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,  or from the

Superintendent  of Documents.
                     6th printing January 1973


          Office of Air Programs Publication No. AP-26
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                                  ii

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                                Chapter  1 — INTRODUCTION

                     NOTE: SEE PREFACE TO THE SIXTH PRINTING ON PAGE iii.
   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
  600r
  500
  400
  300
o
  200
   100
                                  temperature structure. When temperature decreases
                                  with height at a rate higher than 5.4 °F per 1000 ft
                                  (1CC 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.
                                                                                        J	L
                                                                              _L
    -1   0   1
234567

  TEMPERATURE, "C
8   9   10  11   12
3456789

 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  ilida-
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
                     URBAN AREA

                   GRADIENT WIND
  SUBURBS
                                                                                    LEVEL COUNTRY
  Figure 1-2.  Examples of variation of wind with height over different size roughness elements (Tigures 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 C3-, C,, 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, OK, at the point of release. Cramer (1957)
derived a diffusion equation incorporating standard
deviations of  Gaussian distributions:  ;> calculated from
wind measurements  made with a bi-directional
wind vane (bivane).  Values  for diffusion param-
eters based on field diffusion  tests  were suggested
by Cramer, et al.  (1958) (and  also in Cramer 1959a
and 1959b).  Hay  and Pasquill  (1959)  also  pre-
sented a method  for deriving  the spread of pollut-
ants  from records  of  wind  fluctuation.  Pasquill
(1961)  has further proposed a  method  for  esti-
mating diffusion when such detailed wind  data are
not  available.  This method expresses the height
and angular spread of a diffusing plume in terms of
more commonly observed weather parameters. Sug-
gested curves of height and  angular spread as a
function of distance downwind were given  for sev-
eral "stability" classes. Gifford (1961) converted
Pasquill's values of angular spread and height into
standard deviations of plume  concentration distri-
bution, 
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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,y,z;H).
H is the height of  the plume centerline  when it
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 ery and a,,
respectively;  the mean wind speed affecting  the
plume is u; the uniform emission rate of pollutants
is Q; and total reflection of the plume takes place
at the earth's surface, i.e.,  there is no deposition
or reaction at the surface (see problem 9).
  (x,y,z;H) =
                                           (3.1)
*Note: exp —a/b = e~»/b where e is the base of natural logarithms
     and is approximately equal to 2.7183.
                                                                                    (x,-y,Z)
                                                                                    (x,-y,0)
          Figure 3-1.  Coordinate system showing Gaussian  distributions in the horizontal and vertical.
Estimates

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 Any consistent set of units may be used.  The most
 common is:.

    X (g m~3) or, for radioactivity (curies m~s)
    Q (g sec"1) or (curies sec"1)
    u (m sec"1)
     6
1
Day
Night

J,) Incoming Solar Radiation Thinly Overcast
' , .. -' -=0/0

Strong
A
A-B
B
C
C

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

Slight -4/8 Low Cloud
B
C E
C D
D D
D D

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 CT}. 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 o-y and
2 XL; XL is where 2xr,; xr. is where crz = 0.47 L
    The value of 
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10,000
                                                                    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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                                         }                                 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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                                                                                   2 km
                                                     ,-5
                             234 5 4*10
                             CONC.
                             SBOmeters
            Figure 34.  Variations  in concentration  in the vertical beneath a more stable layer.
three cases (where  and u.  The relative confidence
in the IT'S (in decreasing  order) is indicated by the
heavy lines and dashed lines in Figures 3-2 and 3-3.

   Estimates of H, the effective height of the plume,
may be in error because of uncertainties in the esti-
mation of AH, the plume rise. Also, for problems
that require estimates of concentration at a specific
point, the difficulty of determining the mean wind
over a given  time interval and consequently the
location of the x-axis can cause considerable un-
certainty.

GRAPHS FOR ESTIMATES  OF  DIFFUSION

   To avoid repetitious  computations, Figure  3-5
(A through F) gives relative  ground-level concen-
trations times  wind  speed  (x  u/Q)  against down-
wind distances for various effective heights of emis-
sion and limits to the vertical mixing for each sta-
bility class (1 figure for  each stability).  Computa-
tions'were made  from Eq.  (3.3), (3.4), and  (3.5).
Estimates of actual  concentrations may be deter-
mined by multiplying ordinate values by Q/u.
 PLOTTING GROUND-LEVEL
 CONCENTRATION ISOPLETHS

    Often one wishes to  determine the locations
 where concentrations equal or exceed a given mag-
 nitude.  First, the axial position of the plume must
 be determined  by the mean wind direction. For
. plotting isopleths  of  ground-level  concentrations,
 the relationship between  ground-level  centerline
 concentrations and ground-level  off-axis concentra-
 tions can be used:
    x (x,y,0;H)
    x (x,0,0;H)
exp I —
(3.7)
 The y coordinate of a particular isopleth from the
 x-axis can be determined  at  each downwind  dis-
 tance, x.  Suppose that one  wishes  to  know  the
 off-axis distance to the 10~3 g m~8 isopleth at an x
 of 600 m, under stability type B, where the ground-
 level centerline concentration at  this distance  is
 2.9 x 10-3 g m-3.
                             x (x,y,0;H)   _
                             x U,0,0;H)
     10~3
  2.9 x 10-"
               0.345
10
         ATMOSPHERIC DISPERSION ESTIMATES

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                                     PREFACE

     This workbook presents some computational techniques currently used by scientists
working with atmospheric dispersion  problems.  Because the basic working  equations 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 com-
plete do-it-yourself manual for atmospheric, dispersion estimates; all of the .numerous compli-
cations that  arise in making best estimates of dispersion  cannot be so easily  resolved.
Awareness of the possible complexities can enable the user to appreciate the validity of his
"first approximations" and to realize  when the  services of a professional air pollution mete-
orologist are required.

      Since the  initial publication of  this workbook, air  pollution meteorologists affiliated
with the Environmental protection Agency  have turned to using the method of Briggs to de-
termine plume rise in most cases rather than using the plume-rise equation of Holland as set
forth in Chapter 4.  The reader is directed to:
           Briggs, Gary A.  1971: "Some  Recent Analyses of Plume Rise Observations."
           In: Proceedings of the Second International Clean Air Congress. Academic Press,
           New York, N. Y.  pp  1029-1032

           and modified by

           Briggs, Gary A.  1972:   "Discussion,  Chimney Plumes  in Neutral and Stable
           Surroundings." Atmospheric Environment, 6:507-510.
                                          iii

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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 Tunes 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 binomial 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 of 10 minutes. 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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                 1C
                                                         DISTANCE km
       3-5A.  xu/Q with distance  lor various  heights  of  emission (H) and limits to vertical dispersion (L), A stability.
Estimates

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            ^
            oi
                                                  DISTANCE, kin

Figure 3-5B.   \-u 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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                                                           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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             :
                                                  DISTANCE, km




Figure 3-5D.   \u 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,



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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                                                   DISTANCE, k.
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
From Figure 3-2, for stability B and x = 600 m, a,
= 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)
I
ery
        (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"3 x 2/20 = 10-*.  Therefore the xu/Q isopleth
in Figure 3-6B having a value of 10"* 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-* m"2 x u/Q isopleth)  is about 5 x 10* meter2.

CALCULATION OF MAXIMUM
GROUND-LEVEL  CONCENTRATIONS

    Figure  3-9  gives the distance  to the point of
maximum concentration, xmix, and the relative maxi-
mum concentration, x u/Qm», 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 
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CLASS  A   STABILITY
         H = 0
                               3                 4

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

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                             CLASS  B   STABILITY
                                        H = 0
IO'3  10
                                                     3                  4

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

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o
Ml
"0
O
O
on
M
a
                                  CLASS  C  STABILITY
                                           H=0
DOWNWIND DISTANCE |«|,  km
                                             Figure 3-6C.  Isopleths  of xu/Q for a ground-level source, C stability.

