mode. Enter stage constants, one at a time, and
store them in the appropriate registers, see Table 1. After the last
stage constant is stored, record both sides of a magnetic card using following
steps: press ^nd_ rst, insert side 1, press INV 2nd READ, insert side 2, and
then press INV 2nd READ.
Programming Card 4
Turn the calculator on. Press LRN to put the calculator in the
learn mode. Enter the Inverse Normal Function program as listed in the
program listing. After the last instruction is entered, press LRN to
return the calculator to calculate mode. Enter CQ through C5> one at a
time, and store them in the appropriate registers, see Table 2.
11
-------
Record the program on both sides of a magnetic card by following
the same procedure used for Card 1.
USE OF THE DATA REDUCTION PACKAGE
The step by step procedure for using the data reduction package is
given in Table 3. Use of the package is demonstrated in Example 1.
Example 1. Use of Data Reduction Package
An MRI impactor was used to obtain the following data. Use the data
reduction package to reduce the data.
Inlet
Outvie
Q
T
M] + M2
M3
M4
M8(filter)
WIN
= 9.569 1/m
= 92°C
= 0.0146 mg
= 0.0199
= 0.0273
= 0.0080
= 0.0021
= 0.0005
= 0.0003
= 0.3804 mg/1
Q = 33.01 1/m
T = 92°C
0.00005 mg
0.0010
0.0025
0.0014
0.0007
0.0009
0.0014
WQ = 0.00072 mg/1
12
-------
Table 3. STEPS FOR USING SR-52 DATA REDUCTION PACKAGE
Step
1
2
3
4
5
6
7
8
9
10
Procedure
Read sides A and B of
Check to see if card
Enter T
or
Enter Q
or
Initialize
Reset
Calculate dA5Q1
Read sides A and B of
Initialize
Enter M1
Enter
Card 1
read properly
T°C
T°F
Q 1/min
cfm
Card 2
Ml
Mo
Press
RCL 92
A
2nd A1
i
2nd B
E_
2nd rst
D_
E_
A
A
Display
Constant
for 1st
T°C
T°C
Q 1/min
Q 1/min
1.0000
1 . 0000
0.0000
0.0000
1 . 0000
2.0000
Print
stage
Ml
Mo
Mfilter
A
7.0000
Mr
Note: For the MRI and University of Washington impactors, M-j = the sum of
the mass collected on the first two stages. M, and Mp must be added
before the data are entered.
11 Calculate f^
12 Read Side A of Card 3
13 Print Kp f.
0.0000
M-,
JA501
13
JA506
-------
Table 3. STEPS FOR USING DATA REDUCTION PACKAGE (Cont'd)
Step
14
15
16
17
18
19
20
21
22
23
24
25
26
Procedure
Read Card 4 sides A
Initialize
Transform f .
Read Card 5 sides A
Initialize
Calculate log-normal
Read Card 6 sides A
Enter Wy
Enter Id
0
Enter aj
Enter OQ
Enter d y
Enter d
Enter
and B
and B
parameters
and B
WI
w^
0
°I
°0
dgi
d_
Press
Display
Print
"go
27 Calculate Pt(d)
E. 8.0000
A
E 0.0000
A
A
2nd A1
B_
2nd B1
C_
2nd C'
D_
a A
B
r2
dg
a
2n' rst
INV READ
INV READ
0.10000
*<
In ao
lndgl
lndgo
Pt(d)
l-Pt(d)
0.1
9999.00000
Pt(d)
l-Pt(d)
20.0
14
-------
Solution
Step Procedure
Do inlet calculations
Read Card 1
Enter
1
2
3
4
5
6
7
8
9
11
12
13
Check to see if read correctly
92
9.5696
Enter T °C
Enter Q 1/m
Initialize
Reset
Calculate d.,-Q.
Read Card 2
Initialize
Put calculator in fix display mode
10 Enter
M3
M4
M5
M6
M7
M8
Calculate f
0.0146
0.0199
0.0273
0.008
0.0021
0.0005
0.0003
i
Read Card 3 side A only
Print results
Press
2nd rst
2nd READ
RCL 91
A
B
i
2nd rst
D.
2nd rst
E.
INV EE
A
A
A
A
A
A
A
B_
2nd rst
A
Display
READ
.054069
92
9.5696
1 . 0000
1.000
0.00000
2nd READ
0.000000
0.0000
1
2
3
4
5
6
7
0.0000
2nd READ
0.0028
Print
0.0146
0.0199
0.0273
0.0080
0.0021
0.0005
0.0003
0.0727
12.3662
0.7992
6.9199
0.5254
2.9356
0.1499
1.5039
0.0399
0.8840
0.0110
15
-------
Step Procedure
14 Read Card 4
Enter
Press
Display
2nd rst 2nd READ
15
16
17
18
19
Initialize
Transform f .
Read Card 5
Initialize
Calculate
2nd READ
i
A
2nd rst
2nd READ
8.0000
0.0000
2nd READ
0.0000
2.3102
1.1943
-2.2263
0.9978
6.4505
2.3102
A sample print out for inlet calculations is shown in Figure 1.
Repeat for Outlet
Step Procedure
1 Read Card 1
Enter
2
3
4
5
6
7
Check to see if card read correctly
Enter T °C 92
Enter Q 1/m 33.01
Initialize
Reset
Calculate dA5Qi
Read Card 2 and change display
to fix mode
Press
2nd CMS
2nd rst
2nd READ
2nd READ
clr
RCL 91
A
B
2nd rst
D
Display
Print
0.054069
92.0000
33.0100
1.0000
1.0000
0.0000 00
2nd rst 2nd READ
2nd READ INV EE 0.0000
16
-------
0.0146 PRT
0.0199 PRT
0.0273 PRT
0. 0080 PRT
0.0021 PRT
0. 0005 PRT
0. 0003 PRT
0. 0727
12.3662 PRT
0. 7992 PRT
6.9199 PRT
0. 5254 PRT
2. 9356 PRT
0. 1499 PRT
1.5039 PRT
0. 0399 PRT
0. 8840 PRT
0.0110 PRT
0.7144 PRT
0.0041 PRT
1. 1943 PRT
-2.2263 PRT
0. 9978 PRT
6. 4505 PRT
2.3102 PRT
Figure 1. Inlet Cascade Ir.ipactor Data for Example 1Use of SR-52 Data Reduction
Programs
17
-------
Stej
9
Procedure
Enter MI +
M,
Me
M
8(filter)
Enter
0.00005
Press
A
Display
1 . 0000
Print
0.0001
(0.00005
rounded
to
0.0001 be-
0.001
0.0025
0.0014
0.0007
0.0009
0.0014
A
A
A
A
A
A
2
3
4
R
6
7
cause of
printer
command
Card 1)
0.0010
0.0025
0.0014
0.0007
0.0009
0.0014
0.0080
in
10 Calculate f.
11 Read Card 3 side A only
12 Print outlet results
13 Read Card 4 sides A and B
14 Initialize
15 Transform
16 Read Card 5 sides A and B
17
18
Initialize
Calculate
i 0.0000
2nd rset 2nd READ 7
A
2nd rset 2nd READ
2nd READ
I 8.0000
A 0.0000
2nd rset 2nd READ
2.5213
2nd READ
E.
A
0.0000
3.3014
Printer output for the outlet calculations is shown in Figure 2.
Note that r for inlet is 0.9978 and is 0.9384 for outlet.
1.0813
0.0077
0.9384
0.9929
2.5213
1!
-------
0.0001 PRT
0.0010 PRT
0.0025 PRT
0.0014 PRT
0.0007 PRT
0.0009 PRT
0.0014 PRT
0.0080 PRT
6.6583 PRT
0.9937 PRT
3. 7258 PRT
0.8679 PRT
1.5806 PRT
0.5535 PRT
0.8097 PRT
0.3774 PRT
0.4760 PRT
0.2893 PRT
0.3847 PRT
0.1761 PRT
1.0813 PRT
0.0077 PRT
0.9384 PRT
0.9929 PRT
2.5213 PRT
Figure 2. Outlet Cascade Impactor Data for Example 1 - Use
of SR-52 Data Reduction Programs
19
-------
Now calculate Pt(d)
Step Procedure
1 Read Card 6
2
3
4
5
6
7
8
Enter W
Enter W
Enter a
Enter a
I
I
o
Enter d j
Enter dgQ
Calculate Pt(d)
Enter
.3804
.00072
2.3102
2.5213
6.4505
0.9929
Press
2nd rst
2nd READ
2nd READ
2nd Cms
CVr
2nd Fix 5
A
2nd A
B_
2nd B_'_
C.
2nd C'
D
Display
0.00000
0.10000
0.0007Z
0.83733
0.92477
-0.00713
Print
18.75795*
-17.75795
0.10000
For entire printer output see Figure 3.
9999.00000
0.00002
0.99998
20.00000
*The first five or six values of Pt(d) are unreliable because extrapolation
of the data was used to calculate them.
20
-------
18.75795
17. 75795
0.10000
2.08446
-1.08446
0.20000
0.61050
0.38950
0.30000
0.26207
0.73793
0.40000
0.13801
0.86199
0.50000
0.08250
0.91750
0.60000
0.05376
0.94624
0.70000
0.03728
0.96272
0.80000
0. 02709
0.97291
0.90000
0.02043
0.97957
1.00000
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
0.00342
0.99658
2.00000
0.00127
0.99873
3.00000
0.00065
0.99935
4.00000
0.00039
0.99961
5.00000
0. 00026
0.99974
6.00000
0.00019
0.99981
7.00000
0.00014
0. 99986
8.00000
0.00011
0.99989
9.00000
0.00009
0.99991
10.00000
PRT
PRT
' PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
PRT
Figure 3. Penetration as a Function of Particle Diameter
Printer Output for Example 1 - Use of SR-52
Data Reduction Programs
21
-------
0.00007 PRT
0.99993 PRT
11.00000 PRT
0.00006 PRT
0.99994 PRT
12.00000 PRT
0.00005 PRT
0.99995 PRT
13.00000 PRT
0.00004 PRT
0.99996 PRT
14.00000 PRT
0.00004 PRT
0.99996 PRT
15.00000 PRT
0.00003 PRT
0.99997 PRT
16.00000 PRT
0.00003 PRT
0.99997 PRT
17.00000 PRT
0.00003 PRT
0.99997 PRT
18.00000 PRT
0.00002 PRT
0.99998 PRT
19.00000 PRT
0.00002 PRT
0.99998 PRT
20.00000 PRT
Figure 3. (Cont'd)
22
-------
TI-59 PROGRAM SET
GENERAL DISCUSSION
The TI-59 program set is contained on five cards. Four cards are
used to store program instructions and the fifth card is used to store
the impactor stage constants and the constants for the log-normal transformation,
The Master Library Module is used as a subroutine in the data reduction
program set.
