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P.2 

i^m-M-5-m 

WORKBOOK 

OF 

ATMOSPHERIC DISPERSION 

ESTIMATES 

H 

/ 

U.S. ENVIRONMENTAL PROTECTION AGENCY 

»^^iw$i|j§^;. i^S 
P.3 

WORKBOOK OF 

ATMOSPHERIC DISPERSION ESTIMATES 

D. BRUCE TURNER 

Air Resources Field Research Office, 

Environmental Science Services Administration 

V" 

ENVIRONMENTAL PROTECTION AGENCY 

Office of Air Programs 

Research Triangle Park, North Carolina 

Revised 1970 

y 

_"___! 

- •^v^wi-'i.3t%.',^Spji ">i*%S^^-f» ~ ^"«^^>,§S^rfc!;i. •^•kj&Sv-* 

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y" 

The AP series of reports is issued by the Environmental Protection 

Agency to report the results of scientific and engineering studies, 

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

Information presented in this series includes coverage of intramural 

activities involving air pollution research and control technology 

and of cooperative programs and studies conducted in conjunction 

with state and local agencies, research institutes, and industrial 

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

as supplies permit - from the Office of Technical Information and 

Publications, Office of Air Programs, Environmental Protection 

Agency, Research Triangle Park, North Carolina 27711, or from the 

Superintendent of Documents. 

) 

6th printing January 1973 

Office of Air Programs Publication No. AP-26 

For sale by tbe Superintendent of Document*. U.S. Government Printing Office, Washington, D.C. 20*03 - Price 11.00 

Stock Number WB-OOU 

A* i i 

J 

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P.5 

PREFACE 

This workbook presents some computational techniques currently used by scientists 

working with atmospheric dispersion problems. Because the basic working equations are 

general, their application to specific problems usually requires special care and judgment; 

such considerations are illustrated by 26 example problems. This workbook is intended as an 

aid to meteorologists and air pollution scientists who are required to estimate atmospheric 

concentrations of contaminants from various types of sources. It is not intended as a complete do-it-yourself manual for atmospheric dispersion estimates; all of the numerous complications that arise in making best estimates of dispersion cannot be so easily resolved. 

Awareness of the possible complexities can enable the user to appreciate the validity of his 

"first approximations" and to realize when the services of a professional air pollution meteorologist are required. 

Since the initial publication of this workbook, air pollution meteorologists affiliated 

with the Environmental Protection Agency have turned to using the method of Briggs to determine plume rise in most cases rather than using the plume-rise equation of Holland as set 

forth in Chapter 4. The reader is directed to: 

Briggs, Gary A. 1971: "Some Recent Analyses of Plume Rise Observations." 

In: Proceedings of the Second International Clean Air Congress. Academic Press, 

New York, N. Y. pp 1029 -1032 

and modified by 

Briggs, Gary A. 1972: "Discussion, Chimney Plumes in Neutral and Stable 

Surroundings." Atmospheric Environment, 6:507-510. 

/ V M * 

v*. .-•*"•;.•, •.'',-'.'",v'iifc.'..v.-JS'-- i»^r;,-'!'ii

,

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P.6 

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 discussions and review; to Jean J. Schueneman, Chief, Criteria and Standards Development, 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. 

3 

r IV 

) 

•.•U*.^g!1 
CONTENTS 

P.7 

/ 

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 Continuous 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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P.8 

Chapter 1 — INTRODUCTION 

NOTE: SEE PREFACE TO THE SIXTH PRINTING ON PAGE iii. 

During recent years methods of estimating atmospheric dispersion have undergone considerable 

revision, primarily due to results of experimental y 

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. Turhulence induced. b__ buoyancy_iorces 

in the atmosphere is closely related to the vertical 

600 

temperature structure. When temperature decreases 

with height at a rate higher than 5.4°F per 1000 ft 

(J'C P^r

 ir'Q meters), the atmosphere is in unstable equilibrium and vertical motions are enhanced. When temperature decreases at a lower 

rate or increases with height (inversion), vertical 

motions are damped or reduced. Examples of typical variations in temperature and wind speed with 

height for daytime and nighttime conditions are 

illustrated in Figure 1-1. 

500 -

400 -

E 300 -

200 -

100 

-10 ] 2 -3 4 5 6 7 8 9 10 11 12 0 I 

TEMPERATURE, °C 

2345678 9 10 11 

WIND SPEED, m/sec 

Figure 1-1. Examples of variation of temperature and wind speed with height (after Smith, 1963). 

r 

The transfer of momentum upward or downward_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 fewmeters). In addition to thermal turbulence, roughness 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. J 

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 transport) by turbulence is a major factor in the dispersion process. 

The procedures presented here to estimate atmospheric dispersion are applicable when mean wind* 

speed and direction can be determined. J.ut measurements of turbulence" such aa tht* standard deviation of wind direction fluctuations, art* not-available. If such measurements are at hand, techniques 

such as those outlined by Pasquill (1961) are likely 

to give more accurate results. The diffusion param-

-' «f«*«. '^"ft.-!-"''."- '"* '-fk'3^"'^'; 

• -. iJ^fi^JT'7 
P.9 

eters; pi______ted here are most applicable to groundlevel <nr Brow-level releases (from the surface to about 

•> metes]),, although they are commonly applied at 

.ghar dictations without full experiments olidation.. Itt is assumed that stability is the same 

throag$_a__t the diffusing layer, and no turbulent 

transfer occurs through layers of dissimilar stability 

characteristics. Because mean values for wind directions __s__l speeds are required, neither the variation 

of wind speed nor the variation of wind direction 

with fi___^_t Jn the mixing layer are taken into account. TTiais usually is not a problem in neutral or 

unstaftfe {eg., daytime) situations, but can cause 

oyeg^^taBBations of downwind concentrations in 

stabile ramditions. 

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 atmosphere, 15 pp., Brookhaven Lecture Series, 

No. 24, 13 Feb 63, BNL 784 (T-298) Brookhaven National Laboratory. 

^ 

6 GD©n— URBAN AREA SUBURBS LEVEL COUNTRY 

) 

0. 

Figure 1-2. Examples of variation of wind with height over different size roughness elements (figures are percentages 

of gradient wind); (from Davenport, 1963). 

r J 

ATMOSPHERIC DISPERSION ESTIMATES 

•- -*,. ..... ,*v * St-'ttfri-' 
/ 

P.10 

Chapter 2 — BACKGROUND 

For a number of years estimates of concentrations were calculated either from the equations of 

Sutton (1932) with the atmospheric dispersion 

parameters Cr, C„ and n, or from the equations of 

Bosanquet (1936) with the dispersion parameters 

p and q. 

Hay and Pasquill (1957) have presented experimental evidence that the vertical distribution of 

spreading particles from an elevated point is related to the standard deviation of the wind elevation angle, aK, at the point of release. Cramer (1957), 

derived a diffusion equation incorporating standard 

deviations of Gaussian distributions: g. for the 

distribution of .material, in.ihgj>liime_..acrQSSJfflind. 

in_the horizontal, and <r, for the vertical distribution 

Qjjnaterial in tjhejpjume." (See "Appendix 2 for properties of Gaussian distributions.) These statistics 

were related to the standard deviations of azimuth 

angle,YTA7 and elevation angle, (oi?t calculated from 

wind measurements made wi__f a bi-directional 

wind vane (bivane). Values for diffusion parameters based on field diffusion tests were suggested 

by Cramer, et al. (1958) (and also in Cramer 1959a 

and 1959b). Hay and Pasquill (1959) also presented a method for deriving the spread of pollutants from records of wind fluctuation. Pasquill 

(1961) has further proposed a method for estimating 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. Suggested curves of height and angular spread as a 

function of distance downwind were given for several "stability" classes. Gifford (.1.961) converted 

Pasquill's yalue_L_of__ahgular spread and _iei%ht into 

standard ..deviations jof.. plume_^ijcentratiqrL.di5tributjon, vyand_aK Pasquill's method, with .Gifford's 

• conversion incorporated, is used in this.workFook 

" (see Chapter,3) fbTHiffusiorT estimates. 

Advantages of this system are that (1) only two 

dispersion parameters are required and (2) results 

of most diffusion experiments are now being reported 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 stability. If the dispersion parameters from a specific 

experiment are considered to be more representative 

than those suggested in this workbook, the parameter 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 estimating the dispersion of atmospheric contaminants. 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 meteorological 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 dispersion. 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 Atmospheric 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 windborne material. Meteorol. Mag., 90,1063, 

33-49. 

Sutton, 0. G., 1932: A theory of eddy diffusion in 

the atmosphere. Proc. Roy. Soc, A, 135, 143-

165. 

Background 

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vSSET-
P.11 

Chapter 3 —ESTIMATES OF ATMOSPHERIC DISPERSION 

r 

/ -. 

( 

This chapter outlines the basic procedures to 

be used in making dispersion estimates as suggested by Pasquill (1961) and modified by Gifford 

(1961). 

COORDINATE SYSTEM 

j \ In the system considered here thejKigvn ifi„at 

i j jyoundJevel at or beneath „the .point._of emission, 

' \ with the x-axis"extending horizontally in the~direction of the mean wind. The y-axis is in the horizontal 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 ?a^2L_L§£2_£Js__E5#i" 

cle_sJessJhan_a,bautJffi.jnQte 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 

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 distribution in the horizontal and vertical of o> and or,, 

respectively; the mean wind speed affecting the 

plume is u; the uniform emission rate of pollutants 

iS Q; and totaj refWtir.l "* +h° plnmo + _V____plgrp 

at .the earth.'?; surface, j.e., there is no deposition 

or reaction at the surface (see problem 9). 

%*.' x (x,y,z;H) Q 

exp 

z-fH 

I'M 

•)•] ! 

2ir <xT oyU 

z-H 

°_ 

M-M^Y] 

r ] + < *

p

 [-

i 

2 

(3.1). 

*Note: exp —a/b = e -» / b where e is the base of natural logarithms 

and is approximately equal to 2.7183. 

,-y,Z ) 

(x,-y,0) 

Figure 3-1. Coordinate system showing Gaussian distributions in the horizontal and vertical. 

Estimates 

----i_____3_r:'

; 
P.12 

Any consistent set of units may be used. The most 

commo n is: 

X (g m~3) or, for radioactivity (curies m~3) i" 

Q (gsec-1) or (curies sec-1) '/ 

u (msec-1) Y 

<r}, oz, 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 Sutton'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. 

\ is a mean over the same time interval as the time 

interval for which the o's and u are representative. 

The values of both JJV and a_ are evaluated in terms 

of the downvyind distance, x. 

Eq. (3.1) is valid where diffusion in the direction of the plume travel ca_TL.be neglected, that is, 

n^_iig_i§i2____n. the_xjJireciipn. 

• >, This may be assumed if the release is continuous 

:

' or if the duration of release is equal to or greater 

i,than the travel time (x/u) from the source to the 

location of interest. Y< •'',,...,,, - ;->-o~---- *£"*•• -': 

For concentrations calculated at ground level, 

i.e., z = 0, (see problem 3) the equation simplifies 

to: 

x (x,y,0;H) = 

Q 

T Oy <7, U exp 

-[-i(-^r] 

[-M-i-Y] 

(3.2) 

Where the concentration is to be calculated 

along the centerline of the plume (y = 0), (see 

problem-2) further simplification results: 

x (x,0.Q:H) = -

Q 

Vy Oz U I exp [-Mm _i \ Or J > 1(3.3) 

For a ground-level source with no effective plume 

rise (H = 0), (see problem 1): 

Q 

rr o-y o- U (3.4) x (x,0,0;0) = 

EFFECTS OF STABILITY 

The values of ay and az vary with the turbulent 

structure of the atmosphere, height above the surface, 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 

. surface to be relatively open country. The 

bulent structure of the atmosphere and wind 

.eed are considered in the stability classes presented, and the effect of distance from the source is 

considered in the graphs determining the parameter 

values. Values for oy and o, are estimated from the 

stability of the atmosphere, which is in turn estimated from the wind speed at a height of about 

10 meters and, during the day, the incoming solar 

radiation or, during the night, the cloud cover (Pasquill, 1961). Stability< categories .(in six classes) 

are given_JnJX'ablL-___l'.' Class "A is the most unstable, clas$ F the mp^f, ptflhliT class rnr^iriWfiHj liftrft. 

*"" "'"refers to the period from 1 hour before sunset 

to 1 hour after sunrise. Note that the neutral 

class, D, can be assumed for overcast conditions 

during day or night, regardless of wind speed. 

Table 3-1 KEY TO STABILITY CATEGORIES 

Surface Wind 

Speed (at 10 m), 

m sec- 1 

< 2 

2-3 

3-5 

5-6 

> 6 

Day 

Incoming Solar Radiation 

Strong 

A 

A-B 

B 

C 

C 

Moderate 

A-B 

B 

BC 

C-D 

D 

Slight 

B 

C 

C 

D 

D 

Night 

Thinly Overcast 

or 

2=4/8 Low Cloud 

E 

D 

D 

D 

-=3/8 

Cloud 

F 

E 

D 

D 

The neutral class, D, should be assumed tor 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 35c with clear skies. Table 170, Solar 

Altitude and Azimuth, in the Smithsonian Meteorological Tables (list, 1951) can be used in determining the solar altitude. Cloudiness will decrease 

incoming solar radiation and should be considered 

along with solar altitude in determining solar radiation. Incoming radiation that would be strong 

with clear skies can be expected to be reduced to 

moderate with broken (% to % cloud cover) middle 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 represeqfotiye indica- J 

tionISs of i^flhility. rarer .nppn rnnntty nr r^ral arpaa, J 

hut «ry |P_B rplighlo fnr nr h?" „rfye This differ- i 

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 unstable or near neutral to a height several times the 

average building height, with a stable layer above 

(Duckworth and Sandberg, 1954; DeManais, 1961). 

" ^ 

' ) 

J 

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ATMOSPHERIC DISPERSION ESTIMATES 

•>#5&Y 
P.13 

Some preliminary results of a dispersion experiment in St. Louis (Pooler, 1965) showed that the 

dispersion over the city durij_g_J__e*daytime-behaved 

somewhat like types B and Ci_for_pne_night experiment o, 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 or and 

o, as a function of downwind distance from the 

source, x, using Figures 3-2 and 3-3. These values 

of ov and rr,. are representative for a sampling time 

of about 10 minutes. For estimation of concentrations for longer time periods see Chapter 5. Figures 

3-2 and 3-3 apply strictly only to open level country 

and probabh.^_underestimate the. jlume__dispei__ion 

potential.Jrbm lo.w.-Jevel.sources-_Q_built;.up_areas. 

Although the vertical spread may be less than the 

values for class F with very light winds on a clear 

night, quantitative estimates of concentrations are 

nearly impossible for this condition. With very light 

winds on a clear night for ground-level sources free 

of topographic influences, frequent shifts in wind 

direction usually occur which serve to spread the 

plume horizontally. For elevated sources under 

these extremely stable situations, significant concentrations usually do not reach ground level until 

the stability changes. 

A stable layer existing above an unstable layer 

will have the effect of restricting the vertical diffu 

sion. The dispersion computation can be modified 

for this situation by considering the height of th 

base of the stable layer, L. At a height 2.15 oL 

above the plume centerline the concentration is onetenth the plume centerline concentration at the same 

distance. When one-tenth the plume centerline 

concentration extends to the stable layer, at height 

L, it is reasonable to assume that the distribution 

starts being affected by the "lid." The following 

method is suggested to take care of this situation. 

Allow o_ to increase with distance to a value of 

L/2.15 or 0.47 L. At this distance x_, the plume is 

assumed to have a Gaussian distribution in the 

vertical. Assume that by the time the plume travels 

twice this far, 2 x_, the plume has become uniformly 

distributed between the earth's surface and the 

height L, i.e., concentration does not vary with 

height (see Figure 3-4). For the distances greater 

than 2 xi„ the concentration for any height between 

the ground and L can be calculated from: 

X (x,y,z;H) =—= • Q 

(*)'] 

\/2?r Oy L u 

exp 1-+ 

(3.5) 

i 

(see problem 6). Note that Eq. (3.5) assumes normal or Gaussian distribution of the plume only in 

the horizontal plane. The same result can be obtained from the following equation where o._ is an 

effective dispersion parameter because \/2*r L = 

2.5066 L and 0.8 *L — 2.51 L. 

x (x,y,z;H) = — ^ — - [ exp 1—(-^—^)=

 1 

T Oy OlL U |_ I \ (Ty j J 

(3.6) 

for any z from 0 to L 

for x

 >2„L; xf

, is where o. 

The value of o_„ = 0.8 L 

0.47 L 

from any z from 0 to L 

for x >2 xL; xr. is where <r, — 0.47 L 

EVALUATION OF WIND SPEED 

For the wind speed, u, a mean through the vertical extent of the plume should be used. This 

would be from the height H — 2 o. through H -+-

2 oz. Of course, if 2 o. is greater than H then the 

wind can be averaged from the ground to H -j- 2 oz. 

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 ^'"^ggffin."TM i"gjffh+ *"*" a diffusion problem it is often desirable to plot centerline concentrations against distance downwind. A convenient 

procedure is to determine the ground-level centerline concentrations for a number of downwind distances and plot these values on log-log graph paper. 

By connecting the points, one may estimate concentrations for intermediate downwind distances 

(see problem 6). 

ACCURACY OF ESTIMATES 

Because of a multitude of scientific and technical 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 o, 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 atmosphere with a marked inversion above for distances 

out to 10 km or more. Uncertainties in the estimates of oy are in general less than those of o,. 

