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

     tn, is dependent upon both the strength of the
  inversion and the rate of heating at the surface.
  Pooler  (1965) has derived an expression for esti-
  mating  this time:
                                  2   ;    (5.5)

            time required  for the mixing layer  to
            develop from the top of the stack to the
            top of the plume, sec
       PB = ambient air density, g m~*
       cp = specific heat of air at constant pressure,
            cal g-1  °K-'
       R = net rate of sensible heating of an air
            column by solar radiation, cal m~2 sec"1
       SQ
       — = vertical potential temperature gradient,
                     ST
            °K m"1 ~——\- T (the adiabatic lapse
            rate)      Sz
       h, = height of base of the inversion sufficient
            to be above the plume, m
       h = physical height of the stack, m

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

 heated and (—^—L J  js 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):

                                          (5.6)

         t = time required  to eliminate the inver-
            sion to height z, sec
         z = height  to which the inversion has been
            eliminated, m
       K = eddy diffusivity for heat, m* sec"1

Rewriting to compare with Eq. (5.5),

         h,' — h'
           4 K
                                          (5.7)
Hewson (1945) has suggested a value of 3 mz sec"1
for K.

PLUME TRAPPING

   Plume trapping  occurs  when  the plume  is
trapped between the ground surface and  a stable
                                                    layer aloft. Bierly and Hewson (1962) have sug-
                                                    gested the use of an equation that accounts for the
                                                    multiple eddy reflections from both the ground and
                                                    the stable layer:
                                                       X (x,0,z;H) =
                                                       -fexp	-
                                                                     z + H — 2 NL
                                                                     z — H + 2 NL
                                                    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 a, = 0.47 L (see Chapter 3). It is as-
                                                    sumed that  at this distance, XL,  the stable layer
                                                    begins to affect the vertical distribution so that at
                                                    the downwind distance, 2 XL, uniform vertical mix-
                                                    ing has taken place and the following equation can
                                                    be used:

                                                                     Q
                                                                   —   T „  6XP ' —
                                                                      ffy L U
                                          (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-

tance where  a, = ~~F ₯L.  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:
       . O.H)
--HIT]
   xU,0,0)
                       exp —
    H
              y- [1.0 + exp —0.5(2 V2)=]

                       exp —0.5 (V2)-

              4- (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 a, and H such that the concentration
at ground-level at a given distance from the source
is the same as the concentration at plume level.
This condition should occur where:

           H
The value  H/w, = 1.10 satisfies this  expression,
which can be written as ot = 0.91 H (see problem
10).

TOTAL DOSAGE  FROM  A FINITE RELEASE

   The total dosage,  which is  the  integration of
concentration over the time of passage  of a plume
or puff, can be obtained from:
                                         (5.10)
   where DT = total dosage, g sec m 3
   and QT = total release, g
   The a's should be  representative of the time
period over which the release takes place, and care
should be taken to consider the x-axis along the
trajectory or path of the plume or puff travel. Large
errors can easily occur if the  path is not known
accurately. The estimate of this path is usually in-
creasingly difficult with shorter release times.  DT
can also be given in curie sec m~s if QT is in curies.

CROSSWIND-INTEGRATED CONCENTRATION

   The ground-level crosswind-integrated  concen-
tration is  often of interest. For a continuous ele-
vated source this concentration is determined from
Eq. (3.2)  integrated with respect to y from ~x  to
+ v (Gifford 1960a) giving:
                       Xcwi
                                                                  cr. U
                    exp I	^
                    In diffusion experiments the  ground-level cross-
                    wind-integrated concentration is often determined
                    at particular downwind distances from a crosswind
                    line or arc of sampling measurements made at this
                    distance.  When the source strength, Q, and average
                    wind speed, u, are known, a. can be estimated in-
                    directly even though no measurements were made
                    in the vertical. If any  of the tracer is lost through
                    reaction or deposition,  the resulting a, from such
                    estimates will not represent  the vertical dispersion
                    (see problem 18).

                    ESTIMATION  OF CONCENTRATIONS FOR
                    SAMPLING TIMES LONGER THAN  A
                    FEW MINUTES

                       Concentrations directly downwind from a source
                    decrease with sampling time mainly because of a
                    larger 
-------
    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 at  t~°-17.  Note that these estimates were based
 ::pon 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:
                  Xe = X*
                           **
                                         (5.12)
 where XB is  the desired concentration estimate for
 the sampling time, t6; 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
 month to 10 years). A stability wind rose gives the
 same  type of information for each stability class.

   If the wind directions are taken to 16 points and
 it is assumed that the wind directions within each
 sector are distributed randomly over a period of  a
 month or a season, it can further be assumed that
 the effluent  is uniformly distributed in the hori-
zontal within the sector  (Holland, 1953, p.  540).
The appropriate equation for average concentration
is then either:
                           exp
                            f_J_fJLVl
                            [    2 U J J
      2.03Q
      a, ux
                                                                    exp
                          I  ( H  Vl
                          T\~) J
                                                                                             (5.13)
                                                       or
                                                                            2.55 Q
                                         (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 (e,s,N)
     (x,G)
                   N
                                      16
exp
                                         (5.15)
where f (e, S, N) is the frequency during the period
       of interest that the wind is from the  direc-
       tion 6, for the stability condition, S, and
       wind speed class N.
   «r,s is the vertical dispersion parameter evaluated
       at the distance x for the stability condition S.
   UN is the representative wind speed for class N.
   Hu is the effective height of release for the wind
       speed UN.

   Where stability wind rose information cannot be
obtained, a first-order approximation may be made
of seasonal  or  annual average concentrations by
using the appropriate wind rose in the  same man-
ner,  and assuming the neutral stability  class, D,
only.

METEOROLOGICAL  CONDITIONS
ASSOCIATED WITH MAXIMUM
GROUND-LEVEL CONCENTRATIONS
                                 concentra-
1.  For ground-level  sources
   tions occur with stable conditions.
38
       ATMOSPHERIC DISPERSION ESTIMATES

-------
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-
    no/ be estimated from the material presented in
    this workbook.
3. For elevated sources mp*i""im 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 p™*imtim 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
                                                                                     (•.r.H)
                                                                                              UPWIND
                                                           RECEPTOR
                                                           (0,0,0)
                                                    DOWNWIND
                                                                    d.y.O)
                                                    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 ma^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, aro.  A virtual dis-
tance, x7, can  then be found that  will give this
standard deviation.  This is just the distance that
will yield the appropriate value for 
-------
   When estimating concentrations from finite line
sources, one must account for "edge effects" caused
by the end of the line source.  These effects will of
course extend to greater cross-wind  distances as
the distance from the source increases. For concen-
trations from a finite  line  source oriented  cross-
wind, define the x-axis in the direction of the mean
wind and passing through the receptor of  interest.
The limits  of the line source can be defined as ex-
tending from y, to y, where y, is less than y2.  The
equation for concentration (from Button's (1932)
equation (11), p. 154), is:
X (x,0,0;H) =
                                         (5.20)
                       »y         "j
The value of the integral can be determined from
tabulations given in most statistical tables (for ex-
ample, see Burrington (1953), pp. 273-276; also see
problem 24).

INSTANTANEOUS  SOURCES

   Thus far we have considered only sources  that
were emitting continuously or for time periods equal
to or greater than the travel times from the  source
to the point of  interest.  Cases of instantaneous re-
lease, as from an explosion, or short-term releases
on the order of seconds, are often of practical  con-
cern. To determine concentrations at any position
downwind, one must consider  the  time interval
after the time of release and diffusion in the  down-
wind direction  as well as lateral and vertical diffu-
sion. Of considerable importance, but very difficult,
is the  determination of the path or trajectory of
the "puff."  This is most important if concentra-
tions are to be determined at specific points.  Deter-
mining the trajectory is of less importance if knowl-
edge of the magnitude of the concentrations for
particular downwind distances or travel times  is
required without the need to know exactly at what
points  these concentrations occur. Rewriting  Sut-
ton's (1932)  equation (13), p.  155, results in an
equation that may be used for estimates of concen-
tration downwind from  a release from height, H:
     (x,y,0;H) =
(/ir)J/- o, a, a,
               exp
                                      f - -J-
                                      I     2
   -l-Hi-)1]
 (The numerical value of (2»)8/I is 15.75.)
                                    The symbols have the usual meaning, with the
                                 important exceptions that QT represents the total
                                 mass of the release and the a's are not those eval-
                                 uated with respect to the dispersion of a continuous
                                 source at a fixed point in space.

                                    In  Eq. (5.21)  the o's  refer  to dispersion sta-
                                 tistics  following the motion of the expanding puff.
                                 The cz is  the standard deviation of the concentra-
                                 tion distribution in the puff in the  downwind direc-
                                 tion, and t is  the time after release.  Note that
                                 there is no dilution in the downwind direction by
                                 wind speed. The speed of the wind mainly serves
                                 to give the downwind position of the center of the
                                 puff, as shown  by examination of  the exponential
                                 involving  a,. Wind speed may  influence the dis-
                                 persion indirectly because the dispersion parameters
                                 
10
4
1.3
a*
15
3.8
0.75
"J
300
120
35
°t
220
50
7
                REFERENCES

Bierly, E. W., and E. W. Hewson, 1962:  Some re-
   strictive meteorological conditions to be  con-
   sidered in the design of stacks. J. Appl. Mete-
   orol., 1, 3, 383-390.

Burington, R. S., 1953: Handbook of Mathematical
   Tables  and Formulas.  Sandusky, Ohio, Hand-
   book Publishers, 296 pp.

Cramer, H.  E., 1959:  Engineering  estimates  of
   atmospheric dispersal capacity. Amer. Ind. Hyg.
   Assoc. J., 20, 3, 183-189.
Special Topics
                                                                               41
   JS9-60I O - 69 - 4

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

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

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

Hewson, E. W., and G. C. 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., 73, 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 DIFFUSION7 EQUATIONS
   Most other widely used diffusion equations are
variant forms of the ones presented here. With re-
spect to ground-level  concentrations from an ele-
vated source  (Eq. 3.2):
   x U,y,0;H)
                    Q
                 v 
-------
                             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, a, = 190 m
    from Figure 3-2 and 
-------
    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 m«*'T"»™ ground-level concentration  is 5.6
    km, and the man'mum xu/Q is 3.0 x  10—.
           3.0 x KT* 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
   
4
4
4
4
4
4
4.5
u,
m seer1
4.5
4.5
4.5

-------
  2.io-»U
   IJ"
           -400
                  -700     0
                 ceosswixo DISTANCE
                                «JOO
                                       • 400
 Figure 7-2.  Concentration as a function of crosswind
               distance (Problem 7).

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

    Table 7-3   DETERMINATION OF ISOPLETH WIDTHS
                   (PROBLEM 8)
*,
km
0.5
0.8
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
or
m
83
129
157
295
425
540
670
780
890
980
x (centerline),
g m-3
3.8 x 10~5
2.3 x 10-'
2.8x10-'
1.4 x 10-'
7.1 x 10-1
4.0 x 10~5
2.4 x 10~s
1.8 x 10-'
1.4 xlO-»
1.1 x 10-'
X (isopleth)
X (centerline)
0.263
4.35x10-=
3.53x10-'
7.14 x 10-'
1.42x10-'
0.250
0.417
0.556
0.714
0.909
y/
-------
   Table 7-4   DETERMINATION OF CONCENTRATIONS FOR
            VARIOUS HEIGHTS (PROBLEM 9)
                    d.
                               f.
                                           g.
J-H   T	1 / i-H V-'l I+H   f	I/
                                 c. + e.
                                            gin-
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
1.49x
3.55 x



10-'
io-3
10-3
10-'
10-'
10-'
10-"
10-*
10~«
10-'
0.794
0.813
0.875
0.953
1.014
1.024
0.975
0.865
0.716
0.553
0.397
0.261
0.161
0.093
0.050
0.024
2.78 x
2.85 x
3.06 x
3.34 x
3.55 x
3.58 x
3.41 x
3.03 x
2.51 x
1.94 x
1.39 x
9.14 x
5.64 x
3.26 x
1.75 x
8.40 x
10-'
10-'
lfJ-«
10-'
10-'
10-'
10-'
10-'
10-'
10~5
10~5
10-'
10-*
   These values are plotted in Figure 7-4.
   soo
     010
        10"    2-KT*    J-IO'4   4x10"*
           CONCENTRATION. | •-'
Figure 7-4. Concentration as a function of height (Prob-
                    lem 9).
   Verifying:

   X (x,0,0) -
                TT 
-------
          cr (stable)
                151
                      H/8 = 520 + 19 = 539
                (539) 330
      = 8.5 x 10-" g m-8 of SOZ

   -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
   particulate 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 Ib hr> x 0.126  fjf C~*  . — 94.5 g sec'1
                        . ID br~a
   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 summarized
    in Table 7-6, and plotted in Figure 7-5.
« \
IM 1V
S  7
*
9
                        I   I  I   I
      0.5
                    2    3  4
                  WIND SPEED. •
                                   10
                                          20
Figure 7-5.  Maximum concentration  as  a  function of
             wind speed (Problem 14).

