WORKBOOK
OF
ATMOSPHERIC DISPERSION
ESTIMATES
H
U.S. ENVIRONMENTAL PROTECTION AGENCY
-------
WORKBOOK OF
ATMOSPHERIC DISPERSION ESTIMATES
D. BRUCE TURNER
Air Resources Field Research Office,
Environmental Science Services Administration
ENVIRONMENTAL PROTECTION AGENCY
Office of Air Programs
Research Triangle Park, North Carolina
Revised 1970
-------
The AP series of reports is issued by the Environmental Protection
Agency to report the results of scientific and engineering studies,
and information of general interest in the field of air pollution.
Information presented in this series includes coverage of intramural
activities involving air pollution research and control technology
and of cooperative programs and studies conducted in conjunction
with state and local agencies, research institutes, and industrial
organizations. Copies of AP reports are available free of charge -
as supplies permit - from the Office of Technical Information and
Publications, Office of Air Programs, Environmental Protection
Agency, Research Triangle Park, North Carolina 27711.
5th printing March 1972
Office of Air Programs Publication No. AP-26
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402- Price $1.00
Stock Number 5603-0015
-------
PREFACE
This workbook presents some computational techniques currently used by scien-
tists working with atmospheric dispersion problems. Because the basic working equa-
tions are general, their application to specific problems usually requires special care
and judgment; such considerations are illustrated by 26 example problems. This
workbook is intended as an aid to meteorologists and air pollution scientists who are
required to estimate atmospheric concentrations of contaminants from various types
of sources. It is not intended as a complete do-it-yourself manual for atmospheric
dispersion estimates; all of the numerous complications that arise in making best esti-
mates of dispersion cannot be so easily resolved. Awareness of the possible complex-
ities can enable the user to appreciate the validity of his "first approximations" and
to realize when the services of a professional air pollution meteorologist are required.
111
-------
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
-------
CONTENTS
ABSTRACT vii
Chapter 1. INTRODUCTION 1
Chapter 2. BACKGROUND 3
Chapter 3. ESTIMATES OF ATMOSPHERIC DISPERSION _ 5
Coordinate System 5
Diffusion Equations 5
Effects of Stability : 6
Estimation of Vertical and Horizontal Dispersion 7
Evaluation of Wind Speed 7
Plots of Concentrations against Distance _ 7
Accuracy of Estimates 7
Graphs for Estimates of Diffusion 10
Plotting Ground-Level Concentration Isopleths 10
Areas Within Isopleths 17
Calculation of Maximum Ground-Level Concentrations , 17
Review of Assumptions _ 17
Chapter 4. EFFECTIVE HEIGHT OF EMISSION 31
General Considerations _ 31
Effective Height of Emission and Maximum Concentration 31
Estimates of Required Stack Heights _ 31
Effect of Evaporative Cooling 32
Effect of Aerodynamic Downwash 32
Chapter 5. SPECIAL TOPICS 35
Concentrations in an Inversion Break-up Fumigation 35
Plume Trapping 36
Concentrations at Ground Level Compared to Concentrations
at the Level of Effective Stack Height from Elevated Con-
tinuous Sources _ 36
Total Dosage from a Finite Release 37
Crosswind-Integrated Concentration _ 37
Estimation of Concentrations for Sampling Times Longer
than a Few Minutes 37
Estimation of Seasonal or Annual Average Concentrations
at a Receptor from a Single Pollutant Source 38
Meteorological Conditions Associated with Maximum
Ground-Level Concentrations 38
Concentrations at a Receptor Point from Several Sources 39
Area Sources _ 39
Topography 40
Line Sources 40
Instantaneous Sources 41
Chapter 6. RELATION TO OTHER DIFFUSION EQUATIONS 43
Chapter 7. EXAMPLE PROBLEMS 45
Appendices: 57
1 Abbreviations and Symbols _ 59
2 Characteristics of the Gaussian Distribution 61
3 Solutions to Exponentials 65
4 Constants, Conversion Equations, Conversion Tables 69
-------
ABSTRACT
This workbook presents methods of practical application of the binormal con-
tinuous plume dispersion model to estimate concentrations of air pollutants. Estimates
of dispersion are those of Pasquill as restated by Gifford. Emphasis is on the estima-
tion of concentrations from continuous sources for sampling times up to 1 hour. Some
of the topics discussed are determination of effective height of emission, extension of
concentration estimates to longer sampling intervals, inversion break-up fumigation
concentrations, and concentrations from area, line, and multiple sources. Twenty-six
example problems and their solutions are given. Some graphical aids to computation
are included.
vii
-------
Chapter 1INTRODUCTION
During recent years methods of estimating at-
mospheric dispersion have undergone considerable
revision, primarily due to results of experimental
measurements. In most dispersion problems the
relevant atmospheric layer is that nearest the
ground, varying in thickness from several hundred
to a few thousand meters. Variations in both
thermal and mechanical turbulence and in wind
velocity are greatest in the layer in contact with
the surface. Turbulence induced by buoyancy forces
in the atmosphere is closely related to the vertical
temperature structure. When temperature decreases
with height at a rate higher than 5.4°F per 1000 ft
(1°C per 100 meters), the atmosphere is in un-
stable equilibrium and vertical motions are en-
hanced. When temperature decreases at a lower
rate or increases with height (inversion), vertical
motions are damped or reduced. Examples of typ-
ical variations in temperature and wind speed with
height for daytime and nighttime conditions are
illustrated in Figure 1-1.
600r
234567
TEMPERATURE, °C
10 11 12
345678
WIND SPEED, m/sec
10 11
Figure 1-1. Examples of variation of temperature and wind speed with height (after Smith, 1963).
The transfer of momentum upward or down-
ward in the atmosphere is also related to stability;
when the atmosphere is unstable, usually in the
daytime, upward motions transfer the momentum
"deficiency" due to eddy friction losses near the
earth's surface through a relatively deep layer,
causing the wind speed to increase more slowly
with height than at night (except in the lowest few
meters). In addition to thermal turbulence, rough-
ness elements on the ground engender mechanical
turbulence, which affects both the dispersion of
material in the atmosphere and the wind profile
(variation of wind with height). Examples of these
effects on the resulting wind profile are shown in
Figure 1-2.
As wind speed increases, the effluent from a
continuous source is introduced into a greater vol-
ume of air per unit time interval. In addition to
this dilution by wind speed, the spreading of the
material (normal to the mean direction of trans-
port) by turbulence is a major factor in the dis-
persion process.
The procedures presented here to estimate at-
mospheric dispersion are applicable when mean wind
speed and direction can be determined, but meas-
urements of turbulence, such as the standard de-
viation of wind direction fluctuations, are not avail-
able. If such measurements are at hand, techniques
such as those outlined by Pasquill (1961) are likely
to give more accurate results. The diffusion param-
-------
eters presented here are most applicable to ground-
level or low-level releases (from the surface to about
20 meters), although they are commonly applied at
higher elevations without full experimental valida-
tion. It is assumed that stability is the same
throughout the diffusing layer, and no turbulent
transfer occurs through layers of dissimilar stability
characteristics. Because mean values for wind direc-
tions and speeds are required, neither the variation
of wind speed nor the variation of wind direction
with height in the mixing layer are taken into ac-
count. This usually is not a problem in neutral or
unstable (e.g., daytime) situations, but can cause
over-estimations of downwind concentrations in
stable conditions.
REFERENCES
Davenport, A. G., 1963: The relationship of wind
structure to wind loading. Presented at Int.
Conf. on The Wind Effects on Buildings and
Structures, 26-28 June 63, Natl. Physical Lab-
oratory, Teddington, Middlesex, Eng.
Pasquill, F., 1961: The estimation of the dispersion
of wind borne material. Meteorol. Mag. 90,
1063, 33-49.
Smith, M. E., 1963: The use and misuse of the at-
mosphere, 15 pp., Brookhaven Lecture Series,
No. 24, 13 Feb 63, BNL 784 (T-298) Brook-
haven National Laboratory.
600
500
.400
'300
200
100
URBAN AREA
GRADIENT WIND
SUBURBS
LEVEL COUNTRY
GRADIENT WIND
Figure 1-2. Examples of variation of wind with height over different size roughness elements (figures are percentages
of gradient wind); (from Davenport, 1963).
ATMOSPHERIC DISPERSION ESTIMATES
-------
Chapter 2 BACKGROUND
For a number of years estimates of concentra-
tions were calculated either from the equations of
Sutton (1932) with the atmospheric dispersion
parameters Cy, Cz, and n, or from the equations of
Bosanquet (1936) with the dispersion parameters
p and q.
Hay and Pasquill (1957) have presented experi-
mental evidence that the vertical distribution of
spreading particles from an elevated point is re-
lated to the standard deviation of the wind eleva-
tion angle,
-------
Chapter 3 ESTIMATES OF ATMOSPHERIC DISPERSION
This chapter outlines the basic procedures to
be used in making dispersion estimates as sug-
gested by Pasquill (1961) and modified by Gifford
(1961).
COORDINATE SYSTEM
In the system considered here the origin is at
ground level at or beneath the point of emission,
with the x-axis extending horizontally in the direc-
tion of the mean wind. The y-axis is in the hori-
zontal plane perpendicular to the x-axis, and the
z-axis extends vertically. The plume travels along
or parallel to the x-axis. Figure 3-1 illustrates the
coordinate system.
DIFFUSION EQUATIONS
The concentration, x, of gas or aerosols (parti-
cles less than about 20 microns diameter) at x,y,z
from a continuous source with an effective emission
height, H, is given by equation 3.1. The notation
used to depict this concentration is x (x,y,z;H).
H is the height of the plume centerline when it
I
becomes essentially level, and is the sum of the
physical stack height, h, and the plume rise, AH.
The following assumptions are made: the plume
spread has a Gaussian distribution (see Appendix
2) in both the horizontal and vertical planes, with
standard deviations of plume concentration distri-
bution in the horizontal and vertical of af and
-------
Any consistent set of units may be used. The most
common is:
X (g m~a) or, for radioactivity (curies m~3)
Q (g sec~l) or (curies sec"1)
u (m sec"1)
a,, CTZ U
exp
6XP ~
f -
|^ Z
0.2)
Where the concentration is to be calculated
along the centerline of the plume (y = 0), (see
problem 2) further simplification results:
x(x,0,0;H) =
exp
f -- L(J
|^ Z \ 6
Strong
A
A-B
B
C
C
Moderate
A-B
B
B-C
C-D
D
Slight
B
C
C
D
D
Night
Thinly Overcast
-4/8 Low Cloud
E
D
D
D
G/ O
Cloud
F
E
D
D
The neutral class, D, should be assumed for overcast conditions during
day or night.
"Strong" incoming solar radiation corresponds
to a solar altitude greater than 60° with clear skies;
"slight" insolation corresponds to a solar altitude
from 15° to 35° with clear skies. Table 170, Solar
Altitude and Azimuth, in the Smithsonian Mete-
orological Tables (List, 1951) can be used in deter-
mining the solar altitude. Cloudiness will decrease
incoming solar radiation and should be considered
along with solar altitude in determining solar radia-
tion. Incoming radiation that would be strong
with clear skies can be expected to be reduced to
moderate with broken (% to % cloud cover) mid-
dle clouds and to slight with broken low clouds.
An objective system of classifying stability from
hourly meteorological observations based on the
above method has been suggested (Turner, 1961).
These methods will give representative indica-
tions of stability over open country or rural areas,
but are less reliable for urban areas. This differ-
ence is due primarily to the influence of the city's
larger surface roughness and heat island effects
upon the stability regime over urban areas. The
greatest difference occurs on calm clear nights; on
such nights conditions over rural areas are very
stable, but over urban areas they are slightly un-
stable or near neutral to a height several times the
average building height, with a stable layer above
(Duckworth and Sandberg, 1954; DeMarrais, 1961).
ATMOSPHERIC DISPERSION ESTIMATES
-------
Some preliminary results of a dispersion experi-
ment in St. Louis (Pooler, 1965) showed that the
dispersion over the city during the daytime behaved
somewhat like types B and C; for one night experi-
ment try varied with distance between types D and E.
ESTIMATION OF VERTICAL AND
HORIZONTAL DISPERSION
Having determined the stability class from
Table 3-1, one can evaluate the estimates of 2 XL; XL is where 2xL; XL is where az = 0.47 L
The value of (rzL = 0.8 L
EVALUATION OF WIND SPEED
For the wind speed, u, a mean through the ver-
tical extent of the plume should be used. This
would be from the height H 2 CTZ through H -f-
2
-------
1 10
DISTANCE DOWNWIND, km
100
Figure 3-2. Horizontal dispersion coefficient as a function of downwind distance from the source.
ATMOSPHERIC DISPERSION ESTIMATES
-------
1 10
DISTANCE DOWNWIND, km
100
Figure 3-3. Vertical dispersion coefficient as a function of downwind distance from the source.
Estimates
339-901 O - 69 - 2
-------
. 11/11.
1 234 5 6xlO"5
CONC.
SSOmeters
Figure 3-4. Variations in concentration in the vertical beneath a more stable layer.
three cases (where
-------
10
DISTANCE,km
Figure 3-5A. xu/Q with distance for various heights of emission (H) and limits to vertical dispersion (L), A stability.
Estimates
11
-------
100
DISTANCE, km
Figure 3-5B. xu/Q with distance for various heights of emission (H) and limits to vertical dispersion (L), B stability.
12
ATMOSPHERIC DISPERSION ESTIMATES
-------
O.I
DISTANCE, km
Figure 3-5C. xu/Q with distance for various heights of emission (H) and limits to vertical dispersion (L), C stability.
Estimates
13
-------
E
o
DISTANCE, km
Figure 3-5D. xu/Q with distance for various heights of emission (H) and limits to vertical dispersion (L), D stability.
14
ATMOSPHERIC DISPERSION ESTIMATES
-------
DISTANCE, km
Figure 3-5E. xu/Q with distance for various heights of emission (H) and limits to vertical dispersion (L), E stability.
Estimates
15
-------
0.1
100
DISTANCE, km
Figure 3-5F. xu/Q with distance for various heights of emission (H) and limits to vertical dispersion (L), F stability.
16
ATMOSPHERIC DISPERSION ESTIMATES
-------
From Table A-l (Appendix 3) when exp
- °-345' y/ffy = L46
From Figure 3-2, for stability B and x = 600 m, vy
= 92. Therefore y = (1.46) (92) = 134 meters.
This is the distance of the 10~3 isopleth from the
x-axis at a downwind distance of 600 meters.
This can also be determined from:
x(x,o,Q;H)
x(x,y,0;H)
(3.8)
The position corresponding to the downwind dis-
tance and off-axis distance can then be plotted.