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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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N
r o
                                  CLASS  E    STABILITY
                                           H=0
                                                               DOWNWIND DISTANCE (>), km
            1.5 rrr
I
-a
o
O
X
M
Lfl
H
   CLASS   F   STABILITY
 5xlO'4  3KICT4    2xlCT4
I                 2
                                                              DOWNWIND DISTANCE («), km
                                       Figure 3-6E, F.   Isopleths of xu/Q for a ground-level  source, E and F stabilities.

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M


I
                                   CLASS  A   STABILITY

                                           H = IOO
                                                                 3                4


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

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

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i
                                    CLASS  C    STABILITY
                                            H = IOO
                                                                   3                 4

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

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S

w
C/J
                                    CLASS   D   STABILITY


                                             H = IOO
 3                 4



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

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                            CLASS  I  STABILITY

                                     H = IOO
                                                i
                                                                 3                4


                                                               DOWNWIND  DISTANCE (x), km
                           CLASS F  STABILITY

                                   H=IOO
                                                                 3                4


                                                               DOWNWIND DISTANCE (x), km
                                                             5
i j
-1
Figure 3-7E, F.  Isopleths of ,\u Q for a source 100  meters high, E and-F  stabilities.

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     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, 0. 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.
                                                           ATMOSPHERIC DISPERSION  ESTIMATES

-------
rn
If:
            10
         Figure 3-9.   Distance of maximum  concentration and maximum ,\u 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, T»;  and
diameter of the stack opening, d. The meteorolog-
ical factors influencing plume rise are wind speed,
u; temperature of the air, Tu; 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 see"', 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:
2.68 x
                                      » d)  (4.1)
where:
    .AH = the rise of the plume above the stack, m
   v, = stack gas exit velocity, m sec 1
   d = the inside stack diameter, m
   u = wind speed, m sec"1
   p = atmospheric pressure, mb
   Ta = stack gas temperature, °K
   T. = 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 V^^i = H and that at this
distance the  
-------
             B.I
               Figure 4-1.  The product of <*& 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 limit?.  Virtual
distances x,  and x, can be found such that at xy,

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                                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 wanner 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' I
                                                                    ? 15
                                                                         y
                                                                         7(FIWIGATION)
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
required  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 h, (Eq. 5.3).

    tm 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:
   t  _
   tm"
                86
           __
           R~"8T
                     ,       / h + ht \
                     (h'~~ n) V   2   J    (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~s
       cp = specific heat of air at constant pressure,
           cal g-1 °K-1
       R = net rate of sensible heating of an air
           column by  solar radiation, cal m~2 sec"1

      -r- = vertical potential temperature gradient,
                     8T
           °K m"1 ~——(- r (the adiabatic lapse
           rate)      8z
       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 —^—- J is the 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
        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 mz sec"1
forK.

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) —
                                                                       Q
                                                                    2ir U o>
                                                      exp  —
                                                                          [1  / 2_H
                                                                  exP--2-(	7.
                                                   where L is the height of the stable layer and J = 3
                                                   or 4 is sufficient to include  the  important reflec-
                                                   tions. A good approximation of this lengthy equa-
                                                   tion can be made by assuming no effect of the stable
                                                   layer until     x (x,y,z;H) -   — ** '     exp	*
                                                                       Lu
                                                                                            (5.9)
                                                  For distances between XL and 2 XL the best approxi-
                                                  mation to the ground-level centerline concentration
                                                  is that read from a straight line drawn between the
                                                  concentrations for points XL and 2 XL on a log-log
                                                  plot of ground-level centerline concentration as a
                                                  function of distance.

                                                  CONCENTRATIONS  AT  GROUND LEVEL
                                                  COMPARED TO  CONCENTRATIONS AT THE
                                                  LEVEL OF EFFECTIVE STACK  HEIGHT
                                                  FROM ELEVATED CONTINUOUS SOURCES

                                                     There are several interesting relationships be-
                                                  tween ground-level concentrations and concentra-
                                                  tions at the level of the plume centerline.  One of
                                                         ATMOSPHERIC DISPERSION ESTIMATES

-------
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
                  ~~?JF
                       H. This  approximation is
much better for unstable conditions than for stable
conditions. With this approximation, the ratio of
concentration at  plume centerline to that at the
ground is:
   X (x, 0,H)
   X(x,0,0)
                            exp
                                	1  /2H
                                    2  V »,
                  11.0 + exp —0.5(2 V2)=]
                        exp — 0.5 (V2)-
                  (1.0 + 0.0182)
                      0.368
           = 1.38
   This calculation indicates that at the distance
of maximum ground-level concentration the concen-
tration at plume centerline is greater  by  about
one-third.

   It is also of interest to determine the relation-
ship between 
-------
   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 ot 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:
                                          (5.12)
 where x» is the desired concentration estimate for
 the sampling time, t,; x& 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
m'onthio 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:
                           exp  I —
         2.03Q
                                                               UX
                                                                    exp  -
                                                                                  H
                                          (5.13)
                                                       or
                                                                 Q
                         2.55 Q
                         L u x
                                                                                             (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:
      ,   *    ^ ^ ( 2 Q f (9,S,N)
    X (x,e) = *^- -=^ \——
               S   N    V2,r
-------
 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
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 maTi'mnm 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,    does  not appear in this
 equation, since it is assumed that lateral dispersion
 from one segment of the line is compensated by dis-
 persion in  the opposite  direction from adjacent
 segments.  Also y does not appear,  since concentra-
 tion at a given x is the same  for any value of y
 (see problem 23).

    Concentrations from infinite line sources when
 the wind is not perpendicular  to  the line can be
 approximated. If the angle between the wind direc-
 tion and line source is 0,  the equation for concen-
 tration downwind of the line source-is:


 x (x,y,0;H) = -r-*±=	exp  [__L/HVl
               Sin 0 ^/2ar «r,U    F[    2  V »» / I

                                          (5.19)

 This equation should  not be used where 0 is less
 than 45°.
40
                                                           ATMOSPHERIC DISPERSION ESTIMATES

-------
   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 yt to y2 where y, is less than y2.  The
equation  for concentration (from Button's (1932)
equation  (11), p. 154), is:

                 2 q
                         exp
x (x,0,0;H) =
               \X2JTcr, U
f	L_fJLVl
I     2  u. /  j
               exp (—0.5 p2) dp
                                          (5.20)
           where
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:

   The symbols have the usual meaning, with the
important exceptions  that Qr represents the  total
mass of the release and the 
-------
Gifford, F. A.,  1959:  Computation of pollution
   from several  sources.  Int. J. Air Poll., 2, 109-
   110.

Gifford, F. A., 1960s: 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. Gill, 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):

     /_ ., n.u\        **
                 IT 
"r
Bosanquet and Pearson qx "\/2~Px
-2-n
O|ittnn l p 7
ouuon — - cy x f-
•\ f*) a U w v
A*I V' t fl r\ VT A
rnlnrr v

i 2'n
1 P 2
V2 "IA
\/2kvxx
u
                REFERENCES

Bosanquet, C. H., and J.  L. Pearson, 1936:  The
   spread of  smoke  and gases from  chimneys.
   Trans. Faraday Soc., 32, 1249-1263.

Calder, K. L., 1952:  Some recent British work on
   the problem  of diffusion in the lower atmos-
   phere, 787-792 in Air Pollution, Proc. U. S.
   Tech. Conf. Air Poll., New York, McGraw-Hill,
   847 pp.

