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
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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
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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
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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
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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-
-------
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
-------
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
-------
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 -
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9.90E -
9. ME -
8.74E -1
8.25E -t
7.7ZE -I
7.1">£ -1
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9.94E -1
5.34E -1
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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
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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
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9.28E -6
0.04
9.99E
9.90E
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V.44£
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H.64E
H.19E
7.61E
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6.43E
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3.06E
2. ME
2.20E
1.84E
1.92E
1.2SE
1.01E
M. 14E
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•>.11E
3.97E
3.07E
2.34E
1.77E
1.315
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2.6<»E
l.OOE
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9.99E -1
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9.69F -1
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9.04E -1
B.60E -1
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7.99E -1
6.97E -1
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9.76E -I
9.16E -1
4.9BE -1
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1.B1E -1
1.49E •!
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9.91E -2
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3.87E .2
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1.72F -2
1.29F -2
9.99E -3
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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
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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
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T.08E
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9.97E
9.84E
9.62E
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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
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2.83E .1
2.40E .1
2.02E .1
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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
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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
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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.
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