WORKBOOK
                OF
   ATMOSPHERIC DISPERSION
            ESTIMATES
H
      U.S. ENVIRONMENTAL PROTECTION AGENCY

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               WORKBOOK OF
ATMOSPHERIC  DISPERSION ESTIMATES
                   D. BRUCE TURNER

              Air Resources Field Research Office,
           Environmental Science Services Administration
          ENVIRONMENTAL PROTECTION AGENCY
                  Office of Air Programs
            Research Triangle Park, North Carolina
                      Revised 1970

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The AP series of reports is issued by the Environmental Protection

Agency to report the results of scientific and engineering studies,

and information of general interest in the field of air pollution.

Information presented in this  series includes coverage of intramural

activities  involving air pollution research and control technology

and of cooperative programs and studies conducted in conjunction

•with state and local agencies,  research institutes,  and industrial

organizations.   Copies of AP  reports are available free of charge -

as  supplies permit - from the  Office of Technical Information and

Publications,  Office  of Air Programs, Environmental Protection

Agency, Research Triangle Park, North Carolina  27711.
                      5th printing March 1972


         Office of Air Programs Publication No. AP-26
     For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402- Price $1.00
                             Stock Number 5603-0015

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                                   PREFACE

     This workbook presents some  computational techniques currently used by scien-
tists working with atmospheric dispersion problems.  Because the basic working equa-
tions are general,  their application  to  specific problems usually requires special care
and  judgment;  such  considerations  are  illustrated  by 26  example problems.  This
workbook is intended as an aid to meteorologists and air pollution scientists who are
required to  estimate atmospheric  concentrations of contaminants from  various types
of sources. It is not intended as a complete  do-it-yourself  manual  for atmospheric
dispersion estimates; all of the numerous complications that arise in making  best esti-
mates of dispersion cannot  be so  easily resolved.  Awareness of the possible complex-
ities can enable the user to appreciate the validity of his "first approximations" and
to realize when the services of a professional air pollution  meteorologist are required.
                                       111

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                           ACKNOWLEDGMENTS

     The author wishes to express his appreciation to Robert A. McCormick, Paul
A. Humphrey, and other members of the Field Research Office for their helpful dis-
cussions and review;  to  Jean J. Schueneman, Chief, Criteria and Standards Develop-
ment, National Center for Air Pollution Control, who suggested this workbook; to Phyllis
Polland and Frank Schiermeier, who checked the problem solutions; to Ruth Umfleet
and Edna Beasley for their aid; and to the National Center for Air Pollution Control,
Public Health Service, and Air Resources Laboratory, Environmental  Science  Services
Administration, for their support.
                                      IV

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                                    CONTENTS

ABSTRACT 	vii

Chapter 1. INTRODUCTION	  1

Chapter 2. BACKGROUND  	  3

Chapter 3. ESTIMATES OF ATMOSPHERIC  DISPERSION  	_	  5
              Coordinate System	  5
              Diffusion Equations 	  5
              Effects of Stability	:	  6
              Estimation of Vertical and Horizontal Dispersion	  7
              Evaluation of Wind Speed 	  7
              Plots of Concentrations against Distance	_	  7
              Accuracy of Estimates	  7
              Graphs for Estimates of Diffusion 	 10
              Plotting Ground-Level Concentration Isopleths 	 10
              Areas Within Isopleths  	 17
              Calculation of Maximum Ground-Level Concentrations	,	 17
              Review of Assumptions  	_	 17

Chapter 4. EFFECTIVE HEIGHT OF EMISSION  	 31
              General Considerations  	_	 31
              Effective Height of Emission and Maximum Concentration	 31
              Estimates of Required Stack Heights	_	 31
              Effect  of Evaporative Cooling 	 32
              Effect of Aerodynamic Downwash  	 32

Chapter 5. SPECIAL TOPICS 	 35
              Concentrations in an Inversion Break-up Fumigation	 35
              Plume  Trapping 	 36
              Concentrations at Ground Level Compared to Concentrations
              at the  Level of Effective Stack Height from Elevated Con-
              tinuous Sources	_	 36
              Total Dosage from a Finite Release	 37
              Crosswind-Integrated Concentration 	_	 37
              Estimation of  Concentrations for Sampling Times  Longer
              than a Few Minutes 	 37
              Estimation of  Seasonal  or Annual Average Concentrations
              at a Receptor from a Single Pollutant Source	 38
              Meteorological Conditions Associated with Maximum
              Ground-Level Concentrations	 38
              Concentrations at a Receptor Point from Several Sources	 39
              Area Sources 	_	 39
              Topography	 40
              Line Sources 	 40
              Instantaneous Sources	 41
Chapter 6. RELATION TO OTHER DIFFUSION EQUATIONS  	 43

Chapter 7. EXAMPLE PROBLEMS 	 45
Appendices:	 57

            1 — Abbreviations and Symbols	_	 59
            2 — Characteristics of the  Gaussian Distribution	61
            3 — Solutions to  Exponentials	 65
            4 — Constants, Conversion Equations, Conversion Tables 	 69

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                                  ABSTRACT

     This  workbook presents methods of practical application  of  the binormal con-
tinuous plume dispersion model to estimate concentrations of air pollutants.  Estimates
of dispersion are those of Pasquill as restated by Gifford. Emphasis is on the estima-
tion of concentrations from continuous sources for sampling times up to 1 hour.  Some
of the topics discussed are determination of effective height of emission, extension of
concentration  estimates  to longer sampling  intervals, inversion  break-up fumigation
concentrations, and concentrations from area, line, and multiple sources. Twenty-six
example problems and their solutions are given.  Some graphical aids  to  computation
are included.
                                       vii

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                                 Chapter 1—INTRODUCTION
   During recent years methods of estimating at-
mospheric dispersion have undergone considerable
revision,  primarily due  to results  of experimental
measurements.  In  most dispersion  problems  the
relevant  atmospheric layer  is that  nearest  the
ground, varying in thickness  from  several hundred
to a  few thousand meters.   Variations  in both
thermal and mechanical turbulence and in wind
velocity are greatest in the layer  in contact with
the surface. Turbulence induced by buoyancy forces
in the atmosphere is closely related to the vertical
      temperature structure. When temperature decreases
      with height at a rate higher than 5.4°F per 1000 ft
      (1°C per 100 meters), the atmosphere is in  un-
      stable equilibrium  and  vertical motions are  en-
      hanced.  When temperature decreases at a  lower
      rate or increases with height  (inversion), vertical
      motions are damped or reduced.  Examples of typ-
      ical variations in temperature and wind speed with
      height for daytime and nighttime conditions  are
      illustrated in Figure 1-1.
  600r
                234567

                  TEMPERATURE, °C
10   11   12
345678

 WIND SPEED, m/sec
10   11
        Figure 1-1.  Examples of variation of temperature and wind speed with height (after Smith, 1963).
    The transfer  of momentum upward or down-
ward in the atmosphere is also related to stability;
when the atmosphere is unstable, usually in  the
daytime, upward motions transfer the momentum
"deficiency"  due to eddy friction losses near  the
earth's  surface  through a  relatively  deep layer,
causing the  wind speed to  increase more slowly
with height than at night (except in the lowest  few
meters). In addition  to thermal turbulence, rough-
ness elements on the ground engender mechanical
turbulence,  which affects both the dispersion of
material in the atmosphere  and  the wind profile
(variation of wind with height). Examples  of these
effects on the resulting wind profile are shown in
Figure 1-2.
          As wind speed increases, the effluent from a
      continuous source is introduced into a greater vol-
      ume of air per unit time interval. In addition to
      this dilution by wind speed, the  spreading of the
      material (normal  to  the mean  direction  of trans-
      port) by turbulence  is a major factor in the dis-
      persion process.

          The procedures presented here to  estimate  at-
      mospheric dispersion are applicable when mean wind
      speed and direction can be determined, but meas-
      urements of turbulence, such as the standard de-
      viation of wind direction fluctuations, are not avail-
      able. If such measurements are at hand, techniques
      such as those outlined by Pasquill (1961)  are likely
      to give more accurate results. The diffusion param-

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eters presented here are most applicable to ground-
level or low-level releases (from the surface to about
20 meters), although they are commonly applied at
higher elevations without full experimental valida-
tion.   It  is assumed  that stability is the same
throughout the diffusing layer, and no  turbulent
transfer occurs through layers of dissimilar stability
characteristics. Because mean values for wind direc-
tions and speeds are required, neither the variation
of wind speed nor the variation of  wind direction
with height in the mixing  layer are taken into ac-
count. This usually is not a problem in neutral or
unstable (e.g., daytime) situations, but can cause
over-estimations  of downwind concentrations  in
stable conditions.
                REFERENCES

Davenport, A. G., 1963:  The relationship of wind
   structure  to  wind loading.  Presented  at Int.
   Conf. on  The Wind Effects on Buildings and
   Structures, 26-28 June 63, Natl. Physical Lab-
   oratory, Teddington, Middlesex, Eng.

Pasquill, F., 1961:  The estimation of the dispersion
   of wind borne material.   Meteorol.  Mag.  90,
   1063, 33-49.

Smith, M. E., 1963: The use and misuse  of the at-
   mosphere, 15 pp., Brookhaven Lecture Series,
   No.  24, 13 Feb 63, BNL 784  (T-298)  Brook-
   haven National Laboratory.
  600
  500
 .400
 '300
  200
   100
                     URBAN AREA

                   GRADIENT WIND
  SUBURBS
LEVEL COUNTRY
                                                                                     GRADIENT WIND
Figure 1-2.  Examples of variation of wind with height over different size roughness elements (figures are percentages
                                 of gradient wind); (from Davenport, 1963).
                                                            ATMOSPHERIC  DISPERSION ESTIMATES

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                                  Chapter  2 — BACKGROUND
    For a number of years estimates of concentra-
tions were calculated either from the equations of
Sutton (1932)  with the  atmospheric  dispersion
parameters Cy, Cz, and n, or from the equations of
Bosanquet (1936) with the dispersion parameters
p and q.

    Hay and Pasquill (1957) have presented experi-
mental evidence that  the vertical  distribution of
spreading particles from an elevated point is re-
lated to the standard deviation of the wind eleva-
tion angle, 
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                Chapter  3 — ESTIMATES OF ATMOSPHERIC  DISPERSION
   This chapter outlines  the  basic procedures to
be used  in  making  dispersion estimates as sug-
gested by Pasquill (1961) and modified by Gifford
(1961).

COORDINATE SYSTEM

   In the system considered here the origin is at
ground level  at or beneath the point of emission,
with the x-axis extending horizontally in the direc-
tion  of the mean wind.  The y-axis is in the hori-
zontal plane  perpendicular to the x-axis,  and the
z-axis extends vertically. The plume travels along
or parallel to the x-axis.  Figure 3-1 illustrates the
coordinate system.

DIFFUSION  EQUATIONS

   The concentration, x, of gas or aerosols (parti-
cles less than about 20 microns diameter) at x,y,z
from a continuous source with an effective emission
height, H, is given by equation 3.1.  The notation
used to depict this concentration is  x (x,y,z;H).
H is the height of the plume centerline  when  it

                      I
becomes essentially  level,  and is the sum of  the
physical stack height, h, and the plume rise, AH.
The following assumptions are  made:  the plume
spread has a Gaussian distribution (see Appendix
2) in both the horizontal and vertical planes, with
standard deviations  of plume concentration distri-
bution in the horizontal and vertical of af and 
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Any consistent set of units may be used.  The most
common is:

   X (g m~a) or, for radioactivity (curies m~3)
   Q (g sec~l) or (curies sec"1)
   u (m sec"1)
   a,,  CTZ U
         exp  —
   6XP   ~
                                f— -
                                |^    Z
                                            0.2)
   Where  the concentration is to  be calculated
along the centerline  of the  plume  (y = 0),  (see
problem 2)  further simplification results:
x(x,0,0;H) =
     exp
                            f -- L(J
                            |^     Z \  6

Strong
A
A-B
B
C
C

Moderate
A-B
B
B-C
C-D
D

Slight
B
C
C
D
D
Night
Thinly Overcast

-4/8 Low Cloud

E
D
D
D


G/ O
Cloud

F
E
D
D
The neutral class, D, should be assumed for overcast conditions during
day or night.

   "Strong" incoming solar radiation corresponds
to a solar altitude greater than 60° with clear skies;
"slight" insolation  corresponds  to a  solar altitude
from 15° to 35° with clear skies. Table 170, Solar
Altitude  and Azimuth, in  the Smithsonian Mete-
orological Tables (List, 1951) can be used in deter-
mining the solar altitude. Cloudiness will decrease
incoming solar radiation and should be considered
along with solar altitude  in determining solar radia-
tion.  Incoming radiation   that  would  be strong
with clear skies can be expected to be reduced to
moderate with broken (% to % cloud cover)  mid-
dle clouds  and to  slight with  broken low  clouds.
An  objective system of  classifying  stability  from
hourly meteorological observations  based on the
above method has been suggested (Turner, 1961).

   These methods  will give representative indica-
tions of stability over open  country or rural areas,
but are less reliable  for  urban  areas. This differ-
ence is due  primarily to  the influence of the city's
larger surface  roughness and  heat  island effects
upon  the stability  regime  over urban areas.  The
greatest difference occurs on calm clear nights; on
such nights conditions over rural  areas are  very
stable, but over urban areas they are slightly un-
stable or near neutral to a height several times the
average building height,  with a stable layer above
(Duckworth and Sandberg, 1954; DeMarrais, 1961).
                                                             ATMOSPHERIC  DISPERSION ESTIMATES

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   Some preliminary results of a dispersion experi-
ment in St. Louis (Pooler, 1965) showed that the
dispersion over the city during the daytime behaved
somewhat like types B and C; for one night experi-
ment try varied with distance between types D and E.

ESTIMATION OF VERTICAL AND
HORIZONTAL DISPERSION

   Having  determined the  stability class  from
Table 3-1, one can evaluate the estimates of 2 XL; XL is where 2xL; XL is where az = 0.47 L
    The value of (rzL = 0.8 L

EVALUATION OF WIND SPEED

   For the wind speed, u, a mean through the ver-
tical extent of  the  plume  should be used.  This
would  be from the height H — 2 CTZ through  H -f-
2 
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                              1                               10
                                  DISTANCE DOWNWIND, km
100
Figure 3-2.  Horizontal dispersion coefficient  as a function of downwind distance from the source.
                                                     ATMOSPHERIC DISPERSION ESTIMATES

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                                         1                                 10
                                              DISTANCE DOWNWIND,  km
100
         Figure 3-3.   Vertical  dispersion coefficient as a function  of downwind  distance  from the source.
Estimates
   339-901 O - 69 - 2

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                             .  11/11.
                             1  234  5 6xlO"5
                              CONC.
                               SSOmeters
             Figure  3-4.   Variations in  concentration in the vertical beneath a more stable  layer.
three cases (where 
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                 10
                                                        DISTANCE,km
Figure 3-5A.  xu/Q with distance for various heights of emission  (H) and  limits to vertical dispersion (L), A stability.
Estimates
                                                                                                                   11

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                                                                                               100
                                                    DISTANCE, km
Figure  3-5B.  xu/Q with distance  for various heights of emission (H) and limits to vertical dispersion (L), B stability.
12
ATMOSPHERIC DISPERSION ESTIMATES

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                       •  O.I
                                                           DISTANCE, km
Figure 3-5C.  xu/Q with distance  for various  heights  of emission (H) and limits to  vertical dispersion  (L),  C stability.
Estimates
                                                                                                                    13

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          E
          o
                                                   DISTANCE, km
Figure  3-5D.  xu/Q with  distance for various heights  of emission (H) and limits to vertical dispersion (L),  D stability.
14
ATMOSPHERIC DISPERSION ESTIMATES

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                                                       DISTANCE, km
Figure 3-5E.   xu/Q with distance for various heights  of  emission (H) and limits to vertical dispersion (L), E stability.
Estimates
15

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                    0.1
                                                                                            100
                                                     DISTANCE, km
Figure 3-5F.  xu/Q with  distance for various heights of emission (H) and limits to vertical dispersion (L), F stability.
16
ATMOSPHERIC DISPERSION ESTIMATES

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   From Table A-l  (Appendix 3) when exp

                  - °-345' y/ffy = L46
From Figure 3-2, for stability B and x = 600 m, vy
= 92.  Therefore y = (1.46)  (92)  =  134 meters.
This is the distance of the 10~3 isopleth from the
x-axis at a downwind distance of 600 meters.
   This can also be determined from:

                 x(x,o,Q;H)
                 x(x,y,0;H)
(3.8)
The position corresponding to the downwind dis-
tance and  off-axis  distance can  then be plotted.
After a number of points  have been plotted, the
concentration isopleth may be  drawn (see problems
8 and 26).  Figures 3-6 and 3-7  give ground-level
isopleths of xu/Q for various stabilities for sources
at H = 0 and H = 100 meters.  For example,  to
locate  the  10~3 g  m~3  isopleth  resulting  from a
ground-level source of 20 g sec"1  under B stability
conditions  with wind speed 2 m sec"1, one must
first determine the corresponding value of xu/Q since
this is the quantity graphed in Figure 3-6.  xu/Q  =
10-" x  2/20 = 10~4. Therefore the xu/Q isopleth
in Figure 3-6B having a value of 10~4  m'2 corre-
sponds to a x isopleth  with a  value of 10~3 g m"3.