 Table 7-6  MAXIMUM CONCENTRATION AS A FUNCTION OF
             WIND SPED (PROBLEM 14)
Stability
Class
B






D








U' H, XU^mai'
m sec~J m m~2
0.5
1.0
1.5
2
3
5
7
0.5
1.0
1.5
2
3
5
7
10
20
142.2
86.1
67.5
58.1
48.7
41.3
38.0
127.6
78.8
62.6
54.4
46.3
39.8
37.0
34.9
32.4
8.0x10-*
2.0 x 10-'
3.1 x 10-'
4.1 x 10"
5.7 x 10"
7.8 x 10"
8.7 x 10"
4.4 x 10-*
1.42x10-'
2.47x10-'
3.5 x 10-'
5.1 x 10"
7.3x10-'
8.2 x 10"
9.4 x 10"
1.1 x 10-*
Q/u,
gm-i
144
72
48
36
24
14.4
10.3
144
72
48
36
24
14.4
10.3
7.2
3.6
Xmai1
g m~a
1.15x10-'
1.44 x 10-'
1.49 xlO-»«-
1.48 x 10-"
1.37 x 10-8
1.12x10-'
8.96 x 10-'
6.34 x 10-'
1.02 x 10-'
1.19 xlO-'
1.26 x 10-'*-
1.22 x 10-'
1.05x10-'
8.45x10-*
6.77 x 10-*
3.96x10-*
   The wind speeds that give the highest maximum
   concentrations for each stability are, from Fig-
   ure  7-5:  B  1.5, D 2.0.

PROBLEM 15: A proposed  pulp processing plant
   is expected to emit %  ton per day of hydrogen
   sulfide from a single stack. The company prop-
   erty extends a  minimum  of  1500 meters from
   the  proposed location.  The nearest  receptor
   is a small town of 500 inhabitants 1700 meters
   northeast of the plant.  Plant managers  have
   decided  that  it  is  desirable  to  maintain
   concentrations below 20  ppb (parts per billion
   by volume), or approximately  2.9 x 10~* g m"',
   for any period greater than 30 minutes.  Wind
   direction frequencies indicate  that  winds  blow
   from  the proposed location toward this town
   between  10 and  15 per cent of the time.  What
   height stack should be erected? It is assumed
   that a design wind speed of 2 m sec"1 will be
   sufficient, since the effective stack  rise will be
   quite great with  winds  less  than  2 m sec"1.
   Other than this stipulation, assume  that the
   physical  stack height and effective stack height
   are  the  same,  to  incorporate a slight safety
   factor.
SOLUTION:  The source strength is:

   Q _  1000 Ib day"1 x 453.6 g Ib "'
   ^ ~       86,400 sec day-1
   FromEq. (4.2):
           0.117 Q      0.117(5.25)
                                                                                         5.25 g sec"
   a, a, '
            Xd U

          1.06 x 10' m2
                    (2.9 x 10-') 2
   At a design distance of 1500 meters (the limit
   of company property), c, a, = 1.06 x 10' gives
   a point from Figure 4-1 about 0.2 from Class C
   to Class  D along the line x = 1500 m.  From
   Figure 3-3, a. = 80 for this stability.
   H =  \/2"a. = 113 meters

PROBLEM  16:   In problem 15 assume that the
   stack diameter is to be 8 ft, the temperature of
   the effluent 250°  F, and the stack gas velocity
   45 ft  sec"1.  From Holland's equation for effec-
   tive stack height  and the method used in prob-
   lem  15,  determine the physical stack height
   required  to satisfy the conditions in problem 15.
   In estimating AH, use T. «= 68°F and p = 920
   mb.
SOLUTION:  First  determine the relation between
   AH and u from Holland's equation.
     v. = 45 ft sec"1 = 13.7 m sec"1
     d = 8 ft — 2.44 m
    T. - 250°F — 121°C - 394°K
    T. — 68°F = 20°C = 293°K
     p <= 920 mb
AH
                 1.5 +2.68 x 10-'p

          13.7 (2.44)
'1
              u

          394-293
                       1.5 + 2.68 x 10-' (920)
            394
                    (2.44)
50
       ATMOSPHERIC DISPERSION ESTIMATES

-------
[1.5+ (2.46)0.256 (2.44)]


(1.5 + 1.54)
   The relation between a, vt and u is:
       _  0.117 Q __ 0.117 (5.25) _ 2.12x10*
   "'ff* ~   x<» u   ^  2.9 x 10-° u =     u

   The required computations using Figure 4-1 are
summarized in Table 7-7:


   Table 7-7   REQUIRED  PHYSICAL STACK HEIGHT AS A
       FUNCTION OF WIND SPEED (PROBLEM 16)
                                                                          60 sec min"
U, AH,  m m2
0.5
1.0
1.5
2.0
2.5
3.0
5.0
7.0
10.0
15.0
204
102
68
51
41
34
20
15
10
7
4.24 x
2.12 x
1.41 x
1.06 x
8.48 x
7.06 x
4.24 x
3.03 x
2.12 x
1.41 x
10*
10'
10<
10*
10*
103
103
103
10s
10s
Stability to
Give ay a, at
1500m
0.9
0.6
0.9
0.2
0.4
0.6

0.5

0.5
from
from
from
from
from
from
0
from
E
from
A
B
B
C
C
C

D

E
to
to
to
to
to
to

to

to
B
C
C
D
D
D

E

F
Of
m
190
120
96
76
64
56
42
34
28
23
H' =
V2*,.
m
269
170
136
108
91
79
60
48
40
33
h =
H'-AH,
m
65
68
68
57
50
45
40
33
30
26
  The required physical height is 68 meters.


PROBLEM  17:  A dispersion study is being made
   over relatively open terrain  with fluorescent
   particles  whose size  yields 1.8 x 1010 particles
   per gram of tracer.  Sampling is by membrane
   filters through which 9 x 10~s m° of air is drawn
   each minute. A study involving a 1-hour release,
   which can be considered from ground-level, is to
   take place  during  conditions forecast to  be
   slightly unstable  with winds  5 m see"1.   It is
   desirable to obtain a particle  count of at  least
   20 particles upon membrane  filters located at
   ground-level 2.0 km  from  the  plume centerline
   on the sampling arc 8 km from  the source. What
   should the total  release be, in grams, for this
   run?

SOLUTION:  The total dosage at the sampler is
   determined by the total sample in grams divided
   by the sampling rate:
   DT
                         20 particles
                                                                        9 x 10~s m" min"1
                                                                          1200
                                                                        16.2 x 10'
                                                       DT = 7.41 x 1CT6 g sec nT8
                                                       The total dosage is given in g sec m~' from
                                       DT (x,y,0;0)
                                                                               exp
                                                      TT U CTj <7.    *  |    2

                                       where QT is the total release in grams.

                                       Therefore QT
                                                                           - u a' "* DT
                                                                          f	i (  y } 1
                                                                          I     2 U J J
                                                      exp
                                                       For slightly unstable conditions (Class C)  at
                                                       x = 8 km, 
-------
PROBLEM 19:   At a  point directly downwind
   from a ground-level source the 3- to 15-minute
   concentration  is estimated to be 3.4  x 10~3  g
   m~3. What would you estimate the 2-hour con-
   centration  to  be at this point,  assuming no
   change in stability or wind velocity?
SOLUTION:
   min, s = 2


   X 2 liour =
              Using Eq. (5.12) and letting k
              hours, and p = 0.2:
                 2.09
   Letting k  15 min, s = 2 hours, and p = 0.17
   X 2 bour '
                       3.4x10-
              8
                     (3.4 x 10-")
              3.4 x IP"3
                 1.42
                           2.4 x 10-" g m"
   The 2-hour concentration  is estimated to be
   between 1.6 x 10~3 and 2.4 x 10"3 g m~\

PROBLEM  20:   Two sources of S0a 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 S0a 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 SOa 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 SO, at the receptor
   shown in the figure?

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

   For a sunny summer afternoon with wind speed
   6 m sec"1, the stability class to be expected is C.
   The equation to  be used  is Eq. (3.2):
                                                   IECEPTO*
                                                                             SOUICE I
                                                                          i*l).C in
                                                                          r* 4.0 In
                                                   Figure 7-6.  Locations of sources and receptor (Problem
                                                                        20).
                                                      x (x,y,0;H)
                                                                        Q
                                                                     it Oj at U
                                                                              exp I	jr-
                                                      For Source A, x = 24.6 km, y = 8.4 km

                                                      a, «= 1810 m, «r, = 1120 m, u •= 8.5 m sec"

                                                                  1450
XA
    7, 1810 (1120) 8.5  "^  [

8400 \*|     F   _  /  183
                                                                              exp  I—0.5
         l     f   . .  /   183   Vl
         J 6XP I"0'5  (-U20-J J
                                                                               U20

                                                                           [-0.5 (4.
                                                      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.

                                                      a, = 1050 m, a, = 640 m, u = 7.0 m sec-

                                                                 126
                                                      XB =  w 1050 (640) 7  6XP
                                                      exp
                                                               126
                                                                         exp [—0.5 (3.81 )2]
                                                             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~s
                                                      x = XA + XB = 0.56 x 10-* + 6.0 x 10"«
                                                         = 6.6 x 10-» g m "'
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 m"3?

SOLUTION:  A clear night with 4 m sec'1 indi-
   cates  class E stability.  Eq.  (3.4) for ground-
   level concentrations from  a  ground-level source
   is most applicable (See Chapter 5).  At 3 km
   for class E, ay = 140 m, 
-------
    that it is 1600 on a sunny fall afternoon. What
    is the concentration directly downwind from one
    end of the source?
SOLUTION:   Late afternoon at this time of  year
    implies slight insolation, which with  3 m Bee"1
    winds  yields stability class  C.  For C stability
    at x = 400 m, a, = 45 m, 
                 ( J-)

                 ay of
                         /
life given, multiply by exp I
is time and L is half-life.  *
                                                    To determine decay of materials with the half-
                                                                                 Q cog + \
                                                                                  ^ - )
                                                                                  •"    /
                                                                                             where t
Source strength of I1'1.

Q, (curies sec'1) — 1.157 x KT8 (5.3 x 10') exp
/ —0.693 t \
                               L

                         For I1S1 L
                                                                 6.95 x 10° sec
                         For a clear night with wind speed 2.5 m sec'1,
                         class F applies.  Approximate the spreading at
                         the reactor shell by 2.15 af0 = 2.15 o,0 = the
                         radius of the shell = 20 m 
-------
       = 2.7 x 10"" (1.0)  The decay of I131 is insig-
   nificant for 2 hours

   xi = 2.7 x lO"8 curies nr3

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"'. The wind direction is pre-
   dicted to be from 310° :t 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 rrr3
1.2 x 10-'
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 ay0
   to equal the width of the wetted area, 6.1 meters
   (20 feet),  
-------
      Table 7-10   DETERMINATION OF WIDTHS  WITHIN
                   ISOPLETHS (PROBLEM 26)

1
s
.0
.0
J.O
1.0
5.0
6.0
km *
0.14
0.54
1.04
2.04
3.04
4.04
5.04
6.04
, av-
m
5.5
19
35
66
93
120
149
175
% (centerline),
g irr3
13.9

3.6
1.3
7.0
1.
x
X
X
4.8 x
3.5
2.7
X
X
1
10-'
10-'
10-'
10-'
10-'
10-'
X (isopleth)
y
X (centerline) aj.
1.8
2.27
6.94
1.92
3.57
5.20
7.14
9.26
x
x
X
X
X
X
X
X
10-'
10-'
io-=
io->
10-
10-'
10-'
10-'
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
                                                                 SCAlt. km
                                                                    I
                                                        Figure 7-8.  Possible positions of the 2.5 x  1(T g m'
                                                            isopleth and the evacuation area (Problem 26).
56
                                                               ATMOSPHERIC DISPERSION ESTIMATES

-------
                            APPENDICES
tn-m o - e» -

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

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

Symbols
a    ratio  of horizontal eddy  velocity to vertical
     eddy velocity
Cp   specific heat at constant pressure
Cy   Sutton horizontal dispersion parameter
C,   Sutton vertical dispersion parameter
d    inside stack diameter at stack top
DT (x,y,0;H)    Total dosage
e    2.7183, the base of natural logarithms
f (0,S,N)  frequency of wind direction for a given
           stability and wind  speed class
h    physical stack height
hi   height of the base of an inversion
H   effective height of emission
H,,   effective height  of emission  for  a  particular
     wind speed
k    von Karman's constant,  approximately equal
     to 0.4
K   eddy diffusivity
L    two uses:  1. the height of an air  layer that is
                 relatively stable compared to the
                 layer beneath it; a lid
              2. the  half-life  of  a   radioactive
                 material
n    Button'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,   total emission during an entire release
R   net rate of sensible heating of an air column
     by solar radiation
s    the length of the edge of a square area source
S    an index for stability
tk   a short time period
t,,,   time required  for the mixing layer to develop
     from the top  of the stack to the top of the
     plume
tB   a time period
T.   ambient air temperature
TB   stack gas temperature at stack top
u    wind speed
u.v   a mean wind speed for the wind speed class N.
v'   horizontal eddy velocity
vs   stack gas velocity at the stack top
v,   a velocity used by Calder
w'   vertical eddy velocity
x    distance  downwind in the direction  of the
     mean wind
x
-------
     the angle  between the wind  direction and a
     line source
     concentration
     crosswind-integrated  concentration
     a ground-level concentration for design pur-
     poses
     inversion break-up fumigation concentration
     concentration measured over a sampling time,
     tk
     maximum  ground-level  centerline concentra-
     tion with respect to downwind distance
X.   concentration measured over a sampling time,
     t.