Card 1 is used to perform all the calculations performed by Cards
1, 2, 3, 4, and 5 in the SR-52 program set. The card containing the
stage constants is used in conjunction with Card 1.
Cards 2, 3, and 4 are used to calculate the graded penetration
curve and are used in the following order: Cards 2 and 3 for inlet
data, Cards 2 and 3 for outlet data, and then Card 4.
Card 2 is used to enter d50l- and f^ and to set up a spline fit
calculation.
Card 3 is used to complete the spline fit calculation of df./dd.
Card 4 is used to calculate Pt(d) from the values of df^/dd calculated
by Cards 2 and 3.
Two additional sets of programs--one to convert aerodynamic diameter
to physical diameter and one to calculate the viscosity of mixtures of
gases--are included.
The use of all cards is discussed below.
CARD 1
Card 1 in the TI-59 data reduction package replaces Cards 1, 2, 3,
4 and 5 in the SR-52 package. The programs on Card 1 solve the same
23
-------
equations using the same methods as are used in the SR-52 package. The
discussion of equations and methods of solution will not be repeated here.
A data card which contains the impactor stage constants and the
constants for the log-normal transformation are used with Card 1. This
data card is recorded in advance. The steps necessary for recording the
data card are:
1. Store impactor stage constants in R»Q through R^c-
2. Store constants for log-normal fit in R»j through Rc^,
3. Record the constants on magnetic card as follows:
Enter 3
Press 2nd Wri te
Pass a magnetic card through the calculator.
The memory contents for the MRI Impactor are shown in Figure 4. The
steps for entering the cards are shown below.
Step Procedure Enter Press Display
1 Enter side 1 of card Clr 1
containing program
2 Enter side 2 of card Clr 2
containing program
3 Enter card with constants Cl_r 3
The use of the programs contained on Card 1 is demonstrated by Example 2.
24
-------
Value of Constant Register
0.0540$9 40
0.068611 41
0.021484 42
C.0038666 43
C.0010147 44
0.00035065 45
0.00022899 46
2.515517 47
0.802853 48
0.010328 49
1.432788 50
0.189269 51
0.001308 52
Figure 4. Contents of R4Q through R52 for MRI Impactor
25
-------
Example 2. Use of TI-59 Reduction Package
The following data were collected with an MRI Impactor:
T
P
Q
M1 +
M-
3
M4
Mr
5
M6
M7
M« T
= 177°C
= 76 cm Hg
= 11.64 1/m
2 = 7.1 mg
= 4.9
= 4.6
= 1.8
= 0.8
= 0.3
*_ = 0.3
Use the TI-59 program to reduce the data.
Step Procedure
1 Enter side 1 of
card containing
program
2 Enter side 2 of
card containing
program
3 Enter card
containing
constants
4 Enter data
T °C
P cm Hg
Q 1/m
Enter
177
76
11.64
7.1
Clr
Clr
A
R/S
R/S
Display
1
Print
370064
340064
3013363600
3013363600
T=
177
P=
76.00
Q=
11.64
MASS
7.1
26
-------
Step Procedure
M3
M4
Me
Enter
4.9
4.6
1.8
0.8
0.3
0.3
Press
R/S
R/S
R/S
R/S
R/S
R/S
Display
3013363600
3013363600
3013363600
3013363600
3013363600
Print
MASS
4.9
MASS
4.6
MASS
1.8
MASS
0.8
MASS
0.3
MASS
0.3
Mfliter
Program will run for 2 minutes then printing will start
D50
.6989891358
FI
.0151515152
For entire Printout
see Figure 5
SIGMA
3.251912896
3.251912896
Printout for this example is shown in Figure 5.
Note that the impactor data reduction program results are for aero-
dynamic particle diameter. The aerodynamic particle diameter is appropriate
for describing the performance of devices which collect particles by inertial
impaction; e.g., venturi scrubbers. However, the aerodynamic diameter is not
appropriate for many situations; e.g., for describing the performance of
27
-------
177.
P =
76.
Q =
11. 64
MflSS
7. 1
MflSS
4. 9
MflSS
4. 6
MflSS
1.8
MflSS
0. 8
MflSS
0.3
MflSS
0. 3
D50
.6989891358
FI
.0151515152
B50
.8649661038
FI
.0303030303
B50
1.471400832
FI
.0707070707
H50
2.872280107
FI
.1616161616
D50
6.770484356
FI
.3929292939
D50
12.09926647
FI
.6414141414
fl
-1.823399103
B
.8480013495
R**2
0.995740151
DG
8.586844903
SIGMfl
3.251912896
Figure 5. Output from Example 3Use of TI-59 Data
Reduction Package
28
-------
electrostatic precipitators. In such cases the physical particle diameter
is needed.
The physical particle diameter, d, is given by
d = d/^T (20)
where P = the particle density and
C = Cunningham correction factor.
The Cunningham correction factor can be calculated from the mean free path
of the gas, A, and the particle diameter d from
C = 1 + 2 A -| (21)
where
A = 1.246 + 0.42 exp (-0.87d/2x) (22)
The mean free path of the gas, A, can be calculated from
x = xo < r ' iz5&> (23)
where
AQ = mean free path at 23°C and
76 cm Hg = 0.0653 ym for air
P = barometric pressure cm Hg
T = temperature °K
Equation (20) can be solved for d by trial and error.
The TI-59 program for calculating d is given in Appendix C. The program
converts dft to d*, prints dA and corresponding d, prints di and f. , and
*The tolerance for the trial and error solution of equation (20)is
|d. + ] - d.\/d. <0.001.
29
-------
calculates and prints the log-normal fit parameters d,a along with A and B
for y = A + Bx, and the correlation coefficient r .
The use of this program is illustrated in Example 3.
Example 3. Use of Programs to Convert Aerodynamic Diameter to Physical
Diameter
The following data were collected with an MRI impactor.
T
P
Q
M] +
M3
M4
M5
M6
= 100
= 76
= 16
M2 = 8.0
= 5.0
= 4.5
= 2.0
= 0.9
°C
cm Hg
1/m
mg
mg
mg
mg
mg
M7 = 0.45 mg
M8
P
= 0.3
= 2.4
mg
g/cc
Use the TI-59 programs to reduce the data for both aerodynamic and physical
particle diameters.
Step Procedure Enter Press Display Print
1 Enter side 1 of data cir. 1
reduction card
2 Enter side 2 of data cir 2
reduction card
3 Enter card containing cir 3
constants
4 Enter data A 370064 T=
T °C 100 R/S TOO
30
-------
Stej^ Procedure Enter
P cm Hg 76
Q 1/m 16
M] + M2 8.0
M3 5.0
M4 4.5
Me 2.0
0
M6 0.9
M7 0.45
"filter °'3
Program will run for about 2
5 Enter side 1 of card
to calculate d from d^
6 Enter side 2 of card
to calculate d from d^
7 Begin calculation
Enter 2.4
Press
R/S
R/S
R/S
R/S
R/S
R/S
R/S
R/S
R/S
minutes
CLR
CLR
A
R/S
Display
330064
340064
30133663600
30133663600
30133663600
30133663600
301 33663600
30133663600
30133663600
then printing will
3.372605753
1
2
3745710000
Print
P=
76
Q=
16
MASS
8.
MASS
5.
MASS
4.5
MASS
2.
MASS
0.9
MASS
0.45
MASS
0.3
start
D50
.5567597984
SIGMA
3.372605753
Density?
2.4
31
-------
Step Procedure Enter Press Display Print
9.637324556 DA
6.118139795 DP
Printer output for this example is given in Figure 6.
As can be seen from equation (1), dA5Q is a function of gas viscosity.
The TI-59 program uses a relationship developed for air to estimate gas
viscosity at impactor temperature. If the gas being sampled has a composi-
tion significantly different from that of air, the viscosity used in the
program will be in error. In many cases, especially when quick data reduc-
tion at field tests is needed, the error in dA5Q caused by using viscosity
of air is not too important. However, final data reduction should be per-
formed using the best possible estimate of the viscosity of the actual gas
being sampled.
The program given in Appendix D can be used to estimate the viscosity
of gas mixtures. Input data required for this program are: number of
components and the viscosity, molecular weight and mole fraction of each
pure component. The viscosity calculated from this program can be used in
the impactor program by modifying subroutine A'of the impactor program,
as follows:
1. Read TI-59 data reduction program card.
2. Press GTO 2nd A'
3. Press Learn^
4. Starting at program step 339, enter the value of viscosity calculated
from viscosity program
5. After last number for viscosity is entered, press I_NV SBR
6. Press Learn
7. Record modified program
b. Reduce data following instructions for TI-59 programs.
32
-------
T =
100.
P =
76.
Q =
16.
MflSS
8.
MflSS
5.
MflSS
4.5
MflSS
.i
MflSS
0. 9
MflSS
0.45
MflSS
0.3
D50
.5567597984
FI
. 0141843972
D50
.6889640038
FI
.0354609929
I! 50
1.172002237
FI
.0780141844
D50
2.287832545
FI
.1725768322
DSD
5.392835614
FI
.3853427896
DSD
9.637324556
FI
0.621749409
fl
-1.602678119
B
.8225810569
R**2
0.992469079
DG
. 7. 017119575 '
SIGMfl
3.372605753
DENSITY?
2.4
9. 637324556
6. 118139795
5. 392835614
3. 379058333
2. 287832545
1. 376807932
1. 172002237
. 6590790717
. 6889640038
. 3488621786
. 5567597984
0. 264398662
DSD
0. 264398662
FI
.0141843972
DSD
.3488621786
FI
. 0354609929
DSD
.6590790717
FI
. 0780141844
D50
1.376807932
FI
. 1725768322
D50
3. 379058333
FI
. 3853427896
D50
6. 118139795
FI
0.621749409
fl
-1. 125663512
B
0. 749240985
R**2
.9926892225
DG
4.492481161
SIGMfl
3.798795567
Dfl
DP
Dfl
DP
Dfl
DP
Dfl
DP
Dfl
DP
Dfl
DP
Figure 6. Printer Output for Example 3Use of Programs to Convert d. to d
-------
The use of the viscosity program is illustrated in Example 4.
Example 4. Calculation of Viscosity of Gas Mixtures
Calculate the viscosity of a mixture of hydrogen, H2, and carbon
dioxide, C02, at 21°C.
Component Viscosity
H2 0.0876 cp
co2
Step
1
2
3
0.148 cp
Procedure Enter
Read side 1 of viscosity
program
Read side 2 of viscosity
program
Begin calculation
Enter number of 2
components
Enter viscosity of H2 0.0876
Enter molecular 2
weight of H2
Enter mole fraction .413
of H2
Enter viscosity of .1480
co2
34
Molecular Weight
2
44
Press Display
CLR 1
CLR 2
A 3171
R/S
42243671.00
R/S
3043710000
R/S
44710000
R/S_
42243671.00
R/S
3043710000
Mole Fraction
0.413
0.587
Print
N?