After a number of points have been plotted, the
concentration isopleth may be drawn (see problems
8 and 26). Figures 3-6 and 3-7 give ground-level
isopleths of xu/Q for various stabilities for sources
at H = 0 and H = 100 meters. For example, to
locate the 10~3 g m~3 isopleth resulting from a
ground-level source of 20 g sec"1 under B stability
conditions with wind speed 2 m sec"1, one must
first determine the corresponding value of xu/Q since
this is the quantity graphed in Figure 3-6. xu/Q =
10-" x 2/20 = 10~4. Therefore the xu/Q isopleth
in Figure 3-6B having a value of 10~4 m'2 corre-
sponds to a x isopleth with a value of 10~3 g m"3.
AREAS WITHIN ISOPLETHS
Figure 3-8 gives areas within isopleths of ground-
level concentration in terms of x u/Q for a ground-
level source for various stability categories (Gifford,
1962; Hilsmeier and Gifford, 1962). For the exam-
ple just given, the area of the 10~3 g m~3 isopleth
(10~4 m~2 x u/Q isopleth) is about 5 x 104 meter2.
CALCULATION OF MAXIMUM
GROUND-LEVEL CONCENTRATIONS
Figure 3-9 gives the distance to the point of
maximum concentration, xmnx, and the relative maxi-
mum concentration, x u/Q,liax, as a function of
effective height of emission and stability class
(Martin, 1965). This figure was prepared from
graphs of concentration versus distance, as in Fig-
ure 3-5. The maximum concentration can be deter-
mined by finding x u/Q as a function of effective
emission height and stability and multiplying by
Q/u. In using Figure 3-9, the user must keep in
mind that the dispersion at higher levels may differ
considerably from that determined by the ery's and
-------
00
s
I
73
o
o
51
M
00
o
M
C/3
3 4
DOWNWIND DISTANCE (x), km
B
Figure 3-6A. Isopleths of xu/Q for a ground-level source, A stability.
-------
w
tfl
a
CLASS B STABILITY
H = 0
IO'3 IO'4
3 4
DOWNWIND DISTANCE (x), km
Figure 3-6B. Isopleths of xu/Q for a ground-level source, B stability.
-------
I
en
o
d
M
Ol
H
CLASS C STABILITY
H=0
DOWNWIND DISTANCE (x), km
H
K
Figure 3-6C. Isopleths of xu/Q for a ground-level source, C stability.
-------
M
(A
ft
CLASS D STABILITY
H= 0
3 4
DOWNWIND DISTANCE (x), km
Figure 3-6D. Isopleths of xu/Q for a ground-level source, D stability.
-------
CLASS E STABILITY
3 4
DOWNWIND DISTANCE (x), km
H
I
VI
*
s
M
73
"0
W
S8
C/3
w
CA
H
i
>
H
M
CLASS F STABILITY
H=0
3 4
DOWNWIND DISTANCE (x), km
Figure 3-6E, F. Isopleths of xu/Q for a ground-level source, E and F stabilities.
-------
w
t/i
«*
to
CLASS A STABILITY
H = IOO
3 4
DOWNWIND DISTANCE (x), kn
Figure 3-7A. Isopleths of xu/Q for a source 100 meters high, A stability.
-------
2
o
Cfl
o
o
53
B
so
en
B
W3
H
i
>
H
B
73
CLASS B STABILITY
H = IOO
1.7 x IO'5,
DOWNWIND DISTANCE (x), km
Figure 3-7B. Isopleths of xu/Q for a source 100 meters high, B stability.
-------
M
Gfi
o <"
o
o
CLASS C STABILITY
H = 100
3 4
DOWNWIND DISTANCE (x), km
VI
Figure 3-7C. Isopleths of xu/Q for a source 100 meters high, C stability.
-------
re
os
H
3
O
1/1
"B
=
H
2
O
SO
H
01
CLASS D STABILITY
H=IOO
3 4
DOWNWIND DISTANCE (x), km
H
M
Cfl
Figure 3-7D. Isopleths of xu/Q for a source 100 meters high, D stability.
-------
w
<
»
V»
O
CLASS E STABILITY
H = IOO
3 4
DOWNWIND DISTANCE (x), km
CLASS F STABILITY
H=IOO
3 4
DOWNWIND DISTANCE (x), km
hS
-J
Figure 3-7E, F. Isopleths of xii/Q for a source 100 meters high, E and F stabilities.
-------
10
10'
Figure 3-8. Area within isopleths for a ground-level source (from Hilsmeier and Gifford).
Hilsmeier, W. F., and F. A. Gifford, 1962: Graphs
for estimating atmospheric diffusion. ORO-545,
Oak Ridge, Tenn. Atomic Energy Commission,
10pp.
List, R. J., 1951: Smithsonian Meteorological
Tables, Sixth Revised Edition, 497-505, Wash-
ington, D. C., Smithsonian Institution, 527 pp.
Martin, D. O., 1965: Personal communication.
Pasquill, F., 1961: The estimation of the dispersion
of windborne material. Meteorol. Mag., 90,
1063, 33-49.
Pooler, F., 1965: Personal communication.
Sutton, O. G., 1953: Micrometeorology, New York,
McGraw-Hill. 333 pp.
Turner, D. B., 1961: Relationships between 24-
hour mean air quality measurements and mete-
orological factors in Nashville, Tennessee. J.
Air Poll. Cont. Assoc., 11, 483-489.
28
ATMOSPHERIC DISPERSION ESTIMATES
-------
M
vi
tt
(Xu/Q)
10"
Figure 3-9. Distance of maximum concentration and maximum xu/Q as a function of stability (curves) and effective height (meters) of emission
(numbers).
-------
Chapter 4 EFFECTIVE HEIGHT OF EMISSION
GENERAL CONSIDERATIONS
In most problems one must estimate the effec-
tive stack height, H, at which the plume becomes
essentially level. Rarely will this height correspond
to the physical height of the stack, h. If the plume
is caught in the turbulent wake of the stack or of
buildings in the vicinity of the stack, the effluent
will be mixed rapidly downward toward the ground
(aerodynamic downwash). If the plume is emitted
free of these turbulent zones, a number of emission
factors and meteorological factors influence the rise
of the plume. The emission factors are: velocity
of the effluent at the top of the stack, vs; tempera-
ture of the effluent at the top of the stack, Ts; and
diameter of the stack opening, d. The meteorolog-
ical factors influencing plume rise are wind speed,
u; temperature of the air, Ta; shear of the wind
speed with height, du/dz; and atmospheric sta-
bility. No theory on plume rise takes into account
all of these variables; even if such a theory were
available, measurements of all of the parameters
would seldom be available. Most of the equations
that have been formulated for computing the ef-
fective height of emission are semi-empirical. For a
recent review of equations for effective height of
emission see Moses, Strom, and Carson (1964).
Moses and Strom (1961), having compared ac-
tual and calculated plume heights by means of six
plume rise equations, report "There is no one for-
mula which is outstanding in all respects." The
formulas of Davidson-Bryant (1949), Holland
(1953), Bosanquet-Carey-Halton (1950), and Bo-
sanquet (1957) all give generally satisfactory re-
sults in the test situations. The experiments con-
ducted by Moses and Strom involved plume rise
from a stack of less than 0.5 meter diameter, stack
gas exit velocities less than 15 m sec""1, and effluent
temperature not more than 35°C higher than that
of the ambient air.
The equation of Holland was developed with
experimental data from larger sources than those
of Moses and Strom (stack diameters from 1.7 to
4.3 meters and stack temperatures from 82 to
204°C); Holland's equation is used in the solution
of the problems given in this workbook. This equa-
tion frequently underestimates the effective height
of emission; therefore its use often provides a slight
"safety" factor.
Holland's equation is:
T8 Ta
d) (4.1)
\J-.v | *J.\S^J A J.W p m
where:
AH = the rise of the plume above the stack, m
vs = stack gas exit velocity, m sec"1
d = the inside stack diameter, m
u = wind speed, m sec"1
p = atmospheric pressure, mb
Ts = stack gas temperature, °K
Ta = air temperature, °K
and 2.68 x 10~3 is a constant having units of mb"1
m"1.
Holland (1953) suggests that a value between
1.1 and 1.2 times the AH from the equation should
be used for unstable conditions; a value between
0.8 and 0.9 times the AH from the equation should
be used for stable conditions.
Since the plume rise from a stack occurs over
some distance downwind, Eq. (4.1) should not be
applied within the first few hundred meters of the
stack.
EFFECTIVE HEIGHT OF EMISSION AND
MAXIMUM CONCENTRATION
If the effective heights of emission were the
same under all atmospheric conditions, the highest
ground-level concentrations from a given source
would occur with the lightest winds. Generally,
however, emission conditions are such that the ef-
fective stack height is an inverse function of wind
speed as indicated in Eq. (4.1). The maximum
ground-level concentration occurs at some inter-
mediate wind speed, at which a balance is reached
between the dilution due to wind speed and the
effect of height of emission. This critical wind speed
will vary with stability. In order to determine the
critical wind speed, the effective stack height as a
function of wind speed should first be determined.
The maximum concentration for each wind speed
and stability can then be calculated from Figure
3-9 as a function of effective height of emission
and stability. When the maximum concentration
as a function of wind speed is plotted on log-log
graph paper, curves can be drawn for each stability
class; the critical wind speed corresponds to the
point of highest maximum concentration on the
curve (see problem 14).
ESTIMATES OF REQUIRED STACK HEIGHTS
Estimates of the stack height required to pro-
duce concentrations below a given value may be
made through the use of Figure 3-9 by obtaining
solutions for various wind speeds. Use of this figure
considers maximum concentrations at any distance
from the source.
In some situations high concentrations upon the
property of the emitter are of little concern, but
Effective Height
31
-------
maximum concentrations beyond the property line
are of the utmost importance. For first approxima-
tions it can be assumed that the maximum concen-
tration occurs where \/~Z~ <7Z = H and that at this
distance the a's are related to the maximum con-
centration by:
Q
Q
U Xn
(4.2)
Knowing the source strength, Q, and the concen-
tration not to be exceeded xnmx, one can determine
the necessary ay az for a given wind speed. Figure
4-1 shows o-j.
-------
10
100
Figure 4-1. The product of w*. as a function of downwind distance from the source.
Effective Height
33
-------
the height. Values other than 4.3 and 2.15 can be
used. When these values are used 97'/ of the dis-
tribution is included within these limits. Virtual
distances x, and xz can be found such that at xv,
a,. try,, and at xz, ax, - uv,. These x's will differ
with stability. Equations applicable to point sources
can then be used, determining <--,. as a function of
x -f- xy and
-------
Chapter 5 SPECIAL TOPICS
CONCENTRATIONS IN AN INVERSION
BREAK-UP FUMIGATION
A surface-based inversion may be eliminated by
the upward transfer of sensible heat from the
ground surface when that surface is warmer than
the overlying air. This situation occurs when the
ground is being warmed by solar radiation or when
air flows from a cold to a relatively warm surface.
In either situation pollutants previously emitted
above the surface into the stable layer will be mixed
vertically when they are reached by the thermal
eddies, and ground-level concentrations can increase.
This process, called "fumigation" was described by
Hewson and Gill (1944) and Hewson (1945). Equa-
tions for estimating concentrations with these con-
ditions have been given by Holland (1953), Hew-
son (1955), Gifford (1960a), Bierly and Hewson
(1962), and Pooler (1965).
To estimate ground-level concentrations under
inversion break-up fumigations, one assumes that
the plume was initially emitted into a stable layer.
Therefore, + H ton 15"
2 15 °y
'(FUMIGATION)
Figure 5-1. Diagram showing assumed height, hi and «?
during fumigation, for use in equation (5.2).
Eq. (5.4) should not be applied near the stack,
for if the inversion has been eliminated to a height
sufficient to include the entire plume, the emission
is taking place under unstable not stable conditions.
Therefore, the nearest downwind distance to be
considered for an estimate of fumigation concen-
trations must be great enough, based on the time
reqrired to eliminate the inversion, that this por-
tion of the plume was initially emitted into stable
air. This distance is x = utm, where u is the mean
Special Topics
35
-------
wind in the stable layer and tm is the time required
to eliminate the inversion from h, the physical
height of the stack to hi (Eq. 5.3).
tn, is dependent upon both the strength of the
inversion and the rate of heating at the surface.
Pooler (1965) has derived an expression for esti-
mating this time:
Pa Cp 89
R
Sz
h + h.
(5.5)
where tm = time required for the mixing layer to
develop from the top of the stack to the
top of the plume, sec
pa = ambient air density, g m"3
cp = specific heat of air at constant pressure,
cal g-1 OR"1
R = net rate of sensible heating of an air
column by solar radiation, cal m"2 sec"1
80
= vertical potential temperature gradient,
°K m"1 ~
rate)
8T
Sz
+ r (the adiabatic lapse
hi = height of base of the inversion sufficient
to be above the plume, m
h = physical height of the stack, m
Note that hi h is the thickness of the layer to be
heated and f ^L J js tne average height of the
layer. Although R depends on season, and cloud
cover and varies continuously with time, Pooler has
used a value of 67 cal m~2 sec"1 as an average for
fumigation.
Hewson (1945) also suggested a method of esti-
mating the time required to eliminate an inversion
to a height z by use of an equation of Taylor's
(1915, p. 8):
z2
t =
where:
4 K
(5.6)
t = time required to eliminate the inver-
sion to height z, sec
z = height to which the inversion has been
eliminated, m
K = eddy diffusivity for heat, m2 sec"1
Rewriting to compare with Eq. (5.5),
h,2 h2
4 K
(5.7)
Hewson (1945) has suggested a value of 3 m2 sec *
for K.
PLUME TRAPPING
Plume trapping occurs when the plume is
trapped between the ground surface and a stable
layer aloft. Bierly and Hewson (1962) have sug-
gested the use of an equation that accounts for the
multiple eddy reflections from both the ground and
the stable layer:
X (x,0,z;H)
exp
+ exp
+ exp
exp
+ exp
1 (
2 V
1 /
2 V
1 (
2 (
z + H 2 NL
Z-H + 2NL
O-z
z + H + 2 NL
-------
these is at the distance of maximum concentration
at the ground. As a rough approximation the maxi-
mum ground-level concentration occurs at the dis-
1
tance where
-------
Table 5-1 VARIATION OF CALCULATED CONCENTRATION
WITH SAMPLING TIME
Ratio of
Calculated Concentration
2 Q
Sampling Time
3 minutes
15 minutes
1 hour
3 hours
24 hours ....
to 3-minute Concentration
1.00
0.82
0.61
0.51
0.36
This table indicates a power relation with time:
x »c t~°-17. Note that these estimates were based
upon published dispersion coefficients rather than
upon sampling results. Information in the refer-
ences cited indicates that effects of sampling time
are exceedingly complex. If it is necessary to esti-
mate concentrations from a single source for the
time intervals greater than a few minutes, the best
estimate apparently can be obtained from:
= Xk(ir)
(5.12)
where x* is the desired concentration estimate for
the sampling time, ts; Xk is the concentration esti-
mate for the shorter sampling time, tk, (probably
about 10 minutes); and p should be between 0.17
and 0.2. Eq. (5.12) probably would be applied
most appropriately to sampling times less than 2
hours (see problem 19).