AREAS WITHIN ISOPLETHS

   Figure 3-8 gives areas within isopleths of ground-
level concentration  in terms of x u/Q for a ground-
level source for various stability categories  (Gifford,
1962; Hilsmeier and Gifford, 1962).  For the exam-
ple just given,  the  area of the 10~3  g m~3 isopleth
(10~4 m~2 x u/Q isopleth) is about 5 x 104 meter2.

CALCULATION OF MAXIMUM
GROUND-LEVEL  CONCENTRATIONS

    Figure  3-9  gives the distance to the  point  of
maximum concentration, xmnx, and the relative maxi-
mum concentration, x  u/Q,liax, as  a  function  of
effective  height of emission  and  stability class
(Martin, 1965).  This  figure was prepared from
graphs of concentration versus distance, as in Fig-
ure 3-5. The maximum concentration can be deter-
mined  by finding x u/Q as a  function of effective
emission height and stability and multiplying  by
Q/u. In using Figure  3-9, the user must  keep  in
mind that the dispersion at higher levels may differ
considerably from  that determined by the ery's and

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00
s
I
73
o
o
51
M
00
o
M
C/3
                        3                   4

                           DOWNWIND DISTANCE (x), km
B
Figure 3-6A.  Isopleths of xu/Q for a  ground-level  source,  A stability.

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w
tfl
a
                                             CLASS   B   STABILITY


                                                       H = 0
               IO'3  IO'4
                                                                    3                 4




                                                                     DOWNWIND DISTANCE  (x), km
                                              Figure  3-6B.  Isopleths of xu/Q for a ground-level source, B  stability.

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I
en
o

d
M
Ol
H
                                 CLASS   C  STABILITY


                                          H=0
                                                                  DOWNWIND DISTANCE (x), km
H
K
                                            Figure 3-6C.  Isopleths of xu/Q for a ground-level source, C  stability.

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M
(A

ft
                                   CLASS  D   STABILITY


                                             H= 0
                                                                    3                  4




                                                                  DOWNWIND DISTANCE (x), km
                                              Figure 3-6D.  Isopleths of xu/Q for a ground-level  source, D stability.

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                                  CLASS  E   STABILITY
                                                                 3                4




                                                               DOWNWIND DISTANCE (x), km
H

I
VI
*
s
M
73
"0

W
S8
C/3
w
CA
H

i
>
H
M
CLASS   F   STABILITY

          H=0
                              3                4



                           DOWNWIND DISTANCE (x), km
                                      Figure 3-6E, F.  Isopleths of xu/Q for a  ground-level source, E and F stabilities.

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w
t/i
«*



to
                                   CLASS  A   STABILITY


                                            H = IOO
                                                                 3                4



                                                               DOWNWIND DISTANCE (x), kn
                                          Figure 3-7A.  Isopleths of xu/Q for a  source 100 meters high, A stability.

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2
o
Cfl
o

o

53

B
so
en
B
W3
H

i
>
H
B
73
                                   CLASS  B  STABILITY


                                            H = IOO
                        1.7 x IO'5,
                   DOWNWIND DISTANCE (x), km
Figure 3-7B.  Isopleths of xu/Q for a source 100 meters high, B stability.

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   M
   Gfi
o  <"
          o

          o
                                      CLASS  C    STABILITY

                                               H = 100
                                                                      3                 4



                                                                     DOWNWIND DISTANCE (x), km
   VI
                                               Figure 3-7C.  Isopleths of xu/Q for a source 100 meters high, C stability.

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re
os
H
3
O
1/1
"B
=
H

2
O
SO
H
01
                                    CLASS   D   STABILITY

                                             H=IOO
                       3                 4


                      DOWNWIND DISTANCE (x), km
H
M
Cfl
Figure 3-7D.  Isopleths of xu/Q for a source 100 meters high, D stability.

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w
<
»—
V»

O
                            CLASS  E STABILITY

                                     H = IOO
                                                                 3                4

                                                               DOWNWIND  DISTANCE (x), km
                           CLASS  F  STABILITY
                                   H=IOO
                                                                 3                4

                                                               DOWNWIND DISTANCE (x), km
hS
-J
                               Figure 3-7E, F.  Isopleths of xii/Q for a source 100 meters high, E and F stabilities.

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      10
                                           10'
             Figure 3-8.   Area within isopleths for a ground-level source (from Hilsmeier and Gifford).
Hilsmeier, W. F., and F. A. Gifford, 1962:  Graphs
   for estimating atmospheric diffusion.  ORO-545,
   Oak Ridge, Tenn.  Atomic Energy Commission,
   10pp.

List,  R.  J.,  1951:   Smithsonian  Meteorological
   Tables, Sixth Revised Edition, 497-505, Wash-
   ington, D. C., Smithsonian Institution,  527 pp.

Martin, D. O., 1965:  Personal communication.

Pasquill, F., 1961: The estimation of the dispersion
   of  windborne  material.  Meteorol.  Mag., 90,
   1063, 33-49.

Pooler, F., 1965: Personal communication.

Sutton, O. G., 1953: Micrometeorology, New York,
   McGraw-Hill. 333 pp.

Turner, D.  B.,  1961:   Relationships between 24-
   hour mean air quality measurements and mete-
   orological factors in Nashville, Tennessee.  J.
   Air Poll. Cont. Assoc., 11, 483-489.
28
                                                             ATMOSPHERIC  DISPERSION ESTIMATES

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M
vi
tt
                                                                          (Xu/Q)
                                                                                                                                                    10"
        Figure 3-9.  Distance of maximum concentration and  maximum xu/Q as a  function  of  stability (curves)  and effective height (meters) of  emission
                    (numbers).

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                      Chapter 4 —EFFECTIVE  HEIGHT OF  EMISSION
GENERAL CONSIDERATIONS

   In most problems one must estimate the effec-
tive stack height, H, at which the plume becomes
essentially level. Rarely will this height  correspond
to the physical height of the stack, h.  If the plume
is caught in the turbulent wake  of the stack  or of
buildings in the vicinity  of the stack, the effluent
will be mixed rapidly downward toward the ground
(aerodynamic downwash).  If the plume is emitted
free of these turbulent zones, a number of emission
factors and meteorological factors influence the rise
of the  plume. The emission factors are:  velocity
of the effluent at the top of the stack, vs; tempera-
ture of the effluent at the top of  the stack, Ts; and
diameter of the stack opening, d. The meteorolog-
ical factors influencing plume rise are wind speed,
u; temperature of the air, Ta;  shear of the  wind
speed with height,  du/dz;  and  atmospheric  sta-
bility.  No theory on plume rise takes into account
all of these variables; even  if such a theory  were
available, measurements  of  all  of the parameters
would seldom be available. Most of the equations
that have been  formulated  for computing the ef-
fective height of emission are semi-empirical. For a
recent  review  of equations for  effective height of
emission see Moses, Strom, and Carson (1964).

   Moses and Strom (1961), having compared ac-
tual and calculated plume heights by means of six
plume rise  equations, report "There is no one for-
mula which is outstanding  in all respects."   The
formulas  of   Davidson-Bryant   (1949),  Holland
(1953), Bosanquet-Carey-Halton (1950),  and Bo-
sanquet  (1957)  all give  generally satisfactory re-
sults in the test situations.  The  experiments con-
ducted by  Moses and Strom involved plume rise
from a stack of less than  0.5 meter diameter, stack
gas exit velocities less than 15 m  sec""1, and effluent
temperature not more than 35°C higher than that
of the ambient air.

   The equation of Holland was developed  with
experimental  data  from larger sources than those
of Moses and  Strom (stack  diameters from 1.7 to
4.3 meters and stack temperatures  from 82 to
204°C); Holland's  equation is used in the solution
of the problems given in this workbook. This equa-
tion frequently underestimates the effective height
of emission; therefore its use often provides a slight
"safety"  factor.
   Holland's equation is:
                              T8 — Ta
                                       d) (4.1)
           \J-.v |  *J.\S^J A J.W  p    m

where:

   AH = the rise of the plume above the stack, m
   vs = stack gas exit velocity, m sec"1
   d = the inside stack diameter, m
   u = wind speed, m sec"1
   p = atmospheric pressure, mb
   Ts = stack gas temperature, °K
   Ta = air temperature, °K
and  2.68 x 10~3 is a constant having units of mb"1
m"1.
   Holland (1953) suggests that a value between
1.1 and 1.2 times the AH from the equation should
be used for unstable  conditions; a value between
0.8 and 0.9 times the AH from the equation should
be used for stable conditions.
   Since the plume rise from a stack occurs over
some distance downwind, Eq.  (4.1) should not be
applied within the first  few  hundred meters of the
stack.

EFFECTIVE HEIGHT  OF  EMISSION AND
MAXIMUM CONCENTRATION

   If the effective heights  of emission  were the
same under all atmospheric  conditions, the highest
ground-level  concentrations from a  given source
would  occur with the  lightest  winds.  Generally,
however, emission  conditions are such that the ef-
fective stack height is an inverse function of wind
speed as indicated in Eq.  (4.1). The maximum
ground-level  concentration  occurs at some inter-
mediate wind speed, at  which  a  balance is reached
between the dilution  due to wind speed and the
effect of height of emission. This critical wind speed
will vary with stability.  In  order to determine the
critical  wind speed, the  effective stack height as a
function of wind speed  should first be determined.
The  maximum concentration for each wind speed
and  stability can  then  be calculated from Figure
3-9 as a function of  effective height of emission
and  stability. When  the maximum  concentration
as a function of wind speed is  plotted on log-log
graph paper, curves can  be drawn for each stability
class; the critical  wind speed corresponds to the
point of highest  maximum  concentration  on the
curve (see  problem 14).

ESTIMATES OF REQUIRED STACK HEIGHTS

   Estimates of the stack height required to pro-
duce concentrations below a given value may be
made through the use of Figure 3-9 by  obtaining
solutions for various wind speeds. Use of this figure
considers maximum concentrations at any distance
from the source.

   In some situations high concentrations upon the
property of the emitter are of little  concern, but
Effective Height
                                             31

-------
maximum concentrations beyond the property line
are of the utmost importance. For first approxima-
tions it can be assumed that the maximum concen-
tration  occurs where \/~Z~ <7Z = H and that at this
distance the a's are related  to the maximum con-
centration by:
               Q
Q
                          U Xn
                                           (4.2)
Knowing the  source strength, Q, and the concen-
tration not to be exceeded xnmx, one can determine
the necessary ay az for a given wind speed.  Figure
4-1 shows o-j.  
-------
            10
                                                                                             100
               Figure 4-1.   The product of w*. as a function of downwind distance from the source.
Effective Height
33

-------
the height.  Values other than 4.3 and 2.15 can be
used. When these values are used 97'/ of the dis-
tribution  is included within these limits.  Virtual
distances  x,  and xz  can be found such that at xv,
a,. — try,, and at xz,   ax,   -  uv,.  These x's will differ
with stability. Equations applicable to point sources
can then  be used, determining <--,. as  a function of
x -f- xy and  
-------
                                Chapter 5 — SPECIAL  TOPICS
CONCENTRATIONS IN AN INVERSION
BREAK-UP FUMIGATION

   A surface-based inversion may be eliminated by
the  upward  transfer of  sensible heat  from the
ground surface when that surface is warmer than
the overlying air.  This situation occurs when the
ground is being warmed by solar radiation or when
air flows from a cold to a relatively warm surface.
In either situation  pollutants  previously emitted
above the surface into the stable layer will be mixed
vertically when  they are reached by the thermal
eddies, and ground-level concentrations can increase.
This process, called "fumigation" was described by
Hewson and Gill (1944) and Hewson (1945). Equa-
tions for estimating concentrations with these con-
ditions have been  given by  Holland (1953), Hew-
son  (1955), Gifford (1960a), Bierly  and Hewson
(1962), and Pooler (1965).

   To  estimate  ground-level concentrations under
inversion break-up fumigations, one assumes that
the plume was initially emitted into a stable layer.
Therefore,   + H ton 15"
                                                                  2 15 °y
                                                                       '(FUMIGATION)


                                          Figure 5-1.  Diagram showing assumed height, hi and «?
                                               during fumigation, for use in equation  (5.2).

                                             Eq. (5.4) should not be applied near  the stack,
                                          for if the inversion has been eliminated to a height
                                          sufficient to include the entire plume, the emission
                                          is taking place under unstable not stable conditions.
                                          Therefore,  the nearest downwind distance to be
                                          considered  for an  estimate  of  fumigation  concen-
                                          trations must be great enough, based on the time
                                          reqrired  to  eliminate the  inversion, that this  por-
                                          tion of the plume was initially  emitted into stable
                                          air.  This distance is x = utm, where u is the mean
Special Topics
                                                                                       35

-------
 wind in the stable layer and tm is the time required
 to eliminate  the inversion from h,  the physical
 height of the stack to hi (Eq. 5.3).

    tn, is dependent upon both the strength of the
 inversion and the  rate of  heating at the surface.
 Pooler (1965) has derived an expression for esti-
 mating this time:
          Pa Cp   89
           R
                 Sz
                                h + h.
                                (5.5)
 where tm = time required for the  mixing layer to
            develop from the top of the stack to the
            top of the plume, sec
       pa = ambient air density, g m"3
       cp = specific heat of air at constant pressure,
            cal g-1 OR"1
       R = net rate of sensible heating  of an air
            column by  solar radiation, cal m"2 sec"1
       80
      — = vertical potential temperature gradient,
°K m"1 ~
rate)
                      8T
                      Sz
                         + r  (the adiabatic lapse
       hi = height of base of the inversion sufficient
            to be above the plume, m
       h = physical height of the stack, m

Note that hi —h is the thickness of the layer to be

heated and f —^—L J  js tne average height of the

layer.  Although R depends on season, and  cloud
cover and varies continuously with time, Pooler has
used a value of  67  cal m~2 sec"1 as an average for
fumigation.

   Hewson  (1945) also suggested a method of esti-
mating the time required to eliminate an inversion
to a height z by use  of an equation  of Taylor's
(1915, p. 8):
          z2
   t =

where:
         4 K
                                           (5.6)
         t = time required to eliminate the inver-
             sion to height z, sec
         z = height to which the inversion has been
             eliminated, m
        K = eddy diffusivity for heat, m2 sec"1

Rewriting to compare with Eq. (5.5),

          h,2 — h2
           4 K
                                           (5.7)
Hewson (1945) has suggested a value of 3 m2 sec *
for K.