2.0000
I =
2.0000
VIS?
0.0876
MW?
2.0000
X?
0.4130
I
1.0000
VIS?
0.1480
MW?
-------
Step Procedure Enter Press Display Print
Enter molecular 44 R/S 44.0000
weight of C02
4471.0000 X?
Enter mole fraction .587 R/S 0.5870
of C02
After about 30 sec 0.1501 0.1501 VIS
calculator will
print viscosity of
mixture
Printer output for this example is shown in Figure 7.
35
-------
N?
2. 0000
1 =
2. 0000
VIS?
0. 0876
MW?
2. 0000
X?
0.4130
1 =
1.0000
VIS?
0. 1480
MW?
44.0000
X?
0. 5870
0.1501 VIS
Figure 7. Printer Output for Example 4Use of Program to Estimate Viscosity
36
-------
CARDS 2, 3, AND 4 (CALCULATION OF PENETRATION AS A FUNCTION OF PARTICLE
DIAMETER WITH TI-59)
The derivative of the cumulative fraction less than function must
be calculated in order to calculate Pt(d). The derivative can be calculated
either from a curve fit to the impactor data or from differentials
calculated from the tabular impactor data. The curve fit method is
discussed in the SR-52 section of this report. The calculation of
differentials from tabular data is discussed in this section.
A spline function gives the smoothest possible curve through data
2
and gives the best estimate of the derivatives for the tabular data.
The general theory of spline functions and how to fit data with them is
discussed in Reference 3 and will not be covered in this report. The
Spline Function Program given in Reference 3 has been programmed for the
TI-59. The program listing is given in Appendix E. Only the use of the
program will be discussed in this report. This program uses numerical
relaxation to solve the following system of six equations:
= 0
S"
S"
S"
S"
(x2
(x4
^*i+l xi^ ^xi xi-l>
b. = 1/2 (xi " xi-l^
(24)
(25)
(26)
(27)
(28)
(29)
(30)
(31)
37
-------
g. = j | " IT | - | _ - l I- I (32)
for 2 -i -5
and e is a user specified tolerance (0.00001 is adequate).
After the above equations are solved, the following quantity is
calculated:
- xi
Card 2 does the following for j = 1 to 6
1. Finds i such that x^ - t .
-------
for, fj should be entered when Y is asked for, tolerance for numerical
solution should be entered when TOL is asked for, and values of d for which
Pt(d) is to be calculated should be entered when T is asked for. Values
d must be input in order of smallest to largest.
Output df(d)/dd is important for calculation of Pt(d) and is labelled
S'(T) in the printed output.
Penetration for any particle diameter is given by
Pt(d) = "o rdfo(d)/dd1 (38)
The use of this program is best demonstrated by an example.
Example 5
Calculate Pt(d) from the following data:
Inlet Data Outlet Data
WI =
d
13.826
7.7369
3.2822
1.6815
0.98842
0.79876
1.305 g/m3
f
0.8731
0.53299
0.15228
0.071066
0.035533
0.015228
WQ = 0.00492
d
6.5012
3.638
1 . 5433
0.7906
0.4648
0.3756
g/m3
f
0.9645
0.8298
0.5603
0.3688
0.2695
0.1489
Note that d's for calculation of Pt(d) must not exceed 6.5 nor be
less than 0.799.
Solution
Choose values of d for calculation of Pt(d). Use 0.8, 1.0, 1.5, 2,
3, and 6. Do inlet first.
39
-------
Step Procedure
Enter
Press
Display Print
1 Read side 1 of spline 1
fit card
Enter side 2 of spline 2
fit card
2 Clear memory and
initialize
3 Input data in order
from smallest d to
largest d
50
4 Enter tolerance for
numerical solution
The calculator will run for about 3 minutes.
1
2
0. 79876
0.015228
0.98842
0.035533
1.6815
0.071066
3.2822
0.15228
7.7369
0.53299
13.826
0.8731
0.0001
INV 2nd Write 1
INV 2nd Write 2
2nd Cms E -1
A 440071
R/S 450071
R/S 440071
R/S "j0071
R/S 440071
R/S
450071
R/S
.440071
R/S
450071
R/S
440071
R/S
450071
R/S
440071
R/s
450071
R/S
37322771
R/S
X ?
0.79876
0.015228
X ?
0.98842
Y ?
0.035533
X ?
1.6815
Y ?
0.071066
X ?
3.2822
Y ?
0.15228
X ?
7.7369
Y ?
0.53299
X ?
13.826
Y ?
0.8731
TOL?
0.0001
40
-------
Step^ Procedure
5 Input d's for calcula- 0.8
tion of Pt(d)
10
11
Enter
0.8
1.0
1.5
2.0
3.0
6.0
Press
R/S
R/S
R/S
R/S
R/S
R/S
CLR
CLR
Display
376536
376536
376536
376536
376536
376536
300000000
1
2
Print
INPUT T's
0.8
INPUT T's
1.
INPUT T's
1.5
INPUT T's
2.
INPUT T's
3.
INPUT T's
6.
READ CARD 2
Read Card 2
Calculate A_
Calculator will run for about 10 seconds and then print.
See Figure 8
for printer
output
Record results on
magnetic card
Repeat for outlet
Read Card 1 side 1
Read Card 1 side 2
Clear memory and
initialize
Enter data
2nd Write
1
2
0.3756
0.1489
0.4648
0.2695
CLR 1
CLR 2
2nd Cms -1
E.
A
R/S
R/S
R/s
R/S
X ?
0.3756
Y ?
0.1489
X ?
0.4648
Y ?
0.2695
X ?
41
-------
Step Procedure Enter Press.
0.7906 R/S
0.3688 R/S
1.5433 R/S
0.5603 R/S
3.638 R/S
0.8298 R/S
6.5012 R/S
0.9645 R/S
Enter tolerance for 0.0001 R/S
numerical solution
0.8
1.0
1.5
2.0
3.0
6.0
12 Read Card 2 side 1 1 CLR
Card 2 side 2 2 CLR
13 Calculate A
Display Print
0.7906
Y ?
0.3688
X ?
1 . 5433
Y ?
0.5603
X ?
3.638
Y ?
0.8298
X ?
6.5012
Y ?
0.9645
376536 TOL ?
0.0001
376536 INPUT T's
0.8
376536 INPUT T's
1.
376536 INPUT T's
1.5
376536 INPUT T's
2.
376536 INPUT T's
3.
376536 INPUT T's
6.
300000000 READ CARD 2
See Figure
for printer output
42
-------
Print
14
15
16
17
18
19
20
Procedure
Record data on
magnetic card
Read Pt(d) Program
Card side 1
side 2
Calculate
Read inlet card
Read outlet card
Enter inlet mass
concentration
Enter outlet mass
concentration
Enter
Press
2nd Write
CLR
CLR
A
CLR
CLR
1.305 R/S
0.00492 R/S
Display
3
1
2
3
3
2431710000
3241377100
READ INLET DATA
READ OUTLET DATA
MASS IN ?
0.1305
MASS OUT ?
0.000492
D =
0.8
PT(D) =
.0002409147
D =
1.
PT(D) =
.0081617673
17311600
D =
6
PT(D) =
.0021486703
OVERALL PT =
.0037701149
END
Printer output for this example is shown in Figure 8.
43
-------
X ?
0.79876
Y ?
0.015228
X ?
0. 98842
Y ?
0.035533
X ?
1.6815
Y ?
0.071066
X ?
3. 2822
Y ?
0. 15228
X ?
7.7369
Y ?
0.53299
X ?
13.826
Y ?
0.8731
TDL?
0.0001
INPUT T'S
0.8
INPUT T'S
1.
INPUT T'S
1.5
INPUT T'S
2.
INPUT T'S
3.
INPUT T'S
6.
CfiRD 2
T =
0.8
S * *
-.0012980732
SOTXX1)
-. 0333067433
S
.0153685362
S'
. 1133351221
T =
1.
S1 '
-. 1948449069
saxxi)
-.0617716849
son
.0366141743
S'On
0.092230367
T =
1.5
S"
-.0351955372
SOTXX1)
-.0351634566
son
.0650258015
S' Of)
.0347202559
T =
2.
C; I '
.0219602419
S
.1341813579
s1 <:T>
.0614217742
T =
6.
S' '
-. 0002447947
saxxi)
.0010203107
S
.3797336807
S'
-------
T =
X ?
0. 3756
Y ?
0. 1489
X ?
0. 4648
V ?
0. 2695
X ?
0. 7906
Y ?
0. 3688
X ?
1.5433
Y ?
0. 5603
X ?
Y ?
0. 8298
X ?
6.5012
Y ?
0. 9645
TDL?
0.0001
INPUT T'S
0.8
INPUT T'S
1.
INPUT T'S
1.5
INPUT T'S
2.
INPUT T'S
3.
INPUT T'S
6.
REflD CflRD 2
T =
0.8
S1 '
1.156694357
S
0.339892683
S
.3688166869
S ' (T)
.0072403722
T =
1.
S"
.7667973758
S(TXX1>
.2749098528
£
.3907993352
S'
.1995895455
T =
1.5
S"
2079450781
S(TXXl)
1124527771
sen
5458295111
S '
3393026199
2.
S' '
-. 2259175925
saxxn
-. 0843164391
sa>
.6821331141
S1 (T>
.2101228815
T =
3.
S"
-.0804387615
saxxn
-. 0600699672
sa>
.8035436712
S'
.0569447045
T =
6.
S1
.0021665334
S
.0024238777
S
.9380514439
s- a>
.0524085076
ENL
Figure 8>(Cont'd)
45
-------
REFtn INLET DflTfl
RERD OUTLET DflTR
MflSS IN?
0. 1305
MflSS DUT?
0. 000492
D =
0. 8
PTCD) =
. 0002408524
D' =
1.
PT =
. 0194580314
D =
3.
PT
-------
Comparison of Graded Efficiency Calculated from Curve Fit and Spline Fit
"How well does the calculated graded penetration represent the
actual graded penetration?" is not a trivial question. It is as nearly
impossible to answer.
The actual graded penetration for a real particulate control device
is unknown. However, we can create synthetic data from mathematical
models and compare data reduction results with the synthetic data. We
can also compare results of various methods of calculating the graded
penetration with each other when real data are available. Both types of
comparisons are made in this section.
The graded penetration calculated using the spline fit, the log-
normal, and a quadratic log-normal fit methods are compared in Table 4.
o
It appears that the curve fit methods give good results when the r
product is greater than 0.985. This indicates that other types of
distribution (such as the upper limit distribution and the Weibull
distribution) could be useful. The fits for these distributions could
be done by an SR-52 calculator and thus extend the useful range of the
SR-52 program set.
The curve fit methods may have an advantage over the spline fit in
that statistical information on goodness of fit and confidence limits of
fit can be calculated for the curve fit. Such statistical information
is not available from the spline fit. Also, curve fits smooth the data;
spline fits do not.