ESTIMATION OF SEASONAL OR ANNUAL
AVERAGE CONCENTRATIONS AT A
RECEPTOR FROM A SINGLE POLLUTANT
SOURCE
For a source that emits at a constant rate from
hour to hour and day to day, estimates of seasonal
or annual average concentrations can be made for
any distance in any direction if stability wind "rose"
data are available for the period under study. A
wind rose gives the frequency of occurrence for
each wind direction (usually to 16 points) and wind
speed class (9 classes in standard Weather Bureau
use) for the period under consideration (from 1
month to 10 years). A stability wind rose gives the
same type of information for each stability class.
If the wind directions are taken to 16 points and
it is assumed that the wind directions within each
sector are distributed randomly over a period of a
month or a season, it can further be assumed that
the effluent is uniformly distributed in the hori-
zontal within the sector (Holland, 1953, p. 540).
The appropriate equation for average concentration
is then either:
nr
V2.ra.ll
exp I
2.03Q
a, UX
exp
H
(5.13)
or
X =
Q
2.55 Q
Lux
(5.14)
depending upon whether a stable layer aloft is af-
fecting the distribution.
The estimation of x for a particular direction
and downwind distance can be accomplished by
choosing a representative wind speed for each speed
class and solving the appropriate equation (5.13 or
5.14) for all wind speed classes and stabilities. Note
that a SSW wind affects a receptor to the NNE
of a source. One obtains the average concentration
for a given direction and distance by summing all
the concentrations and weighting each one accord-
ing to its frequency for the particular stability and
wind speed class. If desired, a different effective
height of emission can be used for various wind
speeds. The average concentration can be expressed
by:
, , _ 2Qf(9,S,N)
x (x,e) =
(5.15)
exp I
where f (9, S, N) is the frequency during the period
of interest that the wind is from the direc-
tion 0, for the stability condition, S, and
wind speed class N.
-------
2. For elevated sources maximum "instantaneous"
concentrations occur with unstable conditions
when portions of the plume that have undergone
little dispersion are brought to the ground.
These occur close to the point of emission (on
the order of 1 to 3 stack heights). These con-
centrations are usually of little general interest
because of their very short duration; they can-
not be estimated from the material presented in
this workbook.
3. For elevated sources maximum concentrations
for time periods of a few minutes occur with
unstable conditions; although the concentra-
tions fluctuate considerably under these condi-
tions, the concentrations averaged over a few
minutes are still high compared to those found
under other conditions. The distance of this
maximum concentration occurs near the stack
(from 1 to 5 stack heights downwind) and the
concentration drops off rapidly downwind with
increasing distance.
4. For elevated sources maximum concentrations
for time periods of about half an hour can occur
with fumigation conditions when an unstable
layer increases vertically to mix downward a
plume previously discharged within a stable
layer. With small AH, the fumigation can occur
close to the source but will be of relatively short
duration. For large AH, the fumigation will
occur some distance from the stack (perhaps 30
to 40 km), but can persist for a longer time
interval. Concentrations considerably lower than
those associated with fumigations, but of sig-
nificance can occur with neutral or unstable
conditions when the dispersion upward is se-
verely limited by the existence of a more stable
layer above the plume, for example, an inversion.
5. Under stable conditions the maximum concen-
trations at ground-level from elevated sources
are less than those occurring under unstable
conditions and occur at greater distances from
the source. However, the difference between
maximum ground-level concentrations for stable
and unstable conditions is only a factor of 2
for effective heights of 25 meters and a factor
of 5 for H of 75 m. Because the maximum
occurs at greater distances, concentrations that
are below the maximum but still significant can
occur over large areas. This becomes increas-
ingly significant if emissions are coming from
more than one source.
CONCENTRATIONS AT A RECEPTOR POINT
FROM SEVERAL SOURCES
Sometimes, especially for multiple sources, it is
convenient to consider the receptor as being at the
origin of the diffusion coordinate system. The
source-receptor geometry can then be worked out
merely by drawing or visualizing an x-axis oriented
upwind from the receptor and determining the
crosswind distances of each source in relation to this
x-axis. As pointed out by Gifford (1959), the con-
centration at (0, 0, 0) from a source at (x, y, H)
on a coordinate system with the x-axis oriented up-
wind is the same as the concentration at (x, y, 0)
from a source at (0, 0, H) on a coordniate system
with the x-axis downwind (Figure 5-2). The total
concentration is then given by summing the indi-
vidual contributions from each source (see problem
20).
SOURCE
(x,y,H)
UPWIND
RECEPTOR
(0,0,0)
DOWNWIND
(x,y,0)
Figure 5-2. Comparison of source-oriented and receptor-
oriented coordinate systems.
It is often difficult to determine the atmos-
pheric conditions of wind direction, wind speed, and
stability that will result in the maximum combined
concentrations from two or more sources; drawing
isopleths of concentration for various wind speeds
and stabilities and orienting these according to
wind direction is one approach.
AREA SOURCES
In dealing with diffusion of air pollutants in
areas having large numbers of sources, e.g., as in
urban areas, there may be too many sources of most
atmospheric contaminants to consider each source
Special Topics
39
-------
individually. Often an approximation can be made
by combining all of the emissions in a given area
and treating this area as a source having an initial
horizontal standard deviation, becomes great enough, the concentrations
can be assumed to be uniform across the width of
the valley and the concentration calculated accord-
ing to the following equation, where in this case Y
is the width of the valley.
X
2Q
Yu
exp l
(5.17)
LINE SOURCES
Concentrations downwind of a continuously
emitting infinite line source, when the wind direc-
tion is normal to the line, can be expressed by
rewriting equation (12) p. 154 of Sutton (1932):
X (x,y,0;H)
2 q
exp
'2w trz U
(5.18)
Here q is the source strength per unit distance,
for example, g sec"1 m -1. Note that the horizontal
dispersion parameter,
-------
When estimating concentrations from finite line
sources, one must account for "edge effects" caused
by the end of the line source. These effects will of
course extend to greater cross-wind distances as
the distance from the source increases. For concen-
trations from a finite line source oriented cross-
wind, define the x-axis in the direction of the mean
wind and passing through the receptor of interest.
The limits of the line source can be defined as ex-
tending from y, to y., where y, is less than y2. The
equation for concentration (from Button's (1932)
equation (11), p. 154), is:
(x,0,0;H) -
exp _
*
f
2
(5.20)
The value of the integral can be determined from
tabulations given in most statistical tables (for ex-
ample, see Burrington (1953), pp. 273-276; also see
problem 24).
INSTANTANEOUS SOURCES
Thus far we have considered only sources that
were emitting continuously or for time periods equal
to or greater than the travel times from the source
to the point of interest. Cases of instantaneous re-
lease, as from an explosion, or short-term releases
on the order of seconds, are often of practical con-
cern. To determine concentrations at any position
downwind, one must consider the time interval
after the time of release and diffusion in the down-
wind direction as well as lateral and vertical diffu-
sion. Of considerable importance, but very difficult,
is the determination of the path or trajectory of
the "puff." This is most important if concentra-
tions are to be determined at specific points. Deter-
mining the trajectory is of less importance if knowl-
edge of the magnitude of the concentrations for
particular downwind distances or travel times is
required without the need to know exactly at what
points these concentrations occur. Rewriting Sut-
ton's (1932) equation (13), p. 155, results in an
equation that may be used for estimates of concen-
tration downwind from a release from height, H:
(x,y,0;H)
exp
(5.21)
The symbols have the usual meaning, with the
important exceptions that QT represents the total
mass of the release and the a's are not those eval-
uated with respect to the dispersion of a continuous
source at a fixed point in space.
In Eq. (5.21) the -
10
4
1.3
"z
15
3.8
0.75
-------
Gifford, F. A., 1959: Computation of pollution
from several sources. Int. J. Air Poll., 2, 109-
110.
Gifford, F. A., 1960a: Atmospheric dispersion cal-
culations using the generalized Gaussian plume
model. Nuclear Safety, 2, 2, 56-59, 67-68.
Gifford, F. A., 1960b: Peak to average concentra-
tion ratios according to a fluctuating plume dis-
persion model. Int. J. Air Poll., 3, 4, 253-260.
Hewson, E. W., and G. C. GUI, 1944: Meteorolog-
ical investigations in Columbia River Valley
near Trail, B. C., pp 23-228 in Report submitted
to the Trail Smelter Arbitral Tribunal by R. S.
Dean and R. E. Swain, Bur. of Mines Bull 453,
Washington, Govt. Print. Off., 304 pp.
Hewson, E. W., 1945: The meteorological control
of atmospheric pollution by heavy industry.
Quart. J. R. Meteorol. Soc., 71, 266-282.
Hewson, E. W., 1955: Stack heights required to
minimize ground concentrations. Trans. ASME
77, 1163-1172.
Holland, J. Z., 1953: A meteorological survey of
the Oak Ridge area, p. 540. Atomic Energy
Comm., Report ORO-99, Washington, D. C.,
584 pp.
Nonhebel, G., 1960: Recommendations on heights
for new industrial chimneys. J. Inst. Fuel, 33,
479-513.
Pooler, F., 1965: Potential dispersion of plumes
from large power plants. PHS Publ. No. 999-
AP-16, 1965. 13 pp.
Singer, I. A., 1961: The relation between peak and
mean concentrations. J. Air Poll. Cont. Assoc.,
11, 336-341.
Singer, I. A., K. Imai, and R. G. Del Campos, 1963:
Peak to mean pollutant concentration ratios for
various terrain and vegetation cover. J. Air Poll.
Cont. Assoc., 13, 40-42.
Slade, D. H., 1965: Dispersion estimates from pol-
lutant releases of a few seconds to 8 hours in
duration. Unpublished Weather Bureau Report.
Aug. 1965.
Stewart, N. G., H. J. Gale, and R. N. Crooks, 1958:
The atmospheric diffusion of gases discharged
from the chimney of the Harwell Reactor BEPO.
Int. J. Air Poll., 1, 87-102.
Sutton, O. G., 1932: A theory of eddy diffusion in
the atmosphere. Proc. Roy. Soc. London, A,
135, 143-165.
Taylor, G. I., 1915: Eddy motion in the atmos-
phere. Phil. Trans. Roy. Soc., A, 215, 1-26.
42
ATMOSPHERIC DISPERSION ESTIMATES
-------
Chapter 6 RELATION TO OTHER DIFFUSION EQUATIONS
Most other widely used diffusion equations are
variant forms of the ones presented here. With re-
spect to ground-level concentrations from an ele-
vated source (Eq. 3.2):
x (x,y,0;H) =
Q
7T <7y
U
exp
-[--H-f-Vl
(3.2)
Other well-known equations can be compared:
Bosanquet and Pearson (1936):
Q
X (x,y,0;H) - =
pq x2 u
exp I
(6.1)
where p and q are dimensionless diffusion coeffi-
cients.
Sutton (1947):
X (x,y,0;H) =
2 Q
7T Cy Cz X2-" U
exp
H2 \]
C,2 J]
M
(6.2)
where n is a dimensionless constant and Cy and Cz
are diffusion coefficients in m"/2.
Calder (1952):
X (x,y,0;H) =
Q u
2 k2 a vx2 x2
exp I
u
k vx x
(6.3)
where a = 7, the ratio of horizontal eddy velocity
to vertical eddy velocity, k is von Karman's con-
k u
stant approximately equal to 0.4, and vx = TT~
i { \
where z0 is a roughness parameter, m. '~z7'
NOTE: Calder wrote the equation for the con-
centration at (x, y, z) from a ground-level source.
For Eq. (6.3) it is assumed that the concentration
at ground level from an elevated source is the same
as the concentraton at an elevated point from a
ground-level source.
Table 6-1 lists the expressions used in these
equations that are equivalent to ay and
-------
Chapter 7 EXAMPLE PROBLEMS
The following 26 example problems and their
solutions illustrate the application of most of the
techniques and equations presented in this work-
book.
PROBLEM 1: It is estimated that a burning
dump emits 3 g sec"1 of oxides of nitrogen.
What is the concentration of oxides of nitrogen,
averaged over approximately 10 minutes, from
this source directly downwind at a distance of
3 km on an overcast night with wind speed of
7 m sec"1? Assume this dump to be a point
ground-level source with no effective rise.
SOLUTION: Overcast conditions with a wind
speed of 7 m sec"1 indicate that stability class D
is most applicable (Statement, bottom of Table
3-1). For x = 3 km and stability D,
-------
level concentration occur and what is this con-
centration on an overcast day with wind speed
4 m sec"1?
SOLUTION: On an overcast day the stability
class would be D. From Figure 3-9 for D sta-
bility and H of 150 m, the distance to the point
of maximum ground-level concentration is 5.6
km, and the maximum xu/Q is 3.0 x 10~6.
3.0 x 1Q-" x 151
Xmai 4
= 1.1 x 10-" g m~3
PROBLEM 6: For the conditions given in prob-
lem 4, draw a graph of ground-level centerline
sulfur dioxide concentration with distance from
100 meters to 100 km. Use log-log graph paper.
SOLUTION: The frontal inversion limits the mix-
ing to L = 1500 meters. The distance at which
az = 0.47 L = 705 m is XL = 5.5 km. At dis-
tances less than this, Eq. (3.3) is used to calcu-
late concentrations:
x (x,0,0;H) =
Q
7T
-------
E 3*
10"
-400
-200 0 +200
CROSSWIND DISTANCE (y), m
+ 400
Figure 7-2. Concentration as a function of crosswind
distance (Problem 7).
The values necessary to determine the isopleth
half widths, y, are given in Table 7-3.
Table 7-3 DETERMINATION OF ISOPLETH WIDTHS
(PROBLEM 8)
x,
km
0.5
0.8
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
(Ty,
m
83
129
157
295
425
540
670
780
890
980
X (centerline),
g m~3
3.8 x 10-5
2.3 x 10-4
2.8 x 10-*
1.4 x 10-*
7.1 x 10~5
4.0 xlO-5
2.4 X 10-5
1.8 x 10-=
1.4 x 10-5
1.1 x 10-5
X (isopleth)
X (centerline)
0.263
4.35 x 10-2
3.53 x 10-2
7.14 xlO-2
1.42X10-1
0.250
0.417
0.556
0.714
0.909
y/,y
1.64
2.50
2.59
2.30
1.98
1.67
1.32
1.08
0.82
0.44
y,
m
136
323
407
679
842
902
884
842
730
432
The orientation of the x-axis will be toward
225° close to the source, curving more toward
210° to 215° azimuth at greater distances be-
cause of the change of wind direction with
height. The isopleth is shown in Figure 7-3.