£j-  relative concentration
y

£_  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 9 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:
                                         (A.I)
Figure A-2 gives the ordinate value at any distance
from the center of the distribution (which occurs
at x). This information is also given in Table A-l.
Figure A-3 gives the area under the Gaussian curve
from — K to a particular value  of p  where p =
     x — x
   This area is found from Eq. (A.2):

                        F       -
   Area (— ^  to p) =    I        —7=
                                                     exp (—0.5 p=) 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):
   Area (—p


   exp (—0.5 p5) dp
/-HP

-p
                                                                                           (A.3)
               -3
                              Figure A-l.  The Gaussian distribution curve.
Appendix 2
                                             61
    J5S-901 O • »« - »

-------
        0.01
          0.0   0.2  0.4  06  O.e  1.0  1.2   1.4  I »  I.
                           Figure A-2.   Ordinate values of  the  Gaussian distribution.
C2
ATMOSPHERIC DISPERSION  ESTIMATES

-------
4.0
s. s
3.0
2.5
2.0
1.5
1.0
0.5
0
•0.5
-1 0
-1.5
2rt
-2.5
•1.0
•3.5
•4.0
—

—
v
-L-

~-
r~ 	
- *444
- — "
- -T*+
_ ~yl


— <-
—

?
—

>

-
E
-
—
-•-t
a
1
j
•±bt
Tr^
-fit
•;J
— -h
jr
^~

+


**





-T-T
—
"*
1

r*l


g
— •

x


^*-
— rrr


T**j
.^' i

gJJ
• "T4"
^JL

r*t
— 40.
M*l
"ri


j»^
	 T
• ** f
i j i J i
-rt-
u-^i
; • T'l '
Trtr
^V
—



3
v^

f ..-».{ T
" 1 ^ '*
"rrrr
•=f
— »**
J"**~
I j
! . J 1
T i t •
1 	 k-j-t-
TTT~
^PJ-L

— . —


^<

i / ; • i
*^l
-rr
- ~~:
w~
... 4 .
X

|
^
-

j^


"^r


~?
^_.
-r



—
x1

—
           0.01     0,1    0.5 1  2    5   10   20     40    *0     BO   90   95   96  99      99.8   99.99
                      Figure A-3.   Area under the  Gaussian distribution curve from —«  to  p.
Appendix 2
63

-------
        4.5
        4.0
        3.5
                                                                                        dFP
        3.0
        2.5
        2.0
        1.5
        1.0
        0.5
                                                                      ±2
                 Figure A-4. Area under the Gaussian distribution curve between —p and +p.
€4
ATMOSPHERIC DISPERSION ESTIMATES

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

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

-------
Table A-l   SOLUTIONS  TO EXPONENTIALS B = exp [-0.5A2]
          The notation  2.16 E-l means 2.16 x 10~'
t
0.00
0.10
0.20
0.30
0.40
0.90
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.90
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.90
2.60
2.70
2.80
2.90
3.00
3.10
3.20
3.30
3.4«
3.90
3.60
3.70
3.80
3.90
4.00
4.10
4.20
4.30
4.40
4.90
4.60
4.70
4.80
4.90
0.00
B
l.OOE 0
9.9-5E -1
V.81E -1
9.9*E -1
9.21E -1
8.81E -t
B.31E -I
7.8'E -1
7.2*E -1
6.67E -1
6.07E -1
9.4AE -1
4»8"'E -I
4.30E -1
*.7«iE -1
3.2*E -1
2.7BE -1
2.3AE -1
I .QBE -1
1.6«C -1
1.3-iE -1
1.1PE -1
B.floE .2
7. IDE -2
9. ME -2
4.3oE -2
3.41E -Z
'.ME -?
1.9RE -2
l.4«C -Z
1.11E -2
8.1iE -3
9. QBE -?
4.32E -3
3.0<»E -3
Z.loE -3
1.93E -3
1.07E -3
7.3?E -4
4.9BE -4
3.3*E -4
2.24E -4
1.4BE -4
9.6'iE -9
6.2SE -!>
4.01E -9
2.94E -9
1.60E -9
9.93E -6
6. lib -f>
0.01
l.OOE 0
9.94E -1
9.7QF .1
9.93E ~1
9.19F -1
8.78E -1
«.30E -1
7.77E -1
7.20F. -1
6.61E -I
A. OIF -1
9.40E -1
4.S1E -1
4.24F -1
3.70F -1
3.20E -1
2.74£ -1
2.3ZE -1
1.94E -1
1.61F .1
1.33E -1
l.OBF .1
».70F -2
6.94E -2
9.«BE -2
4.29E -2
3.32E -2
2.9*E ~Z
1.93E -2
1.45F -2
l.OBE -2
7.94E -3
>.79F -3
4.18E -3
?.<»9F -3
2. HE -3
'..48F -3
1.03E -3
7.05E -4
*«T''E -4
3.22F. -4
2.19t -4
1.4ZE -4
0.25E -9
5. 986 -9
3.B3C -9
2.43E -9
l.SZE -9
9.46F -6
9.82E -6
0.02
10. OOE -
9.93E -
9.7*E -
9.90E -
9. ME -
8.74E -1
8.25E -t
7.7ZE -I
7.1">£ -1
6.5SE -)
9.94E -1
5.34E -1
4»7*E ~ I
4. IRE -1
3.6*E -I
3.1«E -I
2.69E -I
2.2PE -1
1.91E -1
1.9PE -1
1.30E -I
1.04E -1
8.91E -Z
6.7PE -Z
9.3«E -Z
4.1«E -Z
3.23E -Z
2.4"*E ~Z
1.88E -2
1.41E -2
1.09E -Z
7.70£ -3
3.60E -3
4.04E -3
Z.8°E -3
2.04E -3
1.4?E -3
9.80E -4
6.7°E -4
4.61E -4 ,
3.10E -4
Z.CMt -4
1.3«sE ~4
8.86E -*
S.72E -9
3.66E -9
2.3?E -5
1.45E -5
9.02E -6
9.34E ••>
0.03
10. OOE -1
9.92E -1
9.74E .1
9.47E -1
V.12E -1
B.69E -1
H.20E -1
T.66E -1
7.09E -1
ft.49E -1
9.88E -1
9.28E -1
».69E -1
4.13E -1
3.60E -1
3.10E -1
Z.69E -1
Z.24E -1
1.B7E -l
1.99E -1
1.27E -1
1.04E .1
0.32E -2
6.62E —2
5.22E -2
4.07E -2
3.19E .2
Z.41E -2
1.S2E -2
1.37E -2
1.02E -2
7.46E -3
9.43E -3
3.91E -3
Z.79E -3
1.97E -3
1.38E -3
9.93E -4
6.93E -4
4.43E -4
2.07E -4
I.98E -4
1.30E -4
M.49E -9
5.48E -9
1.90E -9
Z.21E -9
1.39E -9
",99E -6
9.28E -6
0.04
9.99E
9.90E
•».72E
V.44£
o.OBE
H.64E
H.19E
7.61E
'.03E
6.43E
9.«2E
^.2ZE
'*.*>''£
fc.OBE
3.9SE
3.06E
2. ME
2.20E
1.84E
1.92E
1.2SE
1.01E
M. 14E
6.4'E
•>.11E
3.97E
3.07E
2.34E
1.77E
1.315
•>.!»9E
7 . 2 1 E
5.25F
3.7HE
2.6<»E
l.OOE
1.3'IE
9.18E
6.2HE
*.Z6E
Z.B'-E
1.90E
1.29E
S.13E
5.*4E
3.?<.F
Z.11E
1.32E
H. 19£
5.0ZE

.1
.1
-1
-1
.1
.1
.1
.1
-1
-1
.1
-1
-1
-1
-1
-1
.1
-]
-1
-1
.1
.1
.2
-2
-2
.2
.2
>2
-2
-2
-3
-3
.3
.3
.3
-3
.3
.4
-4
•*'
_«.
-<«
.4
_•>
-5
-9
-5
.5
.6
.6
0.09
9.99E -1
9.89E -1
9.69F -1
9.41E -1
9.04E -1
B.60E -1
B.IOE -1
7.99E -1
6.97E -1
6.37E -1
9.76E -I
9.16E -1
4.9BE -1
4.02E -1
3.90E -1
3.01E -1
2.96E -1
2.16E -1
1.B1E -1
1.49E •!
1.22F -1
9.91E -2
7.96E -2
6.32E -2
4.97E -2
3.87E .2
2.99F -2
2.28E -2
1.72F -2
1.29F -2
9.99E -3
7. OOE -3
9.09E -3
3.66E -3
2.60F -3
1.83F -3
1.28E -3
B.84E -4
6.04E -4
4.09E -4
2.74F .«
1.92E -4
1.20F -4
7.78E .9
9.01E -9
3.20F -9
2.02E -9
1.26E -9
7.BOE -6
4.7BE -6
0.06
9.9BE -1
9.87E .1
9.67E .1
9.37E .1
9. OOE -1
8.99E -1
8.04E .1
7.49E -1
6.91E -1
6.31E -1
9.70E .1
9.10E .1
4.92E «1
3.97E -1
3.49E -1
2.96E -1
2.92E -1
2.13E -1
1.77E -1
1.47E -1
1.20E -1.
9.70E -2
7.78E -2
6.17E -2
4.89E -2
3.7BE -2
2.91E -2
2.22E -2
l.67E .2
1.29E .2
9.26E -3
6.79E -3
4.92E -3
3.94E .1
2.91E -3
1.77E -3
1.23E -3
8.91E -4
9.82E -4
3.93E -4
2.63E -4
1.79E -4
1.19E -4
7.49E -9
4.79E -9
3.09E .9
1.93E -9
1.20E -9
7.43E .6
4.99E -6
0.07
9.98C
0.86E
9.64E
9.34E
B.99E
B.30E
7.99E
7.44E
6.89E
6.29E
9.64E
9.04E
4.46E
3.91E
3.39E
2.92E
2.48E
2.09E
1.74E
1.44E
1.17E
0.30E
7.60E
6.03E
4.73E
'.68E
2.83E
2.16E
1.63E
1.22E
8.98E
6.98E
*.77E
3.42E
2.43E
1.71E
1.19E
8.20E
9.60E
3.78E
2.93E
1.68E
1.10E
7.13E
4.38E
2.92E
1.84E
».l 9E
T.08E
4.33E

^
•
«•
.
«
«•

w
^
•
V
w
•
.
-
—
m
.
.
-
-1
.3

-;
-j
• i
.2
^)

.;
-3
-3
.3
-3
.3
-3
-3
.4
• 4
.4
.4
-4
.4

• '
m
.
.
,
»
0.08
9.97E
9.84E
9.62E
9.30E
8.91E
8.45E

T!38E
».79E
».l9E
9.9BE
*.99E
*.4l£
3.B6E
3.35E
2.87E
2.4»E
2.05E
1.71E
1.41E
1 1.19E
! 9.29E
1 7.43E
' 9.89E
! 4.62E
1 3.99E
' 2.76E
• 2. IDE
! 1.98E
' 1.18E
1 8.7tE
6.37E
4.61E
3.31E
2.39E
1.69E
1.19E
T.89E
> 9.3BE
3.63E
2.43E
1.61E
1.09E
6.83E
*.38E
2.70E
1.75E
t . 09E
6.74E
4.12E

.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.2
.2
.2
.2
.2
.2
.2
.2
.2
-3
.3
.3
.3
.3
.3
.3
^4
.4
.4
.4
.4
.4
.9
.9
.9
.9
.9
.6
.6
0.09
9.9»t .1
9.82C .1
9.99C .1
9.27E .1
8.87E .1
8.40E .1
7. BBC .1
7.32E .1
6.73E .1
6.13E .1
9.92C .1
4.93E .1
4.39E .1
3.81C .t
3.30E .1
2.83E .1
2.40E .1
2.02E .1
1.6BE .1
1.38E -1
1.13E .1
9.09E .2
7.27E .2
9.75C .2
4.91E .2
3.49E .2
2.68E .2
2.04E .2
1.34E .2
1.19E .2
8.49E .3
6.17E -3
4.46E .3
3.20E .3
2.27C .3
1.99E -3
1.11E .3
7.6QC .4
3.18E .4
3.49E .4
2.33E .4
1.94E .4
1.01E -4
6.93E .9
4.19E .9
2.66E .9
1.67E -9
1.04E .9
6.42E .6
3.92E .6