Synthetic data were created with the aid of a mathematical model
for electrostatic precipitation. "Perfect" impactors were used to
sample the inlet particle size distribution fed into the model and the
outlet particle size distribution generated by the model. The TI-59
programs were used to reduce the impactor data and calculate the graded
penetration. The results of these calculations are summarized in Table
5.
47
-------
Table 4. COMPARISON OF GRADED PENETRATION CALCULATED USING LINEAR LOG-NORMAL
FIT, QUADRATIC LOG-NORMAL FIT AND SPLINE FIT ON ACTUAL IMPACTOR DATA
d, pmA
0.87
1.24
1.78
2.53
3.62
5.16
2 2
rinX 'out
Case 1
Pt(d)LN Pt(d)LM2 Pt(d)s
0.25
0.18
0.10
0.069
0.050
0.037
= 0.94
= 0.986
0.052
0.028
0.015
0.0070
0.0030
0.0012
0.
0.
0.
0.
0.
0.
0029
023
028
0080
0018
0021
linear log-normal
quadratic
Case 2
Pt(d)LN Pt(d)LN2 Pt(d),.
0.055
0.023
0.0090
0.0050
0.0025
0.0015
2 2
r1nX rout
log-normal
0.048
0.029
0.016
0.0081
0.0038
0.0016
= 0.97
= 0.994
0.016
0.028
0.015
0.0077
0.0040
0.0021
linear log-normal
quadratic log-
normal
Pt(d)LM
0.016
0.029
0.0099
0.0059
0.0030
0.0019
r2 X r2
I i A 1 .
in out
Case 3
Pt(d)LN2
0
0
0
0
0
0
=
=
.075
.031
.014
.0070
.0038
.0021
0.985
0.995
Pt(d)s
0.029
0.035
0.015
0.0070
0.0032
0.0022
linear log-
normal
quadratic 1<
normal
-------
Table 5. COMPARISON OF GRADED PENETRATION CALCULATED
WITH SPLINE AND LOG-NORMAL FITS WITH ACTUAL
GRADED PENETRATIONS FROM ESP MODEL
d
0.45
0.70
1.0
1.5
2.5
4.0
0.45
0.70
1.0
1.5
2.5
4.0
0.45
0.70
1.0
1.5
2.5
4.0
,£t(i)M
0.28
0.26
0.22
0.16
0.094
0.049
0.28
0.27
0.23
0.17
0.10
0.060
0.040
0.035
0.026
0.015
0.0075
0.0021
Case 1
Pt(d)s
0.27
0.25
0.20
0.14
0.071
0.040
Case 2
0.28
0.25
0.21
0.15
0.082
0.052
Case 3
0.040
0.033
0.022
0.012
0.0052
0.00086
A/M
0.036
0.038
0.091
0.125
0.24
0.18
0.0
0.074
0.087
0.12
0.18
0.13
0.0
0.057
0.15
0.20
0.31
0.59
Pt(d)m - Pt(d) from ESP Model
Pt(d)s - Pt(d) from spline fit
AS/M - (Pt(d)M - Pt(d)s)/Pt(d)M
49
-------
The results shown in Table 5 indicate that the graded penetrations
calculated from the spline fit are generally in fair agreement with the
"real" graded penetrations. However, in some cases, especially when the
penetrations are low, the disagreement between the calculated graded
penetration and the "real" graded penetration is substantial. Work to
determine ways to improve the agreement between the calculated and
"real" graded penetrations and to better define the uncertainty in the
calculated graded penetrations is underway and will be reported.
Lawless has suggested that the cumulative size distribution data
be transformed into log-normal space before the spline fit calcinations
are performed. Such a transformation will improve the agrr^ment between
measured and real graded penetration.
The log-normal values f. are available in the memory of the TI-59
if one desires to perform the spline fit calculations in log-normal
space. The log-normal transforms of the f. are stored in registers 30 to
35 (transformed f- is in H, etc.) and may be recovered by pressing 30
INV 2nd List. Value In di is entered when X is asked for and the correspond-
ing value of transformed f. is entered when Y is asked for.
The penetration program must be modified to calculate Pt(d) from
Pt(d.)=Wo {exp [- S(d.)Z/2-\ X S'(d.)> out (39)
Wj {exp [- S(dn.)2/2] X S'(d.)} in
where S(d^) and S'td^) are the output from the spline fit program for d
Recommendations for Running Impactors
No matter what method of data reduction is used, the number of
points available for calculation of the graded penetration is limited by
the number of impactor stages. Also, the values of d for which Pt(d)
50
-------
can be calculated are limited by the range of the impactor stage d5Q's
(extrapolation is prohibited). Data points cannot be created by the
data reduction technique.
The above points lead to the following recommendations on obtaining
impactor data:
1) Six or seven stages covering the range 0.5 - d^5Q
- 15 ymA are probably adequate for most purposes.
2) The particle diameter ranges covered by the inlet
and,outlet impactors are the same or as close to the
same as possible. Otherwise data points are lost.
3) Stages d^5Q for the inlet and outlet impactors should
be as close to each other as possible.
51
-------
REFERENCES
1. Hastings, C., Jr., Approximations for Digital Computers.
Princeton University Press, Princeton, New Jersey, 1955.
2. Walsh, J. L, Ahlberg, J. H., and Nil son, E. N., "Best Approximation
Properties of the Spline Fit", J. Math. & Mecli., 11, 225 (1962).
3. Greville, T. N. E., "Spline Functions, Interpolation, and
Numerical Quadrature", Chapter 8 in Mathematical Methods for Digital
Computers, Vol. II. ed. Ralston, A. and Wolf, H. S. John Wiley -,id
Sons, New York, New York, 1967.
4. Lawless, Phil A., "Analysis of Cascade Impactor Data for Calculating
Particle Penetration", Research Triangle Institute, EPA-600/7-78-189,
September 1978.
52
-------
APPENDIX A
USER INSTRUCTIONS AND PROGRAM LISTING FOR SR-52 DATA REDUCTION PROGRAMS
GENERAL
The data reduction programs are contained on six cards which are
used in order: Cards 1, 2, 3, 4, and 5 for inlet; Cards 1, 2, 3, 4 and
5 for outlet; and Card 6 for combined inlet and outlet results. The
programs use the PC-100A printer.
A-l
-------
USER INSTRUCTIONS FOR SR-52 DATA REDUCTION PACKAGE
Step Procedure
Enter
Press
Display
Print
_f _ * w 1^
1
2
3
4
5
6
7
8
9
10
Note
Read sides
A and B of Card 1
Check to see if card read properly
Enter T
Enter Q
Initialize
Reset
Calculate
Read sides
Initialize
Enter MI
: For the
the mass collec
before the data
11
12
13
Read side
Initialize
Print MT,
T°C or
T°F
Q 1/min or
cfm
RCJL 92
A
2nd A1
B.
2nd B
E
Constant
for 1st stage
T°C
T°C
Q 1/min
Q 1/min
1 . 0000
2nd rst l.OPOu
dA50i
A and B of Card 2
Ml
M2
Mfilter
£
E_
A
A
A
MRI and University of Washington
ted on the first two stages. M-,
are entered.
A of Card 3
fidA50i
E.
0.0000
0.0000
1 . 0000 M1
2.0000 M2
7.0000 Mg
impactors, MI = the sum of
and M2 must be added
0.0000
f MT
A501
JA506
A-2
-------
Step
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Procedure Enter Press
Read Card 4 sides A and B
Initialize E_
Transform f. "~~" A
Read Card 5 sides A and B
Initialize i
Calculate log-normal parameters A
Read Card 6 sides A and B
Enter VL Wr A_
Enter Wn Wn 2nd A1
0 0
Enter aj aj B.
Enter an on 2nd B1
0 0
Enter dgj dgl C
Enter d d 2nd C1
go go
Calculate Pt(D) £
Display Print
f6
8.0000
0.0000
J A
B
2
r
dg
a
2nd rst
INV READ
INV READ
0.10000
Wo
0
In Oj
In a
u
lndgl
lrldgo
Pt(d)
l-Pt(d)
0.1
Pt(d)
l-Pt(d)
9999.00000 20.0
A-3
-------
000
nni
n n 2
003
004
U U ~=
006
007
UUb
009
010
HI 1
012
013
014
f!i=r
r i A
i- ! T
'. i f
CIS
:~ : I"-
i j. T*
C20
C21
r -' -
024
U2b
026
U 2 r'
023
029
030
031
032
:-; -! -:
:": " .-.
U O ""I"
~i "! S)
336
337 f
338
339
340
041
042
043
044
045
046
047
0 4 8
46
1 Q
U 1
44
i J !_l
.-. .-j
36
u U
UU
56
46
10
36
42
fn
flO.
01
44
.-. .;
!_: i
09
56
46
i O
.i '-'
53
01
93
Ub
08
52
94
fii
85
53
no
;-= .
55
U -,'
65
43
00
08
y o
:"": *"":
fix
*~i i±
65
ij £
93
^2
LBL
D 3
1
SUM
ij
.-.
IHD
RCL
0
0
RTH
LBL
^ 3
IHD
orn
- i l_i
9
i
SUM
i
9
RTH
LBL
f : 1
(
i
9
_
b
3
EE
+/ -
4
-i-
,f
Q
-:-
=^
V'
RCL
U
3
4-
.;
-I
':
2
^
050
051
052
:"*! -*i
'-* '-' '-'
054
: : """: "~:
! 1 T: 1":
:": ~ T1
059
06(1
061
062
063
064
065
066
067
068
0 6 9
n 7 M
"~ " ~
071
072
073
074-
075
n "/^ A
1 1 7 '
: ~ ;~:
J O
379
330
381
382
383
334
n:-;h
Ub'b
!~l !-: "/
U b C;
i J O '7
090
0 9 1
i S !-*:
L 9 3
r ~i 4
r 95
: !-H £-.
r 97
C93
0 9 9
n o
=_'i.
=:"
94~-
s"i "?
J-; :
54
"~: f . "*'
46
-; -(
10
O 1
.i --i
^C
00
00
46
37"
19
!^ H
43 :
00
00
*-i !-:
7*7-=
""
07
.95
90
38
4 1
O !'
46
o o
:-: '_'
o i
4- f~i
14
19
65
13
=:=;
H- J
00
: ! H
65
01
j 2
03
!r* ?~!
'": T!
1 0
43
01
f;9
=r
-i
EE
-i-,-- -
i '
!
5
RTH
! ~: :
L- D i
!_.
Lji. T
.Hi_ ;
8 TO
u
0
LBL
i ' a
JJ "
PRT
RCL
;"*!
"{
.