Since the isopleth approximates an ellipse, the
area may be estimated by -n ab where a is the
semimajor axis and b is the semiminor axis.
a =
8600 350
== 4125m
b = 902
A (m2) = TT (4125) (902)
= 11.7 x 106 m2
or A = 11.7 km2
SOURCE
10'
gm"
Figure 7-3. Location of the 1(T5 g m
pleth (Problem 8).
ground-level iso-
PROBLEM 9: For the conditions given in problem
4, determine the profile of concentration with
height from ground level to z = 450 meters at
x = 1 km, y = 0 meters, and draw a graph of
concentration against height above ground.
SOLUTION: Eq. (3.1) is used to solve this prob-
lem. The exponential involving y is equal to 1.
At x = 1 km, o-y = 157 m,
-------
Table 74 DETERMINATION OF CONCENTRATIONS FOR
VARIOUS HEIGHTS (PROBLEM 9)
b.
d.
e.
f.
g.
I Jlexp [--f (^)1±t>t
a» I \ "" / I °»
'z+H
c. + e.
01.36
301.09
600.82
900.55
1200.27
150
180
210
240
270
300
330
360
390
420
450
0.0
0.27
0.55
0.82
1.09
1.36
1.64
1.91
2.18
2.45
2.73
0.397
0.552
0.714
0.860
0.964
1.0
0.964
0.860
0.714
0.552
0.397
0.261
0.161
0.0929
0.0497
0.0241
1.36
1.64
1.91
2.18
2.45
2.73
3.00
3.27
3.54
3.82
4.09
4.36
4.64
4.91
5.18
5.45
0.397
0.261
0.161
0.0929
0.0497
0.0241
1.11 x
4.77 x
1.90 x
6.78 x
2.33 x
7.45 x
2.11 x
5.82 x
1.49 x
3.55 x
io-2
ID"3
io-3
io-4
io-4
10~5
io-5
io-6
io-6
io-7
0.794
0.813
0.875
0.953
1.014
1.024
0.975
0.865
0.716
0.553
0.397
0.261
0.161
0.093
0.050
0.024
2.78 x
2.85 x
3.06 x
3.34 x
3.55 x
3.58 x
3.41 x
3.03 x
2.51 x
1.94 x
1.39 x
9.14x
5.64 x
3.26 x
1.75 x
8.40 x
IO-4
in-4
io-4
IO-4
io-4
IO-4
io-4
io-4
10~4
in-4
io-5
IO-5
io-5
in-5
in-6
These values are plotted in Figure 74.
500
400 -
300 -
200 -
100 -
010
10'* 2xlO'4" 3x|0'4
CONCENTRATION, g m-3
4x10'
Figure 7-4. Concentration as a function of height (Prob-
lem 9).
Verifying:
x (x,0,0) =
Q
TT Oy = 520 m., and
-------
-------
maximum xu/Q as a function of H and stability
from Figure 3-9 and multiplying by the appro-
priate Q/u. The computations are summarized
in Table 7-6, and plotted in Figure 7-5.
5 iir*
10-*
I I
0.5
J LJ L
2 3457
WIND SPEED, m sec'1
10
20
Figure 7-5.
Tabla 7-6
Maximum concentration as a function of
wind speed (Problem 14).
MAXIMUM CONCENTRATION AS A FUNCTION OF
WIND SPEED (PROBLEM 14)
Stability u,
Class m sec"1
B 0.5
1.0
1.5
2
3
5
7
D 0.5
1.0
1.5
2
3
5
7
10
20
H,
m
142.2
86.1
67.5
58.1
48.7
41.3
38.0
127.6
78.8
62.6
54.4
46.3
39.8
37.0
34.9
32.4
X^a,
8.0 x 10-6
2.0 x 10-=
3.1 x 10~°
4.1 x 10-5
5.7 x 10-5
7.8 x 10-=
8.7 x 10-=
4.4 x 10-°
1.42x10-°
2.47x10-°
3.5 x 10-r'
5.1 x 10-°
7.3 x 10-°
8.2 x 10-5
9.4 x 10-=
1.1 x 10-4
Q/u,
g m-i
144
72
48
36
24
14.4
10.3
144
72
48
36
24
14.4
10.3
7.2
3.6
Xmax'
g m~3
1.15 xlO-3
1.44 x 10-3
1.49xlO-3<-
1.48 x 10-3
1.37 x 10-3
1.12 xlO-3
8.96 x 10-4
6.34 x lO"4
1.02 x 10-3
1.19 x 10-3
1.26 x 10-3<-
1.22 x 10-3
1.05 x 10-3
8.45 x 10-4
6.77 x 10-4
3.96 x 10-4
The wind speeds that give the highest maximum
concentrations for each stability are, from Fig-
ure 7-5: B 1.5, D 2.0.
PROBLEM 15: A proposed pulp processing plant
is expected to emit % ton per day of hydrogen
sulfide from a single stack. The company prop-
erty extends a minimum of 1500 meters from
the proposed location. The nearest receptor
is a small town of 500 inhabitants 1700 meters
northeast of the plant. Plant managers have
decided that it is desirable to maintain
concentrations below 20 ppb (parts per billion
by volume), or approximately 2.9 x 10~5 g m"3,
for any period greater than 30 minutes. Wind
direction frequencies indicate that winds blow
from the proposed location toward this town
between 10 and 15 per cent of the time. What
height stack should be erected? It is assumed
that a design wind speed of 2 m sec"1 will be
sufficient, since the effective stack rise will be
quite great with winds less than 2 m sec"1.
Other than this stipulation, assume that the
physical stack height and effective stack height
are the same, to incorporate a slight safety
factor.
SOLUTION: The source strength is:
Q =
1000 Ib day-1 x 453.6 g Ib
= 5.25 g sec
86,400 sec day
FromEq. (4.2):
0.117 Q _ 0.117 (5.25)
^ CTz ~ xa u ~ (2.9 x 10-5) 2
== 1.06 x 104 m2
At a design distance of 1500 meters (the limit
of company property), o>
-------
AH
33.4
u
33.4
u
102
u
[1.5+ (2.46) 0.256 (2.44)]
(1.5 + 1.54)
60 sec min
The relation between cry az and u is:
0.117 Q 0.117 (5.25) 2.12 x 104
2.9xlO"5u
u
The required computations using Figure 4-1 are
summarized in Table 7-7:
Table 7-7 REQUIRED PHYSICAL STACK HEIGHT AS A
FUNCTION OF WIND SPEED (PROBLEM 16)
u, AH,
m see"1 m
0.5
1.0
1.5
2.0
2.5
3.0
5.0
7.0
10.0
15.0
204
102
68
51
41
34
20
15
10
7
CTy CTZ,
m2
4.24 x
2.12 x
1.41 x
1.06 x
8.48 x
7.06 x
4.24 x
3.03 x
2.12 x
1.41 x
104
10*
10*
10*
103
103
103
103
103
103
Stability to
Give
-------
PROBLEM 19: At a point directly downwind
from a ground-level source the 3- to 15-minute
concentration is estimated to be 3.4 x 10"3 g
m"3. What would you estimate the 2-hour con-
centration to be at this point, assuming no
change in stability or wind velocity?
SOLUTION: Using Eq. (5.12) and letting k = 3
min, s = 2 hours, and p = 0.2:
3.4x10
40°
3.4 x IP"3
2.09
(3.4 x 10-3)
= 1.6 x 10"3 g
Letting k 15 min, s = 2 hours, and p = 0.17
X 2 ..our =
3-4 x 10~3
- -£rn- (3-4
3.4 x IP"3
~ 1.42
= 2.4 x 10"3 g nr"
The 2-hour concentration is estimated to be
between 1.6 x 10"3 and 2.4 x 10"3 g m"3.
PROBLEM 20: Two sources of SO2 are shown as
points A and B in Figure 7-6. On a sunny
summer afternoon the surface wind is from 60°
at 6 m sec"1. Source A is a power plant emitting
1450 g sec"1 SO2 from two stacks whose physical
height is 120 meters and whose AH, from Hol-
land's equation, is AH (m) = 538 (m2 sec^/u
(m sec"1). Source B is a refinery emitting 126 g
sec"1 SO2 from an effective height of 60 meters.
The wind measured at 160 meters on a nearby
TV tower is from 70° at 8.5 m sec"1. Assuming
that the mean direction of travel of both plumes
is 245°, and there are no other sources of SO2,
what is the concentration of SO2 at the receptor
shown in the figure?
SOLUTION: Calculate the effective height of
Source A using the observed wind speed at 160
meters.
AH
538
= 63.3
8.5
HA = 120 + 63 = 183 m
QA = 1450 g sec"1
HB = 60 m
QB = 126 g sec"1
For a sunny summer afternoon with wind speed
6 m sec"1, the stability class to be expected is C.
The equation to be used is Eq. (3.2):
SOURCE A
i=24.6 In.
y= 8.4 km
RECEPTOR x.
Figure 7-6. Locations of sources and receptor (Problem
20).
(x,y,0;H) =
Q
7T
-------
PROBLEM 21: A stack 15 meters high emits 3 g
sec"1 of a particular air pollutant. The sur-
rounding terrain is relatively flat except for a
rounded hill about 3 km to the northeast whose
crest extends 15 meters above the stack top.
What is the highest 3- to 15-minute concentra-
tion of this pollutant that can be expected on
the facing slope of the hill on a clear night when
the wind is blowing directly from the stack
toward the hill at 4 m sec"1? Assume that AH
is less than 15 m. How much does the wind
have to shift so that concentrations at this point
drop below 10"7 g m"3?
SOLUTION: A clear night with 4 m sec"1 indi-
cates class E stability. Eq. (3.4) for ground-
level concentrations from a ground-level source
is most applicable (See Chapter 5). At 3 km
for class E, ay = 140 m,
-------
that it is 1600 on a sunny fall afternoon. What
is the concentration directly downwind from one
end of the source?
SOLUTION: Late afternoon at this time of year
implies slight insolation, which with 3 m sec"1
winds yields stability class C. For C stability
at x = 400 m, a? = 45 m, az = 26 m.
Q
90
M 150 150
Eq. (5.20) is appropriate.
= 0.6 g sec"1 m 1
(x,0,0;0)
fp,
2q I 1_
\/2ir trz U I \/2~Jr
J Pi
exp (0.5 p2) dp
75
45
i «7 n - -
~"L67' P2 - ~ -
-
45
= +1.67
x (400,0,0;0) =
2 (0.6)
r+,67
I V2^
J 1.67
exp (0.5 p2) dp
= 6.14 x 10~3 (0.91)
= 5.6 x 10~3 g m"3
For a point downwind of one of the ends of the
line:
+3.33
'+3.33
J
_ y 150
Pi u, P« - 45
X (400,0,0;0) = 6.14 x 10~;
exp (0.5 p2) dp
= 6.14 x 10-3 (0.4995)
= 3.1 x 10-3 g m-3
PROBLEM 25: A core melt-down of a power re-
actor that has been operating for over a year
occurs at 0200, releasing 1.5 x 10e curies of
activity (1 second after the accident) into the
atmosphere of the containment vessel. This
total activity can be expected to decay according
to
; is estimated that about 5.3 x 104
curies of this activity is due to iodine-131, which
has a half-life of 8.04 days. The reactor building
is hemispherically shaped with a radius of 20
meters. Assume the leak rate of the building is
0.1% day"1.
The accident has occurred on a relatively clear
night with wind speed 2.5 m sec"1. What is the
concentration in the air 3 kilometers directly
downwind from the source at 0400 due to all
radioactive material? due to iodine-131?
SOLUTION: Source strength = leak rate x ac-
tivity (corrected for decay)
Leak rate =
0.001 day"1
86400 sec day"1
= 1.157 x 10~8 sec"1
Source strength of all products
QA (curies sec"1) = 1.157 x lO"8 (1.5 x 10s)
[t(aec) ]
t0 (sec) J
0.2
t0 (sec)
= 1.74 x 10-2
(-B
0.2
To determine decay of materials with the half-
rt 14.- i u ( 0.693 t\ ,
life given, multiply by exp I - = - J where t
is time and L is half-life. \ /
Source strength of I131.
Qi (curies sec"1) = 1.157 x 10~8 (5.3 x 104) exp
0.693 t
For I131 L = 6.95 x 105 sec
For a clear night with wind speed 2.5 m sec""1,
class F applies. Approximate the spreading at
the reactor shell by 2.15 o-y0 = 2.15 o-z0 = the
radius of the shell = 20 m
-------
= 2.7 x 10~8 (1.0) The decay of I131 is insig-
nificant for 2 hours
Xi = 2.7 x 10~8 curies m~3
PROBLEM 26: A spill estimated at 2.9 x 10"
grams of unsymmetrical dimethyl hydrazine
occurs at 0300 on a clear night while a rocket
is being fueled. A circular area 60 meters in
diameter built around the launch pad is revetted
into squares 20 feet on a side to confine to as
small an area as possible any spilled toxic liquids.
In this spill only one such 20- by 20-foot area is
involved. At the current wind speed of 2 m
sec"1, it is estimated that the evaporation rate
will be 1100 g sec"1. The wind direction is pre-
dicted to be from 310° ± 15° for the next hour.
Table 7-8 gives the emergency tolerance limits
for UDMH vapor.
Table 7-8 EMERGENCY TOLERANCE LIMITS FOR UDMH
VAPOR VERSUS EXPOSURE TIME
Table 7-9 DETERMINATION OF CONCENTRATION AS A
FUNCTION OF DISTANCE (PROBLEM 26)
Time,
minutes
5
15
30
60
Emergency Tolerance
Limits, g m~3
1.2 x 10-1
8.6 x 10"2
4.9 x 10~2
2.5 x 10-2
What area should be evacuated?
SOLUTION: From Table 3-1, the stability class
is determined to be Class F. This is not a point
source but a small area source. Allowing 4.3 (ry0
to equal the width of the wetted area, 6.1 meters
(20 feet), CTyo = 1.4 meters. In attempting to
determine the virtual distance, x}, it is found to
be less than 100 meters, and will be approxi-
mated by 40 meters. The release will take:
2.9xlO°g 0-. 1A, ...
=^-^ = 2.64 x 103 sec = 44 mm.
1.1 x 103 g sec"1
Therefore the concentration for an exposure
time of 1 hour (2.5 x 10~2 g m~3) is of main
concern.
The equation for calculation of downwind con-
centrations is Eq. (3.4):
x(x,0,0;0) =
Of X + Xy.
Q
7T 0V is a function
X,
km
0.1
0.3
0.6
1
3
6
10
aw
m
2.3
5.6
9.7
14
27
37
47
x + xy,
km
0.14
0.34
0.64
1.04
3.04
6.04
10.04
oy
m
5.5
12.5
22
35
93
175
275
X-
g m~3
13.9
2.5
8.2 x 10-1
3.6 x 10~l
7.0 xlO-2
2.7 x 10~2
1.4 x 10-3
These values of x are graphed as a function of x
in Figure 7-7. The downwind concentration
drops below the critical value of 2.5 x 10~2 at a
distance of 6.5 km.