PLUME TRAPPING

    Plume  trapping  occurs  when  the plume  is
trapped between  the ground surface  and  a stable
                                                    layer aloft.  Bierly and Hewson (1962) have sug-
                                                    gested the use of an equation that accounts for the
                                                    multiple eddy reflections from both the ground and
                                                    the stable layer:
                                                        X (x,0,z;H)
                                                        exp   —
                                                       + exp
+ exp 	
exp
+ exp 	
1 (
2 V
1 /
2 V
1 (
2 (
z + H — 2 NL
Z-H + 2NL
O-z
z + H + 2 NL

-------
these is at the distance of maximum concentration
at the ground. As a rough approximation the maxi-
mum ground-level concentration occurs at the dis-
                   1
tance where  
-------
   Table 5-1   VARIATION  OF CALCULATED CONCENTRATION
                WITH SAMPLING TIME

                               Ratio of
                          Calculated Concentration
                                               2 Q
Sampling Time
3 minutes
15 minutes
1 hour
3 hours
24 hours ....
to 3-minute Concentration
1.00
0.82
0.61
0.51
0.36
This  table indicates  a power  relation with time:
x  »c  t~°-17. Note that these estimates were based
upon  published  dispersion coefficients rather than
upon  sampling results.  Information in the refer-
ences cited indicates  that effects of sampling time
are exceedingly complex.  If it  is necessary to esti-
mate  concentrations  from a single  source for the
time intervals greater than a few minutes, the best
estimate apparently can be obtained from:
= Xk(ir)
                                          (5.12)
where x* is the desired concentration estimate for
the sampling time, ts;  Xk is the concentration esti-
mate for the shorter sampling time, tk, (probably
about 10 minutes); and p should be between 0.17
and  0.2.  Eq. (5.12)  probably  would  be applied
most appropriately to  sampling times less than  2
hours (see problem 19).

ESTIMATION OF  SEASONAL OR ANNUAL
AVERAGE CONCENTRATIONS  AT  A
RECEPTOR  FROM A SINGLE  POLLUTANT
SOURCE

   For a source that emits at a constant rate from
hour to hour and day to day, estimates of seasonal
or annual average concentrations can be made for
any distance in any direction if stability wind "rose"
data are available for  the period under study.  A
wind rose gives  the frequency  of occurrence for
each wind direction (usually to 16 points) and wind
speed class (9 classes in standard Weather Bureau
use) for the period under consideration (from  1
month to 10 years).  A stability wind rose gives the
same type of information  for each stability class.

   If the wind directions are taken to 16 points and
it is assumed that the wind directions within each
sector are distributed randomly over a  period of  a
month or a season, it can further be assumed that
the effluent is uniformly  distributed in the hori-
zontal within the sector (Holland, 1953, p.  540).
The appropriate equation for average concentration
is then either:
                                         nr
                                        V2.ra.ll
                                                          exp  I —
                                        2.03Q
                                                              a, UX
                                                                    exp
                                                                                   H
                                                                         (5.13)
                                                        or
                                                        X =
                                                                  Q
                                                        2.55  Q
                                                         Lux
                                                                                              (5.14)
depending upon whether a stable layer aloft is af-
fecting the distribution.

   The estimation  of x  for a particular direction
and  downwind distance  can be  accomplished by
choosing a representative wind speed for each speed
class and solving the appropriate equation (5.13 or
5.14) for all wind speed classes and stabilities. Note
that a SSW wind affects a receptor to the NNE
of a source.  One obtains  the average concentration
for a given direction and distance by summing all
the concentrations and weighting each one accord-
ing to its frequency for the particular stability  and
wind speed class.  If desired, a different  effective
height of emission  can be used for various wind
speeds. The average concentration can be expressed
by:
     ,         ,   _   2Qf(9,S,N)
   x (x,e) =
                                                                         (5.15)
   exp I  —
                               where f (9, S, N) is the frequency during the period
                                      of interest that the wind is from the direc-
                                      tion  0, for the stability condition, S, and
                                      wind speed class N.
                                   
-------
2. For elevated sources maximum "instantaneous"
   concentrations occur with unstable conditions
   when portions of the plume that have undergone
   little  dispersion  are brought  to  the ground.
   These occur close to the point of emission (on
   the order of 1 to 3 stack heights).  These con-
   centrations  are usually of little general interest
   because of their very short duration; they can-
   not be estimated from the material presented in
   this workbook.

3. For elevated sources maximum concentrations
   for time periods  of a few minutes  occur with
   unstable conditions; although the  concentra-
   tions  fluctuate considerably under these condi-
   tions,  the concentrations averaged  over a few
   minutes are still high compared to those found
   under other conditions.   The distance  of this
   maximum concentration  occurs near the  stack
   (from 1 to 5 stack heights downwind) and the
   concentration drops off rapidly downwind with
   increasing distance.

4. For elevated sources maximum concentrations
   for time periods of about half an hour can occur
   with  fumigation  conditions when an unstable
   layer  increases vertically to mix downward a
   plume previously  discharged  within a  stable
   layer.  With small AH, the fumigation can occur
   close to the  source but will be of relatively short
   duration.  For large AH,  the fumigation will
   occur some distance from the stack  (perhaps 30
   to 40  km), but can persist for a longer time
   interval.  Concentrations considerably lower than
   those associated with fumigations,  but of sig-
   nificance can occur with neutral or unstable
   conditions when  the dispersion upward is  se-
   verely limited by the existence of a  more stable
   layer above the plume, for example, an inversion.

5. Under stable conditions the maximum concen-
   trations at  ground-level  from elevated  sources
   are less  than those occurring under unstable
   conditions and occur at greater distances from
   the source.   However, the  difference between
   maximum ground-level concentrations for stable
   and unstable conditions  is only a  factor of 2
   for effective heights of 25 meters and a factor
   of 5  for H of 75  m. Because the maximum
   occurs at greater  distances, concentrations that
   are below the maximum but still significant can
   occur over large areas. This  becomes increas-
   ingly  significant if emissions are coming from
   more  than  one source.

CONCENTRATIONS AT A  RECEPTOR POINT
FROM SEVERAL SOURCES

   Sometimes,  especially for multiple sources, it is
convenient to consider the receptor as being at the
origin  of  the  diffusion  coordinate system.  The
source-receptor geometry can then be worked out
merely by drawing or visualizing an x-axis oriented
upwind from the receptor  and  determining the
crosswind distances of each source in relation to this
x-axis. As pointed out by Gifford  (1959), the con-
centration at (0, 0, 0) from a source at  (x, y, H)
on a coordinate system with the x-axis oriented up-
wind is the same as the  concentration at (x, y, 0)
from a source at (0, 0, H) on a coordniate system
with the x-axis downwind  (Figure 5-2).  The  total
concentration is then given by summing the  indi-
vidual contributions from each source (see problem
20).
                                  SOURCE
                                  (x,y,H)
                                           UPWIND
       RECEPTOR
        (0,0,0)
 DOWNWIND
                 (x,y,0)
Figure 5-2.  Comparison of source-oriented and receptor-
            oriented  coordinate systems.

   It is often difficult to determine the atmos-
pheric conditions of wind direction, wind speed, and
stability that will result in the maximum combined
concentrations from two or more sources; drawing
isopleths of concentration  for various wind speeds
and  stabilities and  orienting these  according  to
wind direction is one approach.

AREA SOURCES

   In dealing  with  diffusion of air  pollutants  in
areas having large numbers  of sources, e.g., as in
urban areas, there may be too many sources of most
atmospheric contaminants  to consider each source
Special Topics
                                              39

-------
individually. Often an approximation can be made
by combining all of the emissions in a  given area
and treating this area as a source having an initial
horizontal  standard deviation,  becomes great  enough, the concentrations
can be assumed to be  uniform across the width of
the valley and the concentration calculated accord-
ing to the following equation, where in this  case Y
is  the width of the valley.
   X —
            2Q
               Yu
                    exp  l —
                            (5.17)
LINE SOURCES
   Concentrations  downwind  of a  continuously
emitting infinite line source, when the wind direc-
tion  is  normal to the  line,  can be expressed by
rewriting equation  (12) p.  154 of Sutton (1932):
   X (x,y,0;H)
      2 q
     — 	exp
     '2w trz U
                                          (5.18)
Here q is  the source  strength  per unit distance,
for example, g sec"1 m  -1.  Note that the horizontal
dispersion  parameter,  
-------
   When estimating concentrations from finite line
sources, one must account for "edge effects" caused
by the end of the line source.  These effects will of
course extend to greater cross-wind distances  as
the distance from the source increases.  For concen-
trations  from a finite line  source  oriented cross-
wind, define the x-axis in the direction  of the mean
wind and passing through the receptor of interest.
The limits  of the line source can be defined as ex-
tending from y, to y., where y, is less than y2.  The
equation for concentration  (from Button's (1932)
equation (11), p. 154),  is:
 (x,0,0;H) -
                         exp   _
                           *
                                    f
                                    2
                                          (5.20)
The value of the integral can be determined from
tabulations given in most statistical tables  (for ex-
ample, see Burrington (1953), pp. 273-276; also see
problem 24).

INSTANTANEOUS  SOURCES

   Thus far we have considered only sources that
were emitting continuously or for time periods equal
to or greater than the travel times from the source
to the point of interest. Cases of instantaneous re-
lease, as from an explosion, or short-term  releases
on the order of seconds, are often of practical con-
cern.  To determine concentrations at any position
downwind, one must  consider  the  time  interval
after the time of release and diffusion in the down-
wind direction as well as lateral and vertical diffu-
sion. Of considerable importance, but very difficult,
is the  determination of the path or trajectory of
the "puff."  This is  most important if concentra-
tions are to be determined at specific points.  Deter-
mining the trajectory is of less importance if knowl-
edge of the magnitude of the concentrations for
particular downwind distances or travel times is
required without the need to know exactly  at what
points  these concentrations occur. Rewriting Sut-
ton's (1932)  equation (13), p.  155, results  in an
equation that  may be used for estimates of concen-
tration downwind from a release from height, H:
     (x,y,0;H)
                                 exp
                                          (5.21)
   The symbols have the usual meaning, with the
important exceptions that QT represents the total
mass of the release and the a's are not those eval-
uated with respect to the dispersion of a continuous
source at a fixed point in space.

   In  Eq. (5.21) the -
10
4
1.3
"z
15
3.8
0.75

-------
Gifford,  F.  A.,  1959:  Computation of pollution
   from several sources.  Int. J.  Air Poll., 2,  109-
   110.

Gifford, F. A., 1960a:  Atmospheric dispersion cal-
   culations using the generalized Gaussian plume
   model.  Nuclear Safety, 2, 2, 56-59, 67-68.

Gifford, F. A., 1960b:  Peak  to average concentra-
   tion ratios according to a  fluctuating plume dis-
   persion model. Int. J. Air Poll., 3, 4, 253-260.

Hewson, E. W., and G. C. GUI, 1944:  Meteorolog-
   ical investigations in Columbia River  Valley
   near Trail, B. C., pp 23-228 in Report submitted
   to the Trail Smelter Arbitral Tribunal by R. S.
   Dean and R. E. Swain, Bur. of Mines Bull 453,
   Washington, Govt. Print. Off., 304 pp.

Hewson, E. W., 1945: The meteorological control
   of  atmospheric pollution by  heavy industry.
   Quart. J. R. Meteorol. Soc., 71, 266-282.

Hewson, E. W.,  1955:  Stack heights required to
   minimize ground concentrations.  Trans. ASME
   77, 1163-1172.

Holland, J. Z.,  1953:  A meteorological survey of
   the Oak Ridge area, p.  540. Atomic Energy
   Comm., Report  ORO-99, Washington,  D. C.,
   584 pp.
Nonhebel, G., 1960:  Recommendations on heights
   for new industrial chimneys.  J.  Inst. Fuel, 33,
   479-513.

Pooler,  F., 1965:  Potential dispersion  of plumes
   from large power plants.  PHS Publ. No. 999-
   AP-16, 1965. 13 pp.

Singer, I. A., 1961: The relation between peak and
   mean concentrations.  J. Air Poll. Cont. Assoc.,
   11, 336-341.

Singer, I. A., K. Imai, and R. G. Del Campos, 1963:
   Peak to mean pollutant concentration ratios for
   various terrain and vegetation cover. J. Air Poll.
   Cont. Assoc., 13,  40-42.

Slade, D. H., 1965:  Dispersion estimates from pol-
   lutant releases  of a few seconds to 8 hours in
   duration. Unpublished Weather Bureau Report.
   Aug. 1965.

Stewart, N. G.,  H. J. Gale, and R. N. Crooks, 1958:
   The atmospheric diffusion of gases  discharged
   from the chimney of the Harwell Reactor BEPO.
   Int. J. Air Poll.,  1, 87-102.

Sutton, O. G., 1932:  A theory of eddy diffusion in
   the  atmosphere.  Proc.  Roy. Soc.  London,  A,
   135, 143-165.

Taylor, G. I., 1915:  Eddy  motion in the atmos-
   phere. Phil. Trans. Roy. Soc., A, 215, 1-26.
 42
        ATMOSPHERIC DISPERSION ESTIMATES

-------
              Chapter  6 — RELATION TO OTHER  DIFFUSION  EQUATIONS
   Most other widely used diffusion equations are
variant forms of the ones presented here.  With re-
spect to ground-level concentrations from an ele-
vated source  (Eq. 3.2):
   x (x,y,0;H) =
                    Q
                 7T <7y
                       U
                          exp  —
   -[--H-f-Vl
                                         (3.2)
Other well-known equations can be compared:
Bosanquet and  Pearson  (1936):
                      Q
   X (x,y,0;H) - —=
                      pq x2 u
                              exp I  —
                                         (6.1)

where p and q are  dimensionless diffusion coeffi-
cients.
Sutton (1947):

   X (x,y,0;H) =
                      2 Q
                  7T Cy Cz X2-" U
                               exp
              H2  \]
              C,2  J]
M
                                         (6.2)
where n is a dimensionless constant and Cy and Cz
are diffusion coefficients in m"/2.

Calder (1952):

   X (x,y,0;H) =
                     Q  u
                  2 k2 a vx2 x2
                              exp I —
      u
                                       k vx x
                                         (6.3)
where a = —7, the ratio of horizontal eddy velocity
to vertical eddy velocity, k is von Karman's con-
                                         k u
stant approximately equal to 0.4, and vx =	TT~
                                       i  {   \
where z0 is a roughness parameter, m.         '~z7'
                  NOTE:  Calder wrote the equation for the con-
               centration at (x, y, z) from a ground-level source.
               For Eq. (6.3) it is assumed that the concentration
               at ground level from an elevated source is the same
               as the  concentraton at an elevated point from  a
               ground-level source.

                  Table 6-1 lists the expressions used in  these
               equations that are equivalent to ay and 
-------
                             Chapter  7 — EXAMPLE PROBLEMS
   The following 26 example problems and  their
solutions illustrate the application of most of the
techniques and equations presented  in this work-
book.

PROBLEM 1:   It  is  estimated  that a  burning
   dump  emits  3 g sec"1 of oxides of  nitrogen.
   What is the concentration of oxides of nitrogen,
   averaged over approximately 10 minutes,  from
   this source directly downwind at a distance of
   3 km on an overcast night with wind speed of
   7 m sec"1?  Assume this  dump to be a point
   ground-level source with no effective rise.
SOLUTION:  Overcast  conditions  with  a  wind
   speed of 7 m sec"1 indicate that stability class D
   is most applicable (Statement, bottom of Table
   3-1). For x = 3 km and stability D, 
-------
   level concentration occur and what is this con-
   centration on an overcast day with wind speed
   4 m sec"1?
SOLUTION:   On  an overcast  day  the stability
   class would be D.  From Figure 3-9 for D sta-
   bility and H of 150 m, the distance to the point
   of maximum  ground-level concentration  is 5.6
   km, and the maximum xu/Q is 3.0 x  10~6.