-------
•o
•o
n


a.
                                                        Table A 1 (continued)   SOLUTIONS TO EXPONENTIALS
4

9.00
9.10
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
8.7'J
8.80
8.90
;oo
.10
.20
.30
.40
.50
.60
.70
.80
.90
	 0.00
B
3.71E -6
2.25E -6
1.3&E -6
7.9^t -7
*.6*E -7
2.70t -7
l.S^t -7
B.fllE -B
4.9«,E -8
2.76E -9
l.52t -B
8.37E -9
4.50E -9
t, *IE -9
1.29E -9
6.69E-10
3.4BE-10
U7ot-10
9.10E-11
4.SOE-11
2.29E-11
1.13E-11
5i"54E-12
2.6RE.12
1.29E-12
6.10E-13
2.87E-13
l.3fcE-l3
6.HE-14
7.BOE-14
1.27E-14
5.66E-1S

U10E-19
4.77E-16
2.01E-16
8.71E-17
J.67E-17
1.51E-17
6.31E-18
*.58E-18
U04E-1B
4.lflE-19
1.66t-19
6.50E-20
*.53E-20
9|72E-21

l!«OE-21
5.22E-22
o.ot

1.55E -6
2.14E -6
1.28E -6
7.54E -7
4.41E -7
2.56E -7
1.47E -7
B.32E -8
«.68E -8
2.60E -8
1.43E -8
7.R2E -9
4.?3F -9
2.26E -9
1.20F. -9
6.27E-10
3.25E-10
1.67F-1Q
B.50E-U
4.28E-U
2.14E-11
1.05E-M
1.15E-12
Z.49E-12
1.19E-12
5.66E-13
2.66E-13
J.24E-13
S.69E-1*
2.59E-14
1.17E-14
5.22E-13
Z.31E-15
1.01E-15
4.38E-16
1.88E-16
T.99E-17
3.36E-17
1.40E-17
5.77E-18
2.36E-18
9.52E-19
3.81E-19
l.ME-19
5.92E-20
Z.30E-ZO
8.83E-'!
3.36E-*!
1.27E-21
4.73E-Z2
0.02

3.37E -ft
2.0^E ~f>
1.21E -A
7.1-5E -7
4.1PE -7
2.4?c -7
1.39E -7
7«8fE -B
4.41E -B
2.4SE -B
1.39F. -B
7.3SE -•»
3.97E -9
2.12E -9
1.12E -9
5.8"E-10
3.0ISE-10
1 «5*E-10
7.94E-11
4.00E-U
1.99E-11
9. 816-12
4.79E-12
2.32E-12
1.11E-12
5.25E-13
2.46E-13
l.UE-13
5.2(SE-t4
2.39E-U
1.08E-14
4.81E-1S
2.11E-11
9.30E-16
4.03E-16
1.73E-14
7.33E-17
3.04E-17
1.28E-17
5.2RE-1*
2.13E-1B
B.69E-19
3.47E-19
1.37E-19
5.31E-20
2.09E-20
6.02E-21
3.09E-21
1.15E-21
4.21E-22
0.03

3.21E -6
1.9?E -6
1.15E -6
6.7HE -7
J.96E -7
Z.29E -7
1.31E -7
'.42E -8
4.16E -8
Z.31E -8
1.27E -8
ft.92E -9
3.73E -9
1.99E -9
1.05E »9
9.50E-10
Z.B5E-10
1.46E-10
7.42E-11
3.73E-U
1.86E-H
9.UE-12
4.46E-12
Z.15E-12
1.03E-12
4.87E-13
Z.2BE-13
1.06E.13
4.86E-14
Z.21E-14
9.96E-15
4.44E-15
1.96E.15
0.56E-16
3.70E-16
1.59E-16
6.72E-17
Z.82E-17
1.17E-17
4.83E-18
1.97E-18
f.93E-!9
3.17E-19
1.25E-19
4.90E-20
1.90E-20
7.29E-21
2.77E-21
1.04E-21
3.qflE-22
0.04

3.05E -6
1.81E -6
I .OT£ -6
0.05

0.06

2.90E -6 2.76E -6
1.74E -6
1.65E -6
l.O^E -6 9.82E -7
*.<•!£ -' 6.09E -7 5.77E -7
3.7SE -7
Z.l'E -7
1.2<«E -7
7.01E -8
3.91E -8
2. IRE -8
1.20E -8
^.ME -9
3.51E -9
I.R7E -9
9.87E-10
5.16E-10
2.67E.10
1.37E-10
6.93E-11
3.49E-U
1.7^E-11
8.51E-12
4.15E-12
2.00E-12
9.55E-13
4.52E-13
2.11E-13
9.BOE-14
4.50E-14
2.04E-14
9.19E-15
4.09E-15
l.POE-19
7.87E-16
3.4CE-16
1.46E.16
6.17E-17
2.59E-17
1.07E-17
4.41E-18
1.80E-18
7.24E.19
2.89E-19
1.1"E-19
4.46E-20
1.73E-20
4.62E-21
2.51E-21
9.43E-22
3.51E-22
3.55F -7 3.36E -7
2.05E -7
1.17E -7
1.94E -7
L.llE -7
6.62E -8 6.25E -8
3.70E -8 3.49E -8
2.05E -8
1.13E -8
1.94E .8
L.OAE -8
6.12E -9 5.7AE -9
3.29E -9 3.09E -9
1.75E -9
1.63E -9
9.25E-10 8.67E-10
4.83F-10 4.52E-10
2.50E.10 2.34E-10
1.28E-10
1.19E-10
6.47E-11 6.06E-11
3.25E-11 3.03E-11
1.61E-U
L.50E-U
7.92E-12 7.3PE-12
3.86E-12 3.59E-12
1.R6E-12
L.73E-12
8.87E-13 8.23E-13
4.19E-13 3.88E-13
1.96E-13 1.81E-13
9.07E-14 8.39E-14
4.16E-14 3.84E-14
1.89E-14
1.74E-14
8.48E-15 7.82E-19
3.77E-15 3.48E-15
1.66E-15
7.24E-16
3.13E-16
1.34E-16
5.66E-17
2.37E-17
9.83E-18
4.04E-18
1.64E-IR
6.61E-19
2.63E-19
1.04E-19
4.06E-20
.53E-15
.66E-16
.87E-16
.23E-16
.19E-17
.17E.17
.OOE-18
.69E-18
.30E-18
.03E-19
.40E-19
.46E-20
.69E-20
1.57E-20 1.43E-20
6.01E-21 5.46E-21
2.28E-21 2.07E-21
8.55E-22 7.75E-22
• 3.18E-22 2.88E-22
0.07 0.08

2.62E -6 2.49E -6
1.57E -6 l.*9E .6
9.32E -7 8.84E -7
3.47E -7 5.19E -7
3.18E -7 3. OlE -7
1.83E -7 1.73E -7
1.05E -7 ,87E -
5.90E -B .57E •
3.29E - .HE -
1.82E - .72E .
9.98E - .39E -
5.41E - ,09E -
2.91E - Z.73E >
1.55E - 1.45E -
8.13E-10 7.62C-10
4.24E-10 3.77C-10
2.19E-10 2.0*E-10
1.12E-10 1.04E-10
5.64E-11 5.27E-1I
2.82E-11 2.63E-11
1.40E-11 1.3oe-ll
».87E-12 6.J9E-12
3.34E-12 3.10E-12
1.60E-12 1.49E-12
7.64E-13 7.09E-H
3.60E-13 3.S4E.1S
1.68E-13 1.96E.13
7.77E-14 7.19E-14
3.55E-14 3.2§E-14
1.61E-14 1.49E-14
7.22E-15 6.66E.13
3.20E-15 2.95E.19
1.41E-13
6.13E-16
2.64E-16
1.13E-16
4.76E-17
1.99E-17
8.23E-18
3.37E-18
1.37C-19
5.50E-19
2.19E-19
B.61E-20
3.36E-20
1.30E-20
4.95E-21
1.87E-21
7.02E-22
2.60E-22
.30E-15
.64E«16
.43E-16
.03E-16
.36E-17
.82E.17
.53E.18
.08E-18
.25E-18
.02E.19
.99E.19
.84E.20
.05E-20
.18E.20
.90E.21
.70E-21
.36E-22
.36E-22
0.09

2.37E .6
1.42C .6
B.38E .7
4.91E -7
2.85E .7
1.64( .7
9.32E .
9.25E -
2.93E .
1.62E .
8.846 .
4.78E -
2.56C .
1.36C .
7.14C-10
S.71C-10
1.91E-10
9.74E-H
4.92E-11
2.46E-11
1.22C.11
9.95C.12
2.88E-12
1.38C.12
6.98E-13
3.09C.13
1.44E-13
6.65E-14
3.04E.14
1.37E-14
6.14B.15
2.72E-13
1.19E-15
9.18E-16
2.23E-16
t. 496-17
4.00E-17
1.67C.17
6.89C.18
2. 826-18
1.146.18
4.586.19
1.826.19
7.146-20
2.786.20
1.076.20
4.086.21
1.946.21
5.766-22
2.136.22

-------
                         Appendix 4:  CONSTANTS, CONVERSION
                           EQUATIONS, CONVERSION TABLES
                       Constants
                              e = 2.7183 —L_ = 0.3679
                                         e
                              IT == 3.1416 —— = 0.3183
                                         Tr
                             2r = 6.2832 —L_ = 0.1592
                                         2ir
                            \/2T= 2.5066 -j~ = 0.3989

                                        —|=r = 0.7979
                          (27r)3/:!= 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












J^
H
3
o
C/J
"0
X
i
o
o
V)
•fl
DESIRED

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


KNOTS


MKSTAT)
PER DAY

TO CONVERT A
UNITS METERS
PER SEC

1.0000
E 00
3.0480
E-01
5.0800
E-03
2.7778
E-01
4,470*
E-01


5,1479
E-01

1,8627
E-02

VALUE FROM A GIVEN
gj AND BENEATH THE DESIRED UNIT.
V)
O
•x
M
V)
H
H
W
V)


















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
PER MIN

1.9689
E 02
6.0000
E 01
1.0000
E 00
5.4681
E 01
8.8000
E 01


1.013*
E 02

3.6667
E 00

KM
PER HR

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


1.8532
E 00

6.7056
E-02

DESIRED UNIT, MULTIPLY
E-xx MEANS









MKSTAT)
PER HR

2.2369
E 00
6.8182
E-01
1.136*
E-02
6.2137
E-01
1.0000
E 00


1.1916
E 00

4.1667
E-02

THE GIVEN
KNOTS


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


1.0000
E 00

3.6183
E-02

VALUE BY
MKSTAT)
PER DAY

5.3686
E 01
1.6364
E 01
2,7273
E-01
1.4913
E 01
2.4000
E 01


2,7637
E 01

1,0000
E 00

THE FACTOR OPPOSITE THE GIVEN UNITS
10 TO THE -XX POWER.





































-------
•0
•o
8
I
CONVERSION FACTORS
DESIRED UNITS
QtVEN UNITS
GRAMS
PER SEC
GRAMS
PER MIN
KG
PER HOUR
KG
PER DAY
LBS
PER MIN
LBS
PER HOUR
LBS
PER DAY
TONS
PER HOUR
TONS
PER DAY









- EMISSION RATES
GRAMS
PER
1.0000
E 00
1,6667
E-02
2.7778
E-01
1.1574
E-02
T.5599
E 00
1.2600
E-01
5.2499
E-03
2.3200
E 02
1.0500
E 01
GRAMS
SEC PER
6.0000
E 01
1.0000
E 00
1.6667
E 01
6.9444
E-01
4.3339
E 02
7.5599
E 00
3.1499
E-01
1.3120
E 04
6.2999
E 02
KG
MIN PER HOUR
3.6000
E 00
6.0000
E-02
1.000''
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
8.64QO
E 01
1.4400
E 00
2.4000
E 01
1.0000
E 00
6.3317
E 02
1.0886
E 01
4.3339
E-01
2.1772
E 04
9.0718
E 02
LBS
DAY PER M]
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
[N PER HOUR
7.9366
E 00
1.3228
E-01
2.2046
E 00
9.1839
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
2.204ft
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
3.9683
E-03
6.6139
E.09
1.1023
E-03
4.5950
E-09
3.0000
£-02
5.0000
£•04
2.0833
£-09
1.0000
E 00
4.1667
E-02
TONS
PER
9.924Q
E-02
1.5873
E-03
2.6435
E-02
1.1023
E-03
7.2000
E-01
1.2000
E-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.