The ground-level centerline concentrations for these 

Estimates //7 f Wltii,/ ^ t, <h. *•• (Coe^s &*-* /i 4 . i -'* . 

fa I O-r^rU^ "> 

• y»-iiy ,.--.; "it-J:-i-Srifiii.(..- •-: •:.• •..;' . -y:.<rig,-< ;-.-..•: .'.V :•>..\-.fc.vV . . •.•JiwSjjfriSsy.;' •;'-'« .-.-:.*••'..-,;.• "-. .-•* .s 
P.14 

7y WiVt. ' /Y-/,';»'-<.'J''>'.;" •/. / . "ir *sAMj>llfiil> T/r'-tC 

Or /i&OuT 10 W-Ji/Tif 

>000r .„_„p_j|j^l{.:li&^ ^ 

•» •&" .fe 7 6 V 1 

DISTANCE DOWNWIND, km 

Figure 3-2. Horizontal dispersion coefficient as a function of downwind distance from the source. j 

ATMOSPHERIC DISPERSION ESTIMATES 

- *..-• -Y-y.jii'y;;;^. ^ 
P.15 

Ss}x>< ..«;_•._ A : SN t-t* ~

m

.mi 

/,.-••'.c / H->\;I~. 

1,000 

s3= 

;niv;:;,^M_ll__|p5r^

3 ij'.-.._v:J.i.ii^.,:i—.{.:. * .__...-...ii. 

""•:— -TT!?":: 1—;~':,I, ~j Jf?:~^"??V*'l!."'r':7'.•'"'"" "'::,~,

-TM":'*''''"•/* I "j',1" " '' 1:11.11"? ^rH~~~~.*r:i::r! .Ir -1 " . VI .TI i.lTrHY.'.ill."-"--! "JffLJ.I j:r'::i~:~l~.llll-L 

3ESE Egg5=§^ip 

J_^I -

p_^-_^..^..._^r:::-:::j::::::_[::^-.jz;pf:}: 

2 3 -S 5 - -

7

-*-f\ *- J W ' £ fc 7 _-?l( 

DISTANCE DOWNWIND-, km 

100 

Figure 3-3. Vertical dispersion coefficient as a function of downwind distance from the. source. 

Estimates 

339-901 O - 89 - J 

__h 

vW^tc'WjKyt'ty^l. " :. *~ •.•m^yrm -, ^mig-*%-mW*mJ^^^~x.^.r>v^.^fi,.m....*: 
P.16 

y~ 

Figure 3-4. Variations in concentration in the vertical beneath a more stable layer. 

:> 

/ 

three cases (where o. can be expected to be within 

a factor of 2) should be correct within a factor of 3, 

including errors in _-}- and u. The relative confidence 

in the o!s (in decreasing order) is indicated by the 

heavy lines and dashed lines in Figures 3-2 and 3-3. 

Estimates of H, the effective height of the plume, 

may be in error because of uncertainties in the estimation of AH, the plume rise. Also, for problems 

that require estimates of concentration at a specific 

point, the difficulty of determining the mean wind 

over a given time interval and consequently the 

location of the x-axis can cause considerable uncertainty. 

GRAPHS FOR ESTIMATES OF DIFFUSION 

To avoid repetitious computations, Figure 3-5 

(A through F) gives relative ground-level concentrations times wind speed (\ u Q) against downwind distances for various effective heights of emission and limits to the vertical mixing for each stability class (1 figure for each stability). Computa-

"->ns were made from Eq. (3.3), (3.4), and (3.5). 

timates of actual concentrations may be deternined by multiplying ordinate values by Q/u. 

10 

-'.»*k;.-£••--. -.-4i-jB$itU?, 

PLOTTING GROUND-LEVEL 

CONCENTRATION ISOPLETHS 

Often one wishes to determine the locations 

where concentrations equal or exceed a given magnitude. First, the axial position of the plume must 

be determined by the mean wind direction. For 

plotting isopleths of ground-level concentrations, 

the relationship between ground-level centerline 

concentrations and ground-level off-axis concentrations can be used: 

x (x,y,0;H) 

x (x,0,0;H) = exp l-H*.*! (3.7) 

The y coordinate of a particular isopleth from the 

x-axis can be determined at each downwind distance, x. Suppose that one wishes to know the 

off-axis distance to the 10~a g_m~3 isopleth at an x 

of 600 m, under stability*?ypeB7where the groundlevel centerline concentration at this distance is 

2.9 x 10-3 g m-3. 

-[-W]- x (x,y,0;H) 

x (x,0,0;H) 

10"= 

. . *-' 

2.9 x 10-3 0.345 •-O 

/ «.c 

s i cl 

ATMOSPHERIC DISPERSION ESTIMATES 

> i ' 

t Y. 
P.17 

X 

HT 

% 

1 0 " 

,'.!I.U'-r.l,.!.,-ljiV.'-„'-,!.T.'1- !'..'.!'.....'*!< ?.'. . •' .'"!" - .x. -.u__.- yx/,\-.-,,. ..-••-. 

n?rar;ti_itm!r.i_s^^ .•••.EgjgpigEr] saf§_*M :-Ty-imm ".!]—-*i!__T!.JI \\!if , •l

|r.;!h^;:!i:-i:_;_'-;-_!.|:^iP;_i:g^- i.i ..! rr-:i':i/.f'";|!'.:|.^J}_"'J';'Mj"-r^;-^;;^ [ ^{-,.11?! 

8^'vCffi: i tr_;p_5_B ViV: _1if!f; • _ LI _. I! •. F!l! I Vvlifffejllfel^-j T_|i'vj"l il 

w;_a.)?tfiffilUPii§ffi^ fnf Ifr f^-^-v 

*sa. 

___; 

i:::_.:::!:__i:_i:::::.::Lti 

'n—frtT^;"'':: " Y--:;

:::f ^"-H ^ 

*a»iiJI 

::i:V:#a_!_ 

: |- : ••:..=!• . 

i i 

10' 

E 

O 

10"S -33 = 

IO10" 

100 

DISTANCE... 

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

Estimates 

*2ggjg*Y; . . - -._._-. _ t •; m 
(, 

IOO 

". 

/ DISTANCE, km 

Figure 3-5B. vu Q with distance for various heights of emission (H) and limits to vertical dispersion (U, B stability. 

12 ATMOSPHERIC DISPERSION ESTIMATES 

*m& :i^Slfc; -'.L&»y 
P.19 

•"' 

100 

( 

DISTANCE. k> 

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

Estimates 

•.•^.rm^mm.. - - - -

vija^i^. . ^.yti&ry... ••.:. 
P.20 

f~ 

£~ 

( 

liuiyillliffllliii'illig 

DISTANCE, km 

igure 3-5D. ,vu Q with distance for various heights of emission (H) and limits to vertical dispersion (L), D stability. 

J 

14 

<mmx- £$$#£;•:.•-

ATMOSPHERIC DISPERSION ESTIMATES 

___^--
P.21 

( 

IOO 

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 

j^i^Viis.f-rJ--
r 

7-t ry 

DISTANCE, km 

} 

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

16 ATMOSPHERIC DISPERSION ESTIMATES 

.\.:.'4si«Ss'-.. :-^r«SS£.»:-

-S-iilfSJii'A,.-?- iJ^Utii,. L... 

. V 1 .,—^mf.l.' ..... . •..•^^.ym*^..'m:.^m.'.it^m. f •.^-•^'~--..^.m\m^v^^^.^l<^m^-ym*''*^'' _^*P'—iSt^*"''^ -

irr^WTP—m — 
r • 

P.23 

r~-& 

r 

B__onm TTaiHe A-1 (Appendix 3) when exp 

-Mi)'] 0.345 

Fmanm ffigpse 3-2, for stability B and x = ,6p0 m, oy 

= S_L T__H_sefore y = (1.46) (92) =Q34. meters. 

Tinas is ti&ffi distance of the IO-3 isopletiTfrom the 

S-O___E am aa downwind distance of 600 meters. 

also be determined from: 

F — 

[2 2n*[ x (x,0,0;H) 

X (x,y,0;H) (3.8) 

TTBBE passion corresponding to the downwind disaxis distance can then be plotted. 

AffibHr <& _Q_i___ber of points have been plotted, the 

aaiiimenntarfiiDn isopleth may be drawn (see problems 

ffi a_n_l 2S;. - Figures 3-6 and 3-7 give ground-level 

TforgjrJV'tffl"* «s£ jru/Q for various stabilities for sources 

a t H = 0 and H = 100 meters. For example, to 

HcwaBte iflbe 10~3 g m"3 isopleth resulting from a 

g3imiai____r__sw_i source of 20 g sec"1 under B stability 

<nn_«____i_a_)s with wind speed 2 m sec"1, one must 

festtdaEttemnsiae the corresponding value of \u/Q since 

__n_s fe t_J_£ quantity graphed in Figure 3-6. xu/Q = 

l©-"1 __ 2/;'20 = 10~4. Therefore the xu/Q isopleth 

im FSgnine 3-6B having a value of 10~4 m-2 correarf«pmi#»! tt© a x isopleth with a value of 10"' g m~3

. 

ABEAS WITHIN ISOPLETHS 

]F%i__te3-j. gives areas within isopleths of groundheight, the product u o-y <J_ will not change appreciably. The greater the effective height, the more 

likely it is that the stability may not be the same 

from the 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 assumptions, 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 considprfltion. so 

thatj 

(iii) The equation of continuity: 

/ + 30 l+X 

Q = / / x u dy dz (3.9) 

atration in terms of x u/Q f°r a ground- I 

for various stability categories (Gifford ' 

1962; Hiiaaaeier and Gifford, 1962). For the exam 

pile _wsAt given, the area of the 10~3 g m~3 isopleth; 

(1©""" mnT- x u/Q isopleth) is about 5 x 10* meter2-! 

CA1COJLATION OF MAXIMUM 

GEOUMM.EVEL CONCENTRATIONS 

yfetnme 3-9 gives the distance to the point of 

nn__x_in______ concentration, xmnx, and the relative maxi-

__n_s_ concentration, x u/Q„„_, as a function of 

e_£etit_TO£ height of emission and stability class 

(Ma_it_B, 1965). This figure was prepared from 

g_ajj__B of concentration versus distance, as in Figure 3-5L The maximum concentration can be determined by finding x u/Q as a function of effective 

esssissBMHB height and stability and multiplying by 

Q/BL In using Figure 3-9, the user must keep in 

mind t&at the dispersion at higher levels may differ 

co__6M_erably from that determined by the <ry's and 

o_*s used here. As noted, however, since o> generally decreases with height and u increases with 

**H_T denotes natural logarithms, i.e., to the base e. 

is fulfilled, i.e., none of the material emitted is removed from the plume as it moves downwind and 

there is complete reflection at the 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 <r's given in Figures 3-2 and 3-3 represent time periods of about 10 minutes. 

REFERENCES 

DeMarrais, G. A., 1961: Vertical temperature difference 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 dispersion. Nuclear Safety, 2, 4, 47-51. 

Gifford, F. A., 1962: The area within ground-level 

dosage isopleths. Nuclear Safety, 4, 2, 91-92. 

Estunates 
P.24 

X 

( 

S 

o 

o 

03 

«_> 

O 

CO 

~Q3 

OJ 

O 

eo 

K 

o 

<=_ . O v. 

) 

""I '(*) 33NV1SI0 ai.l_lS.0H3 J 

18 

. i^&iym.. 

ATMOSPHERIC DISPERSION ESTIMATES 

.*<f&^l*t!Y* 
61 

''•". vS_J.S3^li>? , f. ••"'•• '• -^t^*«*>'-

sa^Buip_3 

CROSSWIND DISTANCE (y). lim 

C0 

CO 

CT> 

OD 

sr 

o 

C__D . 

= p 

CO 

e 

X 

es N 

O 

o 

—^ 

ai 

OQ 

o 

c= 

s Q . 

CB 

< ro 

^~ on 

o 

cr TM * 

«•> 

CD 

OO 

CA 

o 

o 

£ 

z 

o 

e 

V * 

^ > 

t-» 

J — L 

X 

3 
P.26 

y 

X: 

1 ' , ! • . 

H Mil 

•••• i ! 1 ' 

xrf^—.—' : I '. ! 

1

 . : 1 ] : ; 

, •• . . • I : : 

i • 

. -,I:V : 

I 

t 

1 ' • • 

I 

; i • • r • i 1 j • i - . ! .. 

i 1 j I ' •' : *' 

11 i =^o :" 

i i ' 1 . , ! ! ' 

"I 1 ' • • ' •• 

I'll ; ! i 1 ; i ; i i i-

• 1 . ' ! 1 i 

1

 • • •', ' i • 

1 1 ! 1 : i i i ' 1

 i ' 1

1 ; • ' • 

; : • '

 : : 

i •••;] • 

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i ' • i : ! ' ! ' I ! ! ! 1 : • 1 

1

 i;'' '• 11 

arriv e 

\ \ \i i : . 

• V ' ' \ 1 ' 

i i \ ' i \-L . 

\ • • V 

' 1 ! • i ! ! ' \ 

!

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1

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' ' : i ; ! \ ; ! 

; • • ( • i i ; 

•••-i'i ; 

, • i • ' 

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:

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: . < 1 1 . I 1 

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' 1 : . • • , . 

• : • ( . i : ; • 

1

 ! • • ' •_ . ••'•' , 

'• 1 i h - •''•' * 

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: • —1 ' ' i ' 

' • '1 • CD 1i i ] • ! 

. , ! ! , «_ • .... . 

< • . 1 . .'.'• ! 

try 

• j ; O ' • i ! 

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. . : 1 </l ' ! . ] ! 

: , i , . * T i 

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1 i • i t \ '• • -1 : . 

; ' • : • i • i 

1 ' ; 11 i 11 ! 

' 1 ' i' i 

- — ~ 'T 

.,... , | . 

' • = ... . ' 1 ' '•' ' 

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— 1 1 ' ' 1 f r-i-

<Si ; T.-T+Ttt 

_.^Q1—0.._.,._i.» . .tj r ;_u_;.;. 

-i-\-i-t-r—\- — 

• t \ .LVJ-

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1 V j : •V • : 

t ' \ ; .;„\,,. - i 

i ! • • • • ' i 

i,i ! j! , ... ! 

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L".

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*\r-^L\H-r 

rr~~JV rt~\"i" 

• - y i IV ; ,i 

• : ; 1 \ 

..ill 1 

I 

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-t- H 1 . : •; : 1 ; i | ; 

• "''..'. ' 

; • • ; • . i J 

.Iirtx _.\Y" 

rV.-.-^.rt" 

p;ynnl(^ 

T'-V-!'! i+Tl 

-\ -^V-t— 

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v \ " \ ~ 

-r-n,''ir!\-\ 

1

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! ! I ! : : ! | j 

LxnA 

;.-Y-i> 

• i-'-i-.-•-

.\-fl;Ti HJ: 

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r

k

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V-i-H-Vfr 

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JL-CA-X- , 

liW l V 

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1

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1 , __.! „• \ i 

• ^ — V— ' — • • 

. ; . . i.| i \ i 

i-r_r.r.»--t 

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y-\-L>-n4-r^tit 

4 i \ • i M 

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I 

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i -

l-f 

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. : : . 

. . l- l 

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\

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\ 1 

: :1 .1 

1

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\ \ , 1 . 1 

1 

\ ' \ '• ] I 1 

\

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\ • \ • i • , 

\ I 

^Xfrjf 

11M i ' i •" 

•t+t^^H 1 . ! • • • • 

I •; 1 ! -~ 

1 ! ! !•+. — Y 

.1+1^14 !. 

|i '1 ill ' 

4-.t.-_a!. 

i : i. r — 1 ' : 1 "tJX 

• ! It 7——m 

I • ' ! : •:._•-'-

!! ; 1 ! ! IC. 

1

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! 1 i ' 

• - — 

1 1 : - : • • • 

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i • ; . . n u 

1 : • : '_! 

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K | 

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ll> •' 

-•O-

"ih T 

^ i 

' ; • " 

• ' ' , r 

i • ' ' in ' •' 

• • ' ' ,V»v 

T;'' 

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\ \ \\ A A A \ •: I :

W

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W\

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\\\\ \ \ \ \- V • l / \ \ \ \ \- \ \! \ \ II 

• 

•!6 -

-TVT' 

U"> 

;,; X-rV^W^ - *>< 

;

' ' i i ' ! ' i • =i.-Uv " 

1 • ! ' ' i ! ! ' 1 s< \ 

..:. . | • | . - , • f ^ 

> 

> 

> » 

> 

> 

*r* 

) 

) 

) 

) 

) 

IO 

O 

— 

1 o 

DOWNWIND DISTANCE (>). km 

^ 

(-> e— 

m 

O 

_3 

CO 

!_. o «*~ 

o 

X 

o 

-£_ 

O) 

l^i 

CJ5 

U3 

C O 

t_0 

•"1 (*) 3.NV1SIQ 0NIMSS0JO . 

20 

A^.i&^T'rc^---

ATMOSPHERIC DISPERSION ESTIMATES 
P.27 

'. 

f 

W 

—C 

M 

u. 

Z 

X 

£ 

z 

¥ 

o 

o 

<T3 

CO 

O 

fc <_u > 

= 3 

O 

CO 

a> 

a> > 

• a 

c= 

= o 

ao 

ca 

»_, o 

a 

3 

X 

^_ o 

CO 

-c: 

a> 

o . 

o 

oo — 

Q 

t o 

m 

a> 

oa 

""I '<*) 33NViSI. ONIMSSOW 

Estimates 

,%fifci*ii*.^ ~ :

'';- '.y*?y- .<-~»fc.i5-;JB£t».... - :-»»ij»4_Vi« 

";•;". vYS^~ " •'•• ••Skj?.i»-'. 

21 
i 

S-3 

z 

S 

> 

3 « 

DOWNWIND DISTANCE (>), km 

£•• ! > 

P

;

.IT

 H 

ti?-'' 3 

< .'; o m •fl 

S 

M % M 

i O *l| 

>•. 0 

*fl K TS 

9 CA 

"" _fci__*" . * 

:R 

DOWNWIND DISTANCE («), km 

H 

W Figure 3-6E, F. Isopleths of xu/Q for a ground-level source, E and F stabilities. 