           3.0 x 1Q-" x 151
   Xmai —         4

        = 1.1 x 10-" g m~3

PROBLEM 6:  For the conditions given in prob-
   lem 4, draw a graph  of ground-level  centerline
   sulfur dioxide concentration with distance from
   100 meters to 100 km. Use log-log graph paper.
SOLUTION:   The frontal inversion limits the mix-
   ing to L = 1500 meters. The distance at which
   az = 0.47 L =  705 m is XL  = 5.5 km. At dis-
   tances less than this, Eq. (3.3) is used to calcu-
   late concentrations:
   x (x,0,0;H) =
                     Q
                  7T 
-------
E 3*
   10"
          -400
                 -200      0     +200
                 CROSSWIND DISTANCE (y), m
                                       + 400
Figure 7-2.   Concentration as a function of crosswind
               distance (Problem 7).

   The values necessary to determine the isopleth
   half widths, y, are given in Table 7-3.

    Table 7-3   DETERMINATION OF ISOPLETH WIDTHS
                   (PROBLEM 8)
x,
km
0.5
0.8
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
(Ty,
m
83
129
157
295
425
540
670
780
890
980
X (centerline),
g m~3
3.8 x 10-5
2.3 x 10-4
2.8 x 10-*
1.4 x 10-*
7.1 x 10~5
4.0 xlO-5
2.4 X 10-5
1.8 x 10-=
1.4 x 10-5
1.1 x 10-5
X (isopleth)
X (centerline)
0.263
4.35 x 10-2
3.53 x 10-2
7.14 xlO-2
1.42X10-1
0.250
0.417
0.556
0.714
0.909
y/,y
1.64
2.50
2.59
2.30
1.98
1.67
1.32
1.08
0.82
0.44
y,
m
136
323
407
679
842
902
884
842
730
432
   The orientation  of the x-axis  will be  toward
   225° close to the source, curving more  toward
   210° to 215° azimuth at greater distances be-
   cause  of the  change of wind  direction with
   height. The isopleth is shown in Figure 7-3.

   Since  the isopleth  approximates an ellipse, the
   area may be estimated by -n  ab where a is the
   semimajor axis and b is the semiminor axis.
       a =
            8600 — 350
                         == 4125m
       b = 902
   A (m2) = TT (4125) (902)
       =  11.7 x 106 m2
   or A = 11.7 km2
                                                                                                 SOURCE
                               10'
                                  gm"
                                                     Figure 7-3.  Location of the  1(T5 g m
                                                                      pleth (Problem 8).
                                   ground-level  iso-
                                                     PROBLEM 9:  For the conditions given in problem
                                                        4, determine  the  profile  of  concentration with
                                                        height from ground level to  z = 450 meters at
                                                        x = 1 km, y  = 0 meters, and draw a graph of
                                                        concentration against height above ground.
                                                     SOLUTION:  Eq. (3.1) is used to solve this prob-
                                                        lem. The exponential involving y is  equal to 1.
                                                        At x = 1 km, o-y = 157 m, 
-------
   Table 74   DETERMINATION OF CONCENTRATIONS FOR
            VARIOUS HEIGHTS (PROBLEM 9)
      b.
                    d.
                            e.
f.
                                            g.
I Jlexp [--f (^)1±t>t
   a»   I    \ "" / I °»
                               'z+H
  c. + e.
0—1.36
30—1.09
60—0.82
90—0.55
120—0.27
150
180
210
240
270
300
330
360
390
420
450
0.0
0.27
0.55
0.82
1.09
1.36
1.64
1.91
2.18
2.45
2.73
0.397
0.552
0.714
0.860
0.964
1.0
0.964
0.860
0.714
0.552
0.397
0.261
0.161
0.0929
0.0497
0.0241
1.36
1.64
1.91
2.18
2.45
2.73
3.00
3.27
3.54
3.82
4.09
4.36
4.64
4.91
5.18
5.45
0.397
0.261
0.161
0.0929
0.0497
0.0241
1.11 x
4.77 x
1.90 x
6.78 x
2.33 x
7.45 x
2.11 x
5.82 x
1.49 x
3.55 x

io-2
ID"3
io-3
io-4
io-4
10~5
io-5
io-6
io-6
io-7
0.794
0.813
0.875
0.953
1.014
1.024
0.975
0.865
0.716
0.553
0.397
0.261
0.161
0.093
0.050
0.024
2.78 x
2.85 x
3.06 x
3.34 x
3.55 x
3.58 x
3.41 x
3.03 x
2.51 x
1.94 x
1.39 x
9.14x
5.64 x
3.26 x
1.75 x
8.40 x
IO-4
in-4
io-4
IO-4
io-4
IO-4
io-4
io-4
10~4
in-4
io-5
IO-5
io-5
in-5
in-6
   These values are plotted in Figure 74.

   500
   400 -
   300 -
  200 -
   100 -
     010
            10'*     2xlO'4"    3x|0'4
                CONCENTRATION, g m-3
                                     4x10'
Figure 7-4.  Concentration as a function of height (Prob-
                     lem 9).
   Verifying:

   x (x,0,0)  =
                   Q
                 TT Oy  = 520 m., and
                    
-------
   
-------
    maximum xu/Q as a function of H and stability
    from Figure 3-9  and multiplying  by the appro-
    priate Q/u.  The computations are summarized
    in Table 7-6, and plotted in Figure 7-5.
5 iir*
  10-*
                            I  I
      0.5
                        J	LJ	L
                     2    3457
                   WIND SPEED, m sec'1
                                    10
                                           20
Figure  7-5.
 Tabla 7-6
 Maximum concentration  as a function  of
   wind speed (Problem 14).

MAXIMUM CONCENTRATION AS A FUNCTION OF
   WIND SPEED (PROBLEM 14)
Stability u,
Class m sec"1
B 0.5
1.0
1.5
2
3
5
7
D 0.5
1.0
1.5
2
3
5
7
10
20
H,
m
142.2
86.1
67.5
58.1
48.7
41.3
38.0
127.6
78.8
62.6
54.4
46.3
39.8
37.0
34.9
32.4
X^a,
8.0 x 10-6
2.0 x 10-=
3.1 x 10~°
4.1 x 10-5
5.7 x 10-5
7.8 x 10-=
8.7 x 10-=
4.4 x 10-°
1.42x10-°
2.47x10-°
3.5 x 10-r'
5.1 x 10-°
7.3 x 10-°
8.2 x 10-5
9.4 x 10-=
1.1 x 10-4
Q/u,
g m-i
144
72
48
36
24
14.4
10.3
144
72
48
36
24
14.4
10.3
7.2
3.6
Xmax'
g m~3
1.15 xlO-3
1.44 x 10-3
1.49xlO-3<-
1.48 x 10-3
1.37 x 10-3
1.12 xlO-3
8.96 x 10-4
6.34 x lO"4
1.02 x 10-3
1.19 x 10-3
1.26 x 10-3<-
1.22 x 10-3
1.05 x 10-3
8.45 x 10-4
6.77 x 10-4
3.96 x 10-4
    The wind speeds that give the highest maximum
    concentrations for each stability are, from Fig-
    ure 7-5: B 1.5, D 2.0.

PROBLEM 15:  A proposed  pulp processing plant
    is expected to emit %  ton per day of hydrogen
    sulfide from a single stack. The company prop-
    erty  extends  a  minimum  of 1500 meters from
    the proposed location.  The  nearest  receptor
                                             is a small town of 500 inhabitants 1700 meters
                                             northeast of the plant.  Plant managers have
                                             decided  that  it  is  desirable  to  maintain
                                             concentrations below 20 ppb  (parts per billion
                                             by volume), or approximately 2.9 x 10~5 g m"3,
                                             for any period greater than 30 minutes.  Wind
                                             direction frequencies indicate that winds blow
                                             from the proposed location  toward this town
                                             between  10 and 15 per cent of the time.  What
                                             height stack should be  erected?  It is assumed
                                             that a design wind speed of 2 m sec"1 will be
                                             sufficient, since the effective stack rise will be
                                             quite great with  winds less  than 2  m  sec"1.
                                             Other than this  stipulation,  assume that the
                                             physical  stack height and effective stack height
                                             are  the  same, to  incorporate a slight safety
                                             factor.
                                                     SOLUTION:  The source strength is:
                                             Q =
                                                              1000 Ib day-1 x 453.6 g Ib
                                   = 5.25 g sec
              86,400 sec day
   FromEq. (4.2):
           0.117 Q  _   0.117 (5.25)
   ^ CTz ~   xa u    ~  (2.9 x 10-5) 2
        == 1.06 x 104 m2
   At a design distance of 1500 meters (the limit
   of company property), o> 
-------
   AH
33.4
 u
33.4
 u
102
 u
                [1.5+ (2.46) 0.256 (2.44)]


                (1.5 + 1.54)
                                                                            60 sec min
   The relation between cry az and u is:
           0.117 Q     0.117 (5.25)    2.12 x 104
                       2.9xlO"5u
                                          u
   The required computations using Figure 4-1 are
summarized in Table 7-7:
   Table 7-7   REQUIRED PHYSICAL STACK HEIGHT AS A
        FUNCTION OF WIND SPEED (PROBLEM 16)
u, AH,
m see"1 m
0.5
1.0
1.5
2.0
2.5
3.0
5.0
7.0
10.0
15.0
204
102
68
51
41
34
20
15
10
7
CTy CTZ,
m2
4.24 x
2.12 x
1.41 x
1.06 x
8.48 x
7.06 x
4.24 x
3.03 x
2.12 x
1.41 x
104
10*
10*
10*
103
103
103
103
103
103
Stability to
Give 
-------
PROBLEM 19:  At  a point  directly downwind
   from a ground-level source the 3- to 15-minute
   concentration is estimated  to  be 3.4 x  10"3 g
   m"3. What would  you estimate the 2-hour con-
   centration to be  at  this  point,  assuming no
   change in stability or wind  velocity?

SOLUTION:   Using  Eq.  (5.12) and letting k = 3
   min, s = 2 hours, and p = 0.2:
                        3.4x10
    40°
    3.4 x IP"3
      2.09
                      (3.4 x 10-3)
                         = 1.6 x 10"3 g
   Letting k 15 min, s = 2 hours, and p = 0.17
   X 2 ..our =
                        3-4 x 10~3
- -£rn-  (3-4

    3.4 x IP"3
~    1.42
                         = 2.4 x 10"3 g nr"
   The 2-hour  concentration is estimated to be
   between 1.6 x 10"3 and 2.4 x 10"3 g m"3.

PROBLEM 20:  Two sources of SO2 are shown as
   points A  and B in Figure  7-6.  On a sunny
   summer afternoon the surface wind is from 60°
   at 6 m sec"1.  Source A is a power plant emitting
   1450 g sec"1 SO2 from two stacks whose physical
   height is 120 meters and whose AH,  from  Hol-
   land's equation, is AH (m) = 538 (m2 sec^/u
   (m sec"1).  Source B is a refinery emitting 126 g
   sec"1 SO2 from an effective height of  60 meters.
   The wind measured at 160 meters on a nearby
   TV tower is  from 70° at 8.5 m sec"1.  Assuming
   that the mean direction of travel of both plumes
   is 245°, and there are no other sources of SO2,
   what is the concentration of SO2 at the receptor
   shown in the figure?

SOLUTION:   Calculate  the effective  height  of
   Source  A using the observed wind speed at 160
   meters.
    AH
          538
    = 63.3
           8.5
   HA = 120 + 63 = 183 m
   QA = 1450 g sec"1
   HB = 60 m
   QB = 126 g sec"1

   For a sunny summer afternoon with wind speed
   6 m sec"1, the stability class to be expected is C.
   The equation to be used is Eq. (3.2):
                                                                            SOURCE A
                                                                             i=24.6 In.
                                                                             y= 8.4 km
                                                    RECEPTOR x.
                                          Figure 7-6.  Locations of sources and receptor (Problem
                                                               20).
                                                         (x,y,0;H) =
                                                                         Q
                                                                      7T 
-------
PROBLEM 21:  A stack 15 meters high emits 3 g
   sec"1  of a particular air pollutant.  The sur-
   rounding terrain is relatively flat except for a
   rounded hill about 3 km to the northeast whose
   crest  extends 15 meters  above the stack top.
   What is the highest 3- to 15-minute concentra-
   tion of this pollutant that can  be expected  on
   the facing slope of the hill on a clear night when
   the wind is blowing directly from the  stack
   toward the  hill at 4 m sec"1? Assume that AH
   is less than  15  m.   How much does the wind
   have to shift so that concentrations at this point
   drop below  10"7 g m"3?

SOLUTION:   A clear night with  4  m sec"1 indi-
   cates class E stability.  Eq.  (3.4) for ground-
   level concentrations from a ground-level source
   is most applicable  (See  Chapter 5).  At 3 km
   for class E,  ay = 140 m, 
-------
   that it is 1600 on a sunny fall afternoon. What
   is the concentration directly downwind from one
   end of the source?
SOLUTION:   Late afternoon at this time of  year
   implies slight insolation, which with 3 m sec"1
   winds  yields stability class C.  For C stability
   at x = 400 m, a? = 45 m, az = 26 m.
         Q
               90
   M     150     150
   Eq.  (5.20) is appropriate.
                      = 0.6 g sec"1 m 1
     (x,0,0;0)
                           fp,
                  2q       I     	1_
               \/2ir trz U   I      \/2~Jr
                         J Pi
exp (—0.5 p2) dp
                 —75
               45
                            i «7  n -     -
                         ~"L67' P2 - ~   -
                                               -
                                             45
      = +1.67
   x (400,0,0;0) =
                     2 (0.6)
                             r+,67

                             I         V2^
                            J  —1.67
   exp (—0.5 p2) dp

      = 6.14 x 10~3 (0.91)

      = 5.6 x 10~3 g m"3

   For a point downwind of one of the ends of the
   line:
                                +3.33

                                   '+3.33
                                J
   _         y      150
Pi — u, P« — — -   45
X (400,0,0;0) = 6.14 x 10~;


exp (—0.5 p2) dp

    = 6.14 x 10-3 (0.4995)

    = 3.1 x 10-3 g m-3
PROBLEM 25:   A core melt-down of a power re-
   actor that has been operating for over  a year
   occurs  at  0200, releasing  1.5  x 10e curies  of
   activity (1 second after the accident) into the
   atmosphere  of the  containment vessel.  This
   total activity can be expected to decay according
   to
               ; is estimated that about 5.3 x 104
   curies of this activity is due to iodine-131, which
   has a half-life of 8.04 days.  The reactor building
   is hemispherically shaped with  a  radius of 20
   meters. Assume the leak rate of the building is
   0.1%  day"1.
                                                     The accident has occurred on a relatively clear
                                                     night with wind speed 2.5 m sec"1.  What is the
                                                     concentration in the air 3 kilometers directly
                                                     downwind from the source at 0400 due to  all
                                                     radioactive material?  due to iodine-131?

                                                  SOLUTION:   Source strength =  leak rate x ac-
                                                     tivity (corrected for decay)
                                                     Leak rate =
                                                                     0.001 day"1
                                                                   86400 sec day"1
                                                         = 1.157 x 10~8 sec"1

                                                     Source strength of all products

                                                     QA (curies sec"1) =  1.157 x lO"8 (1.5 x 10s)
                                                           [t(aec)  ]
                                                           t0 (sec)  J
                                                                 —0.2
                                                        t0 (sec)

                                                         = 1.74 x 10-2
                                                                      (-B
                                                                                —0.2
                                                      To determine decay of materials with the half-
                                                      rt   •        14.- i  u      ( — 0.693 t\   ,
                                                      life given, multiply by exp I - = - J where t
                                                      is time and L is half-life.  \         /

                                                      Source strength of I131.