Sutton, O. G., 1947:  The problem of diffusion in
   the lower atmosphere. Quart. J. Roy. Met Soc.,
   73, 257-281.
 Other Equations
                                                                                                43

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                             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 10-* x 151
       = 1.1 x 10-' g m-'

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
   a, =  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
                  - ov a, U
exp
                                   ~H"),
   At distance equal to or greater than 2 XL, which
   is 11 km, Eq. (3.5) is used:
   x (x,0,0;H) =
                       Q
                        y L U
   Solutions for the equations are given in Table
   7-1.  The values of concentration  are  plotted
   against distance in  Figure 7-1.
   :

                  I              10

                  DOWNWIND DISTANCE, km
Figure 7-1.   Concentration as a function  of  downwind
               distance (Problem 6).
                                                        Table 7-1   CALCULATION OF CONCENTRATIONS FOR
                                                               VARIOUS DISTANCES (PROBLEM 6)
x,
km
0.3
0.5
0.8
1.0
2.0
3.0
5.5
x,
km
11.0
30
100
crv.
m sec"1 rn
4
4
4
4
4
4
4.5
u,
m sec"1
4.5
4.5
4.5
52
83
129
157
295
425
720
CFy,
m
1300
3000
8200
m
30
5;
85
110
230
365
705
L,
m
1500
1500
1500
H/CT, expf — 5-(H/
-------
 2»10"* -
  10-'-
          -400
                 -200      0     +JOO

                 CROSSWIND DISTANCE (y), m
                                       MOO
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)
*,
km
0.5
0.8
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Cy-
ril
83
129
157
295
425
540
670
780
890
980
X {centerline),
g m-3
3.8 x 10-"
2.3 X 10-*
2.8xlCh*
1.4 x 10-*
7.1 x 10-5
4.0 xlO-5
2.4 x 10-'
1.8 x 10-5
1.4x10-'
1.1 x 10-5
X (isopletM
X (centerline)
0.263
4.35xlO~s
3.53 x 10~2
7.14x10-=
1.42 xlO-1
0.250
0.417
0.556
0.714
0.909
y/ffr
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 V ab where a is the
    semimajor axis and b is the semiminor axis.
             8600 — 350
                          — 4125 m
       b —902
    A 
-------
   Table 74  DETERMINATION OF CONCENTRATIONS FOR
            VARIOUS HEIGHTS (PROBLEM 9)
 a.
                    d.
                           e.
                      f.
                                          g.
 z.  I-H  r  i / *H \-i *+H   r  i f*+H
 * 	e«pl—r[	] 1-^^wPl—;-(	
 m  a,  I  2 V "• I J "•    I  ' \ »• ,
                        c. + e.
                               gnr>
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



io-j
10-'
10-'
10-*
10-*
10-'
10-"
10-"
io-«
3.55 xlO~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
10-*
10-*
10-*
10-*
10-*
10~*
3.41 x 10-*
3.03x
2.51 x
1.94 x
1.39 x
9.14 x
5.64 x
3.26 x
1.75 x
8.40 x
10-*
10-*
10-*
10-*
10-'
10-'
10-'
10-'
10-
  These values are plotted in Figure 7-4.

  500
  400
_- 300
  ZOO
   100
              I
   I
                                      J_
     010'*
ur*
4x|(r«
                CONCENTRATION, g •-*
Figure 74.  Concentration as a function of height (Prob-
                     lem 9).
   Verifying:

   X (*,0,0) =
Q
                TT 
-------
  ffjf'
         «ry (stable) + H/8
               151
520 + 19 — 539
              4 (539) 330
      = 8.5 x 10-' g m-s of SOX

   Note that the fumigation concentrations under
   these conditions are about 1.3 times the maxi-
   mum ground-level concentrations that occurred
   during  the night (problem 11).

PROBLEM  13:  An air sampling station is located
   at an azimuth of 203° from a cement plant at a
   distance of 1500  meters. The cement plant re-
   leases fine particulates (less than  15 microns
   diameter) at the rate of  750 pounds per hour
   from a 30-meter stack. What is the contribution
   from the cement plant to the total suspended
   participate concentration at the sampling sta-
   tion when the wind is from 30° at 3 m sec"1 on
   a clear day in the late fall at 1600?
SOLUTION:  For this season and time of day the
   C class stability  should apply. Since the sam-
   pling station is off the plume axis, the x and y
   distances can be calculated:

            x = 1500 cos 7° = 1489

            y = 1500 sin 7° = 183

   The source strength is:
   Q = 750 lb hr-1 x 0.126
   At this distance, 1489 m, for stability C, 
-------
   maximum *u/Q as a function of H and stability
   from Figure 3-9  and multiplying by the appro-
   priate Q/u. The computations are sum  larized
   in Table 7-6, and plotted in Figure 7-5.
5 i
-------
   AH =
 u
33.4
 u
102
 u
[1.5+ (2.46) 0.256 (2.44)]


(1.5 + 1.54)
                                                                           60 sec min~
The relation between o> az and u is:
        0.117 Q     0.117 (5.25)   . 2.12 x 10'
   
-------
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-hou  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:
            /  O   \ O.2
                       3.4 x ID"3


                     (3.4 x 10"3)


                        = 1.6 x 10~:1 g m"'
          ~     2.09

   Letting k 15 .min, s = 2 hours, and p = 0.17
              8 0.17

              3.4 x IP"3
                 1.42
                    (3.4 x 10~3)
                         . 2.4 x 10-3 g m
   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 SOZ 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 SOS from two stacks whose physical
   height is 120 meters and whose AH,  from  Hol-
   land's equation, is AH (m)  = 538 (m2 sec^J/u
   (m sec"1). Source B is a refinery emitting 126  g
   sec"1 SOZ 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  S02,
   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.
          538
   AH =
                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):
                                                 RECEPTOR
                                                  Figure 7-6.  Locations of sources and receptor (Problem
                                                                       20).
                                                     X (x,y,0;H) =
                                                                       Q
                                                                       TI U
                                                                            exp  I	5-
                                                     For Source A, x = 24.6 km, y = 8.4 km

                                                     a, = 1810 m, at = 1120 m, u = 8.5 m sec"1

                                                                 1450
                                                     XA
                                                           TT 1810 (1120) 8.5
                                                                             exp I—0.5
                                                             1450
                                                                              1120

                                                                       exp [—0.5 (4.64)2]
                                                       ~  5.42 xlO7
                                                     exp [—0.5 (0.164)2]

                                                       = 2.67 x 10"5) (2.11 x 10"*) (0.987)

                                                     XA = 5.6 x 10"10 g m"3

                                                     For Source B, x = 13.0 km, y = 4.0 km.

                                                     v, = 1050 m, at = 640 m, u = 7.0 m sec"1

                                                                126
                                                     XB
                                                     exp
                                                            1050 (640) 7

                                                                 (*)']
                                                                                  [__ ( 4000 Vl
                                                                                -°-5 how-)  J
                                                               126
                                                                        exp [—0.5'(3.81) =
                                                            1.48 x 107

                                                      exp [—0.5 (0.0938)2]
                                                         = 8.5 x 10^ (7.04 x 10"*)  (0.996)

                                                      XB = 6.0 x 10"° g m"3
                                                      x = XA + XB = 0.56 x 10"9 + 6.0 x 10"9
                                                         — 6.6 x 10-* g m "3
52
                                                          ATMOSPHERIC DISPERSION ESTIMATES

-------
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 mr3?

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, at = 43 m.