100
ft
1
<* 10
o
a.
o
z 1
1
<
oe
t
z
UJ
<«t
Z
Q _|
io-2
0
.... _
\
1 ^~
^!
\^
X
^
^
s
s
^
^
*
*
w
\
s
s
^S
v
\
V
n
N^
1 1 II
Values of the parameters and of x are given in
Table 7-9.
DISTANCE, km
Figure 7-7. Concentration of UDMH as a function of down-
wind distance (Problem 26).
Calculated widths within a given isopleth are
summarized in Table 7-10.
The maximum width of the area encompassed
by an isopleth is about 140 meters from the
downwind position. Since the wind direction is
expected to be from 310° ± 15°, the sector at an
azimuth of 115° to 145° plus a 140-meter rectan-
gle on either side should be evacuated.
See Figure 7-8.
Example Problems
55
-------
Table 7-10 DETERMINATION OF WIDTHS WITHIN
ISOPLETHS (PROBLEM 26)
x,
km
0.1
0.5
1.0
2.0
3.0
4.0
5.0
6.0
x + xy,
km
0.14
0.54
1.04
2.04
3.04
4.04
5.04
6.04
<7V'
m
5.5
19
35
66
93
120
149
175
X (centerline),
g m-:t
13.9
3.6
1.3
7.0
1.1
xlO-'
xlU-1
x 10"^
4.8 x 10--
3.5
2.7
x 10--
x 10~-
X (isopleth)
y
X (centerline) aj.
1.8
2.27
6.94
1.92
3.57
5.20
7.14
9.26
x
x
X
X
X
X
X
X
10-
10-'
10--
10-'
10-1
10-'
10-1
10-1
3.55
2.75
2.31
1.82
1.44
1.14
0.82
0.39
y,
m
20
52
80
120
134
137
122
68
SCALE, km
145"
1
Figure 7-8. Possible positions of the 2.5 x 10~2 g m"
isopleth and the evacuation area (Problem 26).
56
ATMOSPHERIC DISPERSION ESTIMATES
-------
APPENDICES
339-901 O - 69 - 5
-------
Appendix 1: ABBREVIATIONS AND SYMBOLS
Abbreviations
cal calorie
g gram
°K degrees Kelvin
m meter
mb millibar
sec second
Symbols
a ratio of horizontal eddy velocity to vertical
eddy velocity
cp specific heat at constant pressure
Cy Sutton horizontal dispersion parameter
Cz Sutton vertical dispersion parameter
d inside stack diameter at stack top
DT (x,y,0;H) Total dosage
e 2.7183, the base of natural logarithms
f (G,S,N) frequency of wind direction for a given
stability and wind speed class
h physical stack height
hi height of the base of an inversion
H effective height of emission
H,, effective height of emission for a particular
wind speed
k von Karman's constant, approximately equal
to 0.4
K eddy diffusivity
L two uses: 1. the height of an air layer that is
relatively stable compared to the
layer beneath it; a lid
2. the half-life of a radioactive
material
n Sutton's exponent
N an index for wind speed class
p three uses: 1. Bosanquet's horizontal disper-
sion parameter
2. atmospheric pressure
3. a dummy variable in the equa-
tion for a Gaussian distribution.
q two uses: 1. Bosanquet's vertical dispersion
parameter
2. emission rate per length of a line
source
Q emission rate of a source
Q r total emission during an entire release
R net rate of sensible heating of an air column
by solar radiation
s the length of the edge of a square area source
S an index for stability
tk a short time period
t,,,
Ta
TK
u
UN
v'
V«
Vx
W'
X
XL
Xv
y
z
z,,
80
8z~
AH
o
PA
time required for the mixing layer to develop
from the top of the stack to the top of the
plume
a time period
ambient air temperature
stack gas temperature at stack top
wind speed
a mean wind speed for the wind speed class N.
horizontal eddy velocity
stack gas velocity at the stack top
a velocity used by Calder
vertical eddy velocity
distance downwind in the direction of the
mean wind
design distance, a particular downwind dis-
tance used for design purposes
the distance at which crz = 0.47L
a virtual distance so that
-------
0 the angle between the wind direction and a
line source
X concentration
X<;\vi crosswind-integrated concentration
X,, a ground-level concentration for design pur-
poses
XK inversion break-up fumigation concentration
Xk concentration measured over a sampling time,
tk
XIIHIX maximum ground-level centerline concentra-
tion with respect to downwind distance
x» concentration measured over a sampling time,
ts
X relative concentration
y)Z;H) concentration at the point (x, y, z)
from an elevated source with effective
height, H.
x (X>Q) the long-term average concentration at
distance x, for a direction e from a source.
60
ATMOSPHERIC DISPERSION ESTIMATES
-------
Appendix 2: CHARACTERISTICS OF THE
GAUSSIAN DISTRIBUTION
The Gaussian or normal distribution can be de-
picted by the bellshaped curve shown in Figure A-l.
The equation for the ordinate value of this curve is:
exp I ±_
(A.I)
Figure A-2 gives the ordinate value at any distance
from the center of the distribution (which occurs
at x). This information is also given in Table A-l.
Figure A-3 gives the area under the Gaussian curve
from ^ to a particular value of p where p =
This area is found from Eq. (A.2):
Area ( x to p) =
exp (0.5 p-) dp
r -+
I V2^
I -v.
(A.2)
Figure A-4 gives the area under the Gaussian
curve from p to +p. This can be found from Eq.
(A.3):
Area (p to +p) =
exp (0.5 p2) dp
r -j-
/ V2^
J P
(A.3)
-3
Figure A-l. The Gaussian distribution curve.
Appendix 2
61
-------
0.01
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0
Figure A-2. Ordinate values of the Gaussian distribution.
62
ATMOSPHERIC DISPERSION ESTIMATES
-------
4.0
3.5
3.0
2.5
2.0
1 5
1.0
0.5
0
-0 >
-1.0
-1.5
-2.0
-2.5
-3.0
-3 5
-4.0
I- .
_|_.
I
c
1
f
f*
n
:-
EEE-;::::- -:;:;|;:;;:
" ::: ::::::: : x. :: . j :. :_:::
;:; __ .?,i.
_ , i . . . .
~ " ji ' ""
i . . _ ... .
_ ^ _ ^ . i .
i '~~T- '^T
;;;E|:-E|;;:;|=EE
wiiiwf
. "ft" """" '
|::::::::::::|:::::::::|z
r-- -t -.:------- ~ ---;>!i--
....... ft
:::::;!!:::::: .::!:::::::--
::::::::::::::: [::::::: :±:i a
X
;,«
^mm
:::;«f?
rf*
'
L(t
~~ i1'
^- 1-
-fri
F- frt
= (*
^1-
.__
l*i-
~
|
0.01 0.1 0.5 1 2 5 10 20 40
r+P i i
-£= exp (
60 80 90 95 98 99
0.5 p2) dp
99.8 99.99
Figure A-3. Area under the Gaussian distribution curve from <*> to p.
Appendix 2
63
-------
4.5
4.0
3.5
3.0
2.5
? 0
1.5
1.0
0.5
0.0
0.
01
-t T
::;
O.I
__ .1*
0.5
tt^e
1 2
^
1 | | 1 1 IIIIIHIIIIIIIIIIIII mi f
-"I-:::: :::::: |: .:..
T ' -tff"
w- (- |
= «:=!!!£: f :::::::::::|::
5 10 20 30 40 5(
f N/5? oxp
niiiiiiii' : i ;i |ii|iN|imj i j
::: ::|:-|: I,::i.±::-:-
||| j I i ;}||t[|i{j^jjW LH
:::::::::::::: tl::: ::::;--
! i
) 60 70 80 90 95
-0.5 p7) dp
i ff__
. i . _ .
:::::
98 9<
. . . . _
11
\-.-.-
" ~n 1
)
-
9
tit
-1
-t1-'
r
~t::
-f::
- )|r
NN
-; *
- i
r- f
I
9.8
-._
<1_
- "1" JJ
~-t-\
J-j-
r
=
... .
99
Figure A-4. Area under the Gaussian distribution curve between p and +p.
64
ATMOSPHERIC DISPERSION ESTIMATES
-------
Appendix 3: SOLUTIONS TO EXPONENTIALS
Expressions of the form exp [0.5 A2] where
A is H/az or y/cry frequently must be evaluated.
Table A-l gives B as a function of A where B = exp
[0.5 A-']. The sign and digits to the right of the
E are to be considered as an exponent of 10. For
example, if A is 3.51, B is given as 2.11E 03
which means 2.11 x 10~3
Appendix 3 65
-------
a>
O5
Table A-l SOLUTIONS TO EXPONENTIALS B = exp [-0.5A*]
The notation 2.16 E-l means 2.16 x 1Q-1
g
o
o
o
55
H
i
w
3
H
W
CA
A
0.00
0.10
0.20
0.30
0.40
0,50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3.00
3.10
3.20
3.30
3.40
3.50
3.60
3.70
3.80
3.90
4.00
4.10
4.20
4.30
4.40
4.50
4.60
4.70
4.80
4.90
0.00
B
1.00E 0
9.95E .1
V.80E .1
9.5AE -1
9.23E -1
B.8H -1
a.s^E -l
7.8?E -1
7.2AE -1
6.67E -1
6.0?E -1
5,4ftt -1
4.87E -1
4.3PE -1
4.75E -1
3.21E -1
2.7SE -1
2.3ftE -1
1.9BE -1
1.6=C -1
l.3*E -1
1.10E -1
8.89E -2
7.10E -2
5.61E -2
4,?ot: -2
3.41E -?.
i,M£ -2
1.9P.E -2
1.49L -2
unt -2
S.loE -3
5.9RE -?
<..32E -3
3.09E -3
2. lot -3
1.53E -3
1.07E -3
7.3?E -4
«t.98E -4
3.3fcE -4
2.24E -4
1.4RE -4
q.fc*>B -5
6.2SE -b
4.01E -5
2.54E -5
1.60E -5
9.93E -ft
6. lib -6
0.01
l.OOF. 0
9.94E -1
9.78E -1
9.S3E -1
9.19F -1
8.78E -1
R.30E -1
7.77E -1
7.20F. -1
6. ME -1
6. OIF -1
J.40F. -1
4. s IE -i
4.24E -1
3.70E -1
3.20F. -1
2.74F .1
2.32E -1
1.94E -1
1.61E -1
1.33E -1
1.08F -1
R.7QF -2
*.94E -2
5.48E -2
4.29E -2
3.32E -2
2.?4E -2
1.93F -2
1.45F -2
l.OBE -2
7.94E -3
5.79F -3
4.18E -3
2.99F -3
2. HE -3
1..48F. -3
1.03? -3
7.05F -4
4.79F -4
3.22E -4
2.15F -4
1.42E -4
E -5
5.98E -5
3.83E -5
2.43E -5
l.SZE -5
9.46F -6
5.82E -6
0.02
10.00E -1
9.93E -1
9.76E -1
9.50E -1
9.1*E -1
8.74E -1
8.25E -1
7.72E -t
7.15E -1
6.5SE -1
5.94E -1
5.34E -1
4.7?£ -1
4. IRE -i
3.65E -1
3.1?E -1
2.69E -1
2.2PE -1
1.91E -1
1.5PE -1
1.30E -1
1.06E -1
8.51E -2
6.7PE -2
5 3^ E£ ~2
4.19E -2
3.23E -2
2.47E -2
1.88E -2
1.41E -2
1.05E -2
7.7^E -3
5.60E -3
4.04E -3
2.8°E -3
2.04E -3
1.43E -3
9.80£ -4
6.7°E -4
4.61E -4
3.10E -4
Z.Oftf -4
1.36E -'+
8 BftE -">
S.72E -5
3.66E -5
2.3?E -5
1.45l£ -5
9.02E -6
5.54E *>
0.03
10.00E -1
9.92E -1
9.74E -1
9.47E -1
9.12E -1
8.69E -1
H.20E -1
7.66E -1
7.09E -1
&.49E -1
S.88E -1
S.28E -1
".69E -1
4.13E -1
3.60E -1
3.10E -1
2.65E -1
2.24E -1
1.87E -l
1.55E -1
1.27E -1
1.04E -1
H.32E -2
h.62E -2
5.22E -2
4.07E -2
3.15E -2
H.41E -2
1.82E -2
1.37E -2
1.02E -2
'.46E -3
5.43E -3
3.91E -3
2.79E -3
1.97E -3
1.38E -3
9.53E -4
6.53E -4
4.43E -4
2.07E -4
1.98E -4
1.30E -4
«.49E -5
5.48E -5
3.50E -5
Z.21E -5
1.39E -5
^.59E -6
S.28E -6
0.04
9.99E .1
9.90E -1
'J.72E -1
9.44£ -1
".08£ .1
«.64£ -1
8.15E -1
7.61E -1
7.03E -1
.«2E .1
>.22£ -1
'.64E -1
4.0HE -1
3.55E -1
3.0&E -1
2.61E -1
2.20E -)
1.84E -1
) .52E -1
1.2SE -1
J.01-E -1
^. 14£ -2
6. 476 -2
b 1 *"! F » 2
3.97E -2
»!07E -2
2.34E -2
1.77E -2
1.33E -2
^.R'iF. -3
7.2HE -3
S.256 .3
3.78£ -3
2.69E -3
1.90E -3
1.33E -3
9.18E -4
6.28E -4
4.26E -4
Z.lftE -4
1.90E -4
1.25E -4
8.13E -5
5.^4£ .5
3.34r .5
2.11E -5
1.32E -5
H.19E -h
5.02E -6
0.05
9.99E -I
9.89E -1
9.69E -1
9.41E -1
9.04E -1
8.60E -1
8.10E -1
7.55E -1
6.97E -1
6.37E -1
5.76E -1
5.16E -1
4.58E -1
4.02E -1
3.50E -1
3.01E -1
2.56E -1
2.16E -1
1.81E -1
1.49F, -1
1.22F -1
9.91E -2
7.96E -2
6.32E -2
4.97E -2
3.87E -2
2.99E -2
2.28E -2
1.72F. -2
1.29F. -2
9.55E -3
7.00E -3
5.09E -3
3.66E -3
2.60F -3
1.83F -3
1.28E -3
8.84E -4
6.04E -4
4.09E -4
2.74K -4
1.82E -4
1.20F -4
7.78F -5
5.01E -5
3.20E -b
2.02E -5
1.26F. -5
7.80E -6
4.78E -6
0.06
9.98E -1
9.87E -1
9.67E -1
9.37E -1
9.00E -1
8.55E -I
8.04E -1
7.49E -1
6.91E -1
6.31E -1
5.70E -1
5.10E .1
4.52E -1
3.97E -1
3.45E -1
2.96E -1
2.52E -1
2.13E -1
1.77E -1
1.47E -1
1.20E -1.