7
i r i
;~: *
GTQ
f i
LBL
~! 3
^-
HLT
I j-! I
ij
U 5
0 *
_U-
KUL
i~i
9
t
EE
3
=
i :...:
r^ 2
RCL
-;
i-:
-
Impactor Data. Reduction Program Listing Card 1
A-4
-------
4. '-' '_'
101
102
103
104
105
106
107
103
109
110
ill
112
113
114
115
116
117
118
119
120
121
I wLl
123
124
125
126
127
128
129
130 ,
131
132
1 Jo
134
135
136
137
138
139
140
141
142
143
144
145
146
147
143
149
150
151
1 52
153
154
155
156
95
90
13
41
14
46
11
42
00
08
81
46
12
42
00
09
81
46
16
75'
03
03
95
65
05
55
09
95
t i
46
1 "7
i «
55
93
00
03
05
03
02
95
12
46
15
09
01
42
00
00
01
42
U 1
09
uli t^
!3 '£
57
04
31
=-
IFZ
C
GTQ
D
LBL
Fi
STD
0
8
HLT
LEL
B
STQ
0
9
HLT
LBL
fi'
-
3
3
=
X
5
r-
9
=
fl
LBL
B a
-=-
tt
0
3
!^
3
2
B
LBL
E
9
1
STD
0
0
1
STD
L
9
IHV
EE
FIX
4
HLT
Impactor Data Reduction Program Listing Card 1 (Cont'd)
-------
4-6 LBL
11 Fi
98 PRT
36 IHD
034 42 STu
035 00 0
1307 44 SUM
U1 1
09 9
01 1
44 SUM
UU U
014 43 RCL
01i 00 U
021
iQ 0
O1 U! T
_ i : ii_
D!
U22 46 LbL
42 STD
i_i ij M
"0 0
0 0
42 sTfi
42
044
045
046
047
048
049
050
U-~" J
n =. .-,
0 5 3
n=;a
067
063
U !''' U
l"l"? I
:_: : j.
072
073
030
01 1
31 HLT
46 LBL
43 RCL
00 0
fin n
75 -
f!l 1
42 STL
01 i
08 8
46 LBL
36 IHD
43 ROL
Ub 6
44 SUM
_ i
fl7 7
U1 1
22 IHV
44 SUM
01 1
ii i! IN V
44 SUM
Impactor Data Reduction Program Listing Card 2
A-6
-------
031
082
083
084
085
086
087
088
089
090
rm
092
093
094
095
096
097
098
099
100
101
102
103
01
08
43
01
07
==
-' V.'
43
01
09
95
36
42
00
07
i~ --
U i
22
44
00
07
43
00
07
75
i
!~:
!_!
ROL
i
i
f
~
RCL
i
9
I HE
STQ
.-0
:'
1
INV
SUM
0
-f
f
RCL
0
7
-
104 07 7
105 95 =
106 90 IFZ
107 77 4a
108 41 GTD
109 88 2s
110 46 LBL
! -. 1 -J T .-: i
I i i f i t
-, i " O i i-ii T
i i i_ <-= i. rfi_ :
Impactor Data Reduction Progam Listing. Card 2 (Cont'd)
A-7
-------
000 46 LBL 027 °° |J
nSi U P2p °28 9S PRT
ijij^ ^ FHf 029 36 IH:I|
003 4J RUL 030 43 RCL
004 01 031 01 1
005 uy y ,-,32 ,-,9 q
006 22 INV 533 qg PRT
OU7 5i' EE |-|-^4 qq pop
008 98 PRT KM nl 1
29? -? uPT 036 44 SUM
0 U Bl HLT 037 00 0
yll 4t; LBL 038 00 0
Ul£ 1^ B
m? n?
n * 4'
uij H^
me rin n
Ulb UU U ,-[4.-, -- -
,-, i-? nn n -^'- uu '-'
-lr -- u ri44 nn n
018 08 8 ° u
019 42 STD
,-, -.,-! rn 1
UtU Ul 1
I-I---1 nq q | :-1
n-i 4^ i PL °48 22 IHV
:^. ^ L^ 049 90 IFZ
U £.& O i i i-i c; -, c<~? HI
024 36 IND KM ^ RTN
025 43 RCL Ojl Jb R
Impactor Data Reduction Program Card 3
A-8
-------
0 0 0
55 1
U U d
0 0 3
004
005 "
006
007
008
009
010
Oil
012
013
014
015
016
017
013
019
020
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Impactor Data Reduction Epogram Listing Card
A-9
-------
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Impactor Data Reduction Program Listing Card 5
A-ll
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-------
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Impactor Data Reduction Program Listing Card 5 (Cont'd)
A-12
-------
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A-13
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Log-normal Penetration Program Listing
-------
55 -^
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Log-normal Penetration Program Listing (cont'd)
A-15
-------
APPENDIX B
USER INSTRUCTIONS AND PROGRAM LISTING FOR TI-59
IMPACTOR DATA REDUCTION PACKAGE
INTRODUCTION
This program calculates and prints cascade impactor aerodynamic cut
diameters, d^50> cumulative fraction less than and the least-squares
log-normal fit to the data. Input requirements are impactor temperature,
°C, impactor flow rate, 1/m, and mass collected by each impactor stage.
The program uses the PC-100A printer and the Master Library Module.
Nomenclature, in order used by program:
T = impactor temperature, °C
P = impactor pressure, cm Hg
Q = impactor flow rate, 1/m
Mass = mass of parti cul ate collected per stage
D50 = aerodynamic impactor cut diameter, wnA
FI = cumulative fraction less than
A = least-squares fit constant, A, in y = A + Bx
B = least-squares fit constant, B, in y = A + Bx
2
R** = correlation coefficient, r
DG = Aerodynamic mass mean particle diameter of log-
normal size distribution, urnA
SIGMA = geometric standard deviation of log-normal size
distribution
USER INSTRUCTIONS
Step Procedure Enter
1 Read side 1 of card
Read side 2 of Card
Read card with stage constants
B-l
Press
Clr
Clr
Clr
Display
1
2
3
Print
-------
Step Procedure Enter Press DispJay Pri nt
2 Start calculation A 37.0064 T =
Enter temperature °C T°C R/S
Enter pressure cm Hg P cm Hg R/S 330,064 P =
Enter flow rate 1/m R/S 340064 Q =
3013363600 MASS
Enter mass collected M R/S
per stage
30,13363600 MASS
R/S
D50
FI
FI
A
B
R**2
DG
SIGMA
a
B-2
-------
r&'
000
001
002
003
004
005
006
007
008
009
010
Oil
012
013
014
015
L 0 1 6
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^ ^ 021
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^^^ 025
026
027
028
029
030
031
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«Mff4
CTv\ 035
Y^ 036
037
038
039
040
041
042
043
044
045
046
047
048
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76
11
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42
58
69
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03
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051
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056
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060
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062
063
064
065
066
067
068
069
070
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072
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074
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077
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079
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081
082
083
084
085
086
087
088
089
090
091
092
093
094
095
096
097
098
099
100
42 STD
02 02
00 0
42 STD
53 53
42 STD
58 58
07 7
42 STD
00 00
01 1
07 7
42 STD
54 54
76 LBL
87 IFF
69 DP
00 00
03 3
00 0
0 1 1
03 3
03 3
06 6
03 3
06 6
00 0
00 0
69 DP
02 02
69 DP
05 05
91 R/S
99 PRT
72 ST*
54 54
44 SUh
53 53
01 1
44 SUM
54 54
97 DSZ
00 00
87 IFF
07 7
42 STD
00 00
00 0
04 4
00 0
J
r"~
\\
Program Listing TI-59 Cascade Impactor Data ReductionCard T
B-3
-------
aa o
lo'4 44' aTD
135 55 55
141 42 STD
i -1 s -i e <
101 42 STD 151 76- LBL
102 54 54 15>' ft-9 tf
103 01 1 153 73 RC*
104 00 0 154 54 54
105 42 STD 155- 44 SUM
106 55 55 156 5ft 5R
107 76 LBL 157 43 RCL
10S 88 DMS 15ft 5S 58
109 73 RC* 15-5 55 r-
110 54 54 ?60 43 RCL
111 55 -r- 161 53 53
112 43 RCL ?62 95 =
113 02 02 163 72 ST*
114 65 x Ifi4 56- 56
115 16 fl' 165 12 B
Hfc 65 x 166 72 ST*
II7 01 1 !67 57 57
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170 44 SUM
121 34 TX 171 54 54
144 ,-i b'T* 172 44 ft!!M
123 55 55 17^ 56 ~56
124 ul 1 174 44 SUM
Id.j 44 aUM 175 57 57
lib 54 54 176 44 SUM
127 44 SUM 1?7 55 55
I ": l~l C ,-c
r-p
. , C' ' ' J L
e. s( IQQ 73 pr.#
&/»=.- j. - - i - i -
.jo OD 200 54 54
Program Listing TI-59 Cascade Impactor Data Reduction--Card 1 (Cont'd)
B-4
-------
2H1 23 LNX 251 01 01
2H2 32 X!T 252 69 DP
.-fi"-: 73 RC* 253 05 05
2H4 55 55 254 73 RC*
?fi5 73 1+ 255 55 55
206 01 1 256 99 PRT
207 94 +/- 257 01 1
20R 44 SUM 253 94 +/-
209 54 54 259 44 SUM
210 44 SUM 260 54 54
Ml 55 55 261 44 SUM
212 25 CLR 262 55 55
213 97 DSZ 263 25 CLR
214 00 00 264 97 DSZ
215 77 GE 265 00 00
216 01 1 266 73 1+
217 06 6 267 69 DP
213 42 STD 263 00 00
219 54 54 269 01 1
220 02 2 270 03 3
221 09 9 271 69 DP
222 42 SID 272 01 01
223 55 55 273 69 DP
22-i 06 6 274 05 05
225 42 STD 275 69 DP
226 00 00 276 12 12
227 76 LBL 277 99 PRT
22ft 73 2+ 273 69 DP
229 69 DP 279 00 00
2:-m 00 00 230 01 1
2:-:i 01 1 231 04 4
232 06 6 232 69 DP
233 00 0 233 01 01
234 06 6 234 69 DP
23F, HO 0 235 05 05
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237 69 DP 237 12 12
238 01 01 233 32 XJT
?39 69 OP 239 99 PRT
240 ' 05 05 290 69 DP
241" 73 RC* 291 00 00
242 54 54 292 03 3
243 99 PRT 293 05 5
244 02 2 294 05 5
245 '01 1 295 01 1
246 02 2 296 05 5
247 04 4 297 01 1
243 00 0 293 00 0
249 00 0 299 03 3
250 69 DP 300 69 DP
Program Listing TI-59 Cascade Impactor Data ReductionCard 1 (Cont'd)
B-5
-------
301 01 01 351 76 LBL
302 69 OP ' 352 16 fi '
303 05 05 353 53 (
3fi4 6« UP 354 53 (
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306 33 X£ 356 01 01
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310 01 1 360 05 5
311 06 6 361 85 +
312 02 2 362 03 3
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315 01 01 365 65 x
316 69 GP 366 02 2
317 05 05 367 93 .