             Q                3
         TT CTy /2 140
      = 3.46 x 140
      = 484 m.
             484
   tan 9 =
       e
             3000
            9.2°
                      0.1614
   A wind shift of 9.2° is required to reduce the
   concentration to 10~7 g m~3.
PROBLEM 22:  An inventory  of SO2  emissions
   has been conducted  in an urban area by square
   areas,  5000 ft (1524 meters) on a  side. The
   emissions from one  such area are estimated to
   be 6 g sec"1 for the  entire area.  This square is
   composed of  residences and  a few  small com-
   mercial establishments.  What is the concentra-
   tion resulting from this area at the center of the
   adjacent square to the north when the wind is
   blowing from the south on  a thinly overcast
   night with the wind  at 2.5 m sec-1? The average
   effective stack height of these  sources is assumed
   to be 20 meters.
SOLUTION:   A thinly overcast night  with wind
   speed 2.5 m sec"1  indicates stability  of class E.
                                                        (It may actually be more unstable, since this is
                                                       in a built-up area.) To allow for the area source,
                                                       let 
-------
   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, 
-------
        = 2.7 x 10- (1.0) The decay of I1
   nificant for 2 hours
is insig-
    ••
      = 2.7 x 10~8 curies nr
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
Time,
minutes
5
15
30
60
Emergency Tolerance
Limits, g m~:t
1.2 x 10-1
8.6 x 10-=
4.9 x 10-=
2.5 x 10-=
   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 
-------
    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 + xyl
km
0.14
0.54
1.04
2.04
3.04
4.04
5.04
6.04
Of,
m
5.5
19
35
66
93
120
149
175
X (centerline),
g m- '
13.9
1.1
3.6x10-'
1.3 x 10-'
7.0 xlO-2
4.8x10--
3.5 xlO~2
2.7 x 10--
X (isopleth)
X (centerline)
1.8 XlO-3
2.27 x 10~2
6.94 xlO-2
1.92 xlO-1
3.57 x 10- l
5.20 xlO-1
7.14 xlO-1
9.26 x 10-1
y
a,
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
                                                                    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
C,  Sutton horizontal dispersion parameter
d  Sutton vertical dispersion parameter
d    inside stack diameter at stack top
DT (x,y,Q;H)    Total dosage
e    2.7183,  the base of natural logarithms
f (O,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
HM  effective height of emission  for a particular
     wind speed
k    von Karman's constant,  approximately equal
     to 0.4
K  eddy diff usivity
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 i  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 oi a square area source
 S  an index for stability
 tk  a short time period
                                                    t™
                                                    t»
                                                    Ta
                                                    T,
                                                    u
                                                    UN
                                                    V'
                                                    Vs
                                                    vs
                                                    w'
                                                    X
                                                    XL
                                                     xv
                                                     y
                                                     z

                                                     so
                                                     Sz~
                                                     AH

                                                     n
                                                     PA
(x J equals the ini-

(xr) equals the ini-

(xz) equals the ini-
                                                     •Jin
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 
-------
 0   the angle between the wind direction and a
     line source
 X   concentration
 Xcwi crosswind-integrated concentration
 X,i   a  ground-level  concentration for design pur-
     poses
 XK   inversion break-up fumigation concentration
 Xk   concentration measured over a sampling time,
     tk
 Xi,,.» maximum ground-level  centerline concentra-
     tion with respect to downwind distance
XB   concentration measured over a sampling -time,
     t»
y
~-  relative concentration

£"-  relative concentration  normalized  for wind
Q   speed
X (x,y,z;H)   concentration at the point (x, y,  z)
             from an elevated source with effective
             height, H.
X (x,9)   the long-term  average  concentration  at
         distance x, for a direction 6 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:
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):

                          /P
                                —-j=

                          -^
                                                       exp (—0.5p-) dp
                                         (A.2)
   Figure A-4 gives the area under the Gaussian
curve from —p to +p. This can be found from Eq.
(A.3):
                         /+P

                              w
                         —p
          . . r
Area (


exp (—0.5 p2) dp
                                                                                              (A.3)
                                Figure A-l.  The Gaussian distribution curve.
 Appendix 2
                                                                                                 61

-------
1.0

 8
 7
                                                   -i
 O.I
  9
  8
  7
  I
  !

                                                 \
                                                                                             ::;
                                                                I!

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.
                                                           ATMOSPHERIC DISPERSION  ESTIMATES

-------
                          0.5 1   2     5    10    20
                                               + P
0.01
                                                                                              99.8    99.99
                       Figure A-3.  Area under the Gaussian  distribution curve from —»  to p.
Appendix 2
                                                                                                                63

-------
        4.5
        i 0
        3 :
         2.5
        2.0
         1.5
         1.0
         0.5
         0.0
          0.01     0.1    0.5 1  2    5   10   20  30 40 50 60 70  80   90  95   98  99      99.8    99.99

                                         + P
                                            —=—  exp  (-0.5 p) dp

                                         -P
                  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 
-------
A
e>
Table  A-l   SOLUTIONS TO EXPONENTIALS B — exp [-O.SA'1
          The notation 2.16 E-l means 2.16 x 10~'
A

0.00
0.10
0.20
ft. 40
V . 3 »
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

2.00
2.10
2.2"
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3*00
3.10
3.20
3,30
3.4"
3.50
3.60
3.70
3.60
3.90
4,00
4.10
4.20
4.30
4.40
4.50
4*60
4.70
4.80
4.90
o.oo
B
1.00E 0
9.95E -1
*.80E -J
9.21E -1
6. Bit -1
(4.3SIL -1
7.811; -1
7.26E -1

6.0T£ -1
5.4AE -1
4,8'E -1
4.3CE -1

3.2-it -1
2.7flE -1

1 •<>«£ -1
1.6*11 -I
i.3«!E -1
lIinE -1
H.8-3E -2
7.10E -2
5.61E -2
4,3ot: .2
3.41E -Z

U9*E -2

1.11E -2

S^RE -3
4.32E -3
3.09E -3
2.1QE -3
1.53E -3
1.07E -3
7.3?E -4

3.3*>t -4
2^24E -4
V.4RE -4

6!2se .&
4.01E -5
2.54E -5
1.60E -5
9.93E -6
6.111; -6
0.01

l.OOE 0
9.9.4E -1
0.78F. -1
9.19F -1
8.78E -I
*.30E -1
7.77E -I
7.20F. -I
6.61E -1
*. OIF .1
"5.40£ -1
4.«1F -1
4.24E -I
3.7UF -I
3.20E -I
2.74F. -I
2.32E -1
1.94E -1
l»6t£ -I
1.33E -1
1.08): -1
R.70F -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
!>.79f: -3
4.1BE -3
2.19F -3
2.11E -3
1.48E -3
1.03E -3
7.05E -4
4.79E -4
3.22E -4
2. 155 -4
1.42E -4
Q.25E -5
5.98E -5
3.83E -5
2.43E -5
1.52E -5
9.46F -6
5.82P -6
0.02

10. 00£ -1
9.93E -I
9»7*>E ~1
9.1iSE -1
' 8.74E -I
8.25E -I
7.7ZE -I
7. i£ -3
5.60E -I
4.04E -3
2.8o£ -3
2.04E -3
l.4?E -3
9.8QE -4
6.7ȣ -4
4.61E -4
3. me .<,
2.0AE -4
1.36E -4
8.86E -•*
S.72E -5
3.66E -5
2.32E -5
1.45E -5
9.02E -6
5.54E •*•
0.03

1U.OOE .1
V.92E -1
9.74E -1
V.12E -1
H.69E «1
«.20E -V
7.66E -1
'.09E -1
6.49E -1
S.88E -1
».28E -1
«».69E -1
4.13E -1
3.60E -1
1.10E -I
Z.65E -1
Z.24E -1
1.87E -1
1.55E -1
1.27E -i
1.04E -1
H.32E -Z
6.62E -2
5.22E -2
4.07E -2
3.15E -2
2.41E -2
l«fl?E —2
1.37E -2
1.02E -2
'.46E -3
5.43E -3
3.91E -3
2.79E -3
1.97E -3
U38E -3
9.53E -4
6.53E -4
4.43E -4
2.07E -4
1.98E -4
1.30E -4
M.49E -5
S.48E -5
3.50E -5
2.21E -5
1.39E -5
«.59E -6
5.28E -6
0.04