O U 
'. :::.->*_•;.? ^'^."^"^M'ffSS. ;--•;^».^t»'fr-.i 

ez sajuuiijsg 

CROSSWIND DISTANCE (y), km 

ro 

CO 

o 

X 

"V. 

0 

o 

cu 

c/» 

o 

c= 

o 

ro 

s <=> 

3 

ro rm** 

ro 

-. </> 

*-

& *-

£ 

z 

o 

e 

-* > z *"i 

m 

• • " 

—-

3 

cr 
P.30 

ro 

in 

CO 

J=r 

BO 

E __ 

. "TJ 

U J 

Z 

< 

— o 

c. 

z 

NW 

£ 

o 

e> 

c/> 

»_cu . 

a> 

E 

o 

O 

*—* 

o 

o 

_=_ 3 

O 

</> CO 

o 

**~ O 

=3 

» j 

o 

t / . 

. e 

03 

a . 

o CO 

CD 

I - -

ro 

03 

~N 

""I '(<) 3DNV.SIQ QNIMSSO.D 

24 ATMOSPHERIC DISPERSION ESTIMATES 

.. . ~.-. ...&ii*tf>V. jljjgtl'Oi?.: -» - .-?'v*»*'-''--v:

r

:

-!--;.-^T>S,>i»-

_YY. ^ i. ;' .. 'ViS:

"';^i'-"Si-;'-'- - -~*--*SSY 
P.31 

/ 

. a 

E 

~* ANC 

**m 

*r* 

az 

S 

* ' • 

o 

a 

in 

»_O) . 

a> 

E 

cn 

o 

•—« 

a> 

o 

ZS 

O 

CO 

ca 

o 

a ^>. , 3 

O 

CO 

.CT 

<U 

" j ^ 

o 

CO 

a> 

ao 

Estimates 

31S-S0I O - 46 . 1 

" I '(*) 3DNV1SIQ .MMSSOH. 

25 

. >as#i__t^_.---'.-_. _-. &<£---.; "w*Vw^^-***_i;Yr 3S£--;*w-^. *'-V-.#^.^.-rJis-j« •y.i&'zi-'i-*'?'* sv* *'?.. :.rrS 

v^^S^-i •: .;.Si»i,:

i^-.f;: 
P.32 

-r-U - 1 H 

•••• — '• 

r4-

.~ "'"" ' 

. 1 

_._ 

—•• J 

."YrirznY" 

.. ...__. 

— --—•• -

- —;—!•.. . 

—— 

...-...•'.. I ..-:.. ' • '• - 1 

VX^X^l^liV^V^X-^-y^XaX:.-:^ 

.:.:::::.:-aiM'0 :'D:.0:6:'0 : :t>: ::' o -'O: : "'O1' 

£f~~rx7: WH 

_Y.Y__!.: .--:•:-\:-\ 

i.V."£Y-_H 

...:_.—. 

•::::_£H__ \ 

.zrlHrrE 

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, 

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li If 

TY..' :~; : fi 

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" 1 '( x) 3DNV.SI0 ONIMSSOHJ 

2G ATMOSPHERIC DISPERSION ESTIMATES 

. :.M*m.\r^.!>^:;.',Um-,:.m*m*^mpim..m. mim^*^^.... 

r" . ..-.-.-.::-A!.-,i:

:

-';.'-:-»;,-'.'-.-i '5 . .• •••••j?Sv.^ .C-V.-r^f-SjtjJJ.i^; : ...:''^--. 8i&»'--. 
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DOWNWIND DISTANCE («). km 

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- 4 Figure 3-7E, F. Isopleths of ,vu Q for a source 100 meters high, E and F stabilities. 
10' 

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Xu 

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2 

10" 

^ 

Figure 3-8. Area within isopleths for a ground-level source (from Hilsmeier and Gifford). 

Kilsmeier. W. F., and F. A. GifTord, 1962: Graphs 

for estimating atmospheric diffusion. ORO-545, 

Oak Ridge. Tenn. Atomic Energv Commission. 

10 pp. 

List, R. J.. 1951: Smithsonian Meteorological 

Tables, Sixth Revised Edition, 497-505, Washington. D. C, Smithsonian Institution, 527 pp. 

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

Pasquill. F., 1961: The estimation of the dispersion 

of windborne material. Meteorol. Mag., 90, 

1063, 33-49. 

Pooler. F., 1965: Personal communication. 

Sutton. 0. G.. 1953: Micrometeorology, New York, 

McGraw-Hill. 333 pp. 

Turner, D. B., 1961: Relationships between 24-

hour mean air quality measurements and meteorological factors in Nashville, Tennessee. J. 

Air Poll. Cont. Assoc, 11, 483-489. 

28 ATMOSPHERIC DISPERSION ESTIMATES 

~--._;~,:^y*^||^ ^ 
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Estimates 29 

^VW^tT&aj'lBijy^X^-^vt-r*.:*.. ^-"^J* ' -* ^-,,«y'^i •A-r-f.. i¥^§f*'*^r-^^.""; 

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^,£%i^i3_V 
P.36 

Chapter 4—EFFECTIV E HEIGHT OF EMISSION 

y" 

f. 

GENERAL CONSIDERATIONS 

In most problems one must estimate the effective stack height, H, ar 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, v.; temperature of the effluent at the top of the stack, Ts

; and 

diameter of the stack opening, d. The meteorological factors influencing plume rise are wind speed, 

u; temperature of the air, T.,; shear of the wind 

speed with height, du dz; and atmospheric stability. 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 

wouid seldom be available. Most of the equations 

that have been formulated for computing the effective 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 actual and calculated plume heights by means of six 

plume rise equations, report "There is no one formula which is outstanding in all respects." The 

formulas of Davidson-Bryant (1949), Holland 

(1953), Bosanquet-Carey-Halton (19.50), and Bosanquet (1957) all give generally satisfactory results in the test situations. The experiments conducted 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~M 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 equation frequently underestimates the effective height 

of emission; therefore its use often provides a slight 

"safety" factor. 

Holland's equation is: 

AH=-^A(l. 5 + 2.68xlO-=p-^=^-d ) (4.1) 

where: 

AH --= the rise of the plume above the stack, m 

v., = stack gas exit velocity, m sec_: 

d --=* the inside stack diameter, m 

u --= wind speed, m sec-1 

p = atmospheric pressure, mb 

T„ «= stack gas temperature, °K 

T. = air temperature, °K 

and 2.68 x 10-3 is a constant having units of mb-1 

m~l. 

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 effective stack height is an inverse function of wind 

speed as indicated in Eq. (4.1). The TnnYimiiTp 

ground-level concentration occurs at some intermediate 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 m_uri___um concentration 

as a function of wind speed is {dotted on log-log 

graph paper, curves can be drawn for each stability 

class; the critical wind speed corresponds to the 

point of highest maximum comcemtratian on the 

curve (see problem 14). 

ESTIMATES OF REQUIRED STACK HEIGHTS 

Estimates of the stack height required to produce concentrations below a given valine may be 

made through the use of Figure 3-9 by obtaining 

solutions for various wind speeds. Use «_§ this figure 

considers maximum concentrations at any distance 

from the source. 

In some situations high concGratraftmnis upon the 

property of the emitter are of little concern, but 

Effective Height 

«$£&&£?, 

31 
P.37 

maximum concentrations beyond the propert3' line 

are of the utmost importance. For first approxima-

' ons it can be assumed that the maximum concenition occurs where \/2".»-= H and that at this 

distance the a's are related to the maximum concentration by: 

Q 

x u e x-

= - 0.117 Q 

U ,\,„nx (4.2) 

Knowing the source strength, Q, and the concentration not to be exceeded xm«x> one can determine 

the necessary *rr *z for a given wind speed. Figure 

4-1 shows «rr az as a function of distance for the 

various stability classes. The value of <rT <r_ and a 

design distance, Xd (the distance beyond which \ is 

less than some pre-determined value), will determine a point on this graph yielding a stability class 

or point between classes. The a. for this stability 

(or point between stabilities) can then be determined from Figure 3-3. The required effective stack 

height for this wind speed can then be approximated by H = y ^ CT- (see problem 15). Since Eq. 

(4.2) is an approximation, the resulting height 

should be used with Eq. (3.3) to ensure that the 

maximum concentration is sufficiently low. If 

enough is known about the proposed source to 

allow use of an equation for effective height of 

emission, the relation between AH and u can be 

determined. The physical stack height required at 

the wind speed for which H was determined is H — 

.. The same procedure, starting with the deternation of o? a,, must be used with other wind 

speeds to determine the maximum required physical 

stack height (see problem 16). 

EFFECT OF EVAPORATIVE COOLING 

When effluent gases are washed to absorb certain constituents prior to emission, the gases are 

cooled - and become saturated with water vapor. 

Upon release of the gases from the absorption tower, 

further cooling due to contact with cold surfaces 

of ductwork or stack is likely. This cooling causes 

condensation of water droplets in the gas stream. 

Upon release of the gases from the stack, the water 

droplets evaporate, withdrawing the latent heat of 

vaporization from the air and cooling the plume. 

The resulting negative buoyancy reduces the effective stack height (Scorer, 1959). 

EFFECT OF AERODYNAMIC DOWNWASH 

The influence of mechanical turbulence around 

a building or stack can significantly alter the effective stack height. This is especially true with 

hi?h winds, when the beneficial effect of high stack-

"">s velocity is at a minimum and the plume is 

tted nearly horizontally. The region of disturbed 

/ surrounds an isolated building, generally to at 

least twice its height and extends downwind 5 to 10 

times its height. Building the stack 2.5 times the 

height of the highest building adjacent to the stack 

usually overcomes the effects of building turbulence 

(Hawkins and Nonhebel, 1955). Ensuring that the 

exit velocity of the stack gas is more than 1.5 times 

the wind speed will usually prevent downwash in 

the wake of the stack. Most of the knowledge about 

the turbulent wakes around stacks and buildings 

has been gained through wind tunnel studies (Sherlock and Lesher, 1954; Strom, 1955-1956; Strom, 

et al, 1957; and Halitsky, 1962). By use of models 

of building shapes and stacks, one may determine 

the wind speeds required to cause downwash for 

various wind directions. With a wind tunnel the 

meteorological variables most easily accounted for 

are wind speed and wind direction (by rotation of 

the model within the tunnel). The emission factors 

that may be considered are the size and shape of 

the plant building; the shape, height, and diameter 

of the stack; the amount of emission; and the stackgas velocity. 

Through wind tunnel studies, the critical wind 

speeds that will cause downwash from various directions can be determined for a given set of plant 

factors. The average number of hours of downwash 

per year can then be calculated by determining the 

frequency of wind speeds greater than the critical 

speeds for each direction (Sherlock and Lesher, 

1954) if climatological data representative of the 

site are available. 

Maximum downwash about a rectangular structure occurs when the direction of the wind is at an * 

angle of 45 degrees from the major axis of the struc- ;•__ i> 

ture; minimum downwash occurs with wind flow 7^ 

parallel to the major axis of the structure (Sherlock

 3 

and Lesher, 1954). 

Halitsky (1961. 1963) has shown that the effluent from flush openings on flat roofs frequently 

flows in a direction opposite to that of the free 

atmospheric wind, owing to counter-flow along the 

roof in the turbulent wake above the building. In 

addition to the effect of aerodj-namic downwash 

upon the release of air pollutants from stacks and 

buildings, one must also consider the effects of aerodynamic downwash when exposing meteorological 

instruments near or upon buildings. 

Mtri 

Mil* 

ittme wi«o 

r ii.;. 

Where the pollution is emitted from a vent or 

opening on a building and is immediately influenced by the turbulent wake of the building, the 

pollution is rapidly distributed within this turbulent wake. To account for mixing in the turbulent 

wake, one may assume binormal distributions of 

concentrations at the source, with horizontal and 

vertical standard deviations of <r,.„ and a**. The 

standard deviations are related to the width and 

height of the building, for example, letting 4.3 oro 

equal the width of the building and 2.15 <*„. equal 

tauum f_«. 

) 

32 

^ -

ATMOSPHERIC DISPERSION ESTIMATES 
io*r 

S~ 

li;_l_l!;;!ll|'.!!_iaiWii!!H!!;.i.i'l'!|3:.j-! • IfH'lT-i!! ! ••J^!!HBia|!__3;,;!!'!l'l';JiSjj__ i T.1 '.'! yfHII'K.i , i!|: ••_--„!Ha_m_HU|iy___!___i 

i = •-.--£=• •.H.-=;--;:rgltH;ah;='.!_;;!=;;:|:-Li._! \ • •: • jvJTrilMJj::luiiiiHisJidl;!-'":y :;_r-j L j -; •/THgiiHiiiii^Hii^i-i^^sygirg ^ 

IOO 

Distonc t Downwind , km 

Figure 4-1. The product of <r,<r, as a function of downwind distance from the source. 

Effective Height 

iS&U.. • 

:=_*_=r-

.^ASr&C-V •-.-.IHSSQ'SE •• 

33 
( • 

the he-igfai. Values other than 4.3 and 2.15 can be 

••sed.. \6y__ej_ these values are used 97'/', of the dis-

•jautitan is included within these limit?-. Virtual 

-stantees x,- and xz can be found such :_u.c at xy, 

<ry ==• ai*,, smd at x„, <x_, ••= az„. These x's will differ 

with staMity. Equations applicable to point sources 

can trteni be used, determining <?, as a function of 

x -f- x;„ ffiiaiid o,as a function of x + xt. 

REFERENCES 

BosarrqpEefc, C. H., W. F. Carey, and E. M. Halton, 

1955S: Dust from chimney stacks. Proc. Inst. 

Mesab. Eng., 162, 355-367. 

Bosaraqpiet, C. H., 1957: The rise of a hot waste gas 

plniraiE. J. Inst. Fuel, 30, 197, 322-328. 

Davi 

in® 

€ 

H 

F., 1949: The dispersion and spreada£ gases and dust from chimneys. Trans. 

on Ind. Wastes, 14th Ann. Meeting, Ind. 

Found. Amer., 38-55. 

Halitsfcy, J., 1961: Wind tunnel model test of exhau_Et gas recirculation at the NIH Clinical 

Censter. Tech. Rep. No. 785.1, New York Univ. 

Halits&gF,, J-, 1962: Diffusion of vented gas around 

buiMimgs. J. Air Poll. Cont. Assoc, 12, 2, 74-80. 

Halits&y., J., 1963: Gas diffusion near buildings, 

thjffisneiical concepts and wind tunnel model expemmmemts with prismatic building shapes. Geopbigfflical Sciences Lab. Rep. No. 63-3. New 

. Yomk 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 factors 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 

S*/."'.' ' -i6?i 
P.40 

y 

Chapte r 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. 

I n 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 

Kewson and Gill (1944) and Hewson (1945). Equations for estimating concentrations with these conditions have been given by Holland (1953), Hewson (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, a*, and CT. characteristic of stable conditions must be selected for the particular distance 

of concern. An equation for the ground-level concentration when the inversion has been eliminated 

to a height hs is: 

X F (x,y,0;H) = 

Q 1 exp (—0.5 p-) dp 

V2JT oryF u hi 

exp[--H^r] (5.1) 

where p 

-H 

and &-J-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 

maximum by: ' ,.. 

X r (x,y,0;H) Q 

T T - exp V 2JT U' 0>F' hi 

h, — H -f- 2 a, = h + AH + 2 a, 

I 2 U. F J J 

(5.2) 

(5.3) 

A difficulty is encountered in estimating a reasonable 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 

<rT for stable conditions used, the probable result 

would be estimated concentrations higher than actual concentrations. Or, using an approximation 

suggested by Bierly and Hewson (1962) that the 

edge of the plume spreads outward with an angle 

of 15s, the <TyF for the inversion break-up fumigation 

equals the CT, for stable conditions plus one-eighth 

the effective height of emission. The origin of this 

concept can be seen in Figure 5-1 and the following 

equation, where the edge of the plume is the point 

at which the concentration falls to 1/10 that at the 

centerline (at a distance of 2.15 a, from the plume 

center). 

<TyT 

2.15 CTT (stable) + H tan 15° 

oy (stable) 

2.15 

H / 8 (5.4) 

A Gaussian distribution in the horizontal is assumed. 

20- BOUNDARY OF 

STABLE PLUME 

2.15 »y 

'(FUMIGATION) 

Figure 5-1. Diagram showing assumed height, hi and ?7 

during fumigation, for use in equation (52). 

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 concentrations must be great enough, based on the time 

required to eliminate the inversion, that this portion of the plume was initially emitted into stable 

air. This distance is x = utm, where u is the mean 

Special Topics 35 

\«*-*.m*rr'$)rrM,y 
P.41 

wind in the stable layer and t„, is the time required 

r-J-o eliminate the inversion from h, the physical 

ight of the stack to h( (Eq. 5.3). 

tm is dependent upon both the strength of the 

inversion and the rate of heating at the surface. 

Pooler (1965) has derived an expression for estimating this time: 

Pa cp 80 

8z R 8z

 V1(h"

, .- "' « \ m 2 J (5.5) 

where tn, = time required for the mixing layer to 

develop from the top of the stack to the 

top of the plume, sec 

P„ = ambient air density, g m-3 

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 

-r- = vertical potential temperature gradient, 

5 8T K m-1

 ~ — r r (the adiabatic lapse 

rate) Sz 

hi = height of base of the inversion sufficient 

to be above the plume, m 

h = physical height of the stack, m 

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

••ated and [ —^—-) is the average height of the 

yer. 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 estimating the time required to eliminate an inversion 

to a height z by use of an equation of Taylor's 

(1915, p. 8): 

z

2 

(5.6) t = 

where: 

4 K 

t = time required to eliminate the inversion 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,= — h2 

t» — 4 K 

(5.7) 

/ 

Hewson (1945) has suggested a value of 3 m2 sec_i 

for K. 