318 69 GP 363 02 2
319 12 12 369 09 9
320 55 -r 370 02 2
321 32 XJT ' 371 52 EE
322 95 = 372 94
323 94 +/- 373 07
324 22 INV 374 85 +
325 23 LHX 375 01 1
326 99 PRT 376 93 .
327 69 DP 377 06 6
328 00 00 378 08
329 03 3 379 52 EE
330 06 6 380 94 +..- -
331 02 2 381 04 4
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333 02 2 383 92 RTN
334 02 2 384 76 LBL
335 03 3 385 12 B
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340 01 01 390 56 56
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344 12 12 39-4 A3 DP
345 32 KIT 395 86 STF
346 35 1/X 396 01 01
347 22 INV 397 53 (
348 23 LNX 398 01 1
349 99 PRT 399 75 -
350 92 RTN '400 73 RC*
Program Listing TI-59 Cascade Impactor Data ReductionCard 1 (Cont'd)
B-6
-------
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Program Listing TI-59 Cascade Impactor Data ReductionCard 1 (Cont'd)
B-7
-------
APPENDIX C
USER INSTRUCTIONS AND PROGRAM LISTING FOR TI-59 PROGRAM
TO CONVERT AERODYNAMIC DIAMETER TO PHYSICAL DIAMETER
GENERAL
This program converts aerodynamic diameter to physical diameter.
Aerodynamic diameter, d,,, and physical diameter are printed. The program
then calculates and prints cumulative fraction less than for each stage,
and the log-normal fit to the data. Input requirements are particle
density, g/cc. The program uses the PC-100A printer and the
Master Library Module.
Nomenclature, in order used by program:
DENSITY
DA
DP
D50
FI
A
B
R**
DG
SIGMA
particle density, g/cc
aerodynamic particle diameter,
physical particle diameter, ym
physical impactor cut diameter, urn
cumulative fraction less than
least-squares fit constant, A, in y
A + Bx
least-squares fit constant, B, in y = A + Bx
2
correlation coefficient, r
physical mass mean particle diameter of log-
normal size distribution, vim
geometric standard deviation of log-normal size
distribution
USER INSTRUCTIONS
Step Procedure
1 Enter Side 1 of card
Enter Side 2 of card
Begin calculation
Enter density
Enter
P
Press
CLR
CLR
A
R/S ,
C-l
Display
1
2
Print
DENSITY
-------
Step Procedure Enter Press Display Print
dA DA
D DP
C-2
SIGMA
a
-------
051 01 1
000 76 LPL 052 06 6
001 14 D 0=!;-; ill ~~i
002 73 RC* 054 07 7
003 54 54 055 03 3
004 92 RTN 056 01 1
005 76 LBL 057 0:-; 3
006 13 C 058 06 6
007 53 ( 059 n2 2
OOS 01 1 060 04 4
009 85 + 061 69 DP
010 02 2 062 00 00
Oil 65 x 050 59 rjp
012 43 RCL f!64 02 02
013 42 42 065 0>; 3
014 55 - 066 07 7
015 43 RCL 067 04 4
016 40 40 il68 05 5
017 65 x 069 07 7
018 S3 < 070 01 1
019 01 1 071 00 0
020 93 , 072 00 0
021 02 2 073 00 0
022 06 6 074 no 0
023 35 + 075 69 DP
U£4 yy . 076 03 03
025 04 4 077 69 DP
026 02 2 078 05 05
027 65 x 079 91 R/S
028 53 < OHO 99 PRT
029 93 , 081 42 STD
030 08 8 0*2 43 43
031 07 7 OR3 93 .
032 65 x OS4 00 0
033 43 RCL 0*5 06 6
034 40 40 OS6 05 5
035 55 + OS7 03 3
036 53 <. ORR 65 x
037 02 2 089 07 7
038 65 x 090 06 6
039 43 RCL 091 55 +
040 42 42 092 02 2
041 54 ) 093 09 9
042 54 ) 094 06 6
043 94 +/- 095 93 .
044 22 INV 096 02 2
045 23 LHX 097 65 x
046 54 > 098 53 (
047 54 ) 099 43 RP.|_
048 92 RTN 100 =^9 59
049 76 LEL
050 11 fi
Program Listing Program to Convert Aerodynamic Diameter to Physical Diameter
C-3
-------
101 85 + 151 41 41
102 02 2 152 42 STD
103 07 7 153 40 40
104 03 3 154 14 D
105 54 > 155 55 =
106 55 -r 156 53 <
107 43 RCL 157 13 C
10S 36 36 153 65 x
109 95 = 159 43 RCL
110 42 SID 160 43 43
111 42 42 161 54 )
112 01 1 162 34 fX
113 01 1 163 95 =
114 42 STD 164 42 STD
115 54 54 165 41 41
116 06 6 166 75
117 42 STD 167 43 RCL
118 00 00 168 40 40
119 69 DP 169 95 =
120 00 00 170 -50 Ixl
121 93 . 171 55 -r
122 00 0 172 43 RCL
123 00 0 173 40 40
124 01 1 174 95 =
125 32 XJT 175 77 GE
126 76 LBL 176 88 DMS
127 87 IFF 177 01 1
128 98 RDV 178 06 6
129 01 1 179 03 3
130 06 6 180 03 3
131 01 1 181 69 DP
132 03 3 182 04 04
133 69 DP 183 43 RCL
134 04 04 184 41 41
135 73 RC* 185 69 DP
136 54 54 186 06 06
137 69 DP 187 72 ST*
138 06 06 188 54 54
139 55 -r 189 01 1
140 43 RCL 190 44 SUM
141 42 42 191 54 54
142 34 fX 192 97 DSZ
143 95 = 193 00 00
144 42 STD 194 87 IFF
145 40 40 195 36 PGM
146 42 STD 196 01 01
147 41 41 197 71 SBR
148 76 LBL 198 25 CLR
149 38 DMS 199 01 1
150 43 RCL 200 06 6
rogram Listing Program to Convert Aerodynamic Diameter to Physical Diameter (Cont'd)
C-4
-------
201 42 STD 251 01 1
202 54 54 252 69 DP
203 03 3 253 01 01
204 05 5 254 69 DP
205 42 STD 255 05 05
206 55 55 256 73 RC*
207 06 ,6 257 54 54
208 42 STO 25'8 99 PRT
209 00 00 259 69 DP
210 98 flBV 260 00 00
211 76 LBL 261 02 2
212 77 GE 262 01 1
213 73 RC* 263 02 2
214 54 54 264 04 4
215 23 LNX 265 00 0
216 32 XJT 266 00 0
217 73 RC* 267 69 DP
218 55 55 268 01 01
219 78 1+ 269 69 DP
220 01 1 270 05 05
221 94 + /- 271 73 RC*
222 44 SUM 272 55 55
223 54 54 273 99 PRT
224 44 SUM 274 01 1
225 55 55 275 94 +/-
226 25 CLR 276 44 SUM
227 97 DSZ 277 54 54,
228 00 00 278 44 SUM
229 77 GE 279 55 55
230 01 1 280 25 CLR
231 06 6 281 97 BS2
232 42 STD 282 00 00
233 54 54 233 78 2 +
"234 02 2 284 69 DP
235 09 9 285 00 00
236 42 STD 286 01 1
237 55 55 287 03 3
238 06 6 288 69 DP
239 42 STD 289 01 .01
240 00 00 290 69 DP
241 76 LBL 291 05 05
242 78 2+ 292 69 DP
243 69 DP 293 12 12
244 00 00 294 99 PRT
245 On 0 295 69 DP
246 01 1 296 00 ! GO
247 06 6 297 01 1
24ft 00 0 298 04 4
249 06 6 299 69 DP
2*n nn n 300 01 01
Program Listing Program to Convert Aerodynamic Diameter to Physical Diameter (Cont'd)
C-5
-------
301
302
303
304
305
306
307
308
309
310
3 1 i
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
323
329
330
331
;T; 0 2
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
69
05
69
12
32
99
03
05
05
01
05
01
00
03
69
01
69
05
69
13
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99
69
00
01
06
02
02
69
01
69
05
69
12
55
32
95
94
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23
99
03
06
02
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02
02
03
00
01
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05
DP
12
KIT
PRT
3
5
5
1
5
1
0
3
DP
01
DP
05
DP
13
X2
PRT
DP
00
1
6
2
2
DP
01
DP
05
DP
12
-?-
XJT
=
+ / -
IHV
LHX
PRT
3
6
2
4
2
2
3
0
1
351 03 3
352 69 DP
353 ... 01 01
354 69 DP
355 05 05
356 69 DP
3|7 .: 12 12
3"fes 32 X^T
359"* 35 1/X
360 22 IHV
361 23 LHX
362 99 PRT
363 92 RTN
Program listing Program to Convert Aerodynamic Diameter to Physical Diameter (Cont'd)
C-6
-------
APPENDIX D
USER INSTRUCTIONS AND PROGRAM LISTING FOR PROGRAM
TO ESTIMATE VISCOSITY OF MIXTURES
GENERAL
This program estimates the viscosity of mixtures of gases. The
input data requirements are: number of components ( 10 maximum), and
the viscosity, molecular weight and mole fraction of each pure component.
Nomenclature in order used by program:
N = Total number of components
I = Number identifying component for which input data are
required
VIS = Viscosity of component number I
MW = Molecular weight of component number I
X = Mole fraction of component number I
USER INSTRUCTIONS
Step
1
Procedure
Enter
Enter side 1 of card
Enter side 2 of card
Start calculation
Enter number of n
components
3 Enter
Enter MW
n
Press
Clr
Clr
A
R/S
Display
1
2
3171
Pr
N?
n
R/S
R/S
42243671.00
3043710000
4471.0000
I =
n
VIS?
\
MIN?
MIN
n
X?
D-l
-------
Step Procedure Enter Press Display Print
5 Enter X1 X. X..
I =
n-1
Repeat steps 3, 4 and 5 for all components
^mixture ''mixture
D-2
-------
000
001
002
0 0 3
004
005
006
007
008
009
010
on
012
014
015
016
,-i .) -7
018
019
020
021
022
023
024
025
026
027
028
029
030
031
032
fi's'-l
035
036
038
039
040
041
^042
:043
i044
1045
76
p ^7
1 '"'
43
00
94
44
50
44
51
44
52
->c;
5ii
42
40
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5 1
42
41
73
52
42
42
00
42
53
43
00
-. -:
76
88
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59
67
94
44
50
44
51
44
52
25
LBL
IFF
B
RCL
00
+ / -
SUM
50
SUM
51
SUM
52
}""' i r^
"so
STD
40
RC*
5 1
O 1 U
41
RC*
52
STD
42
0
STD
53
RCL
00
xn
Lr~! i
[_: ^
DMS
B
59
EQ
+ x-
SUM
50
SUM
51
SUM
52
CLR
H3i i° 1°
055 54 )
057 65 x
058 53 (
059 73 RC*
061 55 +
062 43 RCL
41 41
45 YX
!^L ^t ±
U68 U5 5
"
073 08 8
075 65
076
9^ 4? RS«r
i^y :± ^
U ^ 1 5 D
082 73 RC*
. j
1* C
12 ..p..
ro KL*
i049 53 < iuu
D50 43 RCL
Program Listing Viscosity Program
D-3
,
^ UD.L'
yy "
12 B
-------
101 88 DNS 151 11 B.