9.99E -1
9.90E -1
•J.72E .1
«I08£ II
H.64E -I
«.\5E -1
7.61E -I
/.03£ -l
6.41E -1
5.02E -1
!>.22£ -1
'*.'i4E -1
4.0HE -1
3.5*E -1
3.06E -1
Z.61E -1
2.20E -3
1.84E -1
1.52E -1
1.21E -1
1.01E -1
h,14£ .2
6»4'E -2
•>,!"£ -2
a.97£ _2
3.07E -2
2.34E -2
1.77E -2
1.3^E -2
t,^«ie -3
vl2^e -3
S.2SE -3
3.7HE -3
Z.69E -3
l.VOE -3
1.3 IE -3
9.1HE -4
6.20E -4
4.26E -*•
Z.S6E -4
1.90E -4
1.25E -4
B.13E -5
5,^«c -5
-l.^^E -5
2.UE -5
J.12E -S
H.19E -6
5.02E -6
0.05

9.99E -I
9.89E -I
9.69E -1
B.41C .1
T . ^ * C *
9.04E -1
8.60E -1
B.IOE -i
7.55E -I
6.97E -I
6.37E -1
5.76E -1
5.16E -1
4.58E -1
4.02E -1
3.50E "1
3.01E -I
2.56E -1
2.16E -1
l.fllE -1
1.49E -1
1.22F -1
9.91E -2
7.96E -2
6.32E -2
4.97E -2
3,87£ .2
2.99E -2
2.2BE -2
1.72F. -2
1.29E -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.R2E -4
l.ZOp -4
7.78E -5
5.01E -5
3.20F -5
2.02E -5
1.26E -5
7.80E -6
4.78E -6
0,06

9.9BE -1
9.87E .1
9.67E .1
Q 37F -1
T • » * b •• ft
9.00E .1
8.55E -1
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
2.96£ .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
4.85E ,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
Z.51E -3
1.77E -3
1.23E -3
6.51E .4
5.B2E -4
3.93E -4
2,63E--4
1.75E' -4
1.15E -4
7.45E -5
4.79E -5
3.05E -5
1.93E -5
1.20E .5
7.43E -6
4.55E -6
0.07

9.986 -I
9.86E .1
9.64E .1
9»4C _i
• *^C • »
8.95E -1
B.50E -1
T.99E -V
7.44E -I
6.85E -1
6.25E -1
5.64E -1
5.04E -1
4.46E <*1
3.91E -1
3.39E -I
2.92E -1
2.48E -1
2.09E -1
1.74E -1
l.^E -1
1.176 -1
".50E -2
7.60E -2
6.03E -2
4.73E -2
3.68E -2
2.B3E -2
2.16E -2
1.63E -2
1.22E -2
B.98E -3
6.58E -3
4.77E -3
3.42E -3
2.43E -3
1.71E -3
1.19E -3
«.2QE -4
5.60E -4
3.78E -4
Z.53E -4
1.68E -4
1.10E -4
7.13E -5
4.58E -5
2.92E -5
I.B4E -5
1.15E -5
7.00E -6
4.33E -6
O.OB

9.97E -1
9.B4E .1
9.62E -1
9.)nP -1
* *ut •*
8.91E -1
8.4JE .1
T.94E -1
T.38E .1
6.79E -t
6.19E -1
5.58E .1
*.99E -i
4.41E .1
3.86E .1
3.35E -1
2.87E .1
2.44E -1
2.05E .1
I. TIE -I
!.<•!£ -1
1.15E -1
9.29E -.2
T.43E .2
5.89E -2
4.62E -2
3.59E -2
2.76E -2
2.10E .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 •*
5.3BE -4
3.63E -*
Z,«3E .4
1.61E -4
1.05E -*
6.83E .5
*.38E -5
2.79E .5
1.75E "5
1.09E -5
6.74E -6
4.12E -6
0,09

9.96C .1
9.82E .1
9.59E .1
9.27E ml
T V • * « ^ •
B.87E .1
8.40E .1
T.88E .1
7.32C .1
6.73E .1
6.13E .1
5.52E .1
4.93E .1
4.35E .1
3.B1E .1
3.30E .1
2.83E .1
2.40E .1
2.02E .1
1.68E .1
1.S8E .1
1.13E .1
9.09E .2
7.27E .2
5.75E .2
4.51E -2
3.49E .2
2.68E .2
2.04E .2
1.54E .2
1.15E .2
8.45E .3
6.17E -3
4.46C .3
3.20E .3
2.27E -3
1.59E -3
1.11E .3
7.60E .4
5.18E -4
3.49E .4
2.33E .4
1.54E -4
1.01E -4
6.S3E .5
4.19E .5
2.66E .5
1.67E .5
1.04E .5
6.42E .6
3.92E .6

-------
                                                         Table A-l (continued)   SOLUTIONS TO EXPONENTIALS
•B
(t

0.
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
6.40
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
8.10
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
6
3,nE -6 •
2.25E -6
1.34C -6
7.9St -7
4.6*E -7
2.70t -7
l.S-it -7
H.81E -H
4.9<>E -8
2.76E. -<>fc:-n
2.29E-11
1.13E-11
5;5V,E-12
2.68E-12
1.29E-12
6.10E-13
2.87E-13
1.34E-13
6.15E-14
P.BOE-14
1.27E-14
5.6AE-15
*.51E-15
1.10E-15
4.77E-16
2.0SE-16
8.71E-17
3.67E-17
1.53E-17
6.31E-18
*.58E-18
1.04E-18
4.VflE-19
1.66t-19
6.50E-20

7.15t -'
4.1PE -7
2.4?£ -7
1.39£ -7
7.8*-e -n
4.41E -1
2.4'5E -«
1.35E -S
7.3^E "5
3.97£ -9
2.12E -9
1.12E -•?
5.8"E-10
3.0SE-10
1.56E-10
7.94E-H
4.00E-11
1.99E-11
9.81E-12
<..79£-12
2.32E-12
1.11E-12
5.25E-13
2.46E-13
l.KE-13
5.2ftE-l*
2.39E-H
1.09E-U
4.81E-15
Z.nE-l-S
9.30E-16
4.03E-1A
l.TIE-U
7.33E-17
3.0?E-17
1.28E-17
5.2SE-19
2.15E-U
8.69E-19
3.47E-19
1.37E-19
5.3")E-20
2.09E-20
8.02E-21
3.05E-21
1.15E-21
4.2RE-22
0.03

3.21E -6
1.9?E -6
1.15E -6
h.7RE -7
1.96E -7
2.29E -7
1.31E -7
'.42E -8
4.16E -8
2.31E -8
1.27E -8
ft.92E -9
3.73E -9
1.99E -9
1.05E -9
5.50E-10
2.85E-10
1.46E-10
'.<»2E-11
3.73E-11
1.86E-11
9.UE-12
4.A6E-12
2.15E-12
1.03E-12
*.87E-13
2.28E-13
1.06E-13
4.86E-U
2.21E-U
9.96E-15
*.A4E-15
1.96E-15
B.56E-16
3.70E-16
1.59E-16
6.72E-17
2.82E-17
1.17E-17
4.S3E-18
1.97E-18
'.93E-19
3.17E-19
1.25E-19
4.90E-20
1.90E-20
7.29E-21
2.77E-21
1.04E-21
3.RHE-22
0.0'«