^LIJiME TRAPPING 

Plume trapping occurs when the plume is 

vapped between the ground surface and a stable 

36 

layer aloft. Bierly and Hewson (1962) have suggested 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 

Q 

2jr U <jy a. 

\-M-^-Y\. 

—[--M^y] 

+ 

N = J 

N —1 

[---H-V"-) 

exp -M 

-*- exp — 

+ exp — 

z + H — 

<<-. 

2 NL ' 

' z — H -f 2 NL 

<T, 

z + H + 2 NL 

r 

1 / Z - H + 2NL \ * 

-H'+ H:

2NLy]H> 

where L is the height of the stable layer and J — 3 

or 4 is sufficient to include the important reflections. A good approximation of this lengthy equation can be made by assuming no effect of the stable 

layer until <r_ = 0.47 L (see Chapter 3). It is assumed that at this distance, x_, the stable layer 

begins to affect the vertical distribution so that at 

the downwind distance, 2 x_, uniform vertical mixing has taken place and the following equation can 

be used: 

X (x,y,z;H) Q 

V2JT oy L u 

exp [-MiY] 

(5.9) 

t 

For distances between xL and 2 x_ the best approximation to the ground-level centerline concentration 

is that read from a straight line drawn between the 

concentrations for points XL and 2 x_, 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 between grrnnntl-lpvpl rnnr-Pntxatinna and r-oncentrations at the level of the plunge rpntg.rline. One of 

ATMOSPHERIC DISPERSION ESTIMATES 

) 

y 

•~:f-t-. 'MX^^S^l^i^^^^^i^i^i^^i^^ ,. 
P.42 

w 

/ 

/ 

6< 

is at the distance of maximum concentration 

a t the ground. As a rough approximation the maxi-

___Q__n grrmnH-jpypl rnnpqn^rntinn OCCUrS at the distanc e where! CT. = —j= H. fThis approximation is 

much better for unstable conditions than for stable 

conditions. With this approximation, the ratio of 

(concentration at plume centerline to that at the 

ground is: 

X (*, 0,H) 

X(x.0,0) 

* [ 1.0 + exp 

1 /2H 

2 V <*z •)•] 

^

x 

1 

0 

exp 

[1.0 + exp4-(-?•)' ^ 

•0.5(2V2) 2] 

exp — 0.5 (v'2)" 

(1.0 + 0.0182) 

0.368 

if 

1.38 

This calculation indicates that at the distance 

| of maximum ground-level concentration the concensus tration at plume centerline is greater by about 

>one-third. 

It is also of interest to determine the relationship between <rz and H such that the concentration 

a t ground-level at a given distance from the source 

is the same as the concentration at plume level. 

This condition should occur where: 

The value H/CT, = 1.10 satisfies this expression, 

which can be written as <*_ = 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: 

DT (x,y,0;H) = 

Q. 

ir ay <r, U exp 

-I-H*)*] 

l-M-i)] 

(5.10) 

where DT = total dosage, g sec m~3 

and QT = total release, g 

The CT'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 patfe 5s usually increasingly difficult with shorter release femes. D_ 

can also be given in curie sec m_J if Q_ is im mmies. 

CROSSWIND-INTEGRATED CONCENTRATION 

The ground-level crosswind-infepgyrattwd concentration is often of interest. Far a. <rain______i_n__. elevated source this concentration is dettB__mi__s_l from 

Eq. (3.2) integrated with respect to y _rao__ "*• to 

+

 v (Gifford 1960a) giving: 

Xcwi 

2 Q 

exp \/2W j u I-H*)* ] fill) 

In diffusion experiments the 

wind-integrated concentration is ©item de&_______ied 

at particular .downwind distances firearm a. <_3_fi__w_t_d 

line or arc of sampling measuronenits _i___d__ _att this 

distance. When the source strength, Q,, and antcrage 

wind speed, u, are known, v_ can be «°«im"_HihwfP indirectly even though no me__sure______i_s wane i___.de 

in the vertical. If any of the tracer os! 

reaction or deposition, the result-Dig w_ imam 

estimates will not represent the vattikal «lli»*jiiwr!ii«w 

(see problem 18). 

ESTIMATION OF CONCENTRAT_©_<S FOX 

SAMPLING TIMES LONGER THAN A 

FEW MINUTES 

Concentrations directly doinnri_a__ fam at wmire 

decrease with sampling time nsainiy Hwjmwft of a. 

larger cy due to increased meander off mmdg___mrtion. 

Stewart, Gale, and Crooks (1958$ uteyu_.tal that 

this decrease in concRntrati"** *«mu__»_ _ ^r.jgfrfr, 

pruggr la w nrifh ...tha c^ffiplmg rim_» ffiirr .EpmiTQHnCT 

periods from about 3 minutes to abcnrit __a_f aaa boar. 

Cramer (1959) indicates that tins _______ punter'law 

applies for sampling times from 3 <»gg«»«fa s© 10 

minutes. Both of these studies WEBS Erased am observations taken near the height off mefease. GilSim. 

(1960b) indicates that ratios of pea_k to mean concentrations are much higher than ttftmse gjweni by 

the above power law where ofasE_^3tt_____s off asaaceatrations are made at heights canBdeoably <___5ere__t 

from the height of release or co___a__ffi_a_bJy _,a___o.ed 

from the plume axis. He also muffin****: fltafc for 

increasing distances from an rf_aEa__eri______aro&_.tlte 

ratios of peak to average OHM-«i-__,lt__»-__. gftaearved 

at ground level approach unity, Scgggr iiSHfeis.) and 

Singer, et al. (1963) show tfiat ________ <_f peak to 

mean concentrations depend also am the s____nf__ty 

of the atmosphere and the type off tanisrin tt&ad. the 

plume is passing over. Nanhdbd ((11960) reports 

that Meade deduced a relation beftawaea c___a___c£ed 

concentrations at ground levd ami tf__e rampfing 

time from "a study of published <_&___ am. l___a__l and 

vertical diffusion coefficients m steady winds." 

These relations are shown in TaMe 5-H. 

Special Topics 37 

*»-—•*-• • 
P.43 

y 

Im2. 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 concentrations are usually of little general interest 

because of their very short duration; they cannot 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 concentrations fluctuate considerably under these conditions, 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 -iH, the fumigation can occur 

close to the source but will be of relatively short 

duration. For large ^H, 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 significance can occur with neutral or unstable 

conditions when the dispersion upward is severely limited by the existence of a more stable 

layer above the plume, for example, an inversion. 

5. Under stable conditions the maximum concentrations 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 increasingly 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 concentration at (0, 0, 0) from a source at (x, y, H) 

on a coordinate system with the x-axis oriented upwind 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 individual contributions from each source (see problem 

20). 

SOURCE 

...H) 

urwiNO 

RECEPTOR 

10.0.0) 

DOWNWIND (x.y.O) 

Figure 5-2. Comparison of source-oriented and receptororiented coordinate systems. 

It is often difficult to determine the atmospheric 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 

;

'»?i______' c%Bgftv;fe^n 

«*. 
P.44 

Table 5-1 VARIATION OF CALCULATED CONCENTRATION 

WITH SAMPLING TIME 

Sampling Time 

Ratio of 

Calculated Concentration 

to 3-minute Concentration 

3 minutes 

15 minutes 

1 hour 

3 hours 

24 hours ... 

1.00 

0.82 

0.61 

0.51 

0.36 

This table indicates a power relation with time: 

Xot_t~217. Note that these estimates were based 

upon published dispersion coefficients rather than 

upon sampling results. Information in the references cited indicates that effects of sampling time 

are exceedingly complex. If it is necessary to estimate concentrations from a single source for the 

time intervals greater than a few minutes, the best 

estimate apparently can be obtained from: 

x» »(*) ' 

(5.12) 

( 

where x* is the desired concentration estimate for 

the sampling time,vt^;x_ is the concentration estimate for the shorter sampling time, tk, (probably 

-'" out 10 minutes): and p should be between 0.17 

i 0.2. Eq. (5.12) probably would be applied 

.iost appropriately to sampling times less than 2 

hours (see problem 19). 

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-

'tal within the sector (Holland, 1953, p. 540). 

. appropriate equation for average concentration 

then either: 

Q 

2TT X exp 

V 2 , a, U ( w f 

2o3M--H-^y] 

[-MZY] 

Or UX (5.13) 

or 

•°m 

2.55 Q 

L u x 

(5.14) 

depending upon whether a stable layer aloft is affecting 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 according 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: 

X (x.©) = 

2 Qf (G.S.N) 

N ) V2ir<rlS 

" * ^ 

exp [--HSwhere f (e, S, N) is the frequency during the period 

of interest that the wind is from the direction e, for the stability condition, S, and 

wind speed class N. 

<J.S is the vertical dispersion parameter evaluated 

at the distance x for the stability condition S. 

u.v is the representative wind speed for class N. 

Hu is the effective height of release for the wind 

speed Ux. 

• Where stability wind rose information cannot be 

obtained, a first-order approximation may be made 

of seasonal or annual average concentrations by 

1 using the appropriate wind rose in the same manner, and assuming the neutral stability class, D, 

jl only. 

METEOROLOGICAL CONDITIONS 

ASSOCIATED WITH MAXIMUM 

GROUND-LEVEL CONCENTRATIONS 

1. For ground-level sources maximum concentrations occur with stable conditions. 

38 ATMOSPHERIC DISPERSION ESTIMATES 

•..-Z#ta$y. ;^$%e».--, .~-.&$ji&3p 
individually. Often an approximation can be made 

by combining all of the emissions in a given area 

^~- nd treating this area as a source having an initial 

jrizontal standard deviation, o}„. A virtual disance, x„ can then be found that will give this 

standard deviation. This is just the distance that 

«sH-»3fie_d the appropriate value for <ry from Figure 

(^-^JValues of xy will vary with stability. Then 

equations for point sources may be used, determining oT as a function of x -f x„ a slight variation of 

the suggestion by Holland (1953). This procedure 

treats the area source as a cross-wind line source 

with a normal distribution, a fairly good approximation for the distribution across an area source. 

The initial standard deviation for a square area 

source can be approximated by • a,„: __: s/Jj ft, "1 ^ 

s is the length of a side of the area (see problem* 

If the emissions within an area are from varying 

effective stack heights, the variation may be approximated by using a a_i;;

 Thus H would be the 

mean effective height of release and ozn the standard 

deviation of the initial vertical distribution of 

sources. A virtual distance, x_, can be found, and 

point source equations used for estimating concentrations, determining o_ as a function of x -f- x_. 

TOPOGRAPHY 

Under conditions of irregular topography the 

.ect ajjplication of a standard dispersion equation 

JS often invalid. In some situations the best one 

may foe able to do without the benefit of in situ 

experiments is to estimate the upper limit of the 

oonceoatrations likely to occur. 

Far example, to calculate concentrations on a 

hillside downwind from and facing the source and 

at abomfe the effective source height, the equation 

for ccHttcentrations at ground-level from a groundilevel siw_rce (Eq. 3.4) will yield the highest expected! concentrations. This would closely approximate tibe situation under stable conditions, when 

the pafatant plume would be most likely to encounter the hillside. Under unstable conditions the 

flow as amore likely to rise over the hill (see problem 

21).. 

downslope flow when the receptor is at a 

lower eDeration than the source, a likely assumption 

_s thadt the flow parallels the slope; i.e., no allowance ns made for the difference between groundlevel iterations at the source and at the receptor. 

Wimx a steep ridge or bluff restricts the horizontal! dispersion, the flow is likely to be parallel 

-to sucfla a bluff. An assumption of complete reflecK

on aft the bluff, similar to eddy reflection at the 

' wmi from an elevated source, is in order. This 

.ay %e accomplished by using: 

x(x,y,0;H) Q 

ir oy o, U exp l-Mi-Y] 

•+• ex p [--H-W])H 

(-s-rll (5.16) 

B is the distance from the x-axis to the restricting bluff, and the positive y axis is defined to be in 

the direction of the bluff. 

The restriction of horizontal dispersion by valley 

sides is. somewhat analogous to restriction of the 

vertical dispersion by a stable layer aloft. When 

the oy becomes great enough, the concentrations 

can be assumed to be uniform across the width of 

the valley and the concentration calculated according to the following equation, where in this case Y 

is the width of the valley. 

2Q f 1 f H v i 

*~ V2;«r.Yu

 P L 2 U J J (5.17) 

UNE SOURCES 

Concentrations downwind of a continuously 

emitting infinite line source, when the wind direction is normal to the line, can be expressed by 

rewriting equation (12) p. 154 of Sutton (1932): 

x (x,y,0;H) = —== 

2 q 

yjltr o, u 

exp l-MSY] 

(5.18) 

Here q is the source strength per unit distance, 

for example, g sec-1 m ~

1

. Note that the horizontal 

dispersion parameter, os, does not appear in this 

equation, since it is assumed that lateral dispersion 

from one segment of the line is compensated by dispersion in the opposite direction from adjacent 

segments. Also y does not appear, since concentration at a given x is the same for any value of y 

(see problerrf?§3)) 

Concentrations from infinite line sources when 

the wind is not perpendicular to the line can be 

approximated. If the single between the wind direction and line source is 0, the equation for concentration downwind of the line source is: 

x <x,y,0;H) 

sin 0 v!.o-_u

 exp [~1r(£) J 

(5.19) 

This equation should not be used where 0 is less 

than 45c. 

3 

m 

fjjft**:r^t,^r 

ATMOSPHERIC DISPERSION ESTIMATES 

«£%!"• 
P.46 

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 concentrations from a finite line source oriented crosswind, 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 extending from y, to y. where y, is less than y2. The 

equation for concentration (from Sutton's (1932) 

equation (11), p. 154), is: 

x (x,0,0;H) v^lu

 exp[—H^r) j 

.—-• exp (—0.5 p2) dp 

\'2TX 

(5.20) 

where p, V

P s =

 ~ 

The value of the integral can be determined from 

tabulations given in most statistical tables (for example, 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 release, as from an explosion, or short-term releases 

on the order of seconds, are often of practical concern. To determine concentrations at any position 

downwind, one must consider the time interval 

after the time of release and diffusion in the downwind direction as well as lateral and vertical diffusion. Of considerable importance, but very difficult, 

is the determination of the path or trajectory of 

the "puff." This is most important if concentrations are to be determined at specific points. Determining the trajectory is of less importance if knowledge 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 Sutton's (1932) equation (13), p. 155, results in an 

equation that may be used for estimates of concentration downwind from a release from height, H: 

X (x,y,0;H) = .

2

. ,

Q T

 exp 

(27.) '- «.„ Oy Ot 

(^),1-I--K40,1 

exp ^__(__ j J ^^^ 

(The numerical value of (2w)3'' is 15.75.) 

[-4 

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 evaluated with respect to the dispersion of a continuous 

source a t a fixed point in space. 

In Eq. (5_21) the a's refer to dispersion statistics following the motion of the expanding puff. 

The ox is the standard deviation of the concentration distribution in the puff in the downwind direction, 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 o*-. Wind speed may influence the dispersion indirectly because the dispersion parameters 

cr_, oy, and ox may be functions of wind speed. The 

<Tj,'s and oz's for an instantaneous source are less 

than those for a few minutes given in Figure 3-2 and 

3-3. Slade (1965) has suggested values for a «rT 

and ot for quasi-instantaneous sources. These are 

given in Table 5-2. The problem remains to make 

best estimates of <J_. Much less is known of diffusion in the downwind direction than is known of 

lateral and vertical dispersion. In general one should 

expect the a, value to be about the same as o>. 

Initial dimensions of the puff, i.e., from an explosion, may be approximated by finding a virtual 

distance to give the appropriate initial standard 

deviation for each direction. Then ay will be determined as a function of x -f- x„ a. as a function of 

x -f x„ and or, as a function of x -f- x,. 

Table 5-2 ESTIMATION OF DISPERSION PARAMETERS FOR 

QUASI-INSTANTANEOUS SOURCES (FROM SLADE, 1965) 

Unstable 

Neutral 

Very Stable 

X = 

"x 

10 

4 

1.3 

100 m 

ot 

15 

3.8 

0.75 

x = 4 km 

Oy o. 

300 220 

120 50 

35 7 

REFERENCES 

Bierly, E. W., and E. W. Hewson, 1962: Some restrictive meteorological conditions to be considered in the design of stacks. J. AppL Meteorol., 1, 3, 383-390. 

Burington, R. S., 1953: Handbook of Mathematical 

Tables and Formulas. Sandusky, Ohio, Handbook Publishers, 296 pp. 

Cramer, H. E., 1959: Engineering estimates of 

atmospheric dispersal capacity. Amer. Ind. Hyg. 

Assoc. J., 20, 3, 183-189. 

Special Topics 

1M-M1 O - 69 - 4 

41 
*** 

Gifford, F. A., 1959: Computation of pollution 

^_ from several sources. Int. J. Air Poll., 2, 109-

110. 

iiord, F. A., 1960a: Atmospheric dispersion calculations using the generalized Gaussian plume 

model. Nuclear Safety, 2, 2, 56-59, 67-68. 

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

Hewson, E. W., and G. C. Gill, 1944: Meteorological 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, *72, 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 pollutant 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: 

the atmosphere. 

135, 143-165. 

A theory of eddy diffusion in 

Proc. Roy. Soc. London, A, 

Taylor, G. I., 1915: Eddy motion in the atmosphere. PhiL Trans. Roy. Soc, A, 215, 1-26. 

3 

....rXttiir*il*m.- L

*»VJ«WR-; 

ATMOSPHERIC DISPERSION ESTIMATES 
P.48 

('••-

Chapter 6 — RELATION TO OTHER DIFFUSION EQUATIONS 

Most other widely used diffusion equations are 

variant forms of the ones presented here. With respect to ground-level concentrations from an elevated source (Eq. 3.2): 

exp [--r(^") =

] (3.2) 

Other well-known equations can be compared: 

Bosanquet and Pearson (1936): 

Q 

x (x,y,0;H) = = 

\'2TT pq x- u 

exp 

(*)'•]-[-£1 

[-

(6.1) 

where p and q are dimensionless diffusion coefficients. 