102 43 RCL 152 69 OP
in:-; 4n 4H 153 00 00
!fi4 55 -^ 154 03 3
105 ' 53 ( 155 01
PCL 156 07
in? 53 53 157 01 1
inn 85 + 158 69 DP
109 01 1 159 02 02
1 in 54 } 160 69 DP
ill 95 = 161 05 05
112 44 SUM 162 91 R/S
113 54 54 163 58 FIX
114 43 RCL 164 04 04
115 58 58 165 99 PRT
116 42 STD 166 42 STD
117 59 59 167 58 58
118 12 B 168 42 STD
119 97 DSZ 169 00 00
120 nn nn 170 42 STD
121 87 IFF 171 59 59
122 13 C 172 00 0
123 91 R/S 173 12 B
124 76 LBL 174 76 LBL
125 12 B 175 38 SIH
126 43 RCL 176 12 B
127 58 58 177 98 flDV
128 85 + 178 69 DP
129 01 1 179 00 00
130 95 = ISO 02 2
131 42 STD 181 04 4
132 50 50 182 06 6
133 43 RCL 183 04 4
134 58 58 184 69 DP
135 85 + 185 02 02
136 01 1 186 69 DP
137 01 1 187 05 05
138 95 = 188 43 RCL
139 42 STD 189 00 00
140 51 51 190 99 PRT
141 43 RCL 191 94 + /-
142 58 53 192 44 SUM
143 85 + 193 50 50
144 02 2 194 44 SUM
145 01 1 195 51 51
146 95 = 196 44 SUM
147 42 STD 197 52 52
148 52 52 19ft 04 4
149 92 RTH 199 02 2
BL 200 02 2
Program Listing Viscosity Program (Cont'd)
D-4
-------
201
202
2Q3
204
205
206
207
208
209
210
211
~' i -~>
li. A L-
213
214
215
216
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2 i 9
220
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235
236
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2 3 '3
240
241
242
243
244
245
246
247
248
249
250
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03 3
06 6
07 7
01 1
69 DP
02 02
69 DP
05 05
91 R/S
99 F'RT
72 ST*
50 50
03 3
0 0 0
04 4
03 3
07 7
01 1
0 0 0
00 0
00 0
00 0
69 DP
02 02
69 DP
05 05
91 R/3
99 PRT
72 ST*
51 51
69 DP
0 0 0 0
04 4
04 4
07 7
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02 02
69 DP
05 05
91 R/S
99 PRT
72 ST*
52 52
97 DSZ
00 00
38 SIN
43 RCL
58 58
Program Listing Viscosity Program (Cont'd)
D-5
-------
APPENDIX E
USER INSTRUCTIONS AND PROGRAM LISTING FOR SPLINE FIT PROGRAM
GENERAL
The spline fit program fits a spline function between six data points,
x and y^ i = 1 to 6. The function can be used to interpolate values of y
between the data points. The spline function also can be used to estimate
the derivative dy/dx anywhere in the interval x, to x.,. The program uses
the PC-100A printer.
Nomenclature, in order used by program:
X = x variable
Y = y variable
TOL = Tolerance for numerical solution (0.0001 is adequate)
T = Value of x for which interpolated values of y are desired
S"(T) = d2y/dx at x = T
S(T) = Value of y at x = T
S'(T) = dy/dx at x = T
USER INSTRUCTIONS
Step Procedure Enter Press Display Print
1 Enter side 1 of Card 1 Clr 1
Enter side 2 of Card 1 Clr 2
2 Clear memory and initialize 2nd_ Cms. E_ -1
3 Enter data A X?
X must be x1 x]
entered in order Y?
from smallest to y-j y-j
largest
E-l
-------
Step Procedure
Enter
Press
Display Print
n
Y?
TOL
4 Program calculates for about 2 minutes
5 Enter T T]
TOL?
TOL
INPUT T's
Tl
6 Finish Card 1
7 Read side 1 of card 2
Read side 2 of Card 1
8 Calculate
'N
READ Card 2
Clr 1
Clr 2
A
T =
Tl
S"
Numbers
S(TXX1)
Numbers
S(T)
Numbers
S'(T)
Numbers
9 Save T^ and S1 (T^ by
recording on magnetic
card for later use
2nd Write
END
E-2
-------
JPLII
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000
001
002
003
004
005
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008
009
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012
013
014
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016
017
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023
024
025
026
027
028
029
030
031
032
033
034
035
036
037
038
039
040
041
042
043
044
045
046
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Spline Fit Card 1
E-3
-------
101
102
103
104
105
106
107
108
109
110
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115
116
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50 50
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42 STD
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42 STO
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152
153
154
155
156
157
158
159
160
161
162
163
164
165
1 66
167
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Spline Fit Card 1 (Cont'd)
-------
202 72 ST*
85
Sd -;d "J 01 1
-'' -" 254 95 =
255 42 STD
256 40 40
257 75 -
258 02 2
259 95 =
260 42 STD
261 41 41
262 HI 1
263 93 .
264 00 0
265 07 7
266 01 1
267 07 7
268 09 9
269 06 6
270 03 8
271 65 x
""" 53 <
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204
205
206
207
208
209
210
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214
215
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56 56
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^^ cTu
Spline Fit Card 1 (Cont'd)
E-5
-------
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
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5
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6
DP
02
DP
05
R/S
Spline Fit Card 1 (Cont'd)
E-6
-------
402
403
404
405
406
407
408
409
410
411
412
413
414
X ? C"
"-7 i J
.-: > £
t i b
i j i
4 i '
418
419
4 2 0
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
.: .: J-J
*T *? U
441
442
443
444
445
446
447
448
449
450
451
452
f £
50
99
01
44
50
97
00
18
69
ou
03
05
01
07
01
03
01
06
00
00
69
01
01
05
01
03
03
05
01
06
00
00
69
02
00
03
00
00
00
00
00
00
00
00
69
03
69
05
01
91
ST*
50
PRT
1
SUM
50.
DS2
00
CE
DP
00
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5
1
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02
0
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0
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0
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n
0
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03
DP
05
1
R/S
Spline Fit Card 1 (Cont'd)
E-7
-------
SPLINE FIT CflRD £ 051 51 51
000 76 LBL °52. 95 =
001 11 R 053 67 EQ
0432 04 4 054- 79 x
003 04 4 055- 22 INV
fin4 42 STD 056 77 GE
005 58 "58 °57 6? EQ
nri6 n:-i ': 058 01 1
007 09 9 059 44 SUM
nOR 42 STD 060 51 51
009 56 56 061 97 DSZ
nin 06 6 062 00 00
Oil 42 STD 063 87 IFF
012 00 fin 064 76 LBL
01:-; 01 1 065 88 DMS
014 42 STD 066 69 DP
015 51 51 067 00 00
016 00 H 068 01 1
017 32 XJT 069 07 7
018 76 LBL 070 03 3
019 87 IFF 071 05 5
020 43 RCL 072 03 3
021 00 00 073 05 5
022 73 RC* 074 03 3
023 56 56 075 02 2
024 42 STD 076 03 3
025 59 59 077 05 5
026 43 RCL 078 69 DP
027 59 59 079 02 02
028 75 - 080 69 DP
029 43 RCL 081 05 05
030 01 01 082 61 GTD
031 95 = 083 69 DP
032 67 EQ 084 76 LBL
033 79 x 085 78 1+
034 22 INV 086 06 6
035 77 GE 087 42 STD
036 88 DMS 088 51 51
037 43 RCL 089 76 LBL
038 59 59 090 67 EQ
039 75 - 091 01 1
040 43 RCL 092 22 INV
041 06 06 093 44 SUM
042 95 = 094 51 51
043 67 EQ 095 76 LBL
044 78 1+ 096 79 x
045 77 GE 097 12 B
046 88 DMS 098 76 LBL
047 43 RCL 099 69 DP
048 59 59 100 01 1
049 75 -
050 73 FT:*
Spline Fit Card Z
E-S
-------
101 44 SUM 151 95 =
102 56 56 152 42 STD
103 01 1 153 54 54
104 42 STD 154 85 +
105 51 51 155 06 6
106 06 6 156 95 =
107 42 STD 157 42 STD
108 00 00 158 55 55
109 43 RCL 159 43 RCL
110 56 56 160 59 59
111 75 - 161 75 -
112 04 4 162 73 RC*
113 05 5 163 51 51
114 95 = 164 95 =
115 22 INV 165 42 STD
116 67 EG! 166 23 23
117 87 IFF 167 01 1
118 69 DP 168 44 SUM
119 00 00 169 51 51
120 01 1 170 43 RCL
121 07 7 171 59 59
122 03 3 172 75 -
123 01 1 173 73 RC*
124 01 1 174 51 51
125 06 6 175 95 =
126 69 DP 176 42 STD
127 02 02 177 24 24
128 69 DP 178 65 x
129 05 05 179 43 RCL
130 92 RTH 180 23 23
131 76 LBL 181 95 =
132 12 B 182 42 STD
133 01 1 183 25 25
134 44 SUM 184 98 flDV
135 58 58 185 69 DP
136 43 RCL 186 00 00
137 51 51 187 03 3
138 85 + 188 07 7
139 06 6 189 00 0
140 95 = 190 00 0
141 42 STD 191 06 6
142 52 52 192 04 4
143 85 + 193 69 DP
144 01 1 194 02 02
145 01 1 195 69 DP
146 95 = 196 05 05
147 42 STD 197 43 RCL
148 53 53 . 198 59 59
149 85 + 199 99 PRT
150 09 9 200 69 DP
Spline Fit Card Z (Cont'd)
-------
201 00 .00 -JSl £3 _m
2H2 03 3 ij£- *' Uh
5no n& fi 253 05 05
204 06 6 254 01 1
2R5 r.5 5 ,255 44 SUM
166 06 6 *256 54 54
?n7 05 P. ^""" -'-' (-
i58 69 DP 258 73 RC*
.209 02 02 f5.? 54 54
21n 69 DP £*u a5 +
211 05 05 261 43 RCL
' '"I £ -! C 1 C 1
212 73 RC* £?£ ;:|1 -'
; i -; c- 4 5 4 i^ t> c! y _' +
214 42 STD «4 43 RCL
215 51 51 £bj ^b -b
216 85 + 266 54 >
217 43 RCL 'be -.- -
21ft 23 23 ^bt: Ob 6
219 65 x 269 95 =
220 73 RC* 270 99 PRT
221 55 55 271 42 STD
222 95 = 272 57 57
223 99 PRT 273 69 DP
?24 42 STD 274 00 00
225 26 26 275 03 3
226 69 DP £76 Ot> fcl
'27 00 00 277 05 5
228 03 3 278 05 5
229 06 6 279 03 3
230 05 5 280 07 7
231 05 5 £»1 '-15 5
232 03 3 282 06 6
233 07 7 283 69 DP
;--;4 04 4 284 02 02
235 04 4 285 69 DP
o-t;g, 04 4 286 05 05
237 04 4 287 73 RC*
238 69 DP 288 52 52
239 02 02 289 85 +
240 00 n 290 43 RCL
241 02 2 291 23 23
242 05 5 292 65 x
243 06 6 293 73 RC*
244 00 0 294 53 53
245 00 0 295 85 +
246 00 0 296 53 <.