3.05E .6
1.83E -6
l.O'JE -6
6.41E »7
3.7-5E -7
2. HE -7
1.2-VE -7
7.01E -fl
3.93E -8
2.1BE -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
1.4»E-ll
1.7TE-11
8.51E-12
4.15E-12
2.00E-12
9.55E-13
E -8
1.13E -8
6.12E -9
3.29E -9
1.75E -9
9.25E-10
4.83F-10
2.50E-10
1.28E-10
6.47E-11
3.25E-H
1.61E-H
7.92E-12
3.86E-12
1.86E-12
8.87E-13
4.19E-13
1.96E-13
9.07E-1*
4.16E-14
1.89E-U
8.4BE-15
3.77E-15
1.66E-15
7.24E-16
3.13E-16
1.34E-U
5.66E-17
2.37E-17
9.83E-18
4.04E-18
1.64E-18
6.61E-19
2.63E-19
1.0*E-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
5.77f .7
3.36E -7
1.94E -7
1.11E -7
6.25E -8
3.49E -B
1.9«E -8
l.OftE -8
5.7ft£ -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-1B
1.50E-1B
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.B8E-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-14
7.22E-15
3.20E-15
1.41E-15
6.13E-U
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. DIE -7
1.73E -7
9.87E -8
5.57E -8
3. HE -8
1.72E -8
9.39E -9
S.09E -9
2.73E .9
1.45E -9
7.62E-10
3.97E-10
2.04E-10
1.04E-10
5.27E-11
2.6JE-H
1.30E-H
6.39E-12
3.10E-12
1.49E-12
7.09E-13
3.34E-13
1.56E-13
T.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
7.53E.18
3.08E-18
1.25E-18
5.02E-19
1.99E-19
T.84E-20
3.05E-20
1.18E.20
4.50E-21
1.70E-21
6.36E-22
2.36E-22
0.09

Z.37E -6
1.42E .6
8.38E .7
4.91E -7
2. BSE -7
1.64E .7
9.32E .8
5.25E -6
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-U
4.92E-11
2.46E-11
1.22E-11
5.95E-12
2.88E-12
1.38C.12
6.58t.l3
3.09E-13
1.44E-13
6.65E-14
3.04E-14
1.37E-14
6.14E-15
2.72E-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
S.76E-22
2.13E-22

-------
                          Appendix 4:  CONSTANTS, CONVERSION


                             EQUATIONS, CONVERSION TABLES

                        Constants


                               e = 2.7183 — -- = 0.3679
                                           e


                               * = 3.1416 -I— = 0.3183
                                   6.2832 -A- = 0.1592
                                 = 2.5066 -4=- — 0.3989
                                          V2-



                                         — =• = 0.7979
                                          \/2-
                           (2T-)=/== 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                                                                               69

-------
CONVERSION FACTORS - VELOCITY
DESIRED UNITS METERS
PER SEC
GIVEN UNITS




ATMOSPHI
£
8
DISPERSION
B
H
i
METERS
PER SEC
FT
PER SEC
FT
PER MIN
KM
PER HR
MKSTAT)
PER HR
KNOTS
MMSTAT)
PER DAY
TO CONVERT A
AND BENEATH


1.0000
E 00
3.0480
E-01
5.0800
E-03
2.7778
E-01
4.470*
E-01
5.1479
E-01
1.8627
E-02
VALUE FROM A GIVEN
THE DESIRED UNIT.


FT
PEP SEC
3.2808
E 00
1.0000
E 00
1.6667
E-02
9.1134
E-01
1.4667
E 00
1.6889
E 00
6.1111
E-02
UNIT TO A
NOTE THAT


FT KM
PER MIN PER HR
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
3.6000
E 00
1.0973
E 00
1.8288
£•02
1.0000
E 00
1.6093
E 00
1.8532
E 00
6.7056
E-02
MKSTAT)
PER HR
2,2369
E 00
6.8182
E-Ol
1.1364
E-02
6.2137
E-Ol
1.0000
E 00
1.1516
E 00
4.1667
E-02
DESIRED UNIT. MULTIPLY THE GIVEN
E-XX MEANS 10 TO THE -XX POWER.






KNOTS
1.9425
E 00
5.9209
E-Ol
9.8681
E-03
5.3999
E-01
8.6839
E-Ol
1.0000
E 00
3.6183
E-02
VALUE BY


MI(5TAT>
PER DAY
5.3686
E 01
1.6364
£ 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



-------
•d
ns
§
a.









CONVERSION FACTORS - EMISSION RATES
DESIRED
GIVEN UNITS
GRAMS
PER SEC
GRAMS
PER WIN
KG
PER HOUR
KG
PER DAY
LBS
PER MIN
LBS
PER HOUR
LBS
PER DAY
TONS
PER HOUR
TONS
PER DAY
UNITS GRAMS
PER
1.0000
e o.o
1.6667
E-02
2.7778
E-01
1.157*
E-02
7.5599
E 00
1.2600
E-01
5.2499
E-03
2.5200
E 02
1.0500
E 01
GRAMS
SEC PER MIN
6.0000
E 01
l.OOOQ
E 00
L.666T
E 01
6.9444
E-01
4.5359
E 02
7.5599
E 00
3.1499
E-01
1.5120
E 04
6.2999
E 02
KG
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
8.6400
E 01
1.4400
E 00
2.4QOO
E 01
1.0000
E 00
6.5317
E 02
1.0886
E 01
4.5339
E-01
2.1772
E 04
9.0718
E 02
LBS
DAY PER
1.3228
E-01
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
MJN PER HOUR
7.9366
E 00
1.3228
E-01
2.20*6
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
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
DA* PER HOUR
3.96B3
E-03
6.6139
£.05
1,1023
£-03
4,5930
£.05
3.0000
£.02
5.0000
£.04
2.0833
E-OS
1.0000
£ 00
4.1667
£.02
TONS
PER
9.9240
E-02
1.9873
E-03
2.6455
E-02
1.1023
E-03
7.2000
E-01
1,2000
£•02
5.0000
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
OTVEN UNITS
CM
MICRON
KILOMETER  INCH
FOOT
YARD
MILE(NAUT)






H
1
*N
O
g
on
&n
1
M
3
H
M
00
METER
CM
MICRON
KILOMETER
INCH
FOOT

YARD
MILE(STAT)

Mil C(NAUT)

TO CONVERT A
AND BENEATH

1.0000
E 00
1.0000
E-02
1.0000
E-06
1.0000
E 03
2.3400
E-02
3.0480
E-01

9.1440
E-01
1.6093
E 03

1.8532
E 03

VALUE FROM A GIVEN
THE DESIRED UNIT,

1.0000
E 02
1.0000
E 00
1.0000
E-04
1.0000
E 09
2.3400
E 00
3.0480
E 01

9.1440
E 01
1.6093
E 09

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 03

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

1.8332
E 00

3.9370
E 01
3.937Q
E-01
3.9370
E-05
3.9370
E 04
1.0000
E 00
1.2000
E 01

3.6000
E 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
3.2806
E-02
3.Z8C8
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
£.02
3.3333
E.01