Sutton (1947): 

X (x,y,0:H) = 

H= 

2 Q 

Wv V>* u 

exp [ x-

_n 

( * + ^) ] (6.2) 

where n is a dimensionless constant and C, and C, 

are diffusion coefficients in m"'2. 

Calder (1952): 

x (x.y,0;H) Q u 

( *

 + »)] 

2 k- a v..

;

 xexp I kv, x 

where a = —-, 

vr 

(6.3) 

the ratio of horizontal eddy velocity 

to vertical eddy velocity, k is von Karman's con 

stant approximately equal to 0.4, and vx = 

where z„ is a roughness parameter, m. 

In A 

z« 

NOTE: Calder wrote the equation for the concentration 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 oy and oz (continuous source) in this paper. 

Table 6-1 EXPRESSIONS EQUIVALENT TO oy AND o, IN 

VARIOUS DIFFUSION EQUATIONS. 

Equation 

Bosanquet and Pearson 

Sutton ^ _ c_ 

Calder

 vT a 

u 

Oy 

q x 

2-n 

x 2 

* v* x 

a . 

vTpx 

i

 2"n 

v r c < *

 2 

V ' l k vx x 

u 

REFERENCES 

Bosanquet, C. H., and J. L. Pearson, 1936: The 

spread of smoke and gases from chimneys. 

Trans. Faraday Soc, 32, 1249-1263. 

Calder, K. L., 1952: Some recent British work on 

the problem of diffusion in the lower atmosphere, 787-792 in Air Pollution, Proc. U. S. 

Tech. Conf. Air Poll., New York, McGraw-Hill, 

847 pp. 

Sutton, O. G., 1947: The problem of diffusion in 

the lower atmosphere. Quart. J. Roy. Met Soc, 

73, 257-281. 

Other Equations 43 

-•-••^? ,*'^:.T.^~?^^ ^ •"i-v-r'Z- Tr*V*/"V,.*> 
P.49 

Chapter 7 —EXAMPLE PROBLEMS 

7 

The follow__q£2£^example problems and their 

solutions illustrate the application of most of the 

techniques and equations presented in this workbook. 

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 _a 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 az = 65 m from Figure 3-3 

Eq. (3.4) for estimation of concentrations directly downwind (y = 0) from a ground-level 

source is applicable: 

Q 3 

•y 

y 

y 

7 

(x,0,0;0) 

1.1 

ar a- oz U - 190 (65) 7 j 

( 

x 10~s g m 3 of oxides of nitrogen. 

PROBLEM 2: It is estimated that 80 g sec-1 of 

sulfur dioxide is being emitted from a petroleum 

refinery from an average effective height of 60 

meters. At 0800 on an overcast winter morning 

with the surface wind 6 m sec-1, what is the 

ground-level concentration directly downwind 

from the refinery at a distance of 500 meters? 

SOLUTION: For overcast conditions, D class stability applies- With D stability at x — 500 m, 

o, = 36 m, «r, = 18.5 m. Using Eq. (3.3): 

Q __._ T 1 / H 

All but the exponential involving y has been 

found in the preceding problem. Therefore: 

X (500, 50,0; 60) = 3.3 x IO-5 

exp [—0.5 (50/36)-] 

— 3.3x10 - (0.381) 

/ = 1.3 x IO"5 g m-3 of SOPROBLEM 4: A power plant burns 10 tons per 

hour of coal containing 3 percent sulfur; the 

effluent is released from a single stack. On a 

sunny summer afternoon the wind at 10 meters 

above ground is 4 m sec-1 from the northeast. 

[

The morning radiosonde taken at a nearby 

Weather Bureau station has indicated that a 

frontal inversion aloft will limit the vertical 

mixing to 1500 meters. The 1200-meter wind is 

from 30° at 5 m sec-1. The effective height of 

emission is 150 meters. From Figure 3-9, what 

is the distance to the. maximum ground-level 

concentration and what is the concentration at 

this point? 

SOLUTION: To determine the source strength, 

the amount of sulfur burned is: 10 tons hr-1 x 

2000 lb ton-1 x 0.03 sulfur = 600 lb sulfur hr-1. 

Sulfur has a molecular weight of 32 and combines with 0, with a molecular weight of 32; 

therefore for every mass unit of sulfur burned, 

there result two mass units of SO,. 

X (x,0,0;H) = , 

=• Or, 0Z U exp i-um 

80 

exp (—0.5 (60/18.5)2] 

Q 

* 36 (18.5) 6 

= 6.37 x IO-3 exp [—0.5 (3.24)2] 

The exponential is solved using Table A-1 (Appendix 3). 

= 6.37 x IO-3 (5.25 x IO-3) # 0 . J*« 

X — 3.3 x KT5 g m-s of SO. 

64 (molecular weight of SO.) 

32 (molecular weight of sulfur) 

600 lb hr-1 (453.6 g lb-1) 

X 

^^j,,^—^3600 sec hr-1 

^15\g^et~' of SO. 

On a sunny summer afternoon the 

should be strong. From Table 3-1, 

lation and 4m sec-1 winds yield clai 

From Figure 3-9, the distam 

insolation 

ng insotability../ 

apgeto e Doint of 

maximum concentration is (junio r class-B sta 

PROBLEM 3: Under the conditions of problem 

2, what is the concentration at the same distance downwind but at a distance 50 meters 

from the x-axis? That is: x (500, 50, 0; 60) =- ? 

SOLUTION: Using Eq. (3.2): 

Q 

bility and effective height of 150 meters. From 

Figure 3-3 at this distance oz = 110 m. This is 

-^ao ^

 muc k ^ess

 than [o.^PET^Therefore, at this dis-

• ^ ' tance, the limit ot mixing of 1500 meters will 

not^ affect the grourt^-lfYfil r.nr

i%ar,h"%iTMn

 From 

Figure 3-9, the maximum x

u

/Q f°r B sl 

and this effective height of 150 m _s_77Ifx 10~_, 

Xoi " x« JL 

u 

7.5 x 10-a x 151 tonjx-'r 

<

! t ^H

> —7^r^[-T\i)j j -*•«no-.*-<_so; v 

PROBLEM 5: For the power plant in problem 4, 

at what distance does the maximum groundExample Problems 45 

.'fcT»*^' —»._.._•'.« • 'mm.mi-'iii jyiji^mif**-... ''--"'- * —*-Y^-*-*i-*? «»'» »*•"•*»•*_ T-*"r* 
P.50 

levdl aorrceratration occur and what is this concenii_Qi_bn_ an an overcast day with wind speed 

4 nnsenr1? 

JLUUltimSfc On an overcast day the stability 

claasffi moii-i be D. From Figure 3-9 for D stabilitbyanrilH of 150 m, the distance to the point 

off _n_Es_j_n____ ground-level concentration is 5.6 

krm. andl tfoe maximum \u/Q is 3.0 x 10—. 

XmOKK " 

x IO-11 x 151 

= ILH __ IO-4 g m~:i X J 

PRO__ffl___»fi @z For the conditions given in problem 4k. aHaaaw a graph of ground-level centerline 

sulffinr diarsade concentration with distance from 

10GDm_atei_5 to 100 km. Use log-log graph paper. 

SOLUJHMHSfc The frontal inversion limits the mixing ttoIL= 1500 meters. The distance at which 

oz = <_Lffi71_ = 705 m is xw^= 5.5 km. At dista__a__£l_e_si_h__n this, Eq. (3^) is used to calculate (gamtmrn illations: 

(

;

s; 

Q 

— ff,. <rz U exp [-nm 

Ait (fiBE_a____e equal to or greater than 2 xL, which 

is, 111 Ifam, Mq. <f3.5Lis used: 

Q X <&0lftS_» — 7== _ 

V 2- ffr L u 

Soik___iiiEi_-B inr the equations are given in Table 

7-IL HHnas -calues of concentration are plotted 

agaiinstt aiBSitance in Figure 7-1. 

2 xo~' 

io-' 

io—s. 

j _..:;__ = !.: '. . 1 'i' lim * 

! ••' .;; " "Z~ . *.'.'. '. '. •'. ] I II I 

,-,.--=:•.!: .T.i_-j.|r 

i - l I-TY^IM 

T ; ! ;TTj 

•

:

 l \4W% x.i-^r-zsm. 

X 

i 7 V • 1 • • " ! '• 

1 1 1 \.i ; .in. 

;-_. _: :: jff: : : ::; : -..-. : ^::\ . . :.: : : :.._=_. 

r it 1 ri '^^"S: 

!• ::#: • : : if 

| :: ":|::::':: 

i | 

t ~~ H 

t .11 . .. 

ll 11 

i -^^ . 

"."'" . •>"-.":• : { .; _ 

xx

::xISfi 

..TT."* ~ T~T~ 

i ' 

... : r _•_*""ZT_T.T: "rrtruJZJ". 

— -t—:—=—f-—!—i--Ji 

i :' • l , 1 •! 

^-----—- • — T-r f 

|i- _ —rr^rj 

:

 ; | i • 

• MM : 

; io 

DOWNWIND DISTANCE, km 

100 

f

 -.res KL. ©smcentration as a function of downwind 

distance (Problem 6). 

Table 7-1 CALCULATION OF CONCENTRATIONS FOR 

VARIOUS DISTANCES (PROBLEM 6) 

a- X, u , 

km m sec- 1 Oy, 

m 

oz. 

m 

H/ff, exp[-^-(H/ffl)=] g m-3 

f*/ 0.3 

0.5 

0.8 

1.0 

2.0 

3.0 

5.5 

4 

4 

4 

4 

4 

4 

4.5 

52 

83 

129 

157 

295 

425 

720 

30 

51 

85 

iifi 

230 

365 

705 

5.0 

2.94 

1.77 

1.3S 

0.65 

0.41 

0.21 

3.73 x 10-

1.33 xlO-4 

0.209 

0.397 **/ 

0.810 

0.919 

0.978 

2.9x10-

3.8x10-

2.3x10-* 

(lirxTcR 

1.4x10-

7.1 x 10-6 

2.1xlO-» 

*. U, ffy, 

km m sec - 1 m 

11.0 4.5 1300 

30 4.5 3000 

100 , '4.5 8200 

L, 

m 

J5DD 

1500 

1500 

Xg nr-3 

6.9 X 10-

3.0x10-

1.1 x 10-

\VEQBLEM 7: For the conditions given in problem 4, draw a graph of ground-level concentration versus crosswind distance at a downwind 

distance of 1 km. 

SOLUTION: From problem 4 the ground-level 

centerline concentration at 1 km is 2.8 x 10— 

g m—. To determine the concentrations at distances y from the x-axis, the ground-level centerline concentration must be multiplied by the 

factor exp I-*(*.1 

<rv = 157 meters q*

 Y

 — I kTM- Values for this 

computation are given in Table 7-2. 

Table 7-2 DETERMINATION OF CROSSWIND 

CONCENTRATIONS (PROBLEM 7) 

y. 

m •i -[-MiY] *TM 

±100 

±200 

±300 

±400 

±500 

0.64 

1.27 

1.91 

2.55 

3.18 

0.815 

0.446 

0.161 

3.87x10-

6.37x10-

2JxlO1.3 x 10-* 

4.5x10-

1.1x10-

1.8x10-

These concentrations are plotted in Figure 7-2. 

PROBLEM 8: For the conditions given in problem 4, determine the position of the 10— g m— 

ground level isopleth, and determine its area. 

SOLUTION: From the solution to problem 6, the 

graph (Figure 7-1) shows that the IO-5 g m -

isopleth intersects the x-axis at approximately 

x = 350 meters and x = 8.6 kilometers. 

^ 

4C ATMOSPHERIC DISPERSION ESTIMATES 
P.5JL 

y 

\— 

i 

r 

e 3-10"*^-

t 

ae * 

*2«I0~**— 

5 ! 

i 

3 ! 1 "T i 

I 

i 

r^mm^r 

-40 0 

1 

-20 0 

1 

\_ 

! 

) '20 0 

1 

MOO 

-

-

-

CROSSWIND DISTANCE ly), m 

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 

km 

0.5 

0.8 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

7.0 

8.0 

ffy, 

m 

83 

129 

157 

295 

425 

540 

670 

780 

890 

980 

DETERMINATION OF ISOPLETH WIDTHS 

(PROBLEM 8) 

-^ (centerline), 

g m-:l 

3.8 x 10-

2.3 x 10"* 

2.8 xlO-1 

1.4 x 10"' 

7.1 x 10-

4.0 x 10-" 

2.4 x 10-

1.8 x 10-

1.4x10-

1.1 x 10~5 

Y (isopleth) 

Y (centerline) 

0.263 

4.35x10"= 

3.53 x 10-= 

7.14x10-

1.42 xlO-' 

0.250 

0.417 

0.556 

0.714 

0.909 

Hi Or 

1.64 

2.50 

2.59 

2.30 

1.98 

1.67 

1.32 

1.08 

0.82 

0.44 

y. 

m 

136 

323 

4ojp 

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 because 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 r ab where a is the 

semimajor axis and b is the semiminor axis. 

8600 — 350 

2 = 4125 m 

b = 902 

A (m2) = - (4125) (902) 

= 11.7 x 10" morA = 11.7 kmSOU&CE 

\-fT,firi*l*r 

V R 

Figure 7-3. Location of the IO"5 g m~3 

pleth (Problem 8). 

ground-level isoROBLEM 9: For the conditions given in problem 

4, determine the profile o^ concentration with 

height from ground level^tQ1 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 problem. The exponential involving y is equal to 1. 

At x = 1 km, ffy =• 157 m, o_ = 110 m. (From 

problem 4). 

2.ff?ff,u - 2.157 1qi0) 4 ° 3.5 ^ g^ 3 

Values for the estimation of x(z) are given in 

Table 7-4. 

PROBLEM 10: For the conditions given in problem 4, determine the distance at which the 

ground-level centerline concentration equals tbe 

centerline concentration at 150 meters above 

ground. Verify by computation of x (*t0,0) 

and x (x,0,15O). 

SOLUTION: The distance at which concentrations at the ground and at-jahnnf. height are 

equal should occur where (a? = 0.91 H_ 

Chapter 5). For B stability and H =="T50 m, 

«r, = 0.91 (150) = 136 m occurs at xj=^ 1-2 km. 

At this distance oy = 181 m. 

Example Problems 47 

^^^^^j^ffi,-,^^ ^ '•^•m*^ „ ' MpBiY I'IY _' rT^i ' _ ' 
r 

Table 7-4 DETERMINATION OF CONCENTRATIONS FOR 

VARIOUS HEIGHTS (PROBLEM 9) 

f. gz-H 

-e»p [-K^']^-[-+(^)1 c. + t. 

XU). 

g m -' 

0-1.36 

30—1.09 

60—0.82 

90—0.55 

120—0.27 

150 0.0 

180 0.27 

210 0.55 

240 0.82 

270 1.09 

300 1.36 

330 1.64 

360 1.91 

390 2.18 

420 2.45 

450 2.73 

0.397

 v 

0.552 

0.714 

0.860 

0.964 

1.0 

0.964 

0.860 

0.714 

0.552 

0.397 

0261 

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 IO-2 

4.77 x IO-3 

1.90 x 10~3 

6.78 x IO-4 

2.33 x 10"* 

7.45 x IO-5 

2.11x10-' 

5.82x10-° 

1.49 x IO-6 

3.55 x 10~T 

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 

2.78xl0-«y 

2.85x10-*

 y 

3.06x10-* J 

3.34x10"* 

3.55x10-*

 v 

3.58 x 10-* 

3.41 x 10"* 

3.03 x IO-' 

2.51 x 10"* 

1.94x10-* 

1.39 x 10"* 

9.14x10-" 

5.64 x 10-" 

3.26 x IO"8 

1.75xlO~s 

8.40 x IO-8 

/T 

These values are plotted in Figure 74. 

500 

400 — 

._- 300 

200 — 

IOO 

4.88 x IO-* exp [— \_ (1.10)2] 

4.88 x IO-* (0.546) 

2.7 x 10"* g m-s H> 

-[--H-ifr)'] ^ 151.,.. 

2* 181 (136) 4 

exp 

48 

-181 (136) 4 

^ ° C H) '°f tl\ 

v.-

V 

V 

[-M&Y]] 

— 2.44 x 10"* j 1.0 + exp [ | - (2.21)21J 

- — 2.44 x IO-* (1.0 + 8.70 x IO-2) 

— 2.44X10-* (1.087) 

— 2.7 x IO-* g m- 3 

PROBLEM 11: For the power plant in problem 4, 

what will the maximum ground-level concentration be beneath the plume centerline and at 

what distance will it occur on a clear night with 

wind speed 4 m sec-1? 

SOLUTION: A clear night with wind speed 4 m 

sec-1 indicates E stability conditions. From Figure 3-9, the maximum concentration should 

occur at a distance of 13 km, and the maximum 

xu/Q is 1.7 x IO-5 

Xm»x ' 

X " 

Q 

Q 1.7 x IO-6

 x 151 

u 4 

6.4 x IO-5 g m- s of SO. 

OUT* 10_* 2"10-* 3il0"* 4x10-* 

CONCENTRATION, g m-l 

Figure-74. Concentration as a function of height (Problem 9). fck %--{\<.*\ 

Verifying: 

(

 —-

s s—-[-w 

PROBLEM 12: For the situation in problem 11, 

what would the fumigation concentration be the 

next morning at this point (x — 13 km) when 

superadiabatic lapse rates extend to include 

most of the plume and it is assumed that wind 

speed and direction remain unchanged? 

SOLUTION: The concentration during fumigation conditions is given by Eq. (5.2) with the 

exponential involving y equal to 1. in this problem. 