9.70E -2
7.78E -2
6.17E -2
3.78E -2
2.91E -2
2.22E -2
1.67E -2
1.25E -2
9.26E -3
6.79E -3
4.92E -3
3.54E -3
2.51E -3
1.77E -3
1.23E .3
8.51E .4
5.82E -4
3.93E -4
2.63E -4
1.75E -4
1.15E -4
7.45E -5
*.79E -5
3.05E -5
1.93E -5
1.20E -5
7.43E .6
4.55E -6
0.07
9.98E -1
9.86E -1
9.64E -1
9.34E -1
8.95F. -1
8.50E -1
7.99E -1
7.44E -1
6.85E -1
6.25E -1
5.64E -1
5.04E -1
4 46E -1
3I91E -1
3.39E -1
Z.9ZE -1
Z.48E -1
2.09E -1
1.74E -1
1.44E -I
1.17E -1
9.50E -2
7.60E -2
6.03E -2
f. 7?C 9
3.68E -2
2.83E -2
2.16E -2
1.63E -2
1.22E -2
8.98E -3
6.58E -3
^.77E -3
3.42E -3
2.43E -3
1.71E -3
1.19E -3
B.ZOE -4
5.60E -4
3.78E -4
Z.53E -4
1.68E -4
1.10E -4
7.13E -5
*.53E -5
2.92E -5
1.84E -5
1.15E -5
7.08E -6
4.33E -6
0.08
9.97E -1
9.84E -1
9.62E -1
9.30E -1
8.91E -1
8.45E -1
7.94E -1
7.38E -1
6.79E -1
6.19E -1
5.58E .1
*.99E -1
3.86E -1
3.35E -1
2.87E -1
2.44E -1
2.05E -1
1.71E -1
1.41E -1
1.15E -1
9.29E -.2
7.43E -2
5.89E -2
3.59E -2
2.76E -2
2. IDE .2
1.58E -2
1.18E -2
8.71E -3
6.37E "3
4.61E -3
3.31E -3
2.35E -3
1.65E -3
1.15E -3
7.89E "*
5.38E -«
3.63E -*
2.43E -4
1.61E -4
1.05E *
6.83E -5
4.38E -5
Z.79E .5
1.75E -5
1.09E -5
6.74E -6
4.12E -6
0.09
9.96E
9.82E
9.59E
9.27E
8.87E
8.40E
7.88E
7.3ZE
6.73E
6.13E
5.5ZE
4.93E
*.35E
3.B1E
3.30E
2.83E
2.40E
2.02E
1.68E
1.38E
1.13E
9.09E
7.27E
5.75E
4.51E
~ J * t
3.49E
2.68E
2.04E
1.54E
1.15E
8.45E
6.17E
4.46E
3.20E
2.27E
1.59E
1.11E
7.6QE
5.18E
3.49E
2.33E
1.54E
1.01E
6.53E
4.19E
2.66E
1.67E
1.04E
6.42E
3.92E
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
1
-1
.1
.2
.2
.2
,2
.2
.2
.2
.2
.2
-3
.3
.3
.3
.3
.3
.3
.4
.4
.4
.4
-4
4
.5
.5
.5
-5
.5
.6
.6
-------
Table A-l (continued) SOLUTIONS TO EXPONENTIALS
a
B.
*'
w
A
5.00
5.10
5.20
5.30
5.40
5.50
5.60
5.70
5.80
5.90
6.00
6.10
6.20
6.30
6.<>0
6.50
6.60
6.70
6.80
6.90
7. 00
7.10
7.20
7.30
7.40
7.50
7.60
7.70
7.80
7.90
8.00
8. 1C
8.20
8.30
8.40
8.50
8.60
8. 70
8.80
8.90
9.00
9.10
9.20
9.30
9.40
9.50
9.60
9.70
9.80
9.90
0.00
B
3.7TE -6
2.25E -6
1.34E -6
7.95t -7
".6/SE -7
2.70t -7
1.5-5U -7
8.S1E -H
4.94E -8
2.76E -1*
1.52E -8
8.3?E -9
4.50E -9
*.41E -9
1.231: -9
6.60t-10
3.4RE-10
l.7ot-10
9.10E-11
4.50E-11
2.2QE-11
1.13t-ll
5;54E-12
2.68E-12
1.29E-12
6.10E-13
2.87E-13
1.34E-13
6.15E-14
7.80E-14
1.27E-14
5.66E-15
Z.51E-15
1.10E-15
4.77E-16
2.0SE-16
8.71E-17
3.67E-17
1.53t-l7
6.3IE-18
7.33E-17
3.0?E-17
1.28E-17
5.21E-13
2.15E-1S
8.69E-19
3.47E-19
1.37E-19
5.3SE-20
2.09E-20
8.02E-21
3.09E-21
1.15E-21
4.2flE-22
0.03
3.21E -6
1.9?E -6
1.15E -6
6.78E -7
3.96E -7
2.29E -7
1.31E -7
'.42E -8
4.16E -8
Z.31E -8
1.27E -8
",92E -9
3.73E .9
1.99E -9
1.05E -9
S.50E-10
2.85E-10
1.46E-10
7.42E-11
3.73E-11
1.86E-U
9.HE-12
4.46E-12
2.15E-12
1.03E-12
4.87E-13
Z.28E-13
1.06E-13
4.86E-14
Z.21E.U
9.96E-15
4.44E-15
1.96E-15
W.56E-16
3.70E-16
1.59E-16
6.72E-17
Z.82E-17
1.17E-17
4.83E-18
1.97E-18
'.93E-19
3.17E-19
1.25E-19
4.90E-20
1.90E-20
7.29E-21
Z.77E-21
1.04E-21
3.08E-22
0.0'+
3.05E .6
l.S^E -6
l.O'JE -6
6.41E -/
i.T>£ -7
Z.17E -7
1.24E -7
7.01E -8
3.93E -8
2.13E -8
1.20E -8
->.51E -9
3.51E -9
1.87E -9
9.87E-10
5.16E-10
2.67E-10
1.37E-10
6.93E-11
3.4SE-11
1.7'E-ll
8.51E-12
4.15E-12
2.00E-12
9.55E-13
4.52E-13
2.HE-13
9.30E-14
4.50E-14
2.04E-14
9.19E-15
*.09E-15
l.POE-15
7.87E-16
3.40E-16
1.46E-16
6.17E-17
2.59E-17
1.07E-17
4.41E-18
1.30E-18
7.24E-19
2.89E-19
1.14E-19
4.46E-20
1.73E-20
S62E-21
2.51E-21
9.43E-22
3.51E-22
0.05
2.90E -6
1.74E -6
1.04f -6
6.09E -7
3.55E -7
2.05E -7
1.17P -7
6.62E -8
3.70E -8
2.0bE -8
1.13E -8
6.12E -9
3.29E -9
1.75E -9
9.25E-10
4.83E-10
2.50E-10
1.28E-10
6.47E-11
3.25E-11
1.61E-U
7.92F-12
3.86E-12
1.86E-12
8.87E-13
4.19E-13
1.96E-13
9.07E-14
4.16E-14
1.89E-14
8.48E-15
3.77E-15
1.66E-15
7.24E-16
3.13E-16
1.34E-16
5.66E-17
2.37E-17
9.83E-18
4.04E-18
1.64E-18
6.61E-19
2.63E-19
1.04E-19
4.06E-20
1.57E-20
6.01E-21
2.28E-21
8.55E-22
3.18E-22
0.06
2.76E -6
1.65E -6
9.82E -7
5.77E -7
3.36E -7
1.94E -7
1.11E -7
6.25E -8
3.49E -8
1.94E -8
1.06E -8
5.76£ .9
3.09E -9
1.65E -9
8.67E-10
4.52E-10
2.34E-10
1.19E-10
6.04E-11
3.03E-11
1.50E-11
7.38E-12
3.59E-12
1.73E-12
8.23E-13
3.88E-13
1.81E-13
8.39E-14
3.84E-14
1.74E-14
7.82E-15
3.48E-15
1.53E-15
6.66E-16
2.87E-16
1.23E-16
5.19E-17
2.17E-17
9.00E-1B
3.69E-18
1.50E-18
6.03E-19
2.40E-19
9.46E-20
3.69E-20
1.43E-20
5.46E-21
2.07E-21
7.75E-22
2.8BE-22
0.07
2.62E -6
1.57E -6
9.32E -7
5.47E -7
3.18E -7
1.83E -7
1.05E -7
5.90E -8
3.29E -8
1.82E -8
9.98E -9
5.41E -9
2.91E -9
1.55E -9
8.13E-10
4.24E-10
2.19E-10
1.12E-10
5.64E-11
2.82E-11
1.40E-11
6.87E-12
3.34E-12
1.60E-12
7.64E-13
3.60E-13
1.68E-13
7.77E-14
3.55E-14
1.61E-U
7.22E-15
3.20E-15
1.41E-15
6.13E-16
2.64E-16
1.13E-16
4.76E-17
1.99E-17
8.23E-18
3.37E-18
1.37E-18
5.50E-19
2.19E-19
8.61E-20
3.36E-20
1.30E-20
4.95E-21
1.87E-21
7.02E-22
2.60E-22
0.08
2.49E -6
1.49E -6
8.84E -7
5.19E -7
3.01E -7
1.73E -7
9.87E -8
5.57E -8
3. HE -8
1.72E -8
9.39E -9
5.09E -9
2.73E -9
1.45E -9
7.62E-10
3.97E-10
2.04E-10
1.04E-10
5.27E-11
2.63E-H
1.30E-U
6.39E-12
3.10E-12
1.49E-12
7.09E-13
3.34E-13
1.56E-13
7.19E-14
3.28E-14
1.49E-14
6.66E-15
2.95E-15
1.30E-15
5.64E-16
2.43E-16
1.03E-16
4.36E-17
1.82E.17
T.53E-18
3.08E-18
1.25E-18
5.02E-19
1.99E-19
7.84E-20
3.05E-20
1.18E.20
4.50E-21
1.70E-21
6.36E-22
2.3AE-22
0.09
2.37E -6
1.42E .6
8.38E .7
4.91E -7
2. BSE -7
1.64E .7
9.32E .8
5.25E -8
2.93E .8
1.62E .8
8.84E .9
4.78E -9
2.56E .9
1.36E .9
7.14E-10
3.71E-10
1.91E-10
9.74E.H
4.92E-11
2.46E-11
1.22E-11
5.95E-12
2.88E-12
1.38E-12
6.58E-13
3.09E-13
1.44E-13
6.65E-14
3.04E-14
1.37E.14
6.14E-15
2.726-15
1.19E-15
5.18E-16
2.23E-16
9.49E-17
4.00E-17
1.67E.17
6.89E.18
2.82E-18
1.14E-18
4.58E-19
1.82E.19
7.14E-20
2.78E-20
1.07E-20
4.08E-21
1.54E-21
5.76E-22
2.13C-22
-------
Appendix 4: CONSTANTS, CONVERSION
EQUATIONS, CONVERSION TABLES
Constants
e
TT 3 1416 *
7T
0 3183
01 5Q9
27T
TT = 2.5066 -j= = 0.3989
2
7= = 0.7979
(27r)3/2 = 15.75
Conversion Equations and Tables
T(°C) = 5/9 (T(°F) 32)
T(°K) =T(°C) +273.16
T(°F) = (9/5T(°C) ) +32
Appendix 4 gg
-------
CONVERSION FACTORS - VELOCITY
.
H
g
0
^
s
H
a
o
o
M
W)
M
H
Cfl
0
2!
H
C/3
H
M
H
M
73
DESIRED
GIVEN UNITS
METERS
PER SEC
FT
PER SEC
FT
PER MIN
KM
PER HR
MIISTAT)
PER HR
KNOTS
MKSTAT)
PER DAY
TO CONVERT A
UNITS METERS
PER SEC
1.0000
E 00
3.0480
E-01
5.0800
E-03
2.7778
E-01
4.4704
E-Oi
5.1479
E-01
1.8627
E-02
VALUE FROM A GIVEN
AND BENEATH THE DESIRED UNIT.
FT
PEP SEC
3.2808
E 00
1.0000
E 00
1.6667
E-02
9.113*
E-01
1.4667
E 00
1.6889
E 00
6.1111
E-02
UNIT TO A
NOTE THAT
FT
PER
1.9685
E 02
6.0000
E 01
1.0000
E 00
5.4681
E 01
8.8000
E 01
1.0134
E 02
3,6667
E 00
DESIRED
KM
MIN PER HR
3.6000
E 00
1.0973
E 00
1.8288
E-02
1.0000
E 00
1.6093
E 00
1.8532
E 00
6.7Q56
E-02
UNIT, MULTIPLY
MI(STAT)
PER HR
2.2369
E 00
6.8182
E-01
1.1364
E-02
6.2137
E-01
1.0000
E 00
1.1516
E 00
4.1667
E-02
THE GIVEN
KNOTS
1.9425
E 00
5.9209
E-01
9.8681
E-03
5.3959
E-01
8.6839
E-01
1.0000
E 00
3.6183
E-02
VALUE BY
MKSTAT)
PER DAY
5.3686
E 01
1.6364
E 01
2.7273
E-01
1.4913
E 01
2.4000
E 01
2.7637
E 01
1.0000
E 00
THE FACTOR OPPOSITE THE GIVEN UNITS
E-XX MEANS 10 TO THE -xx POWER.
-------
a
V
I
CONVERSION FACTORS
DESIRED UNITS
GIVEN UNITS
GRAMS
PER SEC
GRAMS
PER MIN
KG
PER HOUR
KG
PER DAY
LBS
PER MIN
LBS
PER HOUR
LBS
PER DAY
TONS
PER HOUR
TON,S
PER DAY
- EMISSION RATES
GRAMS
PER
1.0000
E 00
1.6667
E-02
2.7778
E-Oi
1.157*
E-02
7.5399
E 00
1.2600
E-01
5.2499
E-03
2.5200
E 02
1.0500
E 01
GRAMS
SEC PER
6.0000
E 01
1.0000
E 00
1.6667
E 01
6.9444
E-01
E 02
7.5599
E 00
3.1499
E-01
1.5120
E 04
6.2999
E 02
KG
MIN PER HOUR
3.6000
E 00
6.0000
E-02
1.0000
E 00
4.1667
E-02
2.7216
E 01
4.5359
E-01
1.8900
E-02
9.0718
E 02
3.7799
E 01
KG
PER DAY
8.6400
E 01
1.4400
E 00
2.4000
E 01
1.0000
E 00
6.3317
E 02
1.0886
E 01
4.5359
E-01
2.1772
E 04
9.0718
E 02
LBS
PER MIN
1.3228
E-Oi
2.2046
E-03
3.6744
E-02
1.5310
E-03
1.0000
E 00
1.6667
E-02
6.9444
E-04
3.3333
E 01
1.3889
E 00
LBS
PER HOUR
7.9366
E 00
1.3228
E-01
2.2046
E 00
9.1859
E-02
6.0000
E 01
1.0000
E 00
4.1667
E-02
2.0000
E 03
8.3333
E 01
LBS
PER DA*
1.9048
E 02
3.1747
E 00
5.2911
E 01
2.2046
E 00
1.4400
E 03
2.4000
E 01
1.0000
E 00
4.8000
E 04
2*0000
E 03
TONS
PER HOUR
3.9683
E-03
6.6139
£05
1.1023
E-03
4.5930
E.03
3.0000
E-02
5.0000
E-04
2.0833
E-03
1.0000
E 00
4.1667
E-02
TONS
PER
9.3240
E-02
1.5873
E-03
2.6455
E-02
1.1023
E-03
7.2000
E-01
1.2000
E-02
3.0000
E-04
2.4000
E 01
1.0000
E 00
TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS
AND BENEATH THE DESIRED UNIT. NOTE THAT E-XX MEANS 10 TO THE -XX POWER.