                                                      Qi (curies sec"1) = 1.157 x 10~8 (5.3 x 104) exp
                                                        — 0.693 t
                                                     For I131 L = 6.95 x 105 sec
                                                      For a clear night with wind speed 2.5 m sec""1,
                                                      class F applies.  Approximate  the spreading at
                                                      the reactor shell by 2.15 o-y0 = 2.15 o-z0 = the
                                                      radius of the shell = 20 m 
-------
      = 2.7 x 10~8 (1.0)  The decay of I131 is insig-
   nificant for 2 hours

   Xi = 2.7 x 10~8 curies m~3

PROBLEM 26:   A spill estimated  at  2.9  x 10"
   grams  of unsymmetrical  dimethyl  hydrazine
   occurs at 0300 on a clear night while a rocket
   is being fueled.  A circular area  60  meters in
   diameter built around the launch pad  is revetted
   into squares  20 feet on a side to confine to as
   small an area as possible any spilled toxic liquids.
   In this spill only one such 20- by 20-foot area is
   involved.  At the current  wind  speed of 2 m
   sec"1, it is estimated  that the evaporation rate
   will be 1100 g sec"1. The wind direction is pre-
   dicted to be from 310° ± 15°  for the  next hour.
   Table 7-8 gives the emergency tolerance limits
   for UDMH vapor.

  Table 7-8   EMERGENCY TOLERANCE  LIMITS FOR UDMH
           VAPOR VERSUS EXPOSURE TIME
                                                       Table 7-9   DETERMINATION  OF CONCENTRATION AS A
                                                              FUNCTION OF DISTANCE (PROBLEM 26)
Time,
minutes
5
15
30
60
Emergency Tolerance
Limits, g m~3
1.2 x 10-1
8.6 x 10"2
4.9 x 10~2
2.5 x 10-2
   What area should be evacuated?

SOLUTION:   From Table 3-1, the stability class
   is determined to be Class F.  This is not a point
   source but a small area source. Allowing 4.3 (ry0
   to equal the width of the wetted area, 6.1 meters
   (20 feet),  CTyo = 1.4  meters.  In attempting to
   determine  the virtual distance, x}, it is found to
   be less than 100 meters, and will be  approxi-
   mated by 40 meters.  The release will take:

      2.9xlO°g      0-.  1A,       ...
  —=——^-^	—— = 2.64 x 103 sec = 44 mm.
   1.1 x 103 g sec"1

   Therefore  the concentration for an exposure
   time of 1  hour  (2.5  x 10~2  g m~3) is  of main
   concern.

   The equation for calculation of downwind  con-
   centrations is Eq. (3.4):
   x(x,0,0;0) =

   Of X + Xy.
                    Q
                 7T 0V  is a function
X,
km
0.1
0.3
0.6
1
3
6
10
aw
m
2.3
5.6
9.7
14
27
37
47
x + xy,
km
0.14
0.34
0.64
1.04
3.04
6.04
10.04
oy
m
5.5
12.5
22
35
93
175
275
X-
g m~3
13.9
2.5
8.2 x 10-1
3.6 x 10~l
7.0 xlO-2
2.7 x 10~2
1.4 x 10-3
                                                        These values of x are graphed as a function of x
                                                        in  Figure 7-7. The  downwind  concentration
                                                        drops below the critical value of 2.5 x 10~2 at a
                                                        distance of 6.5 km.
100
ft
1
<*• 10
o
a.
o
z 1
1—
<
oe
t—
z
UJ
<«t
Z
Q _|
io-2
0

.... _



\
1 — ^~
^!

















	






\^
X
^























^
s























s
















































^























^
























*
























*























w
\
s























s
— ^S

























v
























\

















































V























n
























N^
1 1 II
   Values of the parameters and of x are given in
   Table 7-9.
                     DISTANCE, km

Figure 7-7. Concentration of UDMH as a function of down-
            wind distance (Problem 26).
    Calculated  widths within a given isopleth  are
    summarized in Table 7-10.

    The maximum  width of the area encompassed
    by an isopleth is about 140 meters from  the
    downwind position.  Since the wind  direction is
    expected to be from 310° ± 15°, the sector at an
    azimuth of 115° to 145° plus a  140-meter rectan-
    gle on either side should be evacuated.
    See  Figure  7-8.
Example Problems
                                                                                                   55

-------
    Table 7-10   DETERMINATION OF WIDTHS WITHIN
                  ISOPLETHS (PROBLEM 26)
x,
km
0.1
0.5
1.0
2.0
3.0
4.0
5.0
6.0
x + xy,
km
0.14
0.54
1.04
2.04
3.04
4.04
5.04
6.04
<7V'
m
5.5
19
35
66
93
120
149
175
X (centerline),
g m-:t
13.9

3.6
1.3
7.0
1.1
xlO-'
xlU-1
x 10"^
4.8 x 10--
3.5
2.7
x 10--
x 10~-
X (isopleth)
y
X (centerline) aj.
1.8
2.27
6.94
1.92
3.57
5.20
7.14
9.26
x
x
X
X
X
X
X
X
10-
10-'
10--
10-'
10-1
10-'
10-1
10-1
3.55
2.75
2.31
1.82
1.44
1.14
0.82
0.39
y,
m
20
52
80
120
134
137
122
68
                                                                  SCALE, km
                                                                                        145"
                                                                     1
                                                        Figure 7-8.   Possible positions of the 2.5 x 10~2 g  m"
                                                            isopleth and the evacuation area (Problem 26).
56
                                                                ATMOSPHERIC  DISPERSION  ESTIMATES

-------
                                APPENDICES
339-901 O - 69 - 5

-------
Appendix 1:  ABBREVIATIONS  AND SYMBOLS

Abbreviations
cal    calorie
g      gram
°K    degrees Kelvin
m     meter
mb    millibar
sec    second

Symbols
a    ratio of horizontal eddy  velocity to vertical
     eddy velocity
cp   specific heat at constant pressure
Cy   Sutton horizontal dispersion parameter
Cz   Sutton vertical dispersion parameter
d    inside stack diameter at stack top
DT (x,y,0;H)    Total dosage
e    2.7183, the base of natural logarithms
f (G,S,N)  frequency of wind direction for a given
           stability and wind  speed class
h    physical stack height
hi   height of the base of an inversion
H   effective height of emission
H,,   effective height  of emission  for  a particular
     wind speed
k    von Karman's constant,  approximately equal
     to 0.4
K   eddy diffusivity
L    two uses:  1. the height of an air layer that is
                 relatively stable compared to the
                 layer beneath it; a lid
               2. the  half-life  of a  radioactive
                 material
n    Sutton's exponent
N   an index for wind speed class
p    three uses: 1.  Bosanquet's horizontal  disper-
                   sion parameter
                2.  atmospheric pressure
                3.  a  dummy variable in  the equa-
                   tion for a Gaussian distribution.
q    two uses:  1. Bosanquet's  vertical  dispersion
                 parameter
               2. emission rate per length of a line
                   source
Q   emission rate of a source
Q r   total emission  during an entire release
R   net rate of sensible heating of an air column
     by solar radiation
s    the length of the edge of a square area source
S    an index for stability
tk   a short time period
t,,,
Ta
TK
u
UN
v'
V«
Vx
W'
X
XL

Xv
y
z
z,,
80
8z~
AH

o
PA
time required for the mixing layer to develop
from the  top of the stack  to  the top of  the
plume
a time period
ambient air temperature
stack gas temperature at stack top
wind speed
a mean wind speed for the wind speed class N.
horizontal eddy velocity
stack gas velocity at the stack top
a velocity used by Calder
vertical eddy velocity
distance downwind  in  the  direction  of  the
mean wind
design  distance, a particular  downwind  dis-
tance used for design purposes
the distance at which crz = 0.47L
a virtual distance so  that 
-------
0    the angle between  the wind direction  and a
     line source
X    concentration
X<;\vi crosswind-integrated concentration
X,,   a ground-level  concentration  for  design pur-
     poses
XK   inversion break-up fumigation concentration
Xk   concentration measured over a sampling time,
     tk
XIIHIX maximum  ground-level centerline concentra-
     tion with respect to downwind distance
x»   concentration measured over a sampling time,
     ts

X    relative concentration
y)Z;H)   concentration at the point (x, y, z)
             from an elevated source with effective
             height, H.
x (X>Q)   the long-term average  concentration at
         distance x, for a direction e from a source.
60
       ATMOSPHERIC DISPERSION ESTIMATES

-------
  Appendix 2:   CHARACTERISTICS OF THE
          GAUSSIAN DISTRIBUTION

   The Gaussian or normal distribution can be de-
picted by the bellshaped curve shown in Figure A-l.
The equation for the ordinate value of this curve is:

               exp  I	±_
                                         (A.I)
Figure A-2 gives the ordinate value at any distance
from the center of the distribution  (which occurs
at x). This information is also given in Table A-l.
Figure A-3 gives the area under the Gaussian curve
from — ^ to a particular value of  p where p =
This area is found from Eq. (A.2):


Area (— x  to p) =
                                                      exp (—0.5 p-) dp
                                                                           r    -+
                                                                           I        V2^
                                                                           I   	 -v.
                                      (A.2)
                                                      Figure A-4 gives  the area under  the Gaussian
                                                   curve from —p to +p.  This can be found from Eq.
                                                   (A.3):
                                                      Area (—p to +p) =


                                                      exp (—0.5 p2)  dp
                    r -j-
                    /       V2^
                   J  —P
                                       (A.3)
               -3
                              Figure A-l.  The Gaussian  distribution  curve.
Appendix 2
                                          61

-------
         0.01
           0.0  0.2  0.4  0.6  0.8  1.0   1.2   1.4  1.6   1.8  2.0   2.2   2.4  2.6   2.8  3.0  3.2   3.4  3.6  3.8   4.0
                             Figure  A-2.   Ordinate  values  of the Gaussian  distribution.
62
ATMOSPHERIC DISPERSION ESTIMATES

-------

4.0
3.5
3.0
2.5
2.0
1 5
1.0
0.5
0
-0 •>
-1.0
-1.5
-2.0
-2.5
-3.0
-3 5
-4.0














—I- .
_|_.

I
c





1 —





f





f*



n™

„



:-










EEE-;::::- -:;:;|;:;;:
" ::: ::::::: : x. :: . j :. :_:::
	 ;:; 	 __ 	 .?,i.
	 	 	 _ , i . . . — .
~ 	 	 " ji ' 	 ""
i 	 . . _ ... 	 .
_ ^ _ — 	 	 ^ 	 . 	 i — .



i — — '~~T- •• '^T 	
™;;;E|:-E|;;:;|=EE
wiiiwf
— — . 	 "ft" """" 	 ' 	
|::::::::::::|:::::::::|z
r-- -t •-.:------- ~ ---;>!i--
	 ....... ft 	
:::::;•!!:::::: .::!:::::::--
::::::::::::::: [::::::: :±:i a




X





	 ;,«





^mm
:::;«f?





rf*





'




L(t
~~ i1'
^- 1-
-fri
F- frt
= (*




•^1-

.__



l*i-
	
~
—
|—


           0.01     0.1    0.5  1   2    5   10    20     40




                                             r+P  i       i
                                                 -£=• exp (
  60     80   90   95   98  99





0.5  p2) dp
                                                                                              99.8    99.99
                      Figure A-3.  Area under the Gaussian distribution curve from — <*>  to p.
Appendix 2
                                                     63

-------
4.5

4.0
3.5
3.0
2.5
? 0
1.5
1.0
0.5
0.0
0.



01




—

-t T
::•;



O.I










__ .1*
0.5



tt^e
1 2



^
1 | | 1 1 IIIIIHIIIIIIIIIIIII mi f
-"I-:::: :::::: |: .:..
T 	 ' -tff"
	 w- 	 	 (- 	 |
= «:=!!!£: f :::::::::::|::
5 10 20 30 40 5(
f N/5? oxp
niiiiiiii' : i ;i |ii|iN|imj i j
::: ::|:-|: I,::i.±::-:-
||| j I i ;}||t[|i{j^jjW LH
:::::::::::::: tl::: ::::;--
	 	 	 ! 	 	 i 	
) 60 70 80 90 95
-0.5 p7) dp

— 	
i — ff__
— . i . _ .
	
— :::::
98 9<


. . . . _
11 —
\-.-.- —
" ~n 	 1 —
)


-
9
— tit
-1
-t1-'
— r •
~t::
-f::
- )|r
NN
-; *
- i
r- f
I
9.8

-._
<1_
- "1" JJ
•~-t-\
J-j-
r


=
... .
—
99
                 Figure A-4.  Area under the Gaussian distribution curve between —p and +p.
64
ATMOSPHERIC  DISPERSION ESTIMATES

-------
                          Appendix 3:   SOLUTIONS TO EXPONENTIALS

                             Expressions of the form exp  [—0.5 A2]  where
                          A is H/az or y/cry frequently must be  evaluated.
                          Table A-l gives B as a function of A where B = exp
                          [—0.5 A-']. The sign and digits to the right  of the
                          E are to  be considered as an exponent of 10.  For
                          example,  if A is 3.51, B is given as 2.11E  — 03
                          which means 2.11 x 10~3
Appendix 3                                                                                       65

-------
a>
O5
Table  A-l   SOLUTIONS TO EXPONENTIALS B = exp [-0.5A*]
          The notation 2.16 E-l means 2.16 x  1Q-1
g
o
o
o
55
H
i
w
3
H
W
CA
A

0.00
0.10
0.20
0.30
0.40
0,50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3.00
3.10
3.20
3.30
3.40
3.50
3.60
3.70
3.80
3.90
4.00
4.10
4.20
4.30
4.40
4.50
4.60
4.70
4.80
4.90
0.00
B
1.00E 0
9.95E .1
V.80E .1
9.5AE -1
9.23E -1
B.8H -1
a.s^E -l
7.8?E -1
7.2AE -1
6.67E -1
6.0?E -1
5,4ftt -1
4.87E -1
4.3PE -1
4.75E -1
3.21E -1
2.7SE -1
2.3ftE -1
1.9BE -1
1.6=C -1
l.3*E -1
1.10E -1
8.89E -2
7.10E -2
5.61E -2
4,?ot: -2
3.41E -?.
i,M£ -2
1.9P.E -2
1.49L -2
unt -2
S.loE -3
5.9RE -?
<..32E -3
3.09E -3
2. lot -3
1.53E -3
1.07E -3
7.3?E -4
«t.98E -4
3.3fcE -4
2.24E -4
1.4RE -4
q.fc*>B -5
6.2SE -b
4.01E -5
2.54E -5
1.60E -5
9.93E -ft
6. lib -6
0.01

l.OOF. 0
9.94E -1
9.78E -1
9.S3E -1
9.19F -1
8.78E -1
R.30E -1
7.77E -1
7.20F. -1
6. ME -1
6. OIF -1
•J.40F. -1
4. s IE -i
4.24E -1
3.70E -1
3.20F. -1
2.74F .1
2.32E -1
1.94E -1
1.61E -1
1.33E -1
1.08F -1
R.7QF -2
*.94E -2
5.48E -2
4.29E -2
3.32E -2
2.?4E -2
1.93F -2
1.45F -2
l.OBE -2
7.94E -3
5.79F -3
4.18E -3
2.99F -3
2. HE -3
1..48F. -3
1.03? -3
7.05F -4
4.79F -4
3.22E -4
2.15F -4
1.42E -4
E -5
5.98E -5
3.83E -5
2.43E -5
l.SZE -5
9.46F -6
5.82E -6
0.02

10.00E -1
9.93E -1
9.76E -1
9.50E -1
9.1*E -1
8.74E -1
8.25E -1
7.72E -t
7.15E -1
6.5SE -1
5.94E -1
5.34E -1
4.7?£ -1
4. IRE -i
3.65E -1
3.1?E -1
2.69E -1
2.2PE -1
1.91E -1
1.5PE -1
1.30E -1
1.06E -1
8.51E -2
6.7PE -2
5 3^ E£ ~2
4.19E -2
3.23E -2
2.47E -2
1.88E -2
1.41E -2
1.05E -2
7.7^E -3
5.60E -3
4.04E -3
2.8°E -3
2.04E -3
1.43E -3
9.80£ -4
6.7°E -4
4.61E -4
3.10E -4
Z.Oftf -4
1.36E -'+
8 • BftE -">
S.72E -5
3.66E -5
2.3?E -5
1.45l£ -5
9.02E -6
5.54E •*>
0.03