-------
                                                            KILOMETER  INCH
                                                                                   FOOT
Y*RO
MILE<*AUT>
H
2
O
en
"B
s
PJ
91
on
v>


I

w
V)
H
 CONVERSION FACTORS - LENGTH


      DESIRED UNITS METER      CM         MICRON


 OtVEN UNITS


METER
       CM
       MICRON
       KILOMETER
       INCH
       root
       YARD
       MILCISTAT)
       MIlE(NAUT)
       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.
1.0000
E 00
1.0000
E-02
1,0000
E-06
1,0000
E 03
2.9400
E-02
3.0480
E-01
9.1440
E-01
1.6093
C 03
1.8932
E 03
1.0000
E 02
1.0000
E 00
1.0000
E-04
1.0000
E 05
2.9400
E 00
3.0480
E 01
9.144Q
E 01
1.6093
E 09
1,8932
E 09
1.0000
E 06
1.0000
E 04
1.0000
E 00
1.0000
E 09
2.9400
E 04
3.0480
E 03
9.1440
E 09
1.6093
E 09
1.8932
E 09
1.0000
E-03
1.0000
E-03
1.0000
E-09
1.0000
E 00
2.9400
E-09
3.0480
E-04
9.1440
E-04
1.6093
E 00
1.8932
E 00
3.9370
E 01
3.937Q
E-01
3.9370
E-09
3.9370
E 04
1.0000
E 00
1.2000
E 01
3.6000
E 01
6.3360
E 04
7.2962
E 04
3.2808
E 00
3.2808
E-02
3.2808
E-06
3.2808
E 03
8.3333
E-02
1.0000
E 00
3.0000
E 00
3.2800
E 03
6,0802
E 03
1.0936
E 00
1.0936
E-02
1.0936
E-06
1.0936
E 03
2,7778
E-02
3,3333
E-01
1,0000
E 00
1.7600
E 03
2.0267
E 03
6.213;
E- '4
6,2137
£.06
6,2137
E-10
6,2157
£.01
1.9783
E.09
1.8939
£.04
9.6818
£.04
1,0000
£ 00
1.1916
E 00
9.3939
E-04
3.3999
E-06
3,3939
E-10
3,3999
E-01
1.3706
E-OS
1.6447
E-04
4,9340
E-04
8,6839
E-01
1.0000
E 00
H
M
(/>

-------
I
re
       CONVERSION FACTORS • AREA
DESIRED
6TVEN UNITS
so METER
SO KM
so CM
SO INCH
so FOOT
SO YARD
ACRE
so STAT
MILE
so NAUT
MllE
UNITS SO METER
1,0000
E 00
1.0000
E 06
1.0000
E-04
6.4916
£•04
9.2903
E-02
S. 9613
E-01
4.0469
E 03
2.9900
E 06
3.4349
E 06
SO KM
1.0000
E-06
1.0000
E 00
1.0000
E-10
6.4316
E-10
9.2909
£•09
8.3613
E-07
4.0469
E-03
2.9900
E 00
3.4345
E 00
SO CM
1.0000
E 04
1.0000
E 10
1.0000
E 00
6.4916
E 00
9.2903
E 02
8.3613
E 03
4.0469
E 07
2.9900
E 10
3.4343
E 10
SO INCH
1.9900
E 03
1.9900
E 09
1.9900
E-01
1.0000
E 00
1.4400
E 02
1.2960
E 03
6.2726
E 06
4.0149
E 09
9.3239
E 09
SO 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
4.3960
E 04
2.7878
E 07
3.6969
E 07
SO YARD
1.1960
E 00
1.1960
E 06
1.1960
E-04
7.7160
E-04
1.1111
E-01
1.0000
E 00
4.8400
E 03
3.0976
E 06
4.1076
E 06
ACRE
2.4710
E-04
2.4710
E 02
2.4710
E-08
1.9942
E.07
2.2997
E.09
2.0661
E.04
1.0000
E 00
6.4000
E 02
8.4869
E 02
SO STAT
MILE
9.8610
E-07
9.8610
E-01
9.8610
E-ll
2.4910
E-10
3.987Q
E-08
9.2283
E-07
1.9623
E-03
1.0000
E 00
1.3261
E 00
SO NAUT
MILE
2.9116
E-07
2.9116
E-01
2.9116
E-ll
1.8789
E-10
2.7030
E-08
2.4949
E-07
1.1783
E-03
7.9411
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 BENF.ATH THE DESIRED UNIT.   NOTE THAT E-XX MEANS to TO THE -xx POWER.

-------
CONVERSION FACT07S -


     D^SIRFU U''IT5 CD


GIVEN MNTTS
LITE"      CM INCH    cu Fnnr    cu STAT    cu NAUT    u s FLUID  u s QUART  u 5 GALLON
                                       MILE       MILE      OUNCE











>
H
S
O
V)
•fl
X
I
O
o
55
•d
S
eg
O
S!
S
C/J
H
§
»*b
H
n
en
cu METEO

LITER

cu INCH

cu FOOT

CU 5TAT
MILE
CU 'IAUT
MILE


US FLUID
OUMCF

U S QUART



U S GALLON



TO CONVPRT A
AND BENFATH





1.0000 9
f no
I. 0000 1
F-<13
1.6*87 I
r-"s
2.8417 ?
F-02
*.UB


.7B->3
E O'J


U'lp TO
6.1021
F 0*
6.1025
E 01
1.0000
f 00
1.7280
E 03
2.5*36
F L*
3.8«*2
E 1*


1.80*7
F 00

5.7750
E 07


2.3100
F 02


A DESIRE')
3.531*
E '»!
3. VMS
E-n?
5./H70
E-<>*
l.onoo
E ''O
l.*7?n
E 11
2'.?* 7 8
E U


1.0'»**
E-03

3.3*20
E o*


1.3168
E.ni


UNIT, MULTIPLY
*.3991
E-10
2.3992
E-13
3.9315
E-15
6.793ft
E-12
I. 0000
E 00
1.5270
E 00


7.0950
E-15

2.270*
E-07


9.0817
E-13


THE GIVEN
1.57U
E-10
1.5711
E-13
2.57*6
E-15
*.**fl8
E-12
6.5*46
E-Ol
1.0000
E 00


4.6*62
E-15

l.*868
E-07


5.9*72
E-13


VALUE By
3.381*
E 0*
3.3815
E 01
5.5*12
E-Ol
9.5751
E 02
l.*09*
E 1*
2.1523
E 1*


1.0000
E 00

3.20QO
E 07


1.2800
E 02


THE FACTOR
1.0567
E-03
1.0567
E-06
1.7316
E-08
2.9922
E-05
*.*0*5
E 06
6.7259
E 06


3.1250
E-08

1.0000
E 00


*.oooo
£.06


OPPOSITE
NnTf. THftf E-XX MEANS 10 TO THE -xx POWER.



































2.6*17
E 02
2.6*18
E-Ol
*.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 UNITS







-------
5
IV
0
CONVERSION FACTORS - MASS
DESIRED UNITS GRAM
GIVEN UNITS
GRAM 1.0000
E 00
MICROGRAM i.oooo
E-06
KILOGRAM 1.0000
E 03
METRIC TON 1.0000
E 06
SHORT TON 9.0718
E 05
LONG TON 1.0160
E 06
GRAIN 6,4799
E-02
OUNCE 2.8549
(AVDPl E 01
LB (AvDP) 4.5359
E 02


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


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


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


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
£-13
9.B421
E-04
9,8421
E-01
8.9286
E-Oi
1.0000
E 00
6.3775
E-08
2.7902
E-05
4.4643
E-04


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


OUNCE
IAVDP)
5,5274
E-02
3,5274
E-08
4.5274
E 01
*, 5274
E 04
3,2000
E 04
9.584Q
E 04
2.2857
E-03
1.0000
"E 00
1.6000
E 01


LB (A\
2.2Q46
E-03
2.20*6
E-09
2.2Q46
E 00
2,2046
E 03
2,0000
E 03
2,; o
E 03
1.4286
E-04
E-02
1.0000
E 00
TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT,  MULTIPLY THE  GIVEN  VALUE  BY  THE  FACTOR OPPOSITE THE GIVEN UNITS
AND BENEATH THE DESIRED UNIT.   NOTE THAT E-XX MEANS 10  TO THE  -XX POWER.

-------
CONVERSION FACTORS -  FLO*

     DESIRED UNtTS CU METER    CU METER   LITER      LITER      LITER      CU FT      CU FT      CU FT      CU C1
                      PER  SEC    PER HR     PER SEC    PER WIN    PER HR     PER SEC    PER MIN    PER HR     PER SEC
GIVEN UNITS











Jj,
H
3
o
V)
s
I
o
o
55
•a


-
O
z
w
Cfl
H
3
H
M
J/)
cu METER
PER SEC
cu METER
PER MR
LITER
PER SEC
LITER
PER'MIN
LITER
PER MR
CU FT
PER SEC


cu FT
PER MIN

cu FT
PER MR


cu CM
PE« SEC


TO CONVERT K
AND BENEATH






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


4.7193
E-04

7.8638
E-06


1.0000
E-06


3.6000
E 03
l.OQOo
E 00
3.6001
E 00
6.0002
E-02
1.0000
E-03
1.0194
E 02


1.6990
E 00

2.8317
E-02


3.6000
E-03


VALUE FROM A GIVEN UNIT TO A
THE DESIRED UNIT.






NOTE THAT






9.9997
E 02
2.7777
E-01
1.0000
E 00
1.6667
E-02
2.7778
E-04
2.8316
E 01


4.7194
E-01

7.8636
E-03


9.9997
E-04


DESIRED
9.9998
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


9.9998
E-02


UNIT, MULTIPLY
3.5999
E 06
9.9997
E 02
3.6000
E 03
6.0000
E 01
1.0000
E 00
1.0194
E 03


1.6990
E 03

2.8316
E 01


3.9999
E 00


THE GIVEN
3.9314
E 01
9.8096
E-03
3.3313
E-02
3.8839
E-04
9.8098
E-06
I. 0000
E 00


1.6667
E-02

2.7778
E-04


3.3314
E-05


VALUE BY
2.1189
E 03
3.8837
E.01
2.1189
E 00
3.3313
E-02
3. 8839
E-04
6.0000
E 01


1.0000
E 00

1.6667
E-02


2.1189
E-03


THE FACTOR
1.2713
E 09
9.3314
E 01
1.2714
E 02
2.1189
E 00
9.9313
E-02
9.6000
E 03


6.0000
E 01

1.0000
E 00


1.2713
E-01


OPPOSITE
1.0000
E 06
2.7778
E 02
1.0000
E 03
1.6667
E 01
2.7779
E-01
2,8317
E 04


4.7193
E 02

7.8658
E 00


1.0000
E 00


THE GIVEN UNITS
E-XX MRANS 10 TO THE -XX POWER.











































-------
•0
V
n
a
ft
X









CONVERSION FACTORS - CONCENTRATION, DENSITY
DESIRED
GIVEN UNITS
GRAM PER
CU METER
MG PER
CU METER
MICROGRAM
PER CU M
MICROGRAM
PER LITER
GRAIN PER
CU FT
OUNCE PER
CU FT
LB PER
CU FT
GRAM PER
CU FT
LB PER
CU METER
UNITS GRAM PER
cu METER
1.0000
E 00
l.OQOO
E-03
1.0000
E-06
9.9997
E-04
2.2883
E 00
1.0011
E 03
1.6018
E 04
3.5314
E 01
4,3359
E 02
MG PER
CU METER
1.0000
E 03
1.0000
E 00
1.0000
E-03
9.9997
E-01
2.2883
E 03
1.0011
E 06
1.6018
E 07
3.3314
E 04
4.3359
E 05
MICROGRAM
PER cu M
1.0000
E 06
1.0000
E 03
1.0000
E 00
9.999T
E 02
2,2883
E 06
1,0011
E 09
1.6018
E 10
3.331*
E 07
4.5359
E 08
MICROGRAM
PER LITER
1.0000
E 03
1.0000
E 00
I. 0000
E-03
1.0000
E 00
2.2884
E 03
1.0012
E 06
1.6019
E 07
3.3315
E 04
4.5360
E 05
GRAIN PER
CU FT
4,3700
E-01
4,3700
E-0*
4,3700
E-07
4,3699
E-04
1,0000
E 00
4.3730
E 02
7.0000
E 03
1.5432
E 01
1.9822
E 02
OUNCE PER
CU FT
9.9883
E-04
9.9885
E-07
9,9885
E-10
9.9883
E-07
2,2837
E-03
1.0000
E 00
1,6000
E 01
3.3274
E-02
4.5307
E-01
L8 PER
CU
6.2428
E-05
6.2428
E-08
6.2428
E-ll
6.2427
E-08
1.4286
E-04
6.2500
E-02
1.0000
E 00
2.2046
E-03
2.8317
E-02
GRAM PER
FT CU PT
4,8317
E-02
4.8317
E-03
4,8317
E-08
4.8316
E-05
6.4799
E-02
4.83*9
E 01
4.5359
E 02
1.0000
£ 00
1.284*
E 01
UB PER
CU M
2.2046
E-03
2.2046
E-06
2.2046
E-09
2,2046
E-06
3.U449
E-03
2.2072
E 00
3.3314
E 01
7.7835
E-02
1.0000
E 00
TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT,  MULTIPLY THE  GIVEN VALUE  BY  THE  FACTOR OPPOSITE THE GIVEN UNITS
AND BENFATH THE DFSI9ED UNIT.   NOTE THAT E-XX MEANS 10  TO THE -XX POWER.