Q 

XF (x^m - V^i r U ffyF hi 

For the stable conditions, which were assumed 

to be class E, at x = 13 km, or = 520 m., and 

ff, = 90 m. Using Eq. (5.3) to solve for hi: 

h, = H -f 2 ff. — 150 + 2 (90) = 330 m. 

From the horizontal spreading suggested by Eq. 

(5.4): 

ATMOSPHERIC DISPERSION ESTIMATES 

) 

m.t$titfem%r7r.£..:~r>~ 

mmmmmm'**-* 

i-mien.-

nam 

I- ,, :. ;, ;•_.• .»'_-ck.--.::-. -.-••;vw*3ff<;^ 

.:.:x.u..,m-.;!8i(.«S&&^*^:*^&f'-

W^Sfm PU. -JW * 

••- .••.'-.ilpw-.^.j^g':.: 'Mms^^m, 
P.53 

(:. 

•*•• — ffy (stable) + H/8 — 520 4- 19 = 539 

151 

^ . 4 (539) 330 

= 8.5xlO-sgnr 3ofSO_ 

Mates that the fumigation concentrations under 

ttfcese conditions are about 1.3 times the maxi-

___n_a ground-level concentrations that occurred 

Umamg the night (problem 11). 

H*i_p(___ft.HT__r 13: An air sampling station is located 

a i am azimuth of 203° from a cement plant at a 

alE'HHto.Miiff of 1500 meters. The cement plant releases fine particulates (less than 15 microns 

dfianaeter) at the rate of 750 pounds per hour 

firtnnm a 30-meter stack. What is the contribution 

_3m___ the cement plant to the total suspended 

paatiicailate concentration at the sampling sta-

_a_a_ when the wind is from 30° at 3 m sec-1 on 

a cfleor day in the late fall at 1600? 

SOIOTTON: For this season and time of day the 

C daas stability should apply. Since the sampling station is off the plume axis, the x and y 

distances can be calculated: 

x = 1500 cos 7° 

y — 1500 sin 7° 

Tlie source strength is: 

1489 

183 

Q — 750 lb hr- x 0.126 -MJE 94.5 g sec-1 

At this distance, 1489 m, for stability C, o, = 

150 m, «r_ = 87. The contribution to the concentration can be calculated from Eq. (3.2): 

X (*_F,0-,H) -

Q 

IT Oy ff, U exp 

esp l-M&Y] 

1-M-iY] 

94.5 

exp 

150 (87) 3 

30 

exp 

[-*• OS-)'] 

H (•$•)•] 

—0.5 

94.5 exp [—0.5 (1.22)3

] 1.23 x IO3 

exp [—0.5 (0.345)3 J 

-=7.68 x 10-* (0.475) (0.943) 

— 3.4 x 10"* g m"» 

PROfiLEM 14: A proposed source is to emit 72 g 

seer1 of SO- from a stack 30 meters high with 

a diameter of 1.5 meters. The effluent gases are 

emitted at a temperature of 250°F (394°K) 

with an exit velocity of 13 m sec-1. Plot on loglog paper a graph of maximum ground-level 

concentration as a function of wind speed for 

stability classes B and D. Determine the critical wind speed for these stabilities, i.e., the 

wind speed that results in the highest concentrations. Assume that the design atmospheric 

pressure is 970 mb and the design ambient air 

temperature is 20°C (293°K). 

SOLUTION: Using 

height equation: 

Holland's effective stack 

AH. 

v.d 

u [ 1.5 + 2.68 x IO-8 nJ__l_L_.il 

__.

 1 3 (

u

L 5 )

 j 1.5 -f- 2.68 x IO-3 (970) 

394 

19.5 

u 

19.5 

u 

19.5 

1.5 + 2.6 

[1.5 + 2.6 (0.256) 1.5] 

u 

19.5 (2.5) 

[1.5 + 1.0] 

u 

48.8 

~° u 

The effective stack heights for various wind 

speeds and stabilities are summarized in Table 

7-5. 

Table 7-5 EFFECTIVE STACK HEIGHTS (PROBLEM 14) 

u, 

m sec-1 

0.5 

1.0 

1.5 

2 

3 

5 

7 

10 

20 

Class 0 

AH, 

m 

97.6 

48.8 

32.6 

24.4 

16.3 

9.8 

7.0 

4.9 

2.4 

h + AH, 

m 

127.6 

78.8 

62.6 

54.4 

46.3 

39.8 

37.0 

34.9 

32.4 

Class B 

1.15 AH, 

m 

112.2 

56.1 

37.5 

28.1 

18.7 

I U 

8.0 

h + 1.15 _\H, 

m 

UU 

86.1 

67.5 

58.1 

48.7 

AU 

38.0 

By use of the appropriate height, H, the maximum concentration for each wind speed and 

stability can be determined by. obtaining the 

Example Problems 

RP UWI.U>H_JII. ; i* 
maximum xu/Q as a function of H and stability 

from Figure 3-9 and multiplying by the appropriate Q/u. The computations are s'crn larized 

in Table 7-6, and plotted in Figure 7-5. 

0.5 2 3 4 5 7 

WIND SPEED, m ite-' 

10 20 

Figure 7-5. 

Table 7-6 

Maximum concentration as a function of 

wind speed (Problem 14). 

MAXIMUM CONCENTRATION AS A FUNCTION OF 

WIND SPEED (PROBLEM 14) 

f Stability 

Class 

B 

D 

u, 

m sec-1 

0.5 

1.0 

1.5 

2 

3 

5 

7 

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

U/Q».x. 

IT)- = 

8.0 x IO"9 

2.0 x 10"3 

3.1 x IO"5 

4.1 x 10-5 

5.7 x IO"5 

7.8 x 10-' 

8.7 x 10-s 

4.4 x 10-8 

1.42xl0-5 

2.47x10-' 

3.5 x IO"5 

5.1 x IO"6 

7.3xlO-5 

8.2 x 10"5 

9.4x10-= 

1.1 x 10~* 

Q/u, 

gnr-i 

144 

72 

48 

36 

24 

14.4 

10.3 

144 

72 

48 

36 

24 

14.4 

10.3 

7.2 

3.6 

Xmwt* 

g nrs 

1.15x10-' 

1.44 x IO"3 

1.49xl0~3<<-

1.48 xlO"3 

1.37 x IO"3 

1.12xl0-s 

8.96x10"* 

6.34 x 10"* 

1.02 x IO"3 

1.19 xlO"3 

1.26xl0-3<-

1.22 xlO"3 

1.05 xlO"3 

8.45x10-* 

6.77x10-

3.96x10-* 

Y_ 

T h e wind speeds that give the highest maximum 

concentrations for each stability are, from Figure 7-5: B 1.5, D 2.0. 

PROBLEM 15: A proposed pulp processing plant 

is expected to emit y_ ton per day of hydrogen 

sulfide from a single stack. The company property 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 IO-0 g m -\ 

for any period greater than 30 minutes. Wind 

direction frequencies indicate tha t 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 

tha t 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 tha t the 

physical stack height and effective stack height 

are the same, to incorporate a slight safety 

factor. 

SOLUTION: The source strength is: 

O 1000 lb day 1 x 453.6 g lb -

1 

y

 "°" 86,400 sec day-1 

FromEq. (4.2): 

0.117 Q 0.117 (5.25) 

5.25 g sec" 

Oy O . 

Xou 

1.06 x 10* m2 

(2.9 x 10"s) 2 

At a design distance of 1500 meters (the limit 

of company property), os ot «— 1.06 x 10* gives 

a point from Figure 4-1 about 0.2 from Qass C 

to Class O along the line x =— 1500 m. From 

Figure 3-3, oz = 80 for this stability. 

H = \/2~oz = 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 effective stack height and the method used in problem 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. 

vR — 45 ft sec-1 = 13.7 m sec-1 

d — 8 ft —i 2.44 m 

T. — 250°F — 121 °C — 394°K 

T. =- 68°F — 20°C =- 293°K 

p = 920 mb 

v.d. AH 

u 

1.5 + 2.68 x 10~3 p 

T,—T. 

T. 

13.7 (2.44) 

u 

394-293 

1.5 + 2.68 x IO"3 (920) 

394 

(2.44) 

^ 

) 

50 

•?&-.;•. 

ATMOSPHERIC DISPERSION ESTIMATES 

B M - '-'•— 
P.55 

r

: 

( 

CAH 

33.4 

u 

33.4 

u 

102 

u 

[1.5+ (2.46) 0.256 (2.44)] 

(1.5 + 1.54) 

The relation between o> oz and u is: 

0.117 Q 0.117 (5.25) 2.12 x 10* 

OyOZ 

X d " 2.9 x IO"5

 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) 

u. AH, 

tn sec - 1 m 

0.5 

1.0 

1.5 

20 

25 

3.0 

5.0 

7.0 

10.0 

15.0 

204 

102 

68 

51 

41 

34 

20 

15 

10 

7 

Oy Ov 

m

2 

4.24 x 10* 

2.12 x 10* 

1.41 x 10* 

1.06 x 10* 

8.48 x 103 

7.06 xlO3 

4.24 x10s 

3.03 x IO3 

2.12 x IO3 

1.41 x IO1 

Stability to 

Give ov <yt at 

1500 m 

0.9, from A to B 

0.6 from B to C 

0.9 from B to C 

0.2 from C to D 

0.4 from C to D 

0.6 from C to 0 

D 

0.5 from D to E 

E 

0.5 from E to F 

Oz' 

m 

190 

120 

96 

76 

64 

56 

42 

34 

28 

23 

HLr° 

V

2

 ov 

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 IO10 particles 

per gram of tracer. Sampling is by membrane 

filters through which 9 x IO-3 m3 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 sec-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 (g sec m"3) 20 particles 

1.8 x IO10 particles g" 

60 sec min"1 

9 x IO"3 m3 min" 

1200 

16.2 x IO7 

DT == 7.41 x IO-* g sec m-3 

The total dosage islpven in g sec m"3 from 

DT (x,y,0;0) -f* exp 

— U Oy Os 

where QT is the total release in grams 

Therefore QT - * U " * D T 

H-fc)"] 

1-M-tY] exp 

For slightly unstable conditions (Class C) at 

x = 8 km, o7 = 690 m, oz = 310 m; y — 2000 m, 

u = 5 m sec-1 

Qi 

5 (690) 310 (7.41 x IO"*) 

exp 

1_ / 2000 \ "-1 

2 (, 690 ) J 

24.9 

exp [—0.5 (2.90)=] 

24.9 

1.49 x IO"2 

Q T 1670 g 

No correction has been made for the facts that 

the release is for 1 hour and the standard deviations represent time periods of 3 to 15 minutes. 

PROBLEM 18: A release of 2 kg of fluorescent 

particles is made based on the results of the 

computation in problem 17. The conditions are 

class C stability and wind speed 5 m sec'1. The 

crosswind-integrated ground-level dosage along 

the 8-kni arc is determined from the samplers 

along this arc to be 8.2 x IO-1 g sec m"2. What 

is the effective oz for this run? 

SOLUTION: 

given by: 

Dcwi 

The crosswind-integrated dosage is 

2QT 

= = exp 

V 2 T ot u [-"(•f)'l 

Since the source is at ground-level, the exponential has a value of 1. Solving for a,: 

2 Qr 

oz V2JT DCWI U 

2 (2000) 

V27.0.82) 5 

4000 

10.28 

o_ = 389 m 

Example Problems 

.+_«<&&:' ;.-*;*.;:•' . 

• • :••. -yif.icy-.-. 

::. I'0**rii£i^--*rm' -•"* 
PROBLEM 19: At a point directly downwind 

from a ground-level source the 3- to 15-minute 

concentration is estimated to be 3.4 v i0~3 g 

m

- 3

. What would you estimate the 2-hoir concentration 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: 

\ 120 j 

3.4 x 10" 

40u-

: 

3.4 x 1Q-" 

2.09 

(3.4 x IO"3) 

= 1.6 x 10~" g inLetting k 15 min, s = 2 hours, and p 

x . ..our = (-^- ) °-" 3.4 x IO"3 

(3.4 x IO"3) 

0.17 

8 °-17 

3.4 x 10~3 

1.42 2.4 x IO"' g m" 

The 2-hour concentration is estimated to be 

between 1.6 x 10_:: and 2.4 x 10"" g m-=. 

PROBLEM 20: Two sources of SO= are shown as 

points A and B in Figure 7-6. On a sunny 

summer afternoon the surface wind is from 60° 

a t 6 m sec-1. Source A is a power plant emitting 

1450 g sec-1 SO. from two stacks whose physical 

height is 120 meters and whose AH, from Holland's equation, is A H (m) — 538 (m- sec- 1 )/u 

(m sec- 1 ). Source B is a refinery emitting 126 g 

sec- 1 SO. 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 

tha t the mean direction of travel of both plumes 

is 245°, and there are no other sources of SO., 

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. 

A H = 

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 km 

y= «.4 km 

RECEPTOR 

SCAIE. km 

I 1 — X 

0 2 4 

Figure 7-6. Locations of sources and receptor (Problem 

20). 

x (x,y,0;H) Q 

exp 

[--H-sri 

— Oy Oz U KBr)1 

r i / 

exp 

For Source A, x = 24.6 km, y = 8.4 km 

oy = 1810 m, cr» •= 1120 m, u = 8.5 m sec- 1 

r 1810 (1120) 8.5 exp I —0.5 [ 

1450 

1120 

exp [—0.5 (4.64)2] 5.42 x 10r 

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. 

oT = 1050 m, u_ = 640 m, u = 7.0 m sec- 1 

126 

"N 

XB= -

TT 1050 (640) 7 exp 

exp [-*>(•&)'] 

[-"(w)"] 

126 

exp [—0.5 (3.81)-] 1.48 x IO7 

exp [—0.5 (0.0938)2] 

= 8.5 x IO"* (7.04 x 10"*) (0.996) 

Xix = 6.0 x 10"° g nr 3 

x = XA + XB = 0.56 x 10"8

 + 6.0 x 10-» 

= 6.6 x IO-0 gm' 1 

". 

. -yi}i&:;.iri.'•....... V^&g&VATMOSPHERIC DISPERSION ESTIMATES 
PROBLEM 21: A stack 15 meters high emits 3 g 

sec-1 of a particular air pollutant. The surrounding 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 concentration 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 IO"7 g m-3? 

SOLUTION: A clear night with 4 m sec-1 indicates class E stability. Eq. (3.4) for groundlevel concentrations from a ground-level source 

is most applicable (See Chapter 5). At 3 km 

for class E, or = 140 m, oz = 43 m. 

Q 3 

* JT oy ot u w 140 (43) 4 

X — 3.97 x 10"5 g m"3 

To determine the crosswind distance from the 

plume centeriine to produce a concentration of 

10~7 g m-3 Eq. (3.8) is used: 

= j 2 ln 

— j 2 ln 

x U,0,0) 

x (x,y,0) 

3.97 x IO"5 

tan G 

10~7 

— (21n397)v= 140 

— (2 x 5.98) "Z2 140 

= 3.46 x 140 

— 484 m. 

484 

1 

(140) 

3000 

G = 9.2° 

0.1614 

A wind shift of 9.2° is required to reduce the 

concentration to IO-7 g m-3. 

, PROBLEM 22: An inventory of SO. emissions 

has been conducted in an urban area by square 

areas, 5000 ft (1524 meters) on a side. The 

emissions from one such area are estimated to 

be 6 g sec-1 for the entire area. This square is 

composed of residences and a few small commercial establishments. What is the concentration resulting from this area at the center of the 

adjacent square to the north when the wind is 

blowing from the south on a thinly overcast 

night with the wind at 2.5 m sec-1? The average 

effective stack height of these sources is assumed 

to be 20 meters. 

SOLUTION: A thinly overcast night with wind 

speed 2.5 m sec"1 indicates stability of class" 13. 

s/lei 

(It may actually be more unstable, since this is 

a built-up area.) To allow for the area source, 

let oya = 1524/4.3 = 354. For class E the virtual distance, xy = 8.5 km. For x = 1524 m, 

<r«=-28.5. Forx 

Q 

xy =10,024 m, oy = 410 m. 

X=* IT Oy Ot T

exp[--HTr)'] 

exp[—Hw) ] 

\S 

>r410 (28.5) 2.5 

•=6.54xl<rs (0.783) 

= 5.1 x 10-9 g m"1 

PROBLEM 23: An estimate is required of the 

total hydrocarbon concentration 300 meters 

downwind of an expressway at 1730 on an overcast day with wind speed 4 m sec-1

. The expressway runs north-south and the wind is from 

the west. The measured traffic flow is 8000 

vehicles per hour during this rush hour, and the 

average speed of the vehicles is 40 miles per 

hour. At this speed the average vehicle is expected to emit 2 x 10"* g sec-1

 of total hydrocarbons. 

SOLUTION: The expressway may be considered 

as a continuous infinite line source. To obtain 

a source strength q in grams sec-1 m_l, the number of vehicles per meter of highway must be 

calculated and multiplied.by the emission per 

vehicle. —— _ 

Vehicles/meter — 

Flow (vehicles hour"1) 

Average speed (miles hour-1) 1600 (m mile-1) 

40x1600

 1 '2 5 X 10_ 1 (vehicle s m_1 ) 

q — 1.25 x 10"1 (vehicles nr 1) x 2 x IO"2 

(g sec-1 vehide-1) 

q = 2.5 x lO-^g: sec-1 nr 1) 

Under overcast conditions with wind speed 4 m 

sec-1 stability class D applies. Under D, at x — 

300 meters, o% — 12 m. From Eq. (5.18): 

X (300,0,0;0) 3 

V2i r ff, U 

2 (2.5 x IO"3) 

2.507 (12+4 

— 4.2 x 10"* g nr* of total hydrocarbons. 