10.00E -1
9.92E -1
9.74E -1
9.47E -1
9.12E -1
8.69E -1
H.20E -1
7.66E -1
7.09E -1
&.49E -1
S.88E -1
S.28E -1
".69E -1
4.13E -1
3.60E -1
3.10E -1
2.65E -1
2.24E -1
1.87E -l
1.55E -1
1.27E -1
1.04E -1
H.32E -2
h.62E -2
5.22E -2
4.07E -2
3.15E -2
H.41E -2
1.82E -2
1.37E -2
1.02E -2
'.46E -3
5.43E -3
3.91E -3
2.79E -3
1.97E -3
1.38E -3
9.53E -4
6.53E -4
4.43E -4
2.07E -4
1.98E -4
1.30E -4
«.49E -5
5.48E -5
3.50E -5
Z.21E -5
1.39E -5
^.59E -6
S.28E -6
0.04

9.99E .1
9.90E -1
'J.72E -1
9.44£ -1
".08£ .1
«.64£ -1
8.15E -1
7.61E -1
7.03E -1
.«2E .1
•>.22£ -1
'•.64E -1
4.0HE -1
3.55E -1
3.0&E -1
2.61E -1
2.20E -)
1.84E -1
) .52E -1
1.2SE -1
J.01-E -1
^. 14£ -2
6. 476 -2
b 1 *"! F •» 2
3.97E -2
»!07E -2
2.34E -2
1.77E -2
1.33E -2
^.R'iF. -3
7.2HE -3
S.256 .3
3.78£ -3
2.69E -3
1.90E -3
1.33E -3
9.18E -4
6.28E -4
4.26E -4
Z.lftE -4
1.90E -4
1.25E -4
8.13E -5
5.^4£ .5
3.34r .5
2.11E -5
1.32E -5
H.19E -h
5.02E -6
0.05

9.99E -I
9.89E -1
9.69E -1
9.41E -1
9.04E -1
8.60E -1
8.10E -1
7.55E -1
6.97E -1
6.37E -1
5.76E -1
5.16E -1
4.58E -1
4.02E -1
3.50E -1
3.01E -1
2.56E -1
2.16E -1
1.81E -1
1.49F, -1
1.22F -1
9.91E -2
7.96E -2
6.32E -2
4.97E -2
3.87E -2
2.99E -2
2.28E -2
1.72F. -2
1.29F. -2
9.55E -3
7.00E -3
5.09E -3
3.66E -3
2.60F -3
1.83F -3
1.28E -3
8.84E -4
6.04E -4
4.09E -4
2.74K -4
1.82E -4
1.20F -4
7.78F -5
5.01E -5
3.20E -b
2.02E -5
1.26F. -5
7.80E -6
4.78E -6
0.06

9.98E -1
9.87E -1
9.67E -1
9.37E -1
9.00E -1
8.55E -I
8.04E -1
7.49E -1
6.91E -1
6.31E -1
5.70E -1
5.10E .1
4.52E -1
3.97E -1
3.45E -1
2.96E -1
2.52E -1
2.13E -1
1.77E -1
1.47E -1
1.20E -1.
9.70E -2
7.78E -2
6.17E -2

3.78E -2
2.91E -2
2.22E -2
1.67E -2
1.25E -2
9.26E -3
6.79E -3
4.92E -3
3.54E -3
2.51E -3
1.77E -3
1.23E .3
8.51E .4
5.82E -4
3.93E -4
2.63E -4
1.75E -4
1.15E -4
7.45E -5
*.79E -5
3.05E -5
1.93E -5
1.20E -5
7.43E .6
4.55E -6
0.07

9.98E -1
9.86E -1
9.64E -1
9.34E -1
8.95F. -1
8.50E -1
7.99E -1
7.44E -1
6.85E -1
6.25E -1
5.64E -1
5.04E -1
4 46E -1
3I91E -1
3.39E -1
Z.9ZE -1
Z.48E -1
2.09E -1
1.74E -1
1.44E -I
1.17E -1
9.50E -2
7.60E -2
6.03E -2
f. 7?C 9
3.68E -2
2.83E -2
2.16E -2
1.63E -2
1.22E -2
8.98E -3
6.58E -3
^.77E -3
3.42E -3
2.43E -3
1.71E -3
1.19E -3
B.ZOE -4
5.60E -4
3.78E -4
Z.53E -4
1.68E -4
1.10E -4
7.13E -5
*.53E -5
2.92E -5
1.84E -5
1.15E -5
7.08E -6
4.33E -6
0.08

9.97E -1
9.84E -1
9.62E -1
9.30E -1
8.91E -1
8.45E -1
7.94E -1
7.38E -1
6.79E -1
6.19E -1
5.58E .1
*.99E -1

3.86E -1
3.35E -1
2.87E -1
2.44E -1
2.05E -1
1.71E -1
1.41E -1
1.15E -1
9.29E -.2
7.43E -2
5.89E -2

3.59E -2
2.76E -2
2. IDE .2
1.58E -2
1.18E -2
8.71E -3
6.37E "3
4.61E -3
3.31E -3
2.35E -3
1.65E -3
1.15E -3
7.89E "*
5.38E -«
3.63E -*
2.43E -4
1.61E -4
1.05E •*
6.83E -5
4.38E -5
Z.79E .5
1.75E -5
1.09E -5
6.74E -6
4.12E -6
0.09

9.96E
9.82E
9.59E
9.27E
8.87E
8.40E
7.88E
7.3ZE
6.73E
6.13E
5.5ZE
4.93E
*.35E
3.B1E
3.30E
2.83E
2.40E
2.02E
1.68E
1.38E
1.13E
9.09E
7.27E
5.75E
4.51E
~ • J * t
3.49E
2.68E
2.04E
1.54E
1.15E
8.45E
6.17E
4.46E
3.20E
2.27E
1.59E
1.11E
7.6QE
5.18E
3.49E
2.33E
1.54E
1.01E
6.53E
4.19E
2.66E
1.67E
1.04E
6.42E
3.92E


.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
• 1
-1
.1
.2
.2
.2
,2
.2
.2
.2
.2
.2
-3
.3
.3
.3
.3
.3
.3
.4
.4
.4
.4
-4
• 4
.5
.5
.5
-5
.5
.6
.6

-------
                                                        Table A-l (continued)   SOLUTIONS TO EXPONENTIALS
a
B.

*'

w
A

5.00
5.10
5.20
5.30
5.40
5.50
5.60
5.70
5.80
5.90
6.00
6.10
6.20
6.30
6.<>0
6.50
6.60
6.70
6.80
6.90
7. 00
7.10
7.20
7.30
7.40
7.50
7.60
7.70
7.80
7.90
8.00
8. 1C
8.20
8.30
8.40
8.50
8.60
8. 70
8.80
8.90
9.00
9.10
9.20
9.30
9.40
9.50
9.60
9.70
9.80
9.90
	 0.00
B
3.7TE -6
2.25E -6
1.34E -6
7.95t -7
".6/SE -7
2.70t -7
1.5-5U -7
8.S1E -H
4.94E -8
2.76E -1*
1.52E -8
8.3?E -9
4.50E -9
*.41E -9
1.231: -9
6.60t-10
3.4RE-10
l.7ot-10
9.10E-11
4.50E-11
2.2QE-11
1.13t-ll
5;54E-12
2.68E-12
1.29E-12
6.10E-13
2.87E-13
1.34E-13
6.15E-14
7.80E-14
1.27E-14
5.66E-15
Z.51E-15
1.10E-15
4.77E-16
2.0SE-16
8.71E-17
3.67E-17
1.53t-l7
6.3IE-18

7.33E-17
3.0?E-17
1.28E-17
5.21E-13
2.15E-1S
8.69E-19
3.47E-19
1.37E-19
5.3SE-20
2.09E-20
8.02E-21
3.09E-21
1.15E-21
4.2flE-22
0.03

3.21E -6
1.9?E -6
1.15E -6
6.78E -7
3.96E -7
2.29E -7
1.31E -7
'.42E -8
4.16E -8
Z.31E -8
1.27E -8
",92E -9
3.73E .9
1.99E -9
1.05E -9
S.50E-10
2.85E-10
1.46E-10
7.42E-11
3.73E-11
1.86E-U
9.HE-12
4.46E-12
2.15E-12
1.03E-12
4.87E-13
Z.28E-13
1.06E-13
4.86E-14
Z.21E.U
9.96E-15
4.44E-15
1.96E-15
W.56E-16
3.70E-16
1.59E-16
6.72E-17
Z.82E-17
1.17E-17
4.83E-18
1.97E-18
'.93E-19
3.17E-19
1.25E-19
4.90E-20
1.90E-20
7.29E-21
Z.77E-21
1.04E-21
3.08E-22
0.0'+

3.05E .6
l.S^E -6
l.O'JE -6
6.41E -/
•i.T>£ -7
Z.17E -7
1.24E -7
7.01E -8
3.93E -8
2.13E -8
1.20E -8
->.51E -9
3.51E -9
1.87E -9
9.87E-10
5.16E-10
2.67E-10
1.37E-10
6.93E-11
3.4SE-11
1.7'E-ll
8.51E-12
4.15E-12
2.00E-12
9.55E-13
4.52E-13
2.HE-13
9.30E-14
4.50E-14
2.04E-14
9.19E-15
*.09E-15
l.POE-15
7.87E-16
3.40E-16
1.46E-16
6.17E-17
2.59E-17
1.07E-17
4.41E-18
1.30E-18
7.24E-19
2.89E-19
1.14E-19
4.46E-20
1.73E-20
S62E-21
2.51E-21
9.43E-22
3.51E-22
0.05

2.90E -6
1.74E -6
1.04f -6
6.09E -7
3.55E -7
2.05E -7
1.17P -7
6.62E -8
3.70E -8
2.0bE -8
1.13E -8
6.12E -9
3.29E -9
1.75E -9
9.25E-10
4.83E-10
2.50E-10
1.28E-10
6.47E-11
3.25E-11
1.61E-U
7.92F-12
3.86E-12
1.86E-12
8.87E-13
4.19E-13
1.96E-13
9.07E-14
4.16E-14
1.89E-14
8.48E-15
3.77E-15
1.66E-15
7.24E-16
3.13E-16
1.34E-16
5.66E-17
2.37E-17
9.83E-18
4.04E-18
1.64E-18
6.61E-19
2.63E-19
1.04E-19
4.06E-20
1.57E-20
6.01E-21
2.28E-21
8.55E-22
3.18E-22
0.06

2.76E -6
1.65E -6
9.82E -7
5.77E -7
3.36E -7
1.94E -7
1.11E -7
6.25E -8
3.49E -8
1.94E -8
1.06E -8
5.76£ .9
3.09E -9
1.65E -9
8.67E-10
4.52E-10
2.34E-10
1.19E-10
6.04E-11
3.03E-11
1.50E-11
7.38E-12
3.59E-12
1.73E-12
8.23E-13
3.88E-13
1.81E-13
8.39E-14
3.84E-14
1.74E-14
7.82E-15
3.48E-15
1.53E-15
6.66E-16
2.87E-16
1.23E-16
5.19E-17
2.17E-17
9.00E-1B
3.69E-18
1.50E-18
6.03E-19
2.40E-19
9.46E-20
3.69E-20
1.43E-20
5.46E-21
2.07E-21
7.75E-22
2.8BE-22
0.07

2.62E -6
1.57E -6
9.32E -7
5.47E -7
3.18E -7
1.83E -7
1.05E -7
5.90E -8
3.29E -8
1.82E -8
9.98E -9
5.41E -9
2.91E -9
1.55E -9
8.13E-10
4.24E-10
2.19E-10
1.12E-10
5.64E-11
2.82E-11
1.40E-11
6.87E-12
3.34E-12
1.60E-12
7.64E-13
3.60E-13
1.68E-13
7.77E-14
3.55E-14
1.61E-U
7.22E-15
3.20E-15
1.41E-15
6.13E-16
2.64E-16
1.13E-16
4.76E-17
1.99E-17
8.23E-18
3.37E-18
1.37E-18
5.50E-19
2.19E-19
8.61E-20
3.36E-20
1.30E-20
4.95E-21
1.87E-21
7.02E-22
2.60E-22
0.08

2.49E -6
1.49E -6
8.84E -7
5.19E -7
3.01E -7
1.73E -7
9.87E -8
5.57E -8
3. HE -8
1.72E -8
9.39E -9
5.09E -9
2.73E -9
1.45E -9
7.62E-10
3.97E-10
2.04E-10
1.04E-10
5.27E-11
2.63E-H
1.30E-U
6.39E-12
3.10E-12
1.49E-12
7.09E-13
3.34E-13
1.56E-13
7.19E-14
3.28E-14
1.49E-14
6.66E-15
2.95E-15
1.30E-15
5.64E-16
2.43E-16
1.03E-16
4.36E-17
1.82E.17
T.53E-18
3.08E-18
1.25E-18
5.02E-19
1.99E-19
7.84E-20
3.05E-20
1.18E.20
4.50E-21
1.70E-21
6.36E-22
2.3AE-22
0.09

2.37E -6
1.42E .6
8.38E .7
4.91E -7
2. BSE -7
1.64E .7
9.32E .8
5.25E -8
2.93E .8
1.62E .8
8.84E .9
4.78E -9
2.56E .9
1.36E .9
7.14E-10
3.71E-10
1.91E-10
9.74E.H
4.92E-11
2.46E-11
1.22E-11
5.95E-12
2.88E-12
1.38E-12
6.58E-13
3.09E-13
1.44E-13
6.65E-14
3.04E-14
1.37E.14
6.14E-15
2.726-15
1.19E-15
5.18E-16
2.23E-16
9.49E-17
4.00E-17
1.67E.17
6.89E.18
2.82E-18
1.14E-18
4.58E-19
1.82E.19
7.14E-20
2.78E-20
1.07E-20
4.08E-21
1.54E-21
5.76E-22
2.13C-22

-------
                         Appendix 4:  CONSTANTS, CONVERSION
                           EQUATIONS, CONVERSION TABLES
                       Constants
e
TT — 3 1416 *
7T
— 0 3183
— 01 5Q9
                                         27T
                              TT = 2.5066 -j= = 0.3989
                                          2
                                        —7= = 0.7979
                          (27r)3/2 = 15.75
                       Conversion Equations and Tables
                             T(°C) = 5/9 (T(°F) — 32)
                             T(°K) =T(°C) +273.16
                             T(°F) = (9/5T(°C) ) +32
Appendix 4                                                                              gg

-------
CONVERSION FACTORS - VELOCITY












.
H
g
0
^
s
H
a
o
o
M
W)
M
H
Cfl
0
2!
H
C/3
H
M
H
M
73
DESIRED

GIVEN UNITS
METERS
PER SEC
FT
PER SEC
FT
PER MIN
KM
PER HR
MIISTAT)
PER HR


KNOTS



MKSTAT)
PER DAY


TO CONVERT A
UNITS METERS
PER SEC

1.0000
E 00
3.0480
E-01
5.0800
E-03
2.7778
E-01
4.4704
E-Oi


5.1479
E-01


1.8627
E-02


VALUE FROM A GIVEN
AND BENEATH THE DESIRED UNIT.


