-------
CONVERSION FACTORS - LENGTH
DESIRED UNITS METER
GIVEN UNITS
CM
MICRON
KILOMETER INCH
FOOT
YARD
IILE(STAT) MILE(NAUT)
*t»
LTMOSPHERIC
O
"d
|
1
M
cn
H
§
H
H
Cfl
METER 1.0000
E 00
CM 1.0000
E-02
MICRON 1.0000
E-06
KILOMETER 1.0000
E 03
INCH 2.5400
E-02
FOOT 3.0480
£01
YARD 9.1440
E-01
MILE(STAT) 1.6093
E 03
MIlE(NAUT) 1.8532
E 03
TO CONVERT A VALUE FROM A GIVEN
AND BENEATH THE DESIRED UNIT.
1.0000
E 02
l.OQOO
E 00
1.0000
E-04
1.0000
E 05
2.5400
E 00
3.0480
E 01
9.1440
E 01
1.6093
E 05
1.8532
E 05
UNIT TO A
NOTE THAT
1.0000
E 06
1.0000
E 04
1.0000
E 00
1.0000
E 09
2.5400
E 04
3.0480
E 05
9.1440
E 05
1.6093
E 09
1.8532
E 09
1.0000
E-03
1.0000
E-05
1.0000
E-09
1.0000
E 00
2.5400
E-05
3.0480
E-04
9.1440
E-04
1.6093
E 00
1.8532
E 00
3.9370
E 01
3.9370
E-01
3.9370
E-05
3.9370
E 04
1.0000
E 00
1.2000
E 01
3.6000
£ 01
6.3360
E 04
7,2962
E 04
DESIRED UNIT, MULTIPLY THE GIVEN
E-XX MEANS 10 TO THE -xx POWER.
3.2808
E 00
3.2808
E-02
3.2808
E-06
3.2808
E 03
8*3333
E-02
1.0000
E 00
3.0000
E 00
5.2800
E 03
6.0802
E 03
VALUE BY
1.0936
E 00
1.0936
E-02
1.0936
E-06
1.0936
E 03
2.7778
E.02
3.3333
E-01
1.0000
E 00
1.7600
E 03
2.0267
E 03
THE FACTOR
£. '4
6.2137
£.06
6.2137
E-10
6r2137
£.01
1.5783
£.05
1.8939
£.04
5.6818
£04
1.0000
£ 00
1.1516
E 00
OPPOSITE
5.3959
E-04
5.3959
E-06
5.3959
E-10
5.3959
E-01
1.3706
E-05
1.6447
E-04
4,9340
E-04
8,6839
E-01
1,0000
E 00
THE GIVEN UNITS
-------
V
o
3
&
X
>tt
CONVERSION FACTORS - AREA
DESIRED
GIVEN UNITS
SQ METER
SQ KM
SQ CM
SQ INCH
SQ FOOT
SQ YARD
ACRE
SQ STAT
MILE
so NAUT
Mil E
UNITS SQ METER
1.0000
E 00
1.0000
E 06
1.0000
E-04
6.4516
E-04
9.2903
E-02
8.3613
E-01
4,0469
E 03
2.5900
E 06
3.4345
E 06
SQ KM
1.0000
E-06
1.0000
E 00
1.0000
E-10
6.4516
E-10
9.2903
E.08
8.3613
E-07
4.0469
E-03
2.5900
E 00
3.4345
E 00
SQ CM
1.0000
E 04
1.0000
E 10
1.0000
E 00
6.4516
E 00
9.2903
E 02
8.3613
E 03
4.0469
E 07
2.5900
E 10
3.4345
E 10
SQ INCH
1.5500
E 03
1.5500
E 09
1.5500
E-01
1.0000
E 00
1.4*00
E 02
1.2960
E 03
6.2726
E 06
4.0145
E 09
5.3235
E 09
SQ FOOT
1.0764
E 01
1.0764
E 07
1.0764
E-03
6.9444
E-03
1.0000
E 00
9.0000
E 00
4,3560
E 04
2.7878
E 07
3.6969
E 07
SQ YARD
1.1960
E 00
1.1960
E 06
1.1960
E-04
7,7160
E-04
1.1111
E-01
1.0000
E 00
4.8400
E 03
3.0976
E 06
4.1076
E 06
ACRE
2.4710
E-04
2.4710
E 02
2.4710
E.08
1.5942
E.07
2.2957
£.05
2.0661
£.04
1,0000
E 00
6.4000
E 02
8.4869
E 02
SQ STAT
MILE
3.8610
E-or
3.8610
E-01
3,8610
E-ll
2.4910
£.10
3.5870
E.08
3.2283
£.07
1,5625
£.03
1.0000
£ 00
1.3261
E 00
SQ NAUT
MILE
2.9116
E-07
2.9116
e-oi
2.9116
E-ll
1.8785
E-10
2.7Q50
E-08
2.4345
E-07
1.1783
E-03
7.5411
E-01
1.0000
E 00
TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE GIVEN VALUE By THE FACTOR OPPOSITE THE GIVEN UNITS
AND BENEATH THE DESIRED UNIT. NOTE THAT E-XX MEANS 10 TO THE -XX POWER.
-------
SION FACTORS - VOLUME
D^STREO U.-JJTS cu f'
GIVEN UNITS
LITE" CU IIMCH CU FOOT Cu STAT Cj NAUT j 5 FLUID U 5 QUART U 5 GALLON
MILE MILE OUNCE
>
H
S
O
t/3
"B
a
M
M
M
O
o
5!
*B
M
93
Cfl
O
25
M
Cfl
H
i
H
W
in
cu METEP
LITER
cu INCH
cu FOOT
cu STAT
MTLF
cu NAUT
MILF
U S FLUID
OUMCF
U S QUART
U S GALLON
TO CONVFRT
AND BENFATH
1.0000
F 00
1.0000
E-03
1.6487
r-^5
2. an?
F-02
*.U83H7
E-02
2.R316
E 0.1
4,J.6«1
E U
6.36*9
E I/
2.9573
E-02
9.'»6*3
E Ot>
3.78-J3
E 00
U"IJt TO
NOTt r-)t
6.1023 3
f. 0*
6.1025 3
E 01
1.0000 5
F 00
1.7280 1
E 03
2.5*36 1
E 14
3.8«*2 2
E 1*
1.80*7 1
F 00
5.7750 3
E 07
2.3100 1
F 02
A DESIRE1) UNIT
.531*
E 01
,5ns
E-"2
.7H70
E-04
.0000
E ^0
,*^20
E 11
-.2*78
E 11
.0*/+*
E-03
.3*20
E 0*
.3368
E-01
, MULTIPLY
*.3991
E-10
2.3992
E-13
3.9315
E-15
6.7936
E-12
I. 0000
E 00
1.5270
E 00
7.0950
E-15
2.2704
E-07
9.0817
E-13
THE GIVEN
1.5711
E-10
1.5711
E-13
2.5746
E-15
4.4*88
E-12
6.5486
E-01
1.0000
E 00
4.6*62
E-15
l.*868
E-07
5.9472
E-13
VALUE o^
3.3814
E 04
3.3815
E 01
5.5412
E-Ol
9.5751
E 02
1.4094
E 14
2.1523
E 14
1.0000
E 00
3.2000
E 07
1.2800
E 02
f THE FACTOR
1.0567
E-03
1.0567
E-06
1.7316
E-08
2.9922
E-05
4.4045
E 06
6.7259
E 06
3.1250
E-08
1.0000
E 00
4*0000
E-06
OPPOSITE
2,6417
E 02
2.6418
E-01
4.3290
E-03
7.4805
E 00
1.1011
E 12
1.6815
E 12
7.8125
E-03
2.5000
E 05
1.0000
E 00
THE GIVEN UNITS
a E-XX MEANS 10 TO TrlE -XX POWER.
-------
n
B
ft
CONVERSION FACTORS - MASS
DESIRED UNITS GRAM
GIVEN UNITS
GRAM 1.0000
E 00
MICROGRAM i.oooo
E-06
KILOGRAM 1.0000
E 03
METRIC TON 1.0000
E 06
SHORT TON 9.0718
E 05
LONG TON 1.0160
E 06
GRAIN 6.4799
E-02
OUNCE 2.8349
(AVDP) E 01
LB (AvDP) 4.5359
E 02
MICROGRAM
1.0000
E 06
1.0000
E 00
1.0000
E 09
1.0000
E 12
9.0718
E 11
1.0160
E 12
6.4799
E 04
2.8349
E 07
4.5359
E 08
KILOGRAM
1.0000
E-03
1.0000
E-09
1.0000
E 00
1.0000
E 03
9.0718
E 02
1.0160
E 03
6.4799
E-05
2.8349
E-02
4.5359
E-01
METRIC
1.0000
E-06
1.0000
E-12
1.0000
E-03
1.0000
E 00
9.0718
E-01
1.0160
E 00
6.4799
E-08
2.8349
E-05
4.5359
E-04
TON SHORT TON
1.1023
E-06
1.1023
E-12
1.1023
E-03
1.1023
E 00
1.0000
E 00
1.1200
E 00
7.1428
E-08
3.1250
E-05
5.0000
E-04
LONG TON
9.8421
E-07
9.8421
E-13
9.8421
E-04
9.8421
E-01
8,9286
E-Oi
1.0000
E 00
6.3775
E-08
2.7902
E-05
4.4643
E-04
GRAIN
1.5432
E 01
1.5432
E-05
1.5432
E 04
1.5432
E 07
1.4000
E 07
1.5680
E 07
1.0000
E 00
4,3750
E 02
7.0000
E 03
OUNCE
(AVDP)
3.5274
E-02
3,5274
E-08
3.5274
E 01
3,5274
E 04
3.2000
E 04
3.5840
E 04
2.2857
E-03
1.0000
E 00
1.6000
"E 01
LB
-------
CONVERSION FACTORS - FLOW
DESIRED UNITS CD METER CU METER LITER LITER LITER CU FT CU FT CU FT CU CM
PER SEC PER HR PER SEC PER MIN PER HR PER SEC PER MIN PER HR PER SEC
GIVEN UNITS
j^
H
S
0
f$
a
B
2
ft
a
00
fl
t/3
0
2!
B
C/J
NN
H
B
W)
cu METER
PER SEC
cu METER
PER HR
LITER
PER SEC
LITER
PER'MIN
LITER
PER HR
CU FT
PER SEC
cu FT
PER MIN
cu FT
PER HR
cu CM
PER SEC
TO CONVERT A
AND BENEATH
1.0000
E 00
2.7778
E-04
1.0000
E-03
1.6667
E-05
2.7779
E-07
2.8317
E-02
4.7195
E-04
7.8658
E-06
1.0000
E-06
VALUE FROM A GIVEN
THE DESIRED UNIT.
3.6000
E 03
1.0000
E 00
3.6001
E 00
6.0002
E-02
1.0000
E-03
1.0194
E 02
1.6990
E 00
2.8317
E-02
3.6000
E-03
UNIT TO A
NOTE THAT
9.9997
E 02
2,7777
E-01
1.0000
E 00
1.6667
E-02
2,7778
E-04
2.8316
E 01
4.7194
E-01
7.8656
E-03
9.9997
E-04
DESIRED
5.9998
E 04
1.6666
E 01
6.0000
E 01
1.0000
E 00
1.6667
E-02
1.6990
E 03
2.8316
E 01
4.7194
E-01
5.9998
E-02
UNIT, MULTIPLY
3,5999
E 06
9,9997
E 02
3.6000
E 03
6.0000
E 01
1.0000
E 00
1.0194
E 05
1.6990
E 03
2.8316
E 01
3.5999
E 00
THE GIVEN
3.5314
E 01
9.8096
£.03
3.5315
E-02
5.8859
E-04
9.8098
E-06
1.0000
E 00
1.6667
E-02
2.7778
E-04
3.5314
E-05
VALUE BY
2.1189
E 03
5.8857
E.01
2.1189
E 00
3,5315
E-02
5,8859
E-04
6.0000
E 01
1.0000
E 00
1.6667
£.02
2.1189
E-03
THE FACTOR
1.2713
E 05
3.53U
E 01
1.27U
E 02
<.U89
E 00
3,5315
E-02
3,6000
E 03
6.0000
E 01
1.0000
E 00
1.2713
E-01
OPPOSITE
I. 0000
E 06
2,7778
E 02
1.0000
E 03
1,6667
E 01
2,7779
E-01
2,8317
E 04
4,7195
E 02
7.86*8
E 00
1.0000
E 00
THE GIVEN UNITS
E-XX MEANS 10 TO THE -xx POWER.
-------
d
d
a-
*«.