-------
-1
oo
        CONVERSION FACTORS - DEPOSITION RATF
•SHORT  TON .STAT.  MILE)
             DESIRED UNITS GM PER  SO  KG PER SO  MG PER SO  TON PER SO OZ PER SO  LB PER     GN  PER  SO   *G  PER SO
                             M PER MO  KM PER MO  CM PER MO  MI PER MO  FT PER MO ACRE PERMO   FT PER MO   IN PER MO
        GIVEN UNITS









•^
H
3
O
•3
SC
I
n
g
55
"0
3
Cfl
O

M
cn
N4
H
M
GM PER SO
M PER MO
KG PER SO
KM PER MO
MG PER SO
CM PER MO
TON PER SO
MI PER MO
01 PER SO
FT PER MO


LB PER
ACRE PERMO

GM PER SO
FT PER MO


MG PER SO
IN PER MO


TO CONVERT
AND BENEATH




1.0000
E 00
1.0000
E-03
1.0000
E 01
3.5026
E-01
3.0919
E 02


1.1208
E-01

1.0764
E 01


1.9900
E 00


A VALUE FROM A GIVEN
THE DESIRED UNIT.




I. 0000
E 03
1.0000
E 00
1.0000
E 04
3.9026
E 02
3.0519
E 09


1.1208
E 02

1.0764
E 04


1.9900
E 03


UNIT TO A
NOTE THAT




1.0000
E-01
1.0000
E-04
1.0000
E 00
3.9026
E-02
3.0919
E 01


1.1208
E-02

1.0764
E 00


1.9900
E-01


DESIRED
2.8550
E 00
2.8590
E-03
2.8990
E 01
1.0000
E 00
8.7120
E 02


3.2000
E-01

3.0731
E 01


4.4292
E 00


UNIT. MULTIPLY
E-XX MEANS 10 TO THE -








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


3.6731
E-04

3.9274
E-02


9.0799
E-03


THE GIVEN
XX POWER.




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


1.0000
E 00

9.6033
E 01


1.3829
E 01


VALUE BY





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


1.0413
E-02

1.0000
E 00


1.4400
E.01


THE FACTOR





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


7.2313
E-02

6.9444
E 00


1.0000
E 00


OPPOSITE THE GIVEN UNITS






-------
 CONVERSION FACTORS - PRESSURE

      DESIRED UNITS MILLIBAR   BAR

 GIVEN UNITS
ATMOSPHERE OYNES      KG         LBS        MM MERCURY IN MERCURY
            PER SO CM  PER SO CM  PER SO IN
MILLIBAR
BAR
ATMOSPHERE
DYNES
PER SO CM
KG
PER SO CM
LBS
PER SO IN
MM MERCURY
IN MERCURY
1.0000
E 00
1.0000
E 0)
1.0199
E OS
1.0000
E-09
9.8066
E 02
6,8947
E 01
1.3932
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
». 89*7
E-02
1.3332
E-03
3.3B«4
E-02
9.8692
E-04
9. 8692
E-01
1.0000
E 00
9.8692
E-07
9.6784
E-01
6.8046
E-02
1*3138
E-03
3.3421
E-02
l.OQOO
E 0)
1.0000
E 06
1.0193
E 06
1.0000
E 00
9. 8Q66
E 09
6.8947
E 04
1.3332
E 09
9.9864
E 04
1.0197
E-03
1.0197
E 00
1.0992
E 00
1.0197
E-06
1.0000
E 00
7.0907
E-02
1.9999
E-03
3.4332
E-02
1.4904
E-02
1.4904
E 01
1.4696
E 01
1.4904
E-03
1.4229
E 01
1.0000
E 00
1.9997
E-02
4.9119
E-01
7.9006
C-01
7.9006
E 02
7.6000
E 02
7.3006
E.04
7.3936
E 02
9.1719
E 01
1*0000
E 00
2.9400
E 01
2.9990
E-02
'.9990
E 01
2.9921
E 01
2.999Q
E-09
2.8999
E 01
2,0960
E 00
•.9970
E-02
1.0000
E 00
TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT. MULTIPLY THE GIVEN VALUE  BY  THE  FACTOR OPPOSITE THE GIVEN UNITS
AND BENEATH THE DESIRED UNIT.   NOTE THAT E-XX MEANS 10 TO THE -XX POWER.

-------
CONVERSION FACTORS - TIME
     DESIRED UNITS SECOND
GIVEN UNITS
MINUTE
HOUR
WEEK
MONTH (28) MONTH 











[J,
H
g
O
C/J
"B
a
M
o
2
V)
•fl


«
O
5!
W
V)
H
H
PJ
7)
SECOND

MINUTE

WOUR

WEEK

MONTH (28)

MONTH (30)



MONTH 131)


YEAR (365)



YEAR (366)



TO CONVERT A
AND BENEATH





I. 0000
E 00
1.6667
E-02
2.7778
E-04
1.6534
E-06
4.1336
E-07
3.8980
E-07


3.7336
E-07

3.1710
E-08


3.1623
E-08


VALUE FROM A GIVEN
THE DESIRED UNIT.





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


2.2401
E-05

1.9026
E-06


1*8974
E-06


UNIT TO A
NOTE THAT





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


1.3441
E-03

1.1416
E-04


1.1984
E-04


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


2.2581
E-01

1.9178
E-02


1.9126
E-02


DESIRED UNIT. MULTIPLY
E-xx MEANS





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-Ol

7,6712
E-02


7,6503
E-02


THE GIVEN
2.5920
E 06
4.3200
E 04
7.2000
E 02
4.2857
E 00
1,0714
E 00
1.0000
E 00


9.6774
E-01

8.2192
£-02


8.1967
E-02


VALUE BY
2.6784
E 06
4.4640
E 04
7.4400
E 02
4.4286
E 00
1*1071
E 00
1*0333
E 00


1.0000
E 00

8.4932
E.02


8.4699
E-02


THE FACTOR
3,1936
E 07
5.2360
E 09
8.7600
E 03
5.2143
E 01
1.3036
E 01
1.2167
E 01


1,1774
"E 01

1.0000
E 00


9.9727
E.Ol


OPPOSITE THE
3.1622
E 07
5.2704
E 09
8.7840
E 03
9,2286
E 01
1,3071
E 01
1.2200
E 01


1.1806
E 01

1.0027
E 00


1.0000
E 00


GIVEN UNITS
10 TO THE -XX POWER.































-------
•8
1
rnNi/Fueip.si P
\. LJ" V ^ ^ .^ I '.• ''I ~
DfSlpFO
GfVEM UNITS
WATT
(INT)
Kll OWATT
(INT)
MERAWATT
(INT)
CA| (IMT)
PER SEC
BTU
PER 'UN
BTU
PER MR
JOULES ABS
PER SEC
*ATT uns)
ELECT.
HORSEPOWER
TT0"5 - P"d£3
U'MTS xMT
(INT)
I. o^oo
r n-j
l.ynon
F 03
1.0000
E 06
4.1H7A
F 10
1.7S8H
F 01
2.9313
E-il
9.9081
E-01
9.90H1
F.-Ol
7.4586
f. 02

KILO"*' r
(I'M!
1 .00110
t-0*
1.0000
E 00
1.00'»0
t o*
4.18'6
E-0*
1.75M8
E-OiJ
2.0313
E-04
9.99H1
E-0*
9.09HI
E-0««
'.45M6
E-01

v|F.G««ATr
(INT)
1.0000
E-06
1.0000
F-03
1.0000
F 'JO
4.1-76
F.-O&
1.758fl
F-05
2.9313
F.«-07
9.99H1
E-07
9.9981
E-07
7.4^86
E-04

CAI. tl'JT) dTU
I'EP SFC PEP MI
2.3-«flO 5.6P57
E-'U E-02
2.4HflO 5.6857
E '•?. E 01
2.3'^HO 5.6H5?
E "5 E 04
1
l.OOQO 2.3B10
E "0 E-01
4.2000 1.0000
E '.'0 E 00
7.o;inn 1.6667
E-o? E-02
2.3Hf5 »,6S46
E-rM E-02
2.3H75 5.6846
E-01 E-02
I. '"11 4.2407
E "2 E 01

BTU
N PPR HR
3.4114
E 00
3.4114
E 03
3.4114
E 06
1.4285
E 01
6.0000
E 01
1.0000
E 00
3.4108
E 00
3.4108
E 00
2.5444
E 03

JDULES
PER
1.0002
E 00
1.0002
E 03
1.0002
E 06
4.188*
E 00
1.7591
E 01
2.9319
E-01
1.0000
E 00
1.0000
E 00
7.4600
E 02

ABS wATT (ABS)
SEC
1.0002
E 00
1.0002
E 03
1.0002
E 06
4.188*
E 00
1.7591
E 01
2.9319
E-01
1.0000
E 00
1,0000
E 00
7.4600
E 02

ELECT.
HORSEPI
1.3*0?
E-03
1.3*0?
E 00
1.3*0?
E 03
5.61*5
E-03
2.3581
E-02
3.9301
E-O*
1.3*05
E-03
1.3*05
E-03
1.0000
E 00
TO CQNVrRT A v/A|
AND BENFATH 1ME
FROM A GlVtN UNI" T3 A DESIRF^ UNIT, MULTIPLY THE GIVEN VALUE »Y THE FACTOR OPPOSITE THE GIVEN UNITS
     UNIT.   NOTr. THAT E-X* MFANS 10 TO THE -XX POWER.

-------
I
o
VJ
o
g
35
•«
S
—
o
w
3
 CONVERSION FACTORS - ENERGY. WORK

      DESIRED UNITS ERG        DYNE-C*

 GIVEN UNITS

ERG




DYNE-CM




ABS JOULE
                                                 ASS JOULE  CAL  (INT)  CAL  (15)    INT KW-HR  ABS  KW-HR   BTU
1.0000
E 00
1.0000
E 00
1.0000
C 07
4.1868
E 07
4.1899
E 07
3.6007
E 13
3.6000
E 13
1.0991
E 10
1.0000
E 00
1.0000
E 00
1.0000
E 07
4.1868
E 07
4.1899
E 07
3.6007
E 13
3.6000
E 13
1.0991
E 10
1.0000
E-07
1.0000
E-07
1.0000
E 00
4.1868
E 00
4.1899
E 00
3.6007
E 06
3.6000
E 06
1.0391
E 03
2.3884
E-Ofl
2.3884
E-OB
2.3884
E-01
1.0000
E 00
9.9968
E-01
8.6QOO
E 09
8.9984
E 09
2.9200
E 02
2.3892
E-08
2.3892
E-08
2.3892
E-01
1.0003
E 00
1,0000
E 00
8.6027
E 09
8.6011
E 03
2.9208
E 02
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
2,7778
E-14
2.7778
E-14
2.7778
E-07
1.1630
C-06
1.1626
E-06
1,0002
E 00
1.0000
E 00
2,9307
E-04
9.4781
E-ll
9.4781
E-U
9.4781
E-04
9.96B3
E-03
3,9671
E-03
3.4128
E 03
3.4121
E 03
1,0000
E 00
       CAL (13)
INT KW-HR
       ABS KW-HR
BTU
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.
H
W
V)

-------
        CONVERSION FACTORS - ENERGY PER UNIT AREA
             DESIRED UNITS LANGLEY    CAL  <19»   BTU        INT KM-HR  ABS JOULES
                                       PER SO CM  PER SO FT  PER SO M   PER SO CM
        GIVEN UNITS
LANGLEY
CAL 119)
PER SO CM
BTU
PER SO FT
INT KW-HR
PER SO M
ABS JOULES
PER SO CM
1.0000
E 00
1.0000
E 00
2.7193
E-01
8.6029
E 01
2.3892
E-01
1.0000
E 00
1.0000
E 00
2.7133
E-01
8.6029
E 01
2.3892
E-01
3.6899
E 00
3.6899
E 00
1.0000
E 00
3.1706
E 02
8.8094
E-01
1.1624
E-02
1.1624
E-02
3.1940
E-03
1.0000
E 00
2.7772
E-03
4.1899
E 00
4.1899
E 00
1.1397
E 00
3.6007
E 02
1.0000
E 00
       TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT. MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS
       AND BENEATH THE DESIRED UNIT.   NOTE THAT E-XX MEANS 10 TO THE -XX POWER.
oo
CO

-------
CONVERSION FACTORS - POWER PER UNIT AREA
ARE
OEG)
     DESIRED UNITS CAL PER SO CAL PER SO LANflLEY    CAL PER SO BTU PER SO BTU PER SO ABS HATT
                    M PER SEC CM PER MIN    PER MlN CM PER DAy FT  PER MIN FT PER DAY  PER SO CM
GIVEN UNITS











*
GO
8
9
E
Q
a
i
§
3
M
i
V
O
M
O











H
3
O
CA
TJ
2
2
n
2
CA
TS
CA
0
S!
M
CA
H
H
M
CAL PER SO
M PER SEC
CAL PER SO
CM PER MIN
LANGLEY
PER MIN
CAL PER SO
CM PER DAY
BTU PER SO
FT PER MIN

BTU PER SO
FT PER DAY

ABS WATT
PER SO CM

TO CONVERT A
AND BENEATH








1.0000
E 00
1.6667
E 02
1.6667
E 02
1.1574
E-01
4.5222
E 01

3.140*
E-02

2.3892
E 03

VALUE FROM A GIVEN
THE DESISED UNIT.