247 OH 0 297 43 RCL
24fi 00 0 298 25 25
249 OH n 299 65 x
250 69 DP 300 43 RCL
Spline Fit (iard 2 (Cont'd)
-------
301 57 57
302 54 )
303 95 =
304 99 PRT
305 69 DP
306 00 00
307 03 3
308 06 6
309 06 6
310 05 5
311 05 5
312 05 5
313 03 3
314 07 7
315 05 5
316 06 6
317 69 DP
31S 02 02
319 69 DP
320 05 05
321 73 RC*
322 53 53
323 85 +
324 53 <
325 43 RCL
326 23 23
327 85 +
328 43 RCL
329 24 24
330 54 )
331 65 x
332 43 RCL
333 57 57
334 85 +
335 53 <
336 43 RCL
337 25 25
338 65 x
339 73 RC*
340 55 55
341 55 +
342 06 6
343 54 >
344 95 =
345 99 PRT
346 72 ST*
347 58 58
348 98 flDV
349 92 RTH
Spline Fit Card Z (Cont'd)
E-ll
-------
APPENDIX F
USER INSTRUCTIONS AND PROGRAM LISTING FOR CALCULATION OF PENETRATION
AS A FUNCTION OF PARTICLE DIAMETER PROGRAM FOR TI-59
GENERAL
This program is used in conjunction with the spline fit program to
calculate penetration as a function of particle diameter. Magnetic cards
are used to input the results from the spline fit program needed in this
program. Particle diameter, penetration for that diameter, and overall
penetration are printed on the PC-100A printer.
Nomenclature, in order used by program:
Mass In
Mass Out
D
PT(D)
Overall PT
USER INSTRUCTIONS
= Particulate mass concentration at inlet
= Particulate mass concentration at outlet
= Particle diameter, ym
= Penetration for particle diameter, d, fraction
- Overall penetration,
Step Procedure Enter
1 Read side 1 of card
Read side 2 of card
2 Begin calculation
Read magnetic card with
results from spline fit
for inlet
Read magnetic card with results Clr
from spline fit for outlet R/S
Enter inlet mass concentration, Mj R/S
Enter outlet mass concentration, M R/S.
Press
Clr
Clr
A
Clr
R/S
Display
1
2
3
Print
READ INLET DATA
READ OUTLET DATA
MASS IN?
MASS OUT?
D = number
F-l
-------
Step Procedure Enter Press Display Print
PT(D) =
D =
number
RT(D) =
number
Overall PT
number
END
F-2
-------
051 26 26 ini 01 i
052 92 RTN 102 42 STD
000 76 LBL °53 76 LBL 103 21 21
001 12 B °54 U fl 104 04 4
nri2 69 DP °55 6v DP 105 05 Pi
003 00 00 °56 °° °° 106 42 STD
004 03 3 °-'7 °3 3 107 22 22
005 00 0 05S °5 5 108 07 7
006 01 1 U5y 01 1 109 42 STD
007 03 3 06° 07 7 HO 23 23
008 03 3 061 01 1 HI 06 6
009 06 6 °62 °3 3 112 42 STD
010 03 3 °63 01 1 113 00 00
Oil 06 Ofc>4 °6 6 114 76 LBL
fU2 00 n 065 00 0 115 60 DEC
Hi3 00 0 °66 0° 0 116 73 RC*
ni4 69 DP 06? 69 DP 117 20 20
ni5 01 01 °68 01 01 US 72 ST*
H16 02 2 °69 °2 2 119 21 21
017 H4 4 0?0 °4 4 120 73 RC*
018 03 :-: °71 °3 3 121 22 22
ni9 oi 1 0?£ -01 I 122 72 ST*
020 07 - 7 °73 0£ 2 123 23 23
D21 ni 1 °74 °7 7 124 01 1
n2* HO n °75 01 1 125 44 SUM
n--"-: on 0 °76 07 7 126 20 20
fi?4 00 0 °77 °3 3 127 44 SUM
fi25 Oft 0 07S °7 7 128 21 21
69 DP °79 69 DP 129 44 SUM
02 0^J OSO °2 °2 130 22 22
f,'--i DP OS1 °° ° 131 44 SUM
529 05 05 ??2 00 0 132 23 23
030 91 R/S ua3 01 ! 133 97 DSZ
1131 ^9 PPT °84 °6 6 134 00 00
n« 4-? c;Tn 085 01 1 135 60 DEC
,Voc; ^ "2^ 086 03 3 136 03 3
rr-4 n^ ':" °87 03 3 137 02 2
Ao5 5| 2 088 07 7 138 04 4
036 04 4 089 01 1 139 01 1
,-,37 ni 1 09° °3 3 140 03 3
nog fi^: '-I 091 69 DP 141 07 7
039 07 7 092 °3 °3 142 02 2
040 07 7 °93 69 DP 143 07 7
,-,41 ni 1 °94 °5 °5 144 01 1
00 0 095 03 3 145 07 7
no n 096 91 R/S 146 69 DP
A9 DP °97 °3 3 147 02 02
02 n^ 098 09 9 148 03 3
69 Dr 099 42 STD 149 07 7
04? 05 05 100 20 20 150 00 0
048 91 R/S
049 99 PRT
050 42 STD
Program Listing Pt(d) Program for TI-59
; F-3
-------
l^i m 1 202 43 RCL
~ *~ --i 1-1 r, .-, - /-, .-
I <=.--, nf. f ill.!.;, it, £b
S4 01 1 204 55 *
^ ,-,-tj q 205 43 RCL
<*?
A ' I ' *
206 25 25
256
207 95 = 25
itm £Q rip 208 42 STD £5y
159 03 03 209 27 27 259
1 f n n 1 1 -^ 1'-' Oil £ t- U
JfiV n- i 211 42 STD 261
162 On n 212 20 20 262
163 nn n 213 07 7 zbs
164 nn n 214 42 STD 264
165 66 6 215 21 21 ^t-5
166 00 0 -lb 01 i -^'E'
167 on n 217 03 3 ztf
lf.fi nn n 218 42 STD 268
169 on 6 219 22 22 269
17ii 69 DP 220 06 6 270
171 04 f!4 221 42 STD 271
172 69 Up 222 00 00 272
173 05 05 223 76 LBL 273
174 Oa 3 224 80 GRD 274
175 91 R/S 225 73 RC* 275
176 04 4 226 22 22 276
178 42 STD 228 73 RC* 278
179 22 22 f^9 21 Zl ^79
Iftl 03 3 231 43 RCL 281
182 42 STD 232 27 27 282
183 23 23 233 95 = 283
1*4 06 6 234 42 STD 284
185 42 STD 235 30 30 285
186 On on 236 69 DP 286
187 76 LEL 237 00 00 287
188 70 PflD 238 01 1 288 22 22
189 73 PC* 239 06 6 289 97 DSZ
19TI ?? -? 240 00 0 290 00 00
191 72 ST* 241 00 0 291 80 GRD
19-? 23 23 242 06 6 292 69 DP
193 01 1 243 04 4 293 00 00
194 44 SUM 244 69 DP 294 03 3
195 22 22 245 02 02 295 02 2
196 44 SUM 246 69 DP 296 04 4
197 ?:-; ?-; 247 05 05 297 02 2
198 97 DSZ 248 73 RC* 298 01 1
199 00 OH 249 20 20 299 07 7
2nn 7H RflD 250 99 F'RT 300 03 3
Program Listing Pt(d) Program for TI-59 (Cont'd)
-------
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
-' -: -:
_ - %.'
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
05
01
03
69
01
02
07
02
07
00
00
03
03
03
07
69
02
00
00
06
04
00
00
00
00
00
00
69
03
69
05
43
27
99
69
00
01
07
03
01
01
06
00
00
69
02
69
05
92
5
1
3
DP
01
2
r
.-i
h_
7
0
0
. ,
.;
3
3
?
r
DP
02
0
0
6
4
0
0
0
0
0
0
DP
03
DP
05
RCL
27
PRT
DP
00
1
7
-i
\j
1
1
6
0
0
DP
02
DP
05
RTN
j'rogram Listing ljt(d) Program for TI-59 (Cont'd)
F-5
-------
TECHNICAL REPORT DATA
(Please read Iiianictions on the reverse before completing/
1. REPORT NO.
EPA-600/7-78-226
3. RECIPIENT'S ACCESSION NO.
4 -TITLE AND SUBTITLE Cascade impactor Data Reduction with
SR-52 and TI-59 Programmable Calculators
5. REPORT DATE
November 1978
6. PERFORMING ORGANIZATION CODE
7. AUTHOR1SI
Leslie E. Sparks
8. PERFORMING ORGANIZATION REPORT NO
9. PERFORMING ORGANIZATION NAME AND ADDRESS
U.S. Environmental Protection Agency
Industrial Environmental Research Laboratory
Research Triangle Park, North Carolina 27711
10. PROGRAM ELEMENT NO.
EHE624A
11. CONTRACT/GRANT NO.
NA (Inhouse)
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
User Manual; 5-6/78
14. SPONSORING AGENCY CODE
EPA/600/13
15.SUPPLEMENTARY NOTES Author Sparks' mail drop is 61; his phone is 919/541-2925.
16. ABSTRACT
The report provides useful tools for obtaining particle size distributions
and graded penetration data from cascade impactor measurements. The programs
calculate impactor aerodynamic cut points, total mass collected by the impactor,
cumulative mass fraction less than for each stage, log-normal size distribution
parameters for the data, and graded penetration. These programs are written for
the Texas Instruments SR-52 and TI-59 programmable calculators and the PC-100A
printer. A general discussion of the program, an example problem, program listing,
and user instructions are provided for each program.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATl Field/Group
Pollution
Data Reduction
Impactor s
Particle Size Distribution
Measurement
Dust
Computer Programs
Pollution Control
Cascade Impactors
Graded Penetration
Particulate
13B
09B
131
14B
11G
13. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
111
20. SECURITY CLASS (Thispagt)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
F-6
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