FT
PEP SEC

3.2808
E 00
1.0000
E 00
1.6667
E-02
9.113*
E-01
1.4667
E 00


1.6889
E 00


6.1111
E-02


UNIT TO A
NOTE THAT









FT
PER

1.9685
E 02
6.0000
E 01
1.0000
E 00
5.4681
E 01
8.8000
E 01


1.0134
E 02


3,6667
E 00


DESIRED
KM
MIN PER HR

3.6000
E 00
1.0973
E 00
1.8288
E-02
1.0000
E 00
1.6093
E 00


1.8532
E 00


6.7Q56
E-02


UNIT, MULTIPLY
MI(STAT)
PER HR

2.2369
E 00
6.8182
E-01
1.1364
E-02
6.2137
E-01
1.0000
E 00


1.1516
E 00


4.1667
E-02


THE GIVEN
KNOTS


1.9425
E 00
5.9209
E-01
9.8681
E-03
5.3959
E-01
8.6839
E-01


1.0000
E 00


3.6183
E-02


VALUE BY
MKSTAT)
PER DAY

5.3686
E 01
1.6364
E 01
2.7273
E-01
1.4913
E 01
2.4000
E 01


2.7637
E 01


1.0000
E 00


THE FACTOR OPPOSITE THE GIVEN UNITS
E-XX MEANS 10 TO THE -xx POWER.














































-------
•a
V
I
CONVERSION FACTORS
DESIRED UNITS
GIVEN UNITS
GRAMS
PER SEC
GRAMS
PER MIN
KG
PER HOUR
KG
PER DAY
LBS
PER MIN
LBS
PER HOUR
LBS
PER DAY
TONS
PER HOUR
TON,S
PER DAY









- EMISSION RATES
GRAMS
PER
1.0000
E 00
1.6667
E-02
2.7778
E-Oi
1.157*
E-02
7.5399
E 00
1.2600
E-01
5.2499
E-03
2.5200
E 02
1.0500
E 01
GRAMS
SEC PER
6.0000
E 01
1.0000
E 00
1.6667
E 01
6.9444
E-01
E 02
7.5599
E 00
3.1499
E-01
1.5120
E 04
6.2999
E 02
KG
MIN PER HOUR
3.6000
E 00
6.0000
E-02
1.0000
E 00
4.1667
E-02
2.7216
E 01
4.5359
E-01
1.8900
E-02
9.0718
E 02
3.7799
E 01
KG
PER DAY
8.6400
E 01
1.4400
E 00
2.4000
E 01
1.0000
E 00
6.3317
E 02
1.0886
E 01
4.5359
E-01
2.1772
E 04
9.0718
E 02
LBS
PER MIN
1.3228
E-Oi
2.2046
E-03
3.6744
E-02
1.5310
E-03
1.0000
E 00
1.6667
E-02
6.9444
E-04
3.3333
E 01
1.3889
E 00
LBS
PER HOUR
7.9366
E 00
1.3228
E-01
2.2046
E 00
9.1859
E-02
6.0000
E 01
1.0000
E 00
4.1667
E-02
2.0000
E 03
8.3333
E 01
LBS
PER DA*
1.9048
E 02
3.1747
E 00
5.2911
E 01
2.2046
E 00
1.4400
E 03
2.4000
E 01
1.0000
E 00
4.8000
E 04
2*0000
E 03
TONS
PER HOUR
3.9683
E-03
6.6139
£•05
1.1023
E-03
4.5930
E.03
3.0000
E-02
5.0000
E-04
2.0833
E-03
1.0000
E 00
4.1667
E-02
TONS
PER
9.3240
E-02
1.5873
E-03
2.6455
E-02
1.1023
E-03
7.2000
E-01
1.2000
E-02
3.0000
E-04
2.4000
E 01
1.0000
E 00
TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS
AND BENEATH THE DESIRED UNIT.   NOTE THAT E-XX MEANS 10 TO THE -XX POWER.

-------
CONVERSION FACTORS - LENGTH
     DESIRED UNITS METER
GIVEN UNITS
CM
MICRON
KILOMETER  INCH
FOOT
                                            YARD
IILE(STAT)  MILE(NAUT)





*t»
LTMOSPHERIC
O
"d
|
1
M
cn
H
§
H
H
Cfl
METER 1.0000
E 00
CM 1.0000
E-02
MICRON 1.0000
E-06
KILOMETER 1.0000
E 03
INCH 2.5400
E-02
FOOT 3.0480
£•01
YARD 9.1440
E-01
MILE(STAT) 1.6093
E 03

MIlE(NAUT) 1.8532
E 03
TO CONVERT A VALUE FROM A GIVEN
AND BENEATH THE DESIRED UNIT.

1.0000
E 02
l.OQOO
E 00
1.0000
E-04
1.0000
E 05
2.5400
E 00
3.0480
E 01
9.1440
E 01
1.6093
E 05

1.8532
E 05
UNIT TO A
NOTE THAT

1.0000
E 06
1.0000
E 04
1.0000
E 00
1.0000
E 09
2.5400
E 04
3.0480
E 05
9.1440
E 05
1.6093
E 09

1.8532
E 09
1.0000
E-03
1.0000
E-05
1.0000
E-09
1.0000
E 00
2.5400
E-05
3.0480
E-04
9.1440
E-04
1.6093
E 00

1.8532
E 00
3.9370
E 01
3.9370
E-01
3.9370
E-05
3.9370
E 04
1.0000
E 00
1.2000
E 01
3.6000
£ 01
6.3360
E 04

7,2962
E 04
DESIRED UNIT, MULTIPLY THE GIVEN
E-XX MEANS 10 TO THE -xx POWER.



3.2808
E 00
3.2808
E-02
3.2808
E-06
3.2808
E 03
8*3333
E-02
1.0000
E 00
3.0000
E 00
5.2800
E 03

6.0802
E 03
VALUE BY

1.0936
E 00
1.0936
E-02
1.0936
E-06
1.0936
E 03
2.7778
E.02
3.3333
E-01
1.0000
E 00
1.7600
E 03

2.0267
E 03
THE FACTOR

£. '4
6.2137
£.06
6.2137
E-10
6r2137
£.01
1.5783
£.05
1.8939
£.04
5.6818
£•04
1.0000
£ 00

1.1516
E 00
OPPOSITE

5.3959
E-04
5.3959
E-06
5.3959
E-10
5.3959
E-01
1.3706
E-05
1.6447
E-04
4,9340
E-04
8,6839
E-01

1,0000
E 00
THE GIVEN UNITS


-------
V
•o
3
&
X
>tt
CONVERSION FACTORS - AREA
DESIRED
GIVEN UNITS
SQ METER
SQ KM
SQ CM
SQ INCH
SQ FOOT
SQ YARD
ACRE
SQ STAT
MILE
so NAUT
Mil E
UNITS SQ METER
1.0000
E 00
1.0000
E 06
1.0000
E-04
6.4516
E-04
9.2903
E-02
8.3613
E-01
4,0469
E 03
2.5900
E 06
3.4345
E 06
SQ KM
1.0000
E-06
1.0000
E 00
1.0000
E-10
6.4516
E-10
9.2903
E.08
8.3613
E-07
4.0469
E-03
2.5900
E 00
3.4345
E 00
SQ CM
1.0000
E 04
1.0000
E 10
1.0000
E 00
6.4516
E 00
9.2903
E 02
8.3613
E 03
4.0469
E 07
2.5900
E 10
3.4345
E 10
SQ INCH
1.5500
E 03
1.5500
E 09
1.5500
E-01
1.0000
E 00
1.4*00
E 02
1.2960
E 03
6.2726
E 06
4.0145
E 09
5.3235
E 09
SQ FOOT
1.0764
E 01
1.0764
E 07
1.0764
E-03
6.9444
E-03
1.0000
E 00
9.0000
E 00
4,3560
E 04
2.7878
E 07
3.6969
E 07
SQ YARD
1.1960
E 00
1.1960
E 06
1.1960
E-04
7,7160
E-04
1.1111
E-01
1.0000
E 00
4.8400
E 03
3.0976
E 06
4.1076
E 06
ACRE
2.4710
E-04
2.4710
E 02
2.4710
E.08
1.5942
E.07
2.2957
£.05
2.0661
£.04
1,0000
E 00
6.4000
E 02
8.4869
E 02
SQ STAT
MILE
3.8610
E-or
3.8610
E-01
3,8610
E-ll
2.4910
£.10
3.5870
E.08
3.2283
£.07
1,5625
£.03
1.0000
£ 00
1.3261
E 00
SQ NAUT
MILE
2.9116
E-07
2.9116
e-oi
2.9116
E-ll
1.8785
E-10
2.7Q50
E-08
2.4345
E-07
1.1783
E-03
7.5411
E-01
1.0000
E 00
      TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE GIVEN VALUE By THE FACTOR OPPOSITE  THE GIVEN UNITS
      AND BENEATH THE DESIRED UNIT.   NOTE THAT E-XX MEANS  10 TO THE -XX POWER.

-------
      SION FACTORS - VOLUME

     D^STREO U.-JJTS cu f'

GIVEN UNITS
LITE"      CU IIMCH    CU FOOT    Cu  STAT     Cj  NAUT    j 5 FLUID  U 5 QUART  U 5 GALLON
                                        MILE        MILE      OUNCE











>
H
S
O
t/3
"B
a
M
M
M
O
o
5!
*B
M
93
Cfl
O
25
M
Cfl
H
i
H
W
in
cu METEP

LITER

cu INCH

cu FOOT

cu STAT
MTLF
cu NAUT
MILF


U S FLUID
OUMCF

U S QUART



U S GALLON



TO CONVFRT
AND BENFATH






1.0000
F 00
1.0000
E-03
1.6487
r-^5
2. an?
F-02
*.U83H7
E-02
2.R316
E 0.1
4,J.6«1
E U
6.36*9
E I/


2.9573
E-02

9.'»6*3
E Ot>


3.78-J3
E 00


U"IJt TO
NOTt r-)t






6.1023 3
f. 0*
6.1025 3
E 01
1.0000 5
F 00
1.7280 1
E 03
2.5*36 1
E 14
3.8«*2 2
E 1*


1.80*7 1
F 00

5.7750 3
E 07


2.3100 1
F 02


A DESIRE1) UNIT
.531*
E 01
,5ns
E-"2
.7H70
E-04
.0000
E ^0
,*^20
E 11
-.2*78
E 11


.0*/+*
E-03

.3*20
E 0*


.3368
E-01


, MULTIPLY
*.3991
E-10
2.3992
E-13
3.9315
E-15
6.7936
E-12
I. 0000
E 00
1.5270
E 00


7.0950
E-15

2.2704
E-07


9.0817
E-13


THE GIVEN
1.5711
E-10
1.5711
E-13
2.5746
E-15
4.4*88
E-12
6.5486
E-01
1.0000
E 00


4.6*62
E-15

l.*868
E-07


5.9472
E-13


VALUE o^
3.3814
E 04
3.3815
E 01
5.5412
E-Ol
9.5751
E 02
1.4094
E 14
2.1523
E 14


1.0000
E 00

3.2000
E 07


1.2800
E 02


f THE FACTOR
1.0567
E-03
1.0567
E-06
1.7316
E-08
2.9922
E-05
4.4045
E 06
6.7259
E 06


3.1250
E-08

1.0000
E 00


4*0000
E-06


OPPOSITE
2,6417
E 02
2.6418
E-01
4.3290
E-03
7.4805
E 00
1.1011
E 12
1.6815
E 12


7.8125
E-03

2.5000
E 05


1.0000
E 00


THE GIVEN UNITS
a E-XX MEANS 10 TO TrlE -XX POWER.











































-------
n
B
ft
CONVERSION FACTORS - MASS
DESIRED UNITS GRAM
GIVEN UNITS
GRAM 1.0000
E 00
MICROGRAM i.oooo
E-06
KILOGRAM 1.0000
E 03
METRIC TON 1.0000
E 06
SHORT TON 9.0718
E 05
LONG TON 1.0160
E 06
GRAIN 6.4799
E-02
OUNCE 2.8349
(AVDP) E 01
LB (AvDP) 4.5359
E 02


MICROGRAM
1.0000
E 06
1.0000
E 00
1.0000
E 09
1.0000
E 12
9.0718
E 11
1.0160
E 12
6.4799
E 04
2.8349
E 07
4.5359
E 08


KILOGRAM
1.0000
E-03
1.0000
E-09
1.0000
E 00
1.0000
E 03
9.0718
E 02
1.0160
E 03
6.4799
E-05
2.8349
E-02
4.5359
E-01


METRIC
1.0000
E-06
1.0000
E-12
1.0000
E-03
1.0000
E 00
9.0718
E-01
1.0160
E 00
6.4799
E-08
2.8349
E-05
4.5359
E-04


TON SHORT TON
1.1023
E-06
1.1023
E-12
1.1023
E-03
1.1023
E 00
1.0000
E 00
1.1200
E 00
7.1428
E-08
3.1250
E-05
5.0000
E-04


LONG TON
9.8421
E-07
9.8421
E-13
9.8421
E-04
9.8421
E-01
8,9286
E-Oi
1.0000
E 00
6.3775
E-08
2.7902
E-05
4.4643
E-04


GRAIN
1.5432
E 01
1.5432
E-05
1.5432
E 04
1.5432
E 07
1.4000
E 07
1.5680
E 07
1.0000
E 00
4,3750
E 02
7.0000
E 03


OUNCE
(AVDP)
3.5274
E-02
3,5274
E-08
3.5274
E 01
3,5274
E 04
3.2000
E 04
3.5840
E 04
2.2857
E-03
1.0000
E 00
1.6000
"E 01


LB 
-------
CONVERSION FACTORS - FLOW

     DESIRED UNITS CD METER   CU METER   LITER      LITER      LITER       CU FT       CU FT       CU  FT       CU  CM
                      PER SEC    PER HR     PER SEC    PER MIN     PER  HR     PER  SEC     PER  MIN     PER  HR      PER  SEC
GIVEN UNITS











j^
H
S
0
f$
a
B
2
ft
a
00
•fl

t/3
0
2!
B
C/J
NN
H
B
W)
cu METER
PER SEC
cu METER
PER HR
LITER
PER SEC
LITER
PER'MIN
LITER
PER HR
CU FT
PER SEC


cu FT
PER MIN


cu FT
PER HR


cu CM
PER SEC


TO CONVERT A
AND BENEATH





1.0000
E 00
2.7778
E-04
1.0000
E-03
1.6667
E-05
2.7779
E-07
2.8317
E-02


4.7195
E-04


7.8658
E-06


1.0000
E-06


VALUE FROM A GIVEN
THE DESIRED UNIT.





3.6000
E 03
1.0000
E 00
3.6001
E 00
6.0002
E-02
1.0000
E-03
1.0194
E 02


1.6990
E 00


2.8317
E-02


3.6000
E-03


UNIT TO A
NOTE THAT





9.9997
E 02
2,7777
E-01
1.0000
E 00
1.6667
E-02
2,7778
E-04
2.8316
E 01


4.7194
E-01


7.8656
E-03


9.9997
E-04


DESIRED
5.9998
E 04
1.6666
E 01
6.0000
E 01
1.0000
E 00
1.6667
E-02
1.6990
E 03


2.8316
E 01


4.7194
E-01


5.9998
E-02


UNIT, MULTIPLY
3,5999
E 06
9,9997
E 02
3.6000
E 03
6.0000
E 01
1.0000
E 00
1.0194
E 05


1.6990
E 03


2.8316
E 01


3.5999
E 00


THE GIVEN
3.5314
E 01
9.8096
£.03
3.5315
E-02
5.8859
E-04
9.8098
E-06
1.0000
E 00


1.6667
E-02


2.7778
E-04


3.5314
E-05


VALUE BY
2.1189
E 03
5.8857
E.01
2.1189
E 00
3,5315
E-02
5,8859
E-04
6.0000
E 01


1.0000
E 00


1.6667
£.02


2.1189
E-03


THE FACTOR
1.2713
E 05
3.53U
E 01
1.27U
E 02
<.U89
E 00
3,5315
E-02
3,6000
E 03


6.0000
E 01


1.0000
E 00


1.2713
E-01


OPPOSITE
I. 0000
E 06
2,7778
E 02
1.0000
E 03
1,6667
E 01
2,7779
E-01
2,8317
E 04


4,7195
E 02


7.86*8
E 00


1.0000
E 00


THE GIVEN UNITS
E-XX MEANS 10 TO THE -xx POWER.




