6.0000
E-03
1.0000
E 00
1.0000
E 00
ft. 9444
E-04
2.7133
E-01

1.8843
E-0*

l.*335
E 01

UNIT TO A
NOTE THAT








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

1.8843
E-04

1.4339
E 01

DESIRED
8.6400
E 00
1.4400
E 03
1.440Q
E 03
1.0000
E 00
3.9072
E 02

2.7133
E-01

2.0643
E 04

UNIT, MULTIPLY
2.2113
E-02
3.6835
E 00
3.6855
E 00
2.5594
E-03
1.0000
E 00

6.9445
E-04

5,2833
E 01

THE GIVEN
3.1843
E 01
5.3071
E 03
3.3071
E 03
3.6855
E 00
1.4400
E 03

1.0000
E 00

7,6079
E 04

VALUE BY
4.1855
E.04
6.9758
E-02
6.9758
E-02
4.8443
E-05
1.8928
E-02

1.3144
E-03

1.0000
E 00

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









































-------

 AP-26
 ENVIRONMENTAL HEALTH SERIES
 Air Pollution
              WORKBOOK
                    OF
    ATMOSPHERIC DISPERSION
               ESTIMATES
H
   U. S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE
                Public Health Service
       Consumer Protection and Environmental Health Service

-------
                WORKBOOK OF
ATMOSPHERIC DISPERSION  ESTIMATES
                   D. BRUCE TURNER

              Air Resources Field Research Office,
           Environmental Science Services Administration
    U. S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE
                    Public Health Service
         Consumer Protection and Environmental Health Service
            National Air Pollution Control Administration
                      Cincinnati, Ohio
                      Revised 1969

-------
      The ENVIRONMENTAL HEALTH SERIES of reports was established  to re-
port the results of scientific and engineering studies of man's environment:  The com-
munity, whether urban, suburban, or rural, where he lives, works, and plays; the air,
water, and earth he uses and re-uses; and the wastes he produces and must  dispose of
in a way that  preserves these natural  resources.  This SERIES of reports provides for
professional users a central source of information on the intramural research activities
of the Centers  in the  Bureau of Disease Prevention and  Environmental  Control, and
on their cooperative activities with state and local agencies,  research institutions, and
industrial organizations. The general  subject area  of each report is indicated by the
letters that appear in the publication  number; the  indicators are

                         AP — Air Pollution
                        RH — Radiological Health
                       UIH — Urban and Industrial Health

      Triplicate tear-out abstract cards are provided with reports in  the SERIES  to
facilitate information retrieval. Space is provided on the cards for the user's accession
number and additional key words.

      Reports in the SERIES will be distributed to requesters, as supplies permit. Re-
quests should be directed to the Center identified on the title page.
                  Public Health Service Publication No. 999-AP-26

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                                  PREFACE

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

Chapter 1.  INTRODUCTION  	  1

Chapter 2.  BACKGROUND 	  3

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

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

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

Chapter 7.  EXAMPLE PROBLEMS 	-	 45
Appendices:	 57

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

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                                  ABSTRACT

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

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                                 Chapter  1 — INTRODUCTION
    During recent years methods of estimating at-
mospheric dispersion have undergone considerable
revision, primarily due to results of experimental
measurements.  In most  dispersion  problems the
relevant  atmospheric layer is that  nearest the
ground, varying in thickness from several hundred
to  a few thousand  meters.  Variations in  both
thermal  and mechanical  turbulence and in  wind
velocity  are greatest in the layer in contact with
the surface. Turbulence induced by buoyancy forces
in the atmosphere is closely related to the vertical
                                    temperature structure. When temperature decreases
                                    with height at a rate higher than 5.4°F per 1000 ft
                                    (1°C per  100 meters),  the  atmosphere  is in un-
                                    stable  equilibrium and vertical motions are en-
                                    hanced. When temperature decreases at a lower
                                    rate  or increases with height  (inversion), vertical
                                    motions are damped  or reduced. Examples of typ-
                                    ical variations in temperature and wind speed with
                                    height for  daytime and  nighttime  conditions are
                                    illustrated in Figure  1-1.
  600r
  500
  400
  300
o
  200
  100
    0
    -I
23456

  TEMPERATURE. °C
                                   7   8   9  10  II   12
1    2
3   4   5   6   7   8

 WIND SPEED,  m/»«c
9   10  II
        Figure 1-1.  Examples of variation of temperature and wind speed with height (after Smith, 1963).
    The  transfer of momentum upward or down-
 ward in  the atmosphere is also related to stability;
 when  the  atmosphere  is  unstable, usually in the
 daytime, upward motions transfer the momentum
 "deficiency" due to eddy friction  losses near the
 earth's  surface through  a relatively deep  layer,
 causing  the wind  speed  to increase  more slowly
 with height than at night (except in the lowest few
 meters). In addition to thermal turbulence, rough-
 ness elements  on the ground engender mechanical
 turbulence, which  affects both the  dispersion of
 material in the atmosphere and  the wind profile
 (variation  of wind with height). Examples of these
 effects on  the  resulting wind profile are shown in
 Figure 1-2.
                                       As wind  speed  increases,  the effluent from a
                                    continuous source is introduced into a greater vol-
                                    ume of air per unit time interval.  In addition  to
                                    this  dilution  by wind speed, the spreading of the
                                    material (normal to the mean direction of trans-
                                    port) by turbulence is a major factor in the dis-
                                    persion process.

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

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eters presented here are most applicable to ground-
level or low-level releases (from the surface to about
20 meters), although they are commonly applied at
higher elevations without full experimental valida-
tion.  It is  assumed that stability IB  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,—
                    URBAN AREA
  SUBURBS
LEVEL COUNTRY
                                                   GRADIENT WIND
      1-2.  Examples of variation of wind with height over different size roughness elements (ngures are percentages
                                of gradient wind); (from Davenport 1963).
                                                           ATMOSPHERIC DISPERSION ESTIMATES

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                                  Chapter 2 —BACKGROUND
    For a number of years estimates of concentra-
 tions were calculated either from the equations of
 Sutton  (1932)  with  the  atmospheric dispersion
 parameters Cy, Cf, 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, <7K, at the point of release. Cramer (1957)
 derived a diffusion equation incorporating standard
 deviations of  Gaussian distributions:  a, for  the
 distribution of material in the plume across wind
 in the horizontal,  and ot for the vertical distribution
 of material in the  plume.  (See Appendix 2 for prop-
 erties of Gaussian distributions.)  These statistics
 were related to the standard deviations of azimuth
 angle, CTA, and elevation angle, *K, 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, a, and  OE.  Pasquill's method,  with Gifford's
conversion incorporated, is used in  this workbook
 (see Chapter 3) for diffusion estimates.

   Advantages of this system are that (1) only two
dispersion parameters are required and (2) results
of most  diffusion experiments are now being  re-
ported in terms of the standard deviations of plume
spread. More field dispersion experiments are being
conducted and will be  conducted under conditions
of varying surface roughness and atmospheric  sta-
bility.  If the dispersion parameters from a specific
experiment are considered to be more representative
than those suggested in this workbook, the param-
eter values can  be used with the equations given
here.

                REFERENCES

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

Cramer, H. E., 1957:  A practical method for esti-
    mating the dispersion of atmospheric contami-
    nants.  Proc.  1st Natl. Conf. on Appl. Meteorol.
    Amer. Meterol. Soc.

Cramer, H. E., F.  A. Record, and H. C. Vaughan,
    1958:  The study of the  diffusion of gases  or
    aerosols in the  lower atmosphere.  Final Report
    Contract AF  19(604)-1058 Mass. Inst. of Tech.,
    Dept. of Meteorol.

Cramer, H. E., 1959a:  A brief survey of the mete-
    orological aspects of atmospheric pollution. Bull.
    Amer. Meteorol. Soc., 40, 4,  165-171.

Cramer,  H. E.,  1959b:  Engineering estimates  of
    atmospheric dispersal capacity. Amer. Ind. Hyg.
    Assoc. J., 20, 3, 183-189.

Gifford, F.  A., 1961:  Uses of routine meteorological
    observations  for estimating atmospheric disper-
    sion.  Nuclear Safety, 2, 4, 47-51.

Hay, J. S., and F.  Pasquill, 1957: Diffusion from a
    fixed source at a height of a few  hundred feet
    in the atmosphere.  J. Fluid Mech., 2, 299-310.

Hay, J. S., and F.  Pasquill, 1959: Diffusion from a
    continuous source in relation to the spectrum
    and scale of turbulence,  pp 345-365 in  Atmos-
    pheric Diffusion and Air Pollution, edited by
    F.  N. Frenkiel  and P. A. Sheppard, Advances
    in Geophysics,  6, New  York, Academic Press,
    471 pp.

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

Sutton, O.  G., 1932:  A theory of eddy diffusion  in
    the atmosphere. Proc. Roy. Soc., A, .735,  143-
    165.
Background

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                Chapter  3 —ESTIMATES OF  ATMOSPHERIC DISPERSION
   This  chapter  outlines the basic procedures to
be used  in making dispersion estimates as sug-
gested by Pasquill (1961) and modified by Gifford
(1961).

COORDINATE SYSTEM

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

DIFFUSION EQUATIONS

   The concentration, x, of  gas or aerosols (parti-
cles less  than  about 20 microns diameter) at x,y,z
from a continuous source with an effective emission
height, H, is given by equation 3.1.  The notation
used to  depict this concentration is  x (x,y,z;H).
H is the height  of the plume centerline  when it
                      7
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 a, 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 (x,y,z;H)
                                           (3.1)
'Note: exp —a/b = e~«/b where e is the base ol 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"-) or, for radioactivity (curies m~s)
    Q (g sec"1) or (curies sec"1)
    u (m sec"1)
    CTy, a,, H,x,y, and z (m)

This equation is the same as equation (8.35) p. 293
of Sutton (1953) when a's are substituted for Sut-
ton's parameters through equations like  (8.27) p.
286. For evaluations of the  exponentials found in
Eq. (3.1) and those that  follow, see  Appendix 3.
x is a mean over the same time interval as the time
interval for which the  a's and u are representative.
The values of both a, and a, are evaluated in terms
of the downwind distance, x.

    Eq.  (3.1) is valid where  diffusion in the direc-
tion of the plume travel can be neglected, that is,
no diffusion in the x direction.

This may be assumed if the  release is continuous
or if the duration of release  is equal to or greater
than the travel time (x/u) from the source to the
location of interest.

    For  concentrations calculated at ground level,
i.e., z = 0, (see problem 3) the equation simplifies
to:
   X (x,y,0;H)
                    a, a, U
   exp
[-4(^)1
                                           (3.2)
   Where  the concentration is  to be  calculated
along the centerline of the plume (y = 0), (see
problem  2)  further simplification  results:
                                           (3.3)
   For a ground-level source with no effective plume
rise (H = 0), (see problem  1):

                     Q
   x U,0,0;0)
                  ir a, a, U
                                           (3.4)
EFFECTS  OF  STABILITY
   The values of af and a, vary with the turbulent
structure of the atmosphere, height above  the sur-
face, surface roughness, sampling  time over  which
the concentration is to be estimated,  wind speed,
and distance from the source.  For the parameter
values given here, the sampling time is assumed to
be about 10 minutes, the height to be the lowest
several  hundred  meters of  the  atmosphere, and
the surface to be relatively open country.  The
turbulent  structure  of  the atmosphere and wind
speed are considered in the stability  classes pre-
sented, and the effect of distance from the source is
considered in the graphs determining the parameter
values. Values for o, and  6

Day

^ Incoming Solar Radiation
Strong
A
A-B
B
C
C
Moderate
A-B
B
B-C
C-D
D
Slight
B
C
C
D
D
Night
Thinly Overcast
s^/8 Low Cloud

E
D
D
D

-=3/8
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 (Last, 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 2lL; XL is where c.
                           The value of ctL = 0.8 L
                              0.47 L
       for any z from 0 to L
       for x >2 XL; XL is where ot = 0.47 L
                       EVALUATION OF WIND SPEED

                          For the wind speed, u, a mean through the ver-
                       tical extent of  the plume  should be used.  This
                       would be from the height H — 2 a, through  H +
                       2 az. Of course,  if 2 a, is greater than H then the
                       wind can be averaged from the ground to H + 2 at.
                       However, the "surface wind" value may be all that
                       is available. The surface wind is most  applicable
                       to surface or low-level emissions, especially under
                       stable conditions.
PLOTS OF CONCENTRATIONS
AGAINST  DISTANCE

   To gain maximum insight into a diffusion prob-
lem it is often desirable to plot centerline concen-
trations against  distance downwind.  A  convenient
procedure is to determine the ground-level center-
line concentrations for a number of downwind dis-
tances and plot these values on log-log graph paper.
By connecting the points,  one may  estimate con-
centrations  for  intermediate downwind distances
(see problem 6).