1*0000
E 00
1*7600
E 03

2.0267
E 03

THE FACTOR

6.2)3',
E- '4
6.2137
£.06
6.2137
£.10
6.7137
£.01
1.3783
£.05
1.8939
£.04

9.6818
£.04
1,0000
£ 00

1.1916
E 00

OPPOSITE THE

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

GIVEN UNITS


-------
•a
•a
n
a
       CONVERSION FACTORS - AREA


             DESIRED UNITS


       GIVEN UNITS


       so METER






       .SO KM






       SO CM






       SO INCH






       SO FOOT






       SO YARD





       ACRE





       SO STAT             2.5900     2.5900     2.5900     4.0145     2.787B     3.09T6     6.4000     1.0000     7.5*11

       MILE                 E 06       E 00       E 10       E 09       E 07       E 06       E 02       £00       £-01
SO METER
1.0000
E 00
1.0000
E 06
1,0000
E-04
6.4516
E-04
9.2903
E-02
8.3619
E-01
4.0469
E 03
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
SQ CM
1.0000
E 04
1.0000
f. 10
1.0000
E 00
6.4516
E 00
9.2903
E 02
8.3613
E 03
4.0469
E 07
SQ INCH
1.5500
E 03
1.5500
E 09
1.5300
E-01
1.0000
E 00
1.4400
E 02
1.2960
E 03
6.2726
E 06
50 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
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
ACRE
2.4710
E-04
2.4710
E 02
2,4710
E-08
1.5942
E-07
2.2957
E.05
2.0661
E.04
1*0000
E 00
SQ STAT
1IUE
3.8610
E-07
4.8610
E-01
3.8610
E-ll
2.4910
E-10
3.5870
E.OB
3.2283
E-07
1.5625
E-03
SQ NAUT
MILE
2.9116
E-07
2,9116
E-01
2,9116
E-li
1.8785
E-10
2.7Q50
E-08
2.4345
£-07
1.1783
E-03
       so NAUT

       Mil E
3.4345     3.4345     3.4345     5.3235     3.6969     4.1076     8,4869     1,3261     I.0000

 E 06       E 00       E 10       E 09       E 07       E 06       E 02       E 00       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 BENF.ATH THE DESIRED UNIT,   NOTE THAT E-XX MEANS 10 TO THE -xx POWER.

-------
   rp - .VPLU'-IE

IT'ITS CU ''ETES    LITE"      CU INCH    CU  FOOT
                                                                            5TAT    CU  NAUT     j 5 FLUID  J 5  QUART   U S GALLON
                                                                               MILE        MILE      DUNCE












J^
H
g
0
C/3
19
a
§
o
1

1
M
O

8
GIVEN UNITS
CU M£TE»

L'lTf.R

cu INCH

cu FOOT

cu STAT
MtLF
CU NAUT
MtLF


U S FLUID
OUMCF

U S QUART


U S GALLON


TO CONVFRT A
AND BENFATH

1,0000 9.99<»7
F "0 E 0^
1.0000 t.OO^O
E-13 E 00
I. 6187 1.63H7
t-15 E-OS2
2.8417 2.B316
F-02 £ 01
4.U8/ 4.16*1
£ 09 E I/
6,3650 6.164V
F 09 E I/


2.9574 2.9573
F-05 £-02

9, 4635 9.4613
E 02 E 0->

3,7854 1,78r>3
E-03 £ 00

VAl UP FROM A GIVEN UNP TO A
THE DESIRED UNIT. NflTr. THAT

6.1023
E 04
6.1"25
E 01
I. 0000
F 00
1.7280
E 03
2.5436
E 14
3.8«4?
E 14


1.8047
P. 00

5.7750
E 07

2.3100
E 02

DESIRED

S.SS^
E 01
3.5*15
E-D2
5.^70
E-04
l.OOQQ
E 00
1.4720
E 11
2', 2478
E 11


1.0444
E-03

3.1420
E 04

1.316B
E-Oi

UNIT, MULTIPLY

2,3991
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
4,4488
E-12
6.54R6
E-01
1,0000
E 00


4,6462
E-15

1.4868
E-07

5.9472
E-13

VALJE 0^

3.38l«
£ 04
3.3815
E Oi
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
£.06

OPPOSITE

2.6*17
E 02
2.6418
E-01
4,3290
E-03
7.*805
E 00
1.1011
E 12
1.6815
E 12


7.8125
E-03

2.5000
E 05

1,0000
E 00

THE GIVEN 1
E-XX MEAMS 10 TO THE -XX POWER.
VI

-------
•a
•O
n
a
9









CONVERSION FACTORS - MASS
DESIRED
GIVEN UNITS
GRAM
MICROGRAM
KILOGRAM
METRIC TON
SHORT TON
LONG TON
GRAIN
OUNCE
(AVDP)
LB (AvDPj
UNITS GRAM
1,0000
E 00
1.0000
E-06
1.0000
E 03
1.0000
E 06
9.0718
E 05
1.0160
E 06
6.4799
E-02
2.8349
E 01
4,5559
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
i.oooo
E-06
1.0000
E-12
1.0000
E-03
1.0000
E 00
9.0718
E-Ol
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
9.0421
E-07
9.8421
E-13
9.8421
E-04
9.8421
£-01
8.9286
£-01
1.0000
E 00
6,3775
E-08
2,7902
E-05
4.4643
E-04
GRAIN
1.5432
£ 01
1.5432
E-05
1.5432
E 04
1.5432
E 07
1.4000
E 07
1.5680
£ 07
1.0000
E 00
4,3750
E 02
7,0000
E 03
OUNCE
(AVDP)
3.5274
E-02
3,5274
£•08
3,5274
E 01
3,3274
£ 04
3.2000
E 04
3.5840
£ 04
2.2857
£.03
1.0000
E 00
1.6000
"E 01
IB (A
2,2046
E-03
2.2046
E-09
2.2Q46
E 00
2.2046
E 03
2.0000
E 03
2.2400
E 03
1.4286
E-04
0.^500
E-02
1.0000
E 00
TO CONVERT A VALUE FROM A GIVEN UNjT 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 - FLOW

             DESIRED UNITS CU ^ET£R   CU METER   LITER      LITER      LITER      CU FT      CD FT      CU FT      CU C"l
                              PER SEC    PER HR     PER SEC    PER MlN    PER HR     PER SEC    PER MIN    PER HR     PER SEC
        GIVEN UNITS


>
0
en
0
|
i
2
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
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
A VALUE FROM A GH
3.6000
E 03
1.0000
E 00
3.6001
E 00
6.0002
£•02
1.0000
£•03
1.0194
E 02
1.6990
E 00
2.8317
E-02
3.6000
E-03
/EN UNIT TO A
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 I
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
JNIT, MULTII
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
»LY THE GIVI
3,5314
E 01
9.8096
E-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
:N VALUE BY
2.1189
E 03
5.8857
E-01
2.1189
E 00
3.5315
E-02
5,8859
6,0000
E 01
1,0000
E 00
1,6667
£•02
2,1189
E-03
THE FACTOR
1,2713
E 05
9,5314
E 01
1.2714
E 02
'.1189
E 00
9,5315
E-02
9,6000
E 03
6,0000
e. 01
1.0000
£ 00
1.2713
£•01
OPPOSITE Tl
1.0000
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
«E GIVEN i
       AND BENEATH THE DESIRED UNIT.   NOTE THAT E-XX MEANS 10 TO THE -XX POWER.
W5

-------
13
It
P

f
>&.
         CONVERSION FACTORS - CONCENTRATION, DENSITY

              DESIRED UNITS GRAM PER   «G PER     MICROGRAM  MjCROGRAM  GRAIN PER  OUNCE PER  LB PER     GRAM PER   LB  PER
                              cu METER   cu METER   PER cu M  PER LITER      cu FT      cu FT      cu FT      cu FT   cu IETER
         GIVEN UNITS
GRfcW PER
CU METER
MS PER
CU METER
MICROGRAM
PER CU l»
MICROGRAM
PER LITER
GRAIN PER
CU FT
OUNCE PER
CU FT
LB PER
CU FT
SRAM PER
CU FT
LB PER
CU METER
I. 0000
E 00
1.0000
E-03
1.0000
E-06
9.999?
E-04
2.2863
E 00
1.0011
E 03
1.6018
E 0*
3.531*
E 01
4,5359
E 02
1.0000
E 03
1.0000
E 00
1.0000
E-03
9,9997
E-01
2.2883
E 03
1.0011
E 0«
1.4.018
E Of
3,5314
E 0
-------
00
         CONVERSION FACTORS -  DEPOSITION RATf?
(SHORT TON ,STAT.  MILE)
              DESIRED UNITS GM PER SQ  KG PER SO  MG PER SO  TON PER SO OZ PER SO  IB PER     GM PER SQ  16 PER SO.
                              M PER MO  KM PER MO  CM PER MO  Ml PER MO  FT PER MO ACRE PERMO  FT PER MO  IN PER MO
         GIVEN UNITS



>
1
o
d
I
1
H
1
X
GM PER SO
M PER MO
KG PER SO
KM PER MO
MG PER SO
CM PER MO
TON PER SO
MI PER MO
OZ PER SO
FT PER MO
LB PER
ACRE PERMO
GM PER SO
FT PER MO
MG PER SO
IN PER MO
TO CONVERT A
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
VALUE FROM A GIVEN
THE DESIRED UNIT.