-------
•d
•d
a-









*«.
CONVERSION FACTORS - CONCENTRATION, DENSITY
DESIRED
GIVEN UNITS
GRAM PER
CU METER
MG PER
CU METER
MICROGRAM
PER CU M
MICROGRAM
PER LITER
GRAIN PER
CU FT
OUNCE PER
CU FT
LB PER
CU FT
GRAM PER
CU FT
LB PER
CU METER
UNITS GRAM PER
CU METER
1.0000
E 00
1.0000
E-03
1.0000
E-06
9.9997
E-04
2.2883
E 00
1.0011
E 03
1.6018
E 04
3.5314
E 01
4.5359
E 02
MG PER
CU METER
1.0000
E 03
1.0000
E 00
1.0000
E-03
9.9997
E-01
2.2883
E 03
1.0011
E 06
1.6018
E 07
3.5314
E 04
4.5359
E 05
MICROGRAM
PER CU M
1.0000
E 06
1.0000
E 03
1.0000
E 00
9.9997
E 02
2.2883
E 06
1.0011
E 09
1.6018
E 10
3.5314
E 07
4.5359
E 08
MICROGRAM
PER LITER
1.0000
E 03
1.0000
E 00
1.0000
E-03
1.0000
E 00
2.2884
E 03
1.0012
E 06
1.6019
E 07
3.5315
E 04
4.5360
E 05
GRAIN PER
CU FT
4.3700
E-01
4.3700
E-04
4.3700
E-07
4.3699
E-04
1.0000
E 00
4.3750
E 02
7.0000
E 03
1.5432
E 01
1.9822
E 02
OUNCE PER
CU FT
9.9.885
E-04
9.9885
E-07
9.9885
E-10
9.9883
E-07
2.2857
E-03
1.0000
E 00
1,6000
E 01
3.5274
E-02
4.5307
E-01
LB PER
CU
6.2428
E-05
6.2428
E-08
6.2428
E-ll
6.2427
E-08
1.4286
E-04
6.2500
E-02
1.0000
E 00
2.2046
E-03
2.8317
£.02
GRAM PER
FT CU FT
E-02
E-05
'.8317
E-08
'.8316
E-05
6.^799
E-02
'.8349
E 01
4.5359
E 02
1.0000
E 00
1.2844
E 01
LB PER
CU Ml
2.2046
E-03
2.2046
E-06
2.2046
E-09
2.2046
E-06
5,0*49
E-03
2.2072
E 00
3.5314
E 01
7.7855
E-02
1,0000
E 00
        TO  CONVERT  A  VALUE  FROM  A  GIVEN  UNIT  TO  A  DESIRED  UNIT,  MULTIPLY  THE  GIVEN  VALUE  BY  THE  FACTOR OPPOSITE THE GIVEN UNITS

        AND BENEATH THE  DFSIRED  UNIT.    NOTE  THAT  E-XX  MEANS  10  TO THE  -XX POWER.

-------
-J
00
         CONVERSION  FACTORS - DEPOSITION RATF
(SHORT TON ,5TAT.  MILE)
              DESIRED UNITS GM PER SQ  KG PER SQ  MG PER SO.  TON PER SO OZ PER SQ  LB PER     GM PER SO  *IG PER SO
                              M PER MO  KM PER MO  CM PER MO  MI PER MO  FT PER MO ACRE PERMO  FT PER MO  IN PER MO
         GIVEN UNITS









Jj,
H
S
O
Cfl
a
M
5
o
o
55

H
8
OQ
O

M
cw
H
H
H
GM PER SO
M PER MO
KG PER SO
KM PER MO
MG PER SQ
CM PER MO
TON PER SO
MI PER MO
OZ PER SQ
FT PER MO


LB PER
ACRE PERMO


GM PER SO
FT PER MO


MG PER SQ
IN PER MO


TO CONVERT
AND BENEATH




1.0000
E 00
1.0000
E-03
1.0000
E 01
3.5026
E-01
3.0515
E 02


1.1208
E-01


1.0764
E 01


1.5500
E 00


A VALUE FROM A GIVEN
THE DESIRED UNIT.




1.0000
E 03
1.0000
E 00
l.OQOO
E 04
3.5026
E 02
3.0515
E 09


1.1208
E 02


1.0764
E 04


1.5500
E 03


UNIT TO A
NOTE THAT




1.0000
E-01
1.0000
E-04
1.0000
E 00
3.5026
E-02
3.0515
E 01


1.1208
E-02


1.0764
E 00


1.5500
E-01


DESIRED
2.8550
E 00
2.8550
E-03
2.8550
E 01
1.0000
E 00
8.7120
E 02


3.2000
E-01


3.0731
E 01


4.4252
E 00


UNIT, MULTIPLY
E-XX MEANS 10 TO THE -








3.2771
E-03
3.2771
E-06
3.2771
E-02
1.1478
E-03
1.0000
E 00


3.6731
E-04


3.5274
E-02


5.0795
E-03


THE GIVEN
XX POWER.




8.9218
E 00
8.9218
E-03
8.9218
E 01
3.1250
E 00
2.7225
E 03


1.0000
E 00


9.6033
E 01


1.3829
E 01


VALUE BY





9.2903
E-02
9.2903
E-05
9.2903
E-01
3.2541
E-02
2.8349
E 01


1.0413
E-02


1.0000
E 00


1.4400
E-01


THE FACTOR





6.4516
E-01
6.4516
E-04
6.4516
E 00
2.2598
E-01
1.9687
E 02


7.2313
E-02


6.9444
E 00


1.0000
E 00


OPPOSITE THE GIVEN UNITS






-------
•a
        CONVERSION  FACTORS  -  PRESSURE

              DESIRED  UNITS  MILLIBAR    BAR

        GIVEN UNITS
ATMOSPHERE DYNES      KG         LBS        MM MERCURY IN MERCURY
            PER SO CM  PER SO CM  PER SO IN
MILLIBAR
BAR
ATMOSPHERE
DYNES
PER SO CM
KG
PER SO CM
LBS
PER SO IN
MM MERCURY
IN MERCURY
1.0000
E 00
1,0000
E 03
1.0133
E 03
1.0000
E-03
9.8066
E 02
6.8947
E 01
1.3332
E 00
3.386*
E 01
1.0000
E-03
1.0000
E 00
1.0133
E 00
1.0000
E»06
9.8066
E-01
6.89*7
E-02
1.3332
E-03
3.3864
E-02
9.8692
E-04
9.8692
E-01
1.0000
E 00
9.8692
E-07
9.6784
E-01
6.8046
E-02
1.3158
E-03
3.3421
E-02
1.0000
E 03
1.0000
E 06
1.0133
E 06
1.0000
E 00
9.8Q66
E 05
6.8947
E 04
1.3332
E 03
3.3864
E 04
1.0197
E-03
1.0197
E 00
1.0332
E 00
1.0197
E-06
1.0000
E 00
7.0307
£•02
1.3595
E-03
3.4532
E-02
1.4504
E-02
1.4504
E 01
1.4696
E 01
1.4504
E-05
1.4223
E 01
1.0000
E 00
1.9337
E-02
4.9115
E-01
7.5006
E-01
7.5006
E 02
7.6000
E 02
7.5006
E-04
7.3556
E 02
5.1715
E 01
1.0000
E 00
2.5400
E 01
2.9530
E-02
2.9530
E 01
2.9921
E 01
2.9530
E-05
*,8959
E 01
2.0360
E 00
3.9370
E-02
1.0000
E 00
        TO CONVERT  A  VALUE  FROM  A  GIVEN  UNIT  TO  A  DESIRED  UNIT,  MULTIPLY  THE  GIVEN  VALUE  BY  THE  FACTOR  OPPOSITE  THE  GIVEN  UNITS
        AND  BENEATH THE  DESIRED  UNIT.    NOTE  THAT  E-XX  MEANS  10  TO  THE  -XX  POWER.

-------
CONVERSION FACTORS - TIME



     DESIRED UNITS SECOND



GIVEN UNITS
MINUTE
HOUR
WEEK
MONTH (28)  MONTH <3oi  MONTH on  YEAR  (365>  YEAR  <366»











g
0
Ml

35


O
M
0>
M
»

M
o
^
H
cn
H
2
H
H
SECOND

MINUTE

HOUR

WEEK

MONTH (28)

MONTH (SO)

MONTH (31)


YEAR (365)




YEAR (366)



TO CONVERT A
AND BENEATH




1.0000
E 00
1.6667
E-02
2.7778
E-04
1.6534
E-06
4.1336
E-07
3.8580
E-07
3.7336
E-07

3.1710
E-08



3.1623
E-08


VALUE FROM A GIVEN
THE DESIRED UNIT.




6.0000
E 01
1.0000
E 00
1.6667
£.02
9.9206
£.05
2.4802
£-05
2.3148
£-05
2.2401
£.05

1.9026
E-06



1.8974
£.06


UNIT TO A
NOTE THAT




3.6000
E 03
6.0000
E 01
1.0000
E 00
5.9524
E-03
1.4881
E-03
1.3889
E-03
1.3441
E-03

1.1416
E-04



1.1384
E-04


DESIRED
6.0480
E 05
1.0080
E 04
1.6800
E 02
1.0000
E 00
2.5000
E-01
2.3333
E-01
2.2581
E-01

1.9178
E-02



1.9126
E-02


UNIT. MULTIPLY
2.4192
E 06
4.0320
E 04
6.7200
E 02
4.0000
E 00
1.0000
E 00
9.3333
E-01
9.0323
E-01

7.6712
E-02



7.6503
E-02


THE GIVEN
2.5920
E 06
4,3200
E 04
7.2000
E 02
4.2857
E 00
1.0714
£ 00
1.0000
E 00
9.6774
E-01

8.2192
£-02



8.1967
E-02


VALUE BY
2.6784
E 06
4.4640
E 04
7.4400
E 02
4.4286
E 00
1*1071
E 00
1.0333
E 00
1.0000
E 00

8.4932
E-02



8.4699
£.02


THE FACTOR
3.1536
E 07
9.2560
E 05
8.7600
E 03
5.2143
E 01
1.3036
E 01
1.2167
E 01
1.1774
E 01

1.0000
E 00



9.9727
£.01


OPPOSITE THE
3.1622
E 07
5.2704
E 05
8.7840
E 03
5,2286
E 01
1,3071
E 01
1.2200
E 01
1.1806
E 01

1.0027
E 00



1.0000
E 00


GIVEN UNITS
E-XX MEANS 10 TO THE -xx POWER.





























-------
•a
•e
n
D
ft.
CONvERSlCiM F'
DFSlBFi)
GIVEN UNITS
VJATT
( INT)
Kli OWATT
(INT)
MEGAWATT
(INT)
CA| (INT)
PER SEC
BTU
PER MIN
BTU
PER HR
JOULES ABS
PER SEC
ijAjT (ANSI
ELECT.
HORSEPOWER

'.CTO^S - POivES
LIMITS AiATT
(INT)
I. 0^00
F .10
F. 03
1.0000
E 06
F. 00
1.7588
F 01
2,9313
E-ol
9.9081
E-01
9.9981
E-01
7.4586
F 02


KILO" AT r
! I'll )
1 .0000
£-03
l.OOUO
E 00
1.0000
E Or)
4.18/6
E-0?
1.75H8
E-02
2, "3 1.3
E-04
9.99H1
E-04
'E!s:1
E-Ol


(IiNT)
1.0000
E-06
1.0000
F-03
1.0000
F 00
F-06
1.7583
E-05
2.9313
9.9981
E-07
9.9931
E-07
7.4586
E-04


CAI. (INT)
HER sr.c
2.3'iaO
E-'U
2,'IHSO
E '
-------
00
to
        CONVERSION FACTORS - ENERGY.  WORK


             DESIRED UNITS ERG         DYNE-CM


        GtVEN UNITS
ABS JOULE  CAL (INT)  CAL (15)   INT KW-HR  ABS KW-HR  8TU










H
g
O
s
B
2
n
g
53
"8
Not
0
2!
H
VI
H
§
H
H
73
ERG 1.0000
E 00
DYNE-CM i.oooo
E 00
ABS JOULE 1.0000
E 07
CAL (INT) 4.1868
E 07
CAL (15) 4.1855
E 07
INT KW-HR 3,6007
E 13

ABS KW-HR 3.6000
E 13

BTU 1.0551
E 10

TO CONVERT A VALUE FROM A GIVEN
AND BENEATH THE DESIRED UNlT,








1.0000
E 00
1.0000
E 00
1.0000
E 07
4.1868
E 07
4.1855
E 07
3,6007
E 13

3.6000
E 13

1.0551
E 10

UNIT TO A
NOTE THAT








1.0000 2
E-07
1.0000 2
E-07
1.0000 2
E 00
4.1868 1
E 00
4.1855 9
E 00
3.6007 8
E 06

3.6000 8
E 06

1.0551 2
E 03

DESIRED UNIT
.3884
E-08
.3884
E-08
.3884
E-01
.0000
E 00
.9968
E-01
.6000
E 05

.5984
E 05

.5200
E 02

. MULTIPLY
E-xx MEANS 10 TO THE -
















2.3892
E-08
2,3892
E-08
2,3892
E-01
1.0003
E 00
1.0000
E 00
8.6027
E 05

8.6011
E 05

2.5208
E 02

THE GIVEN
XX POWER.








2,7773
E-14
2,7773
E-14
2,7773
E-07
1.1628
E-06
1.1624
E-06
1.0000
E 00

9.9981
E-01

2.9302
E-04

VALUE BY









2.7778
E-14
2.7778
E-14
2.7778
E-07
1,1630
E-06
1.1626
E-06
1.0002
E 00

1.0000
E 00

2.9307
E-04

THE FACTOR









9,4781
E-ll
9,4781
E-ll
9.4781
E-04
3.9683
E-03
3.9671
E-03
3.4128
E 03

3.4121
E 03

1.0000
E 00

OPPOSITE THE GIVEN UNITS










-------
•a
•a
 a
 0

 &
         CONVERSION FACTORS - ENERGY PER UNIT AREA



              DESIRED UNITS LANQ1.EY



         GIVEN UNITS
CAL (15)   BTU        INT KW-HR  ABS JOULES

 PER SQ CM  PER SQ FT  PER SQ M   PER SO CM
LANGLEY

CAL (15)
PER SO CM
BTU
PER SO FT
INT KW-HR
PER SO M
ABS JOULES
PER SQ CM
1.0000
E 00
1.0000
E 00
2.7133
E-01
8.6029
E 01
2.3892
E-01
1.0000
E 00
1.0000
E 00
2.7133
E-01
8.6029
E 01
2.3892
E-01
3.6855
E 00
3.6855
E 00
1.0000
E 00
3.1706
E 02
8.805
-------
CONVERSION FACTORS - POWER PER UNIT AREA    










H
g
o
en
"fl
JjJ
M
M
O
o
M
WJ

M
75
O
2

B
cn
H
§
S
H
CAL PER SO
M PER SEC
CAL PER SQ
CM PER MIN
LANGLEY
PER MIN
CAL PER SQ
CM PER DAY
BTU PER SQ
FT PER MIN

BTU PER SQ
FT PER DAY


ABS WATT
PER SQ CM


TO CONVERT A
AND BENEATH











1.
E
1.
E
1.
E
1.
0000
00
6667
02
6667
02
157*
E-01
4t
E

3.
5222
01

1*0*
E-02


2.
E




3892
03


VALUE FROM A GIVEN
THE DESIRED UNIT.






















6.0000
E-03
1.0000
E 00
1.0000
E 00
6.9444
E-04
2,7133
E-01

1.8843
E-04


1.4335
E 01


UNIT TO A
NOTE THAT











6.0000
E-03
1.0000
E 00
1.0000
E 00
6.9444
E-04
2.7133
E-01

1.8843
E-04


1.4335
E 01


8.
E
1.
E
1.
E
1.
E
3.
E

2.
6400
00
4400
03
4400
03
0000
00
9072
02

7133
E-01


2.
E


DESIRED UNIT,
E-XX MEANS











10













0643
04


MULTIPLY
TO THE -











2.2113
E-02
3.6855
E 00
3.6855
E 00
2.5594
E-03
1.0000
E 00

6,9445
E-04


3.2833
E 01


THE GIVEN
XX POWER.











3.1843
E 01
5.3071
E 03
5.3071
E 03
3.6855
E 00
1.4400
E 03

1.0000
E 00


7.6079
E 04


VALUE BY












4.1855
E-04
6.9758
E-02
6.9758
E-02
4.8443
E-05
1.8928
E-02

1.3144
E-05


1.0000
E 00


THE FACTOR OPPOSITE THE GIVEN UNITS













-------