PROBLEM 24: A line of burning agricultural 

waste can be considered a finite line source 150 

m long. It is estimated that the total emission 

of organics is at a rate of 90 g sec'1. What is the 

3- to 15-minute concentration of organics at a 

distance of 400 m directly downwind from the 

center of the line when the wind is blowing at 

3 m sec"' perpendicular to the line? Assume 

Example Problems 

SiAiv-;-: 

ssssas1-
that it is 1600 on a sunny fall afternoon. What 

is the concentration directly downwind from one 

' end of the source? 

JLUTION: 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, <ry = 45 m, oz = 26 m. 

Q 90 

M

 150 150 

Eq. (5.20) is appropriate. 

= 0.6 g sec-1 m" 

x (x,0,0;0) = 

V2 

exp (—0.5 p2) dp 

fp. 3 j 

'2*r a. U I 

J P. 

1 

XT* 

— +1.67 

—75 . R7 y 

A- = 1-67, p2 = = 

4 5 Oy 

75 

45 

X (400,0,0,0) = 

2 (0.6) f

+1'67 

J —1.67 \'2* \/2W26)3 

exp (—0.5 p2) dp 

= 6.14 xlO"3 (0.91) 

= 5.6 x IO"3 g m"3 

For a point downwind of one of the ends of the 

line: 

Pi — 0, p, 

_y_ 

Oy 

150 

45 +3.33 

/ ; 

-3.33 

V2T. 

X (400,0,0;0) = 6.14 x IO"3 

exp (—0.5 p=) dp 

= 6.14 x IO"3 (0.4995) 

= 3.1 x 10-r g m"3 

PROBLEM 25: A core melt-down of a power reactor that has been operating for over a year 

occurs at 0200, releasing 1.5 x 10° 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 ( * ) 

-° =. It is estimated that about 5.3 x IO4 

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 

0.17c 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 

tivity (corrected for decay) 

0.001 day-1 

leak rate x acLeak rate 86400 sec day-1 

— 1.157 x IO"8 sec"1 

Source strength of all products 

QA (curies sec"1) = 1.157 x 10~8 (1.5 x 10r) 

—0.2 [ t (sec) ] 

[ to (sec) J 

= 1.74 x IO"2 '(4-) —0.2 

To determine decay of materials with the half-

... ... , , /—0.6931\ 

life given, multiply by exp I = J 

ic tim e nnrl T. io Violf-lifo \ / 

where t 

Qi (curies sec-1) 

—0.693 t 

L 

For I m L = 

Qi = 6.13 x IO"4 exp (-

is time and L is half-life. 

Source strength of I131. 

1.157 x 10"8 (5.3 x 104) exp 

/ —0.693 t \ 

6.95 x 10s sec 

—0.693 t \ 

6.95 x 10s ) 

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 <xy0 — 2.15 oto = the 

radius of the shell = 20 m <ryo —» <r.o = 9-3 m. 

The virtual distances to account for this are: 

xy = 250 m, xx = 560 m. 

At x = 3000 m. x + xT = 3250 m, oT = 100 m. 

x + x, = 3560 m, oz = 29 m. 

0 Q X (x,0,0;0) = 

W Oy Ot U 

= 4.4 x 10"5 Q 

» 100 (29) 2.5 

For concentration at 0400, 3000 m downwind 

due to all radioactivity, t = 7200 seconds. 

XA = 4.4 x 1(TS

 (1.74 x IO"2) (7200)-0-

2 

= 7.66 x 10"7 (0.17) 

XA — 1.3 x 10"7 curies m"3 

The concentration at 0400, 3000 m downwind 

due to I1S1 is: 

Xi = 4.4 x 10~s (6.13 x 104) exD [—0.997 x 10-

(7200)] ) 

54 

•*&r -

:-&$ : • 

ATMOSPHERIC DISPERSION ESTIMATES 
P.59 

= 2.7 x IO-1 (1.0) The decay of I131 is insignificant for 2 hours 

Xi 2.7 x 10_S

 curies m~ 

PROBLEM 26: A spill estimated at 2.9 x IO* 

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~!, it is estimated that the evaporation rate 

will be 1100 g sec-1. The wind direction is predicted to be from 310° = 15° for the next hour. 

Table 7-8 gives the emergency tolerance limits 

for UDMH vapor. 

Table 7-8 EMERGENCY TOLERANCE LIMITS FOR UDMH 

VAPOR VERSUS EXPOSURE TIME 

Time, 

minutes 

Emergency Tolerance 

Limits, g nr 3 

5 

15 

30 

60 

1.2 x IO"1 

8.6 x 10"= 

4.9 x lOr2.5 x IO"5 

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 o>o 

to equal the width of the wetted area, 6.1 meters 

(20 feet), oy{, = 1.4 meters. In attempting to 

determine the virtual distance, x,-, it is found to 

be less than 100 meters, and will be approximated by 40 meters. The release will take: 

2.9 x 10" g 

1.1 x 10" g sec 

2.64 x 10:' sec = 44 min. 

Therefore the concentration for an exposure 

time of 1 hour (2.5 x 10"-' g m~") is of main 

concern. 

The equation for calculation of downwind concentrations is Eq. (3.4): 

Q X (x,0,0;0) 

of X + xv. 

If Oy 0Z XX 

where oy is a function 

Values of the parameters and of x are given in 

Table 7-9. 

Table 7-9 DETERMINATION OF CONCENTRATION AS A 

FUNCTION OF DISTANCE (PROBLEM 26) 

X, 

km 

0.1 

0.3 

0.6 

1 

3 

6 

10 

oz. 

m 

2.3 

5.6 

9.7 

14 

27 

37 

47 

x -r xv, 

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-

_ m - 3 

13.9 

2.5 

8.2 x IO"1 

3.6 x 10-* 

7.0x10"* 

2.7 x 10"2 

1.4 x IO"2 

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. 

1. 

o 

10 

1X1 

10 

IT1 

-* 

p—i—i—''i i 

" . 

' i i ; ! ; ! 

I ' I ' ! ! J 

i i : ' : ' 

M M M 

v ! i Hli!l 

*S_ ' i i i '" • i 1 

V i : ' ' i \ ! ! ... 

i X i '' 

1 ! N 

. -

• > ! 

• 

i ! i I ^ ; 

i • 1 

I 

i 

I 

i i I ; ! •, 

i | | II ! 

I 1 MM ! 

! i i ! Iii 

-• -

:

 II I ' ' 

' I ! 

i | 

i j 

1 

r 

• i . 

! •' . I 1 l 

I 

| 

1 

1 ; 

i 1 

X 

-V-• I 

,..,_ 

"^. ! 

1 "N if 

| 

i . 

y i 

1 

0.1 1 

DISTANCE, km 

10 

Figure 7-7. Concentration of UDMH as a function of downwind 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 310P± 15°, the sector at an 

azimuth of 115° to 145° plus a 140-meter rectangle on cither side should be evacuated. 

See Figure 7-8. 

Example Problems 

''••*m%tym?y • 
P.60 

km 

0.1 

0.5 

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

Table 7-10 DETERMINATION OF WIDTHS 

ISOPLETHS (PROBLEM 26) 

X + Xy , 

km 

0.14 

0.54 

1.04 

2.04 

3.04 

4.04 

5.04 

6.04 

<ry. 

ni 

5.5 

19 

35 

66 

93 

120 

149 

175 

x (centerline), 

g m-:l 

13.9 

1.1 

3.6 x 10"' 

1.3 xlO" 1 

7.0 x 10~-

4.8 x 10"-

3.5 x 10--

2.7 x 10-J 

y (isopleth) 

X (centerline) 

1.8 xlO-;! 

2.27 x 10"-

6.94 x 10"-

1.92 x IO"1 

3.57 x IO"1 

5.20 x IO"1 

7.14 x IO"1 

9.26 x IO"1 

WITHIN 

y 

Oy 

3.55 

2.75 

2.31 

1.82 

1.44 

1.14 

0.82 

0.39 

y. 

IB 

20 

52 

80 

120 

134 

137 

122 

68 

SCALE, km 

ITIIITIIIII ' I : 

M 5 * 

Figure 7-SL Possible positions of the 2.5 x IO""2 g m~s 

isqpfeth and the evacuation area (Problem 26). 

(

: -. 

56 

• .^-v^^'fW-VwJ'*, 

ATMOSPHERIC DISPERSION ESTIMATES 

•a?**? 

"•#£-.•-
P.61 

APPENDICES 

C": 

139-901 O - 69 - I 

•".-•TSgSJ 

--^ssSLy?. ..JW&tii-
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 

c,, specific heat at constant pressure 

C, Sutton horizontal dispersion parameter 

C_ Sutton vertical dispersion parameter 

d inside stack diameter at stack top 

DT (x,y,0;H) Total dosage 

e 2.71S3, the base of natural logarithms 

f (0,S,N) frequency of wind direction for a givenstability 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 

n 

N 

P 

/ 

Q 

Qr 

R 

s 

S 

tk 

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 

Sutton's exponent 

an index for wind speed class 

three uses: 1. Bosanquet's horizontal dispersion parameter 

2. atmospheric pressure 

3. a dummy variable in the equation for a Gaussian distribution. 

two uses: 1. Bosanquet's vertical dispersion 

parameter 

2. emission rate per length of a line 

source 

emission rate of a source 

total emission during an entire release 

net rate of sensible heating of an air column 

by solar radiation 

the length of the edge of a square area source 

an index for stability 

a short time period 

tm 

T. 

T. 

u. 

UN 

V

7 

V* 

V, 

w' 

X 

X i . 

Xx 

Xy 

x,, 

y 

z 

z.. 

SO 

sT 

AH 

PA 

"A 

OK 

o*i.. 

Oy 

Oyl | 

Ozl. 

Or,, 

time required for- the mixing layer to develop* 

from the top of th e stack to the top; of the 

plume 

a time period 

ambient air temperature 

stack gas temperature- a t stack top 

wind speed 

a mean wind speed for the wind speed class. N~„ 

horizontal eddy vefoeity 

stack gas velocity at the stack top 

a velocity used by Calder 

vertical eddy velocity 

distance downwind in the direction of the.1 

mean wind 

design distance, a particular downwind distance used, for design purposes 

the distance at which <rx = 0.47L 

a virtual distance so that <*„ (x_) equals the initial standard deviation, irx„ 

a virtual distance so that _•,. (xv) equals the initial standard deviation, _•.,.„ 

a virtual distance so. that ov (x_) equals the initial standard deviation, o,.„ 

crosswind distance 

height above ground level 

roughness parameter 

the rate of: change of potential temperature 

with height 

the rise of the plume, centerline above the stack: 

top 

two uses: 1. wind'direction-azimuth or sector 

2. potential temperature 

3.1416 

ambient air density 

the standard deviation of. azimuth (wind direction) as determined from a wind vane or bidirectional vane 

the standard deviation of wind elevation angle 

as determined from a bi-directional vane 

the standard deviation in the downwind direction of a puff concentration distribution 

an initial downwind standard deviation 

the standard deviation in the crosswind direction of the plume concentration distribution "w"1

^'-* 

an initial crosswind standard deviation 

the standard deviation in the vertical of the 

plume concentration distribution - ...;.*«...'•«•*, 

an effective oz equal to 0:8 L 

an initial vertical standard deviation 

the vertical standard deviation of the plume 

concentration at a particular downwind distance for the stability, S. 

Appendix 1 

.'w4^i^Bfr.'«i-"i*£-- •.•a^f^f.iir*-
P.63 

p the angle between the wind direction and a 

line source 

concentration 

V1;YVI crosswind-integrated concentration 

,\-<i a ground-level concentration for design purposes 

Xi- inversion break-up fumigation concentration 

Xk concentration measured over a sampling time, 

tk 

Xiiins maximum ground-level centerline concentration with respect to downwind distance 

XK concentration measured over a sampling time, 

t. 

y 

£— relative concentration 

|L- relative concentration. normalized for wind 

" speed 

X (x,y,z;H) concentration at the point (x, y, z) 

from an elevated source with effective 

height, H. 

X (x,e) the long-term average concentration at 

distance x, for a direction 0 from a source. 

J 

60 ATMOSPHERIC DISPERSION ESTIMATES 

*_^w"£^-*. - •-• w.V . .•*... .•;5^«jsijiiy-..i. . ..^yU^.y^Y'y^hr -' '-.:*-

 !^"^.yffiy^ 
P.64 

Appendix 2: CHARACTERISTICS OF THE 

GAUSSIAN DISTRIBUTION 

The Gaussian or normal distribution can be depicted by the bellshaped curve shown in Figure A-1. 

The equation for the ordinate value of this curve is: 

y = J - exp f L ( *—~* ) 1 

V2r . [ 2 1 6 ) \ (A.1) 

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-1. 

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 (-

exp (—0.5 p-) dp 

^

t0P)= J _ ~fe-

(A.2) 

Figure A-4 gives the area under the Gaussian 

curve from —p to -j-p. This can be found from Eq. 

(A.3): 

Area (—p to +p ) = 

exp (—0.5 p2) dp 

i-P

 v" 

(A.3) 

( 

Figure A-1. The Gaussian distribution curve. 

Appendix 2 61 

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0.0 0.2 0.4 0.6 0.8 1.0 12 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. 

f 

j 

ATMOSPHERIC DISPERSION ESTIMATES 

•••iM 
0.01 0.1 0.5 1 2 5 10 20 40 60 80 90 95 98 99 99.8 99.99 

/ : 

P

 -4=_ .<p (-0.5 p3) lip 

Figure A-3. Area under the Gaussian distribution curve from — <* to p. 

Appendix 2 

H*P^r" 3ip W*.% •' 

. - . .,'._rT , L 

' •' \___ ^c.-' 

63 
P.67 

/' 

99.8 99.99 

/ ••-'-• • 

Figure A-4. Area under the Gaussian distribution curve between —p and -fp. 

64 ATMOSPHERIC DISPERSION ESTIMATES 

. .;-#*ai-r*-"-

*§if 

.=__=_«. 

*____ 
P.68 

Vpp.-mlix 3: SOLUTIO.NS TO EXPONENTIALS 

Expressions of the form exp [—0.5 A:] where 

A is H o-7. or y/oy frequently must be evaluated. 

Table A-1 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.HE — 03 

which means 2.11 x IO"3 

/ 

Appendix 3 65 

',^».-.--;- •.-&&*&*••'' ' 

•••':• • •.•.'.,:,'.;•->• 

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P.69 

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GC ATMOSPHERIC DISPERSION ESTIMATES 

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5.1 0 

5.2 0 

5.3 0 

5.4 0 

5.5 0 

5.6 0 

5.7 0 

5.8 0 

5.9 0 

6.0 0 

6.1 0 

6.2 0 

6.3 0 

6.4 0 

6.5 0 

6.6 0 

6.7 0 

6.6 0 

6.9 0 

7.0C 

7.1 0 

7.2 0 

7.3 0 

7.4 0 

7.5 0 

7.6 0 

7.7 0 

7.8 0 

7.9 0 

B.00 

B.1C 

8.2 0 

8.3 0 

8.4 0 

8.5 0 

8.6 0 

8.7 0 

8.8 0 

8.9 0 

9.0 0 

9.1 0 

9.2 0 

9.3 0 

9.4 0 

9.5 0 

9.6 0 

9.7 0 

9.8 0 

9.9 0 

_ O.OO 

B 

3.M E 

2.2SE 

1.34C 

7.9S t 

**.6 HE 

2.70 c 

1.55c 

8.R1E 

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2.7K.E 

1.52 t 

8.3. E 

4.50E 

<!.41E 

1.291. 

6.6QE3.4QE1.7a_ -

9.10E -

* . 5 .t -

2.20E -

1.13E5454E2.68E1.29E6.10E2.87E1.3*E -

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- 6 

- 6 

- 7 

- 7 

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- . 

. 8 

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. 8 

- 9 

- 9 

- 9 

- 9 

10 

10 

10 

11 

11 

11 

11 

•12 

12 

.12 

• 13 

• 13 

• 13 

• 14 

• 14 

• 14 

•15 

15 

1.10E-1 5 

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2.0.E -

• 16 

• 16 

8.71E-1 7 

3.67E-• 17 

1.53E-1 7 

6.31E-1 8 

<.58E1.04E4.1BEl.64t -

6.50E-

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6.27E3.25E1.67F8 . . o_-

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- 9 

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• 12 

• 13 

13 

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15 

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3.36E-1 7 

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8.83E3.36E1.27E4.73E . 

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4.79E2.32E-

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• 16 

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1.73E7.33E-

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1.28E-1 7 

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B.69E3.47E1.37E5.31E2.09E8.02E3,OBELISE -

4.2A_ -

•19 

• 19 

•19 

•20 

• 20 

•21 

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22 

VI (cont 

0.0 3 

J.21E 

1.93E 

1.15E 

h . 7 .E 

1.96E 

2.29E 

1.31E 

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2.31E 

1.27E 

6.92E 

1.73E 

1.99E 

1.05E 

nuiid 

- 6 

- 6 

- 6 

- 7 

- 7 

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- 8 

- 8 

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5.50E-1 0 

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10 

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2.21E- U 

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1.96E-

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3.70E1.59E-• 16 

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6.72E-1 7 

Z.82E-1 7 

1.17E-1 7 

4.83E-1 8 

1.97E. •18 

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3.17E1.25E4.90E1.90E-

• 19 

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3.8RE-

• 21 

,21 

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) SOLUTION! 

0.0 4 

3.05 £ -A 

1.81E - 6 

l.O.E - 6 

*.<>TE - 7 

J.75E . 7 

2.1' E - 7 

1.24E - 7 

?.01E - 8 

J.93E - 8 

2.18E - 8 

1.20E - 8 

6.51E - 9 

3.51E - 9 

l.BTE - 9 

9.87E-1 0 

5.16E-1 0 

2.6'£-1 0 

1.37E-1 0 

6.93E-1 1 

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9.80E-1 * 

4.50E-1 4 

2.0.E-1* . 