1.0000
E 03
1.0000
E 00
i.oooo
E 04
3.5026
E 02
3.0515
E 05
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
2.8550
E 00
2.8550
£•03
2.8550
E 01
1.0000
E 00
8.7120
E 02
3.2000
£•01
3.0731
E 01
4.4252
E 00
DESIRED 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
£•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

S
         CONVERSION FACTORS - PRESSURE


              DESIRED UNITS MILLIBAR   BAR


         GIVEN UNITS
ATMOSPHERE DYNES      *G
            PER SO CM  PER SO CM
IBS        MM MERCURY IN MERCURY

 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
I. 0000
E 03
1.0139
E 03
1.0000
£•03
9.8066
E 02
6.89*7
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
3.386*
E-02
9,8692
E-0*
9,8692
E-01
1,0000
E 00
9.8692
E-07
9.678*
E-01
6.80*6
E-02
1.3158
E-03
3.3*21
E-02
1.0000
E 03
1.0000
E 06
1.0133
E 06
1.0000
E 00
9.8066
E 03
6.89*7
E 0*
1.3332
E 03
3.386*
E 0*
1.0197
E-03
1.0197
E 00
1.0332
E 00
1,0197
E-06
I. 0000
E 00
7.0307
E-02
1.3595
E-03
3.*932
E-02
l.*50*
E-02
l.*50*
E 01
l.*696
E 01
1.*SO*
£-05
1«*223
E 01
1.0000
E 00
1.9337
E-02
*.911S
E-01
7.5006
E-Ol
7.5006
E 02
7.6000
E 02
7.5006
E-0*
7.39.56
E 02
5,1715
E 01
1.0000
E 00
2.5*00
E 01
*,9530
E-02
'.9530
E 01
2,9921
E 01
*.95»0
E-05
$.8999
E 01
2.0360
E 00
4.9370
E-02
1.0000
E 00
        TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE GIVEN
        AND BENEATH THE DESIRED UNIT.   NOTE THAT E-XX MEANS 10 TO THE -XX POWER.
                                 VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS

-------
         CONVERSION FACTORS - TIME
              DESIRED UNITS SECOND
         GIVEN UNITS
                               MINUTE
HOUR
WEEK
MONTH <28» MONTH  MONTH on YEAR (365> YEAR <366)





>
1
3
I
1
SECOND
MINUTE
HOUR
WEEK
MONTH (26)
MONTH ISO)
MONTH (3D
YEAR 1365}
YEAR (366)
TO CnNUFRT A VA
1.0000
E 00
1.6667
E-02
2.7778
E-04
1.6534
E-06
4.1336
£-07
3*8580
E-07
3.7336
E-07
3.1710
E-08
3.1623
E-08
LUF FROM A GIY
6.0000
E 01
1.0000
E 00
1.6667
E-02
9.9206
E-05
2.4802
E-05
2.3148
E-05
2.2401
E-05
1.9026
E-06
1.8974
£-06
/EN UNIT TO
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
A DESIRED I
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
INlTi MIlLTIf
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
>l Y THE GIVf
2.5920
E 06
4.3200
E 04
7.2000
E 02
4.2857
E 00
1.0714
E 00
1.0000
E 00
9.6774
E-01
8.2192
E-02
8.1967
E-02
•N 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
E.02
THE FACTOR
3.1936
E 07
9.2560
E 05
B. 7600
E 03
9.2143
E 01
1.3036
E 01
1.2167
E 01
1.1774
"E 01
1.0000
E 00
9.9727
E.01
OPPOSITE Tk
3.1622
E 07
5,2704
E 09
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
IE GIVEN I
£
AND BENEATH THE DESIRED UNIT.   NOTE THAT E-XX MEANS 10 TO THE -XX POWER.
yi

-------
•a
X)
re
a.
*»•
CnNvf ^sir:\i t-'f"r
GIVEN UMTS
(IMT)
Kll OWATT
(IMT)
MEGAWATT
(INT)
CA| (INT)
PER r,Ec
BTU
PER 'UN
BTU
PER MR
JOULES A8S
PER SEC
H/ATT (Ansi
ELECT.
HORSEPOWER

,"S - -?-.*=«
IT'S *MT.
( p; n '
I. 0^00
r i )
F 03
1.0000
'E ot
4.1876
F 1 0
1 ^"JflR
F 01
2.9313
F-01
9.9odl
E-01
9.9PH1
F-01
7.4586
F 02


; E 01


BTU
IN PER HR
3.4114
E 00
3.4114
E 03
3.4114
E 06
1.4286
E 01
6.0000
E 01
1.0000
E 00
3.4108
E 00
3.41Q8
E 00
Z.5444
E 03


J3JLE5
PER
1.00Q2
E 00
1.0002
E 03
1.0002
E 06
4.1884
E 00
E 01
2.9319
E-01
1.0000
E 00
1.0000
E 00
7.4600
E 02


AB5 WATT (ABS)
SEC
1.0002
E 00
1.0002
E 03
1.0002
E 06
4.1884
E 00
1.7591
E 01
2.9319
E-01
1.0000
E 00
1.0000
E 00
7.4600
E 02


ELECT.
HORSEPi
1,3407
E-03
1.3407
E 00
1.3407
E 03
5.6145
E-03
2.3581
E-02
3.9301
E-04
1.3405
E-03
1.3405
E-03
1.0000
E 00
TO CONVTRT A \/AI u<~ FROM A GIVEN UMII  TJ  A  DESIRF^
AND Bt'NFATH THE JPStRED UNIT.   NOTr.  THAT  E-X)
JNIT, MULTIPLY THE GWEM VALUE »Y THE  FACTOR  OPPOSITE THE GIVEN UNITS
   10 TO THE -XX PO^ER.

-------
CONVERSION FACTORS - ENtRQY, WORK
     DESIRED UNITS ERG        DYNE-CM
GTVEN UNITS
ABS JOULE  CAL (INT)   CAL (15)    INT KW-HR  ABS KW-HR  8TU










>

Ss!
o ,
C/3
•fl
s
»
ft
g
55
IS
g
£
o
2
M
Cfl
H
8 •
ERG 1.0000
I 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 UNIT.





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
£13

1.0551
E 10


UNIT TO A
NOTE THAT





1.0000
E-07
1.0000
E-07
1.0000
E 00
4.1868
E 00
4.1855
E 00

3.6007
E 06



3.6000
E 06

1.0551
E 03


DESIRED
2.3884
E-08
2.3884
E-08
2.3884
E-01
1.0000
E 00
9.9968
E-01

8.6QOO
E 05



8.5984
E 05

2.5200
E 02


UNIT, MULTIPLY
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
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
£.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
£.11
9.4781
£•11
9.4781
£-04
3.9683
£•03
3.9671
£•03

9.4128
£ 03



3.4U1
E 03

1.0000
E 00


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































-------