ACCURACY OF  ESTIMATES

   Because of a  multitude  of scientific and techni-
cal limitations the  diffusion  computation method
presented in this manual may provide  best estimates
but not infallible predictions.  In the unstable and
stable cases, severalfold  errors  in estimate of  o,
can occur for the longer travel  distances.  In some
cases the «r, may be expected to be correct within a
factor of 2, however.  These are: (1) all stabilities
for distance of travel out to a few hundred meters;
(2) neutral to moderately  unstable  conditions for
distances out to a few kilometers; and (3) unstable
conditions  in the lower 1000  meters  of  the atmos-
phere with a marked  inversion  above for distances
out to 10 km or more. Uncertainties  in the esti-
mates of a,, are  in  general less than those  of 
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10,000
                                    1                              10
                                        DISTANCE DOWNWIND, km
100
        Figure 3-2.  Horizontal dispersion coefficient as a function of downwind distance from the source.
                                                           ATMOSPHERIC DISPERSION ESTIMATES

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                                        I                                10
                                            DISTANCE DOWNWIND, km
100
        Figure  3-3.  Vertical  dispersion  coefficient as a function of downwind distance from the  source.
Estimates
   IN-101 O - «» - 1

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                            , I  234 $ 6«10"5
                              CONC.
                              SSOmeleri
             Figure 3-4.  Variations  in concentration  in the vertical beneath a more stable layer.
three cases (where a, can be expected to be within
a factor of 2) should be correct within a factor of 3,
including errors in ay and u. The relative confidence
in the 
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                 10'
                    0.1
Figure 3-5A.   xu/Q with distance for various  heights of emission (H) and limits to vertical dispersion (L), A stability.
Estimates
11

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               10
               10
               10
                                                    DISTANCI. ki
Figure  3-5B.  xu-'Q with distance for various heights of emission (H) and limits to vertical dispersion (L), B stability.
12
ATMOSPHERIC DISPERSION ESTIMATES

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                                                           •ISTAMCE. k.
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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                                                  BISTAKCE, km



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

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              10'
                                                      •ISTANCi. IIP



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

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                \0
                10
                   •.I                      1
                                                   USTAKCE. k.


Figure 3-5F.  xu/Q with distance for various heights of emission (H) and limits to vertical dispersion (I), F stability.



16                                                              ATMOSPHERIC DISPERSION ESTIMATES

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   From Table A-l  (Appendix 3) when exp

                         5, y/a, - 1.46
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~" isopleth from the
x-axis at a downwind distance of 600 meters.
   This can also be determined from:
21r*[ x(«.Q.Q;H)
       X(x,y,0;H)
                            1)
                            Jj
(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 see"1 under B stability
conditions with wind speed 2 m sec"5, 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~:  corre-
sponds to a x isopleth with  a value of 10~3 g m~B.

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~s g m~s isopleth
(10~4 nr2 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, xml),, 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 a,'s and
a.'s used here.  As noted, however, since  ot  gener-
ally decreases  with  height  and  u increases with
height, the product u a, ot will not change appreci-
ably.  The greater the  effective height, the  more
likely it is that the stability may not be the  same
from tne  ground  to this height.  With  the longer
travel distances such as the points of maximum
concentrations for stable conditions (Types  E or
F), the stability  may  change before the plume
travels the entire distance.


REVIEW  OF  ASSUMPTIONS

   The  preceding has  been based  on these as-
sumptions, which should be clearly understood:

   (i)  Continuous  emission  from  the  source or
emission times equal to or greater than travel times
to the downwind position under  consideration, so
that diffusion in the direction of transport may be
neglected.

   (ii) The material diffused  is a  stable gas or
aerosol (less than  20 microns diameter) which re-
mains suspended in the air over long periods of time.

   (iii) The equation  of continuity:
                                              Q
                    /h»   j +co

                         I  xudydz

                    0  J  -°°
                                           (3.9)
*"ln" denotes natural logarithms, i.e., to the base e.
                                          is fulfilled, i.e., none of the material emitted is re-
                                          moved from the plume as it moves downwind and
                                          there is complete reflection at th2 ground.

                                              (iv) The  mean  wind  direction specifies  the
                                          x-axis, and a mean wind speed representative of
                                          the diffusing layer  is chosen.

                                              (v)  Except where specifically  mentioned,  the
                                          plume constituents are distributed normally in both
                                          the cross-wind and vertical directions.

                                              (vi) The IT'S given in Figures 3-2 and 3-3 repre-
                                          sent time periods of about 10 minutes.

                                                          REFERENCES

                                          DeMarrais, G. A., 1961: Vertical temperature  dif-
                                              ference observed over an urban area. Bull. Amer.
                                              Meteorol.  Soc.,  42, 8, 548-554.

                                          Duckworth, F. S., and J. S. Sandberg,  1954:  The
                                              effect  of cities  upon horizontal and  vertical
                                              temperature gradients. Bull. Amer. Meteorol.
                                              Soc., 35, 5, 198-207.

                                          Gifford, F. A.,  1961: Use of routine meteorological
                                              observations for estimating atmospheric disper-
                                              sion. Nuclear Safety, 2, 4, 47-51.

                                          Gifford, F. A.,  1962:  The area within ground-level
                                              dosage isopleths.  Nuclear Safety,  4, 2, 91-92.
Estimates
                                                                                                 17

-------
H



O
|
8
H
                                   CLASS A  STABILITY


                                             H»0
3                 4




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

-------
                                     -FH-H4  fTFRfflffi+
                             CLASS   B   STABILITY
IO'3  IO'4
                                                    3                 4


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

-------
r>

1
                                 CLASS  C   STABILITY
                                         H»0
                                                                 DOWNWIND DISTANCE (i). k«
                                            Figure 3-6C.  Isopleths of xu/Q for a ground-level source, C stability.

-------
a

I
                                   CLASS  D   STABILITY
                                            H- 0
                                                                   3                 4

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

-------
           10
       -i   o.$
                                 CLASS  E    STABILITY
                                          H»0
                                                                3               4


                                                              DOWNWIND DISTANCE (i), km
o
o
                                  CLASS   F   STABILITY
                                            H«0
                           |0*  5x10-"*  3,10*    2x10
                                                                3                4


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

-------
I
                                   CLASS  A   STABILITY
                                                                   3                 4



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

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

-------
CLASS  C   STABILITY
            IOO
                               I                 4

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

-------
H

3
o
I
•0
8
H
                                   CLASS   D   STABILITY


                                            H«IOO
  3                 4



DOWNWIND DISTANCE (i). km
                                            Figure 3-70.  Isopleths of xu/Q for a source 100 meters high, D stability.

-------
•   0.5
                     CLASS E  STABILITY
                             H«IOO
                                                          3                 4

                                                        DOWNWIND  DISTANCE (i), ki
    1.0
    I.S
    1.0
    0.5
CLASS  F  STABILITY
        H-IOO
                                                          3                 4

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

-------
   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. 0., 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.
28
                                                            ATMOSPHERIC DISPERSION ESTIMATES

-------
                                                                          (x./o)     --»
                                                                                 mot,
•*       Figure 3-9.  Distance of maximum concentration  and maximum xu/Q as a function  of  stability (curves)  and effective  height (meters) of emission
                    (numbers).

-------
                      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
 tp.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, v,; 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, Ta; shear of the wind
 speed  with  height,  du/dz;  and   atmospheric  sta-
 bility.  No theory on plume rise takes into account
 all of these  variables; even if such a theory were
 available, measurements  of  all of the  parameters
 would  seldom be available. Most of  the equations
 that have been  formulated for computing  the ef-
 fective height of emission are semi-empirical. For a
 recent review  of equations for effective height of
 emission see Moses, Strom, and Carson (1964).

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

   The equation of Holland was developed with
experimental  data from larger sources than those
of Moses and Strom (stack diameters from 1.7 to
4.3  meters and stack temperatures from 82 to
 204 °C); Holland's equation is used in the solution
of the problems given in this workbook. This equa-
tion frequently underestimates the effective height
of emission; therefore its use often provides a sb'ght
"safety" factor.

   Holland's equation is:


AH ~-^J- (1.5 + 2.68 x  10-' p T' ~ T' 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 see"1
    p = atmospheric pressure, mb
    TB = stack gas temperature, °K
    T. = air temperature, °K
 and 2.68 x 10~3 is  a constant having units of mb~l
 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 Jine
 are of the utmost importance. For first approxima-
 tions it can be assumed that the maximum concen-
 tration occurs  where vTTa, = H and that at this
 distance the 
-------
            10 Q
             0.
               Figure 4-1.  The product of "^ as a function of downwind distance from the source.
Effective Height

-------
the height. Values other than 4.3 and 2.15 can be
used. When these values are used 97 % of the dis-
tribution is included within these limits. Virtual
distances x, and  x, can be found such that at x<,
a,  = a,,, and at x,,  at>  = atu.  These x's will differ
with stability. Equations applicable to point sources
can then be used, determining «v as  a function of
x +  x, and ot as a function of x + x,.

                REFERENCES

Bosanquet, C.  H., W. F. Carey, and E. M. Halton,
   1950:  Dust from chimney stacks. Proc.  Inst.
   Mech. Eng., 162, 355-367.

Bosanquet, C. H., 1957:  The rise of a hot waste gas
   plume.  J. Inst. Fuel, 30, 197, 322-328.

Davidson, W. F., 1949:  The dispersion and spread-
   ing of gases and dust from chimneys.  Trans.
   Conf. on Ind.  Wastes, 14th Ann. Meeting, Ind.
   Hygiene Found. Amer., 38-55.

Halitsky, J., 1961:  Wind tunnel model test of ex-
   haust  gas  recirculation at  the  NIH  Clinical
   Center. Tech. Rep.  No. 785.1, New York Univ.

Halitsky, J., 1962:  Diffusion of vented gas around
   buildings. J. Air Poll. Cont. Assoc., 12, 2, 74-80.

Halitsky, J., 1963:  Gas diffusion near  buildings,
   theoretical  concepts and wind tunnel model ex-
   periments with prismatic building shapes.  Geo-
   physical Sciences Lab. Rep.  No. 63-3.   New
   York  Univ.
Hawkins, J. E., and G. Nonhebel, 1955: Chimneys
   and the  dispersal of smoke.  J.  Inst. Fuel, 28,
   530-546.

Holland, J.  Z., 1953:  A meteorological survey of
   the Oak Ridge area.  554-559  Atomic Energy
   Comm.,  Report  ORO-99,  Washington,  D.C.,
   584 pp.

Moses, H., and G. H. Strom, 1961:  A comparison
   of observed plume  rises with values obtained
   from well-known  formulas.  J. Air Poll.  Cont.
   Assoc., 11, 10, 455-466.

Moses, H.,  G. H. Strom, and J. E. Carson,  1964:
   Effects of meteorological and engineering fac-
   tors on stack plume rise. Nuclear  Safety, 6, 1,
   1-19.

Scorer, R. S., 1959: The behavior of plumes. Int.
   J. Air Poll., 1, 198-220.

Sherlock, R. H., and E. J. Lesher,  1954:  Role of
   chimney  design  in  dispersion of waste  gases.
   Air Repair, 4, 2, 1-10.

Strom, G. H., 1955-1956: Wind tunnel scale  model
   studies of air pollution from industrial plants.
   Ind. Wastes, Sept. - Oct. 1955, Nov. - Dec. 1955,
   and Jan. - Feb. 1956.

Strom, G. H., M. Hackman, and E. J. Kaplin, 1957:
   Atmospheric dispersal of industrial stack gases
   determined by concentration measurements in
   scale  model wind  tunnel  experiments. J.  Air
   Poll. Cont. Assoc.,  7, 3, 198-203.
34
       ATMOSPHERIC DISPERSION ESTIMATES

-------
                                Chapter  5 — SPECIAL TOPICS
CONCENTRATIONS IN  AN  INVERSION
BREAK-UP FUMIGATION

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

   To estimate  ground-level  concentrations under
inversion break-up fumigations,  one  assumes that
the plume was initially emitted into a stable layer.
Therefore, o7 and F is discussed below.

Values for the integral in brackets can be found in
most statistical tables. For example, see pages 273-
276, Burington  (1953).  This factor accounts for
the portion of the plume that is mixed downward.
If the inversion is eliminated up to the effective
stack height, half  of the plume is presumed to be
mixed downward,  the other half remaining in the
stable air above.  Eq. (5.1) can be approximated
when the  fumigation  concentration  is  near its
                    Q
XF (x,y,0;H)
               \/2Tu
exp I — -5-
                                          (5.2)
                                          (5.3)
   A difficulty is encountered in estimating a rea-
sonable value for the horizontal  dispersion since in
mixing the stable plume through a vertical depth
some additional horizontal  spreading  occurs  (see
problem 12).  If this spreading is ignored and  the