CONVERSION FACTORS - CONCENTRATION, DENSITY
DESIRED
GIVEN UNITS
GRAM PER
CU METER
MG PER
CU METER
MICROGRAM
PER CU M
MICROGRAM
PER LITER
GRAIN PER
CU FT
OUNCE PER
CU FT
LB PER
CU FT
GRAM PER
CU FT
LB PER
CU METER
UNITS GRAM PER
CU METER
1.0000
E 00
1.0000
E-03
1.0000
E-06
9.9997
E-04
2.2883
E 00
1.0011
E 03
1.6018
E 04
3.5314
E 01
4.5359
E 02
MG PER
CU METER
1.0000
E 03
1.0000
E 00
1.0000
E-03
9.9997
E-01
2.2883
E 03
1.0011
E 06
1.6018
E 07
3.5314
E 04
4.5359
E 05
MICROGRAM
PER CU M
1.0000
E 06
1.0000
E 03
1.0000
E 00
9.9997
E 02
2.2883
E 06
1.0011
E 09
1.6018
E 10
3.5314
E 07
4.5359
E 08
MICROGRAM
PER LITER
1.0000
E 03
1.0000
E 00
1.0000
E-03
1.0000
E 00
2.2884
E 03
1.0012
E 06
1.6019
E 07
3.5315
E 04
4.5360
E 05
GRAIN PER
CU FT
4.3700
E-01
4.3700
E-04
4.3700
E-07
4.3699
E-04
1.0000
E 00
4.3750
E 02
7.0000
E 03
1.5432
E 01
1.9822
E 02
OUNCE PER
CU FT
9.9.885
E-04
9.9885
E-07
9.9885
E-10
9.9883
E-07
2.2857
E-03
1.0000
E 00
1,6000
E 01
3.5274
E-02
4.5307
E-01
LB PER
CU
6.2428
E-05
6.2428
E-08
6.2428
E-ll
6.2427
E-08
1.4286
E-04
6.2500
E-02
1.0000
E 00
2.2046
E-03
2.8317
£.02
GRAM PER
FT CU FT
E-02
E-05
'.8317
E-08
'.8316
E-05
6.^799
E-02
'.8349
E 01
4.5359
E 02
1.0000
E 00
1.2844
E 01
LB PER
CU Ml
2.2046
E-03
2.2046
E-06
2.2046
E-09
2.2046
E-06
5,0*49
E-03
2.2072
E 00
3.5314
E 01
7.7855
E-02
1,0000
E 00
TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS
AND BENEATH THE DFSIRED UNIT. NOTE THAT E-XX MEANS 10 TO THE -XX POWER.
-------
-J
00
CONVERSION FACTORS - DEPOSITION RATF
(SHORT TON ,5TAT. MILE)
DESIRED UNITS GM PER SQ KG PER SQ MG PER SO. TON PER SO OZ PER SQ LB PER GM PER SO *IG PER SO
M PER MO KM PER MO CM PER MO MI PER MO FT PER MO ACRE PERMO FT PER MO IN PER MO
GIVEN UNITS
Jj,
H
S
O
Cfl
a
M
5
o
o
55
H
8
OQ
O
M
cw
H
H
H
GM PER SO
M PER MO
KG PER SO
KM PER MO
MG PER SQ
CM PER MO
TON PER SO
MI PER MO
OZ PER SQ
FT PER MO
LB PER
ACRE PERMO
GM PER SO
FT PER MO
MG PER SQ
IN PER MO
TO CONVERT
AND BENEATH
1.0000
E 00
1.0000
E-03
1.0000
E 01
3.5026
E-01
3.0515
E 02
1.1208
E-01
1.0764
E 01
1.5500
E 00
A VALUE FROM A GIVEN
THE DESIRED UNIT.
1.0000
E 03
1.0000
E 00
l.OQOO
E 04
3.5026
E 02
3.0515
E 09
1.1208
E 02
1.0764
E 04
1.5500
E 03
UNIT TO A
NOTE THAT
1.0000
E-01
1.0000
E-04
1.0000
E 00
3.5026
E-02
3.0515
E 01
1.1208
E-02
1.0764
E 00
1.5500
E-01
DESIRED
2.8550
E 00
2.8550
E-03
2.8550
E 01
1.0000
E 00
8.7120
E 02
3.2000
E-01
3.0731
E 01
4.4252
E 00
UNIT, MULTIPLY
E-XX MEANS 10 TO THE -
3.2771
E-03
3.2771
E-06
3.2771
E-02
1.1478
E-03
1.0000
E 00
3.6731
E-04
3.5274
E-02
5.0795
E-03
THE GIVEN
XX POWER.
8.9218
E 00
8.9218
E-03
8.9218
E 01
3.1250
E 00
2.7225
E 03
1.0000
E 00
9.6033
E 01
1.3829
E 01
VALUE BY
9.2903
E-02
9.2903
E-05
9.2903
E-01
3.2541
E-02
2.8349
E 01
1.0413
E-02
1.0000
E 00
1.4400
E-01
THE FACTOR
6.4516
E-01
6.4516
E-04
6.4516
E 00
2.2598
E-01
1.9687
E 02
7.2313
E-02
6.9444
E 00
1.0000
E 00
OPPOSITE THE GIVEN UNITS
-------
a
CONVERSION FACTORS - PRESSURE
DESIRED UNITS MILLIBAR BAR
GIVEN UNITS
ATMOSPHERE DYNES KG LBS MM MERCURY IN MERCURY
PER SO CM PER SO CM PER SO IN
MILLIBAR
BAR
ATMOSPHERE
DYNES
PER SO CM
KG
PER SO CM
LBS
PER SO IN
MM MERCURY
IN MERCURY
1.0000
E 00
1,0000
E 03
1.0133
E 03
1.0000
E-03
9.8066
E 02
6.8947
E 01
1.3332
E 00
3.386*
E 01
1.0000
E-03
1.0000
E 00
1.0133
E 00
1.0000
E»06
9.8066
E-01
6.89*7
E-02
1.3332
E-03
3.3864
E-02
9.8692
E-04
9.8692
E-01
1.0000
E 00
9.8692
E-07
9.6784
E-01
6.8046
E-02
1.3158
E-03
3.3421
E-02
1.0000
E 03
1.0000
E 06
1.0133
E 06
1.0000
E 00
9.8Q66
E 05
6.8947
E 04
1.3332
E 03
3.3864
E 04
1.0197
E-03
1.0197
E 00
1.0332
E 00
1.0197
E-06
1.0000
E 00
7.0307
£02
1.3595
E-03
3.4532
E-02
1.4504
E-02
1.4504
E 01
1.4696
E 01
1.4504
E-05
1.4223
E 01
1.0000
E 00
1.9337
E-02
4.9115
E-01
7.5006
E-01
7.5006
E 02
7.6000
E 02
7.5006
E-04
7.3556
E 02
5.1715
E 01
1.0000
E 00
2.5400
E 01
2.9530
E-02
2.9530
E 01
2.9921
E 01
2.9530
E-05
*,8959
E 01
2.0360
E 00
3.9370
E-02
1.0000
E 00
TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS
AND BENEATH THE DESIRED UNIT. NOTE THAT E-XX MEANS 10 TO THE -XX POWER.
-------
CONVERSION FACTORS - TIME
DESIRED UNITS SECOND
GIVEN UNITS
MINUTE
HOUR
WEEK
MONTH (28) MONTH <3oi MONTH on YEAR (365> YEAR <366»
g
0
Ml
35
O
M
0>
M
»
M
o
^
H
cn
H
2
H
H
SECOND
MINUTE
HOUR
WEEK
MONTH (28)
MONTH (SO)
MONTH (31)
YEAR (365)
YEAR (366)
TO CONVERT A
AND BENEATH
1.0000
E 00
1.6667
E-02
2.7778
E-04
1.6534
E-06
4.1336
E-07
3.8580
E-07
3.7336
E-07
3.1710
E-08
3.1623
E-08
VALUE FROM A GIVEN
THE DESIRED UNIT.
6.0000
E 01
1.0000
E 00
1.6667
£.02
9.9206
£.05
2.4802
£-05
2.3148
£-05
2.2401
£.05
1.9026
E-06
1.8974
£.06
UNIT TO A
NOTE THAT
3.6000
E 03
6.0000
E 01
1.0000
E 00
5.9524
E-03
1.4881
E-03
1.3889
E-03
1.3441
E-03
1.1416
E-04
1.1384
E-04
DESIRED
6.0480
E 05
1.0080
E 04
1.6800
E 02
1.0000
E 00
2.5000
E-01
2.3333
E-01
2.2581
E-01
1.9178
E-02
1.9126
E-02
UNIT. MULTIPLY
2.4192
E 06
4.0320
E 04
6.7200
E 02
4.0000
E 00
1.0000
E 00
9.3333
E-01
9.0323
E-01
7.6712
E-02
7.6503
E-02
THE GIVEN
2.5920
E 06
4,3200
E 04
7.2000
E 02
4.2857
E 00
1.0714
£ 00
1.0000
E 00
9.6774
E-01
8.2192
£-02
8.1967
E-02
VALUE BY
2.6784
E 06
4.4640
E 04
7.4400
E 02
4.4286
E 00
1*1071
E 00
1.0333
E 00
1.0000
E 00
8.4932
E-02
8.4699
£.02
THE FACTOR
3.1536
E 07
9.2560
E 05
8.7600
E 03
5.2143
E 01
1.3036
E 01
1.2167
E 01
1.1774
E 01
1.0000
E 00
9.9727
£.01
OPPOSITE THE
3.1622
E 07
5.2704
E 05
8.7840
E 03
5,2286
E 01
1,3071
E 01
1.2200
E 01
1.1806
E 01
1.0027
E 00
1.0000
E 00
GIVEN UNITS
E-XX MEANS 10 TO THE -xx POWER.
-------
a
e
n
D
ft.
CONvERSlCiM F'
DFSlBFi)
GIVEN UNITS
VJATT
( INT)
Kli OWATT
(INT)
MEGAWATT
(INT)
CA| (INT)
PER SEC
BTU
PER MIN
BTU
PER HR
JOULES ABS
PER SEC
ijAjT (ANSI
ELECT.
HORSEPOWER
'.CTO^S - POivES
LIMITS AiATT
(INT)
I. 0^00
F .10
F. 03
1.0000
E 06
F. 00
1.7588
F 01
2,9313
E-ol
9.9081
E-01
9.9981
E-01
7.4586
F 02
KILO" AT r
! I'll )
1 .0000
£-03
l.OOUO
E 00
1.0000
E Or)
4.18/6
E-0?
1.75H8
E-02
2, "3 1.3
E-04
9.99H1
E-04
'E!s:1
E-Ol
(IiNT)
1.0000
E-06
1.0000
F-03
1.0000
F 00
F-06
1.7583
E-05
2.9313
9.9981
E-07
9.9931
E-07
7.4586
E-04
CAI. (INT)
HER sr.c
2.3'iaO
E-'U
2,'IHSO
E '
-------
00
to
CONVERSION FACTORS - ENERGY. WORK
DESIRED UNITS ERG DYNE-CM
GtVEN UNITS
ABS JOULE CAL (INT) CAL (15) INT KW-HR ABS KW-HR 8TU
H
g
O
s
B
2
n
g
53
"8
Not
0
2!
H
VI
H
§
H
H
73
ERG 1.0000
E 00
DYNE-CM i.oooo
E 00
ABS JOULE 1.0000
E 07
CAL (INT) 4.1868
E 07
CAL (15) 4.1855
E 07
INT KW-HR 3,6007
E 13
ABS KW-HR 3.6000
E 13
BTU 1.0551
E 10
TO CONVERT A VALUE FROM A GIVEN
AND BENEATH THE DESIRED UNlT,
1.0000
E 00
1.0000
E 00
1.0000
E 07
4.1868
E 07
4.1855
E 07
3,6007
E 13
3.6000
E 13
1.0551
E 10
UNIT TO A
NOTE THAT
1.0000 2
E-07
1.0000 2
E-07
1.0000 2
E 00
4.1868 1
E 00
4.1855 9
E 00
3.6007 8
E 06
3.6000 8
E 06
1.0551 2
E 03
DESIRED UNIT
.3884
E-08
.3884
E-08
.3884
E-01
.0000
E 00
.9968
E-01
.6000
E 05
.5984
E 05
.5200
E 02
. MULTIPLY
E-xx MEANS 10 TO THE -
2.3892
E-08
2,3892
E-08
2,3892
E-01
1.0003
E 00
1.0000
E 00
8.6027
E 05
8.6011
E 05
2.5208
E 02
THE GIVEN
XX POWER.
2,7773
E-14
2,7773
E-14
2,7773
E-07
1.1628
E-06
1.1624
E-06
1.0000
E 00
9.9981
E-01
2.9302
E-04
VALUE BY
2.7778
E-14
2.7778
E-14
2.7778
E-07
1,1630
E-06
1.1626
E-06
1.0002
E 00
1.0000
E 00
2.9307
E-04
THE FACTOR
9,4781
E-ll
9,4781
E-ll
9.4781
E-04
3.9683
E-03
3.9671
E-03
3.4128
E 03
3.4121
E 03
1.0000
E 00
OPPOSITE THE GIVEN UNITS
-------
a
a
a
0
&
CONVERSION FACTORS - ENERGY PER UNIT AREA
DESIRED UNITS LANQ1.EY
GIVEN UNITS
CAL (15) BTU INT KW-HR ABS JOULES
PER SQ CM PER SQ FT PER SQ M PER SO CM
LANGLEY
CAL (15)
PER SO CM
BTU
PER SO FT
INT KW-HR
PER SO M
ABS JOULES
PER SQ CM
1.0000
E 00
1.0000
E 00
2.7133
E-01
8.6029
E 01
2.3892
E-01
1.0000
E 00
1.0000
E 00
2.7133
E-01
8.6029
E 01
2.3892
E-01
3.6855
E 00
3.6855
E 00
1.0000
E 00
3.1706
E 02
8.805
-------
CONVERSION FACTORS - POWER PER UNIT AREA
H
g
o
en
"fl
JjJ
M
M
O
o
M
WJ
M
75
O
2
B
cn
H
§
S
H
CAL PER SO
M PER SEC
CAL PER SQ
CM PER MIN
LANGLEY
PER MIN
CAL PER SQ
CM PER DAY
BTU PER SQ
FT PER MIN
BTU PER SQ
FT PER DAY
ABS WATT
PER SQ CM
TO CONVERT A
AND BENEATH
1.
E
1.
E
1.
E
1.
0000
00
6667
02
6667
02
157*
E-01
4t
E
3.
5222
01
1*0*
E-02
2.
E
3892
03
VALUE FROM A GIVEN
THE DESIRED UNIT.
6.0000
E-03
1.0000
E 00
1.0000
E 00
6.9444
E-04
2,7133
E-01
1.8843
E-04
1.4335
E 01
UNIT TO A
NOTE THAT
6.0000
E-03
1.0000
E 00
1.0000
E 00
6.9444
E-04
2.7133
E-01
1.8843
E-04
1.4335
E 01
8.
E
1.
E
1.
E
1.
E
3.
E
2.
6400
00
4400
03
4400
03
0000
00
9072
02
7133
E-01
2.
E
DESIRED UNIT,
E-XX MEANS
10
0643
04
MULTIPLY
TO THE -
2.2113
E-02
3.6855
E 00
3.6855
E 00
2.5594
E-03
1.0000
E 00
6,9445
E-04
3.2833
E 01
THE GIVEN
XX POWER.
3.1843
E 01
5.3071
E 03
5.3071
E 03
3.6855
E 00
1.4400
E 03
1.0000
E 00
7.6079
E 04
VALUE BY
4.1855
E-04
6.9758
E-02
6.9758
E-02
4.8443
E-05
1.8928
E-02
1.3144
E-05
1.0000
E 00
THE FACTOR OPPOSITE THE GIVEN UNITS
------- |