9.19E-1 5 

4.09E-1 5 

1.60E-1 5 

7.87E-1 6 

3.«0£.1 6 

1.46E-1 6 

6.17E-1 7 

2.59E-1 7 

1.07E-1 7 

A. .IE-I B 

1.80E-1 8 

7.24E-1 9 

2.89E-1 9 

l.l^E-1 9 

4.46E-.20 

1.73E-2 0 

6.62E-2 1 

2.51E-2 1 

9,<»3E-22 

3.51E-2 2 

> TO EXPONEN 

0.0 5 

2.90E - 6 

1.7<.E - 6 

1.0*E - 6 

6.09E - 7 

3.55,. - 7 

2.05E - 7 

1.17E - 7 

6.62E - 8 

3.70E - 8 

2.0. E - 8 

1.13E - 8 

6.12 . - 9 

3.29E - 9 

1.75E - 9 

9.2bE-1 0 

<i.83F-10 

2.S0E-1O 

1.28E-1 0 

6.A7E-1 1 

3.25E- U 

1.61.-1 1 

7.92E-1 2 

3.86E-1 2 

1.R6E-12 

8.87E-1 3 

<,.19E-13 

1.96E-1 3 

9.07E-1 * 

4.16E- K 

1.89E- 1 . 

8.48E-1 5 

3.77E-1 5 

1.66E-1 5 

7.2<»E-16 

3.13E-1 6 

1.34E-1 6 

5.66E-1 7 

2.37E-1 7 

9.83E-1 8 

4.04E-1 8 

1.6«E-1 8 

6.61E-1 9 

2.63E-1 9 

1.0*E-1 9 

..06E-2 0 

1.57E-2 0 

6.01E-2 1 

2.28E-2 1 

8.55E-2 2 

3.13E-2 2 

TIALS 

0.0 6 

2.76E - 6 

1.65E - 6 

9.82E - 7 

5.77E - 7 

3.36E - 7 

1.9<-E - 7 

1.11E - 7 

6.25E - 8 

3 , .9E - 8 

1.94E - 8 

1.06E - 8 

5.76E - 9 

3.09E - 9 

1.65E - 9 

8.67E-1 0 

4.52E-1 0 

2.3«E-1 0 

1.19E-1 0 

6.04E-1 1 

3.03E-1 1 

1.50E-1 1 

7.38E-1 2 

3.59E-1 2 

1.73E-1 2 

8.23E-1 3 

3.88E-1 3 

1.81E-1 3 

8.39E-1 * 

3.84E- H 

1.7.E-1 * 

7.82E-1 5 

3.*8E-1 5 

1.53E-1 5 

6.66E-1 6 

2.87E-1 6 

1.23E-1 6 

5.19E-1 7 

2.17E-1 7 

9.00E-1 8 

3.69E-1 B 

1.50E-1 8 

6.03E-1 9 

2.40E-1 9 

9,«6E-2 0 

3.69E-2 0 

l.*3E-2 0 

5,<»6E-21 

2.07E-2 1 

7.75E-2 2 

2.BBE-22 

0.0 7 0.0 8 

2.62E - 6 2.49E - 6 

1.57E - 6 .49E - 6 

9.32E - 7 8.84E - 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-1 0 

*.2<>E-10 

2.19E-1 0 -

1.12E-1 0 

5.64E- U ! 

2.82E-1 1 > 

1.40E-1 1 1 

6.B7E-1 2 t 

3.34E-1 2 • 

1.60E-1 2 

7.64E-1 3 1 

3.60E-1 3 2 

1.68E-1 3 1 

7.77E-1 4 1 

3.55E-1 4 

1.61E-1 4 

7.22E-1 5 < 

3.20E-1 5 * 

1.41E-1 5 1 

6.13E-1 6 ! 

2.64E-1 6 J 

1.13E-1 6 

*.76E-1 7 ' 

1.99E-1 7 

8.23E-1 8 1 

3.37E-1 B 

1.37E-1 8 1 

5.50E-1 9 '• 

2.19E-1 9 

8.61E-2 0 1 

3.36E-2 0 • 

1.30E-2 0 

4.95E-2 1

 4 

1.87E-2 1 

7.02E-2 2 < 

2.60E-2 2 * 

M 9 E - 7 

J.OlE - 7 

1.73E - 7 

J.87E - 8 

>.57E - 8 

>.11E . 8 

1.72E - 8 

>.39E - 9 

>.09E - 9 

?.73E - 9 

l.«5E - 9 

'.62E-1 0 

I.97E-1 0 

J.04E-1 0 

I.04E-1 0 

>.27E- U 

S.63E- H 

1.30E- U 

W39E-1 2 

l.lOE-1 2 

l.*9E-1 2 

'.09E- H 

I.34E-1 3 

1.56E-13 

M9E-1 * 

I.28E-1 * 

l.*9E-l * 

,.66E-1 ' 

!.95E-1 5 

.30E-1 5 

1.64E-16 

!.43E-1 * 

1.03E-16 

•.36E-1 7 

1.82E.1 7 

r,53E- U 

I.OsE-1 8 

1.25E-18 

I.02E.1 9 

I.99E-1 9 

'.84E-2 0 

I.05E-2 0 

1.18E-2 0 

• .50E-2 1 

1.70E-2 1 

i.36£-2 2 

E.36E-2Z 

0*0 9 

2.37E - 6 

1.42E . 6 

B.38E . 7 

4.91E - 7 

2.BSE . 7 

1.64E . 7 

9.32E . 8 

5.25E . 8 

2.93E . 8 

I.62E . 8 

B.84E . 9 

4.78E . 9 

2.56E . 9 

1.36E . 9 

7.14E-1 0 

3.71E-1 0 

1.91E-1 0 

9.74E-1 1 

4.92E-1 1 

2.46E-1 1 

1.22E-1 1 

5.95E-1 2 

2.88E-1 2 

1.38C-1 2 

6.58E-1S 

3.09E-1 3 

1.44E-1 3 

6.6JE-1 4 

3.04E-1 4 

1.37E-1 4 

6.14E-1 5 

2.72E-1 5 

1.19E-1 5 

5.18E-1 6 

2.23E.1 6 

9.49E-1 7 

4.00E-1 7 

1.67E-1 7 

6.89E-1 8 

2.82E-1 8 

1.14E-1 8 

4.38E-1 9 

1.82E.1 9 

7.14E-2 0 

2.78E-2 0 

1.07E-2 0 

4.08E-2 1 

1.54C-2 1 

5.76E-2 2 

2.13C2 2 
P.71 

Appendix 4: CONSTANTS, CONVERSION 

EQUATIONS, CONVERSION TABLES 

Constants 

e = 2.7183 — 0.3679 

a- = 3.1416 = 0.3183 

2:r = 6.2832 

\/27 = 2.5066 

V2-

2 

— 0.1592 

= 0.3989 

— 0.7979 

(2-yr- = 15.75 

Conversion Equations and Tables 

T(°C) =5/ 9 (T(°F) —32) 

T(°K) =T(°C) +273.16 

T(°F) = (9/5T(°C) ) +3 2 

Appendix 4 

J-'n.Hlf.m T -

69 
•a 

o 

Y 

r.-

CONVERSION FACTORS - VELOCITY 

* 

*& 

im- j. 

GIVEN UNITS 

METERS 

PER SEC 

FT 

PER SEC 

FT 

PER MIN 

KM 

PER HR 

MKSTAT) 

PER HR 

KNOTS 

MKSTAT) 

PER DAY 

METERS 

PER 

1,0000 

E 00 

3.0.8 0 

E-Ol 

9.080 0 

E-03 

2.777 8 

E-Ol 

A,470 * 

E-Ol 

5.147 9 

E-Oi 

1,8627 

E-02 

FT 

SEC PEP 

3.2808 

E 00 

1.0000 

E 00 

1.6667 

E-02 

9.1134 

E-Ol 

1.4667 

E 00 

1.6889 

E 00 

6.1111 

E-02 

FT 

SEC PER MIN 

1.9689 

E 02 

6.000 0 

E 01 

1.0000 

E 00 

5.468 1 

E 01 

8.800 0 

E 01 

1.0134 

E 02 

3.6667 

E 00 

KM 

PER HR 

3.600 0 

E 00 

1.0973 

E 00 

1.8288 

E-02 

1.0000 

E 00 

1.6093 

E 00 

1.8532 

E 00 

6.7096 

E-02 

MKSTAT) 

PER HR 

2,236 9 

E 00 

6.818 2 

E-Ol 

1.1364 

E-02 

6.213 7 

E-Ol 

1.0000 

E 00 

1.1516 

E 00 

4.166 7 

E-02 

KNOTS 

1.9425 

E 00 

5.920 9 

E-Ol 

9.868 1 

E-03 

5,3959 

E-Ol 

8.6839 

E-Ol 

1.0000 

E 00 

3.6183 

E-02 

MKSTAT) 

PER DAY 

5.3686 

E 01 

1.6364 

E 01 

2.7273 

E-Ol 

1.4913 

E 01 

2.400 0 

E 01 

2,763 7 

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 

ANO BENEATH THE DESIRED UNIT. NOTE THAT E-XX MEANS 10 TO THE -XX POWER. 

^ ••s_ > 
\ 

li. s • •O •9 ti 

a 

cu 

CONVERSION FACTORS - EMISSION RATES 

DESIRED UNITS GRAMS GRAMS KG KG LBS LBS LBS TONS TONS 

PER SEC PER MIN PER HOUR PER DAY PER MIN PER HOUR PER DA* PER HOUR PER DAY 

GIVEN UNITS 

•Mu 

m 

!; 

te 

GRAMS 

PER SEC 

GRAMS 

PER MIN 

KG 

PER HOUR 

KG 

PER DAY 

LBS 

PER MIN 

LBS 

PER HOUR 

LBS 

PER OAY 

TONS 

PER HOUR 

TONS 

PER DAY 

1.0000 

E 00 

1,6667 

E-02 

2,7778 

E-Ol 

1.1374 

E-02 

7,5599 

E 00 

1.2600 

E-Ol 

5.2499 

E-03 

2.5200 

E 02 

1.0500 

E 01 

6.0000 

E 01 

1.0000 

E 00 

1.6667 

E 01 

6.9444 

E-Ol 

4.535<j 

E 02 

T.5599 

E 00 

3.1499 

E-Ol 

1.3120 

E 04 

6.2999 

E 02 

3.6000 

E 00 

6.0000 

E-02 

1.0000 

E 00 

4,1667 

E-02 

2.7216 

E 01 

4.5339 

E-Ol 

1.8900 

E-02 

9.0718 

E 02 

3.7799 

E 01 

8,6400 

E 01 

1.4400 

E 00 

2.4000 

E 01 

I.oooo 

E 00 

6.9317 

E 02 

1.0886 

E 01 

4.3339 

E-01 

2.1772 

E 04 

9.0718 

E 02 

1,3228 

E-Ol 

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 

7.9366 

E 00 

1.3228 

E-Ol 

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 

1.9048 

E 02 

3.1747 

E 00 

9,2911 

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 

3.9683 

E-03 

6.6139 

E-05 

1.1023 

E-03 

4,3930 

E-05 

3,0000 

E-02 

9.0000 

E-04 

2,0833 

E-05 

1,0000 

E 00 

4.1667 

E-02 

9,9240 

E-02 

1.3873 

E-03 

2,6493 

E-02 

1.1023 

E-03 

7.2000 

E-Ol 

1,2000 

E-02 

9,0000 

E-04 

2,4000 

E 01 

1,0000 

E 00 

TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MULTIPLY THE 6IVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS 

ANO BENEATH THE DESIRED UNIT, NOTE THAT E-XX MEANS 10 TO THE -XX POWER, 

? >*:• • 
• • $ 

> 

_ 

o 

c/1 

"B 

X 

a 

SB 

r* 

o 

CONVERSION FACTORS - LENGTH 

DESIRED UNITS METER CM 

GIVEN UNITS 

METER 

CM 

MICRON 

KILOMETER 

INCH 

FOOT 

YARD 

MILECSTAT) 

MilEjNAUT) 

MICRON KILOMETER INCH FOOT YARD MRE(STAT) MILE(NAUT) 

1.0000 

E 00 

1.0000 

E-02 

1,0000 

E-06 

1,0000 

E 03 

2.5400 

E-02 

3,0480 

E-Ol 

9,1440 

E-Ol 

1.6093 

E 03 

1.8332 

E 03 

I.OOOO 

E 02 

I.OOOO 

E 00 

1.0000 

E-04 

1.0000 

E 03 

2.5400 

E 00 

3.04B0 -

E 01 

9.1440 

E 01 

1.6093 

E 09 

1.8532 

E 05 

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 

2.9400 

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-0' 

3,9370 

E-05 

3,9370 

E 04 

1,0000 

E 00 

1.2000 

E 01 

3.6000 

E 01 

6.3360 

E 04 

7,2962 

E 04 

3.2808 

E 00 

3.2808 

E-02 

3.28C8 

E-06 

3.2808 

E 03 

8.3333 

E-02 

1.0000 

E 00 

3.0000 

E 00 

9,2800 

E 03 

6,0802 

E 03 

1.0936 

E 00 

1.0936 

E.02 

1.0936 

E-06 

1,0936 

E 03 

2.7778 

£.02 

3.3333 

E-Ol 

1.0000 

E 00 

1.7600 

£ 03 

2.0267 

E 03 

6,213V 

E - 4 

6,2137 

£.06 

6,2137 

E-10 

6,2137 

E.01 

1.9783 

E-09 

1.8939 

£.04 

9.6818 

E-04 

1.0000 

E 00 

1.1516 

E 00 

3,3959 

E-04 

5,3959 

E-06 

5,3939 

E-10 

5.3959 

E-Oi 

1.3706 

E-05 

1.6447 

E-04 

4,9340 

E-04 

8,6839 

E-Ol 

1,0000 

E 00 

TO CONVERT A VALUE FROM A GIVEN UNIT TO A DESIRED UNIT, MUUTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS 

AND BENEATH THE DESIRE O UNIT, NOTE THAT E-XX MEANS 10 TO THE -XX POWER, 

yy 
V 

•»•! ! 

& : 

IS 

a 

Mo 

X 

lb. 

CONVERSION FACTORS DESIRED UNITS 

GIVEN UNITS 

SO METER 

SO KM 

SO CM 

SO INCH 

SO FOOT 

SO YARD 

ACRE 

50 STAT 

MILE 

SO NAUT 

j. MllE 

- AREA 

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-Ol 

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 

'.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 

3.4343 

E 10 

SQ INCH 

1.3500 

E 03 . 

1.5500 

E 09 

1.5500 

E-Ol 

1.0000 

E 00 

1.4400 

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 

I.OOOO 

E 00 

9,0000 

E 00 

4,3560 

E 04 

2.787S 

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-Ol 

1.0000 

E 00 

4.B400 

E 03 

3.0976 

E 06 

4,1076 

E 06 

ACRE 

2.4710 

£-04 

2.4710 

E 02 

2.4710 

£.08 

1.5942 

E-07 

2.2957 

E.05 

2.0661 

E-04 

1.0000 

E 00 

6.4000 

E 02 

8,4869 

E 02 

SQ STAT 

1ILE 

3.8610 

E-07 

3.8610 

E-Ol 

3.8610 

E-ll 

2.4910 

E-10 

3.5870 

£.08 

3,2283 

£.07 

1,5625 

E-03 

1.0000 

E 00 

1.3261 

E 00 

SQ NAUT 

MILE 

2.9116 

E-07 

2.9116 

E-Ol 

2,9116 

E-ll 

1,8785 

E-10 

2,7050 

E-08 

2,4345 

E-07 

1.1783 

E-03 

7,5411 

E-Ol 

1,0000 

E 00 

ISD C K2! H

A THF L Dfsfo « LVr^ unil I2_T pE_ »««> ^ l T. MULTIPLY THE GIVEN VALUE BY THE FACTOR OPPOSITE THE GIVEN UNITS 

AI\D BENEATH THE DESIRED UNIT, NOTE THAT E-XX MEANS 10 TO THE -XX POWER, 

1***1 mn • m -*t 

«r> 
'., 

-r 

CONVER.IO M rACTO?s - v?LU:-lE 

U

rSlRFi_ U-!ITS CU '*ETCP LITE" 

GlVEM UNITS 

CU METEP I.OOOO 

F no 

0.9997 

E OZ 

C'.l INC. CU FOOT 

6.102 1 

. 04 

3.5314 

E OJ 

Cu STAT Cu NAUT j S FLUID U S QUART 

MILE MILE OUNCE 

*.399 1 

E-10 

1.5711 

E-10 

3.3814 

E 04 

1,0567 

E-03 

U S GALLON 

2,6417 

E 02 

» ! • 

LITFR 

CU INCH 

CU FOOT 

CU STAT 

MILE 

1.0000 

E-13 

1,61_7 

2.811 7 

F-02 

H.U8 Z 

f 09 

l.nooo' 

E OU 

1.63H7 

E-02 

2.1316 

E or 

4.161 1 

E U 

6.1"2 5 

E 01 

1.0000 

F 00 

1.7280 

E 03 

2.5436 

E 14 

3.5'U . 

E-o? 

5.7X70 

E-«'4 

1.0000 

E ''O 

1.4720 

E H 

2.3992 

E-13 

3,9315 

E-15 

6.7936 

E-12 

1.0000 

E 00 

1.57 U 

E-13 

2.5746 

E-15 

4,4488 

E-12 

6,5486 

E-Ol 

3,3815 

E Ol 

5.5412 

E-Ol 

9.575 1 

E 02 

1.4094 

E 14 

1,0567 

E-06 

1.7316 

E-08 

2.9922 

E-05 

4,404 5 

E 06 

2,6418 

E-Ol 

4,329 0 

E-03 

7,4805 

E 00 

1.1011 

E 12 

CU NAUT 

M1LF 

6,365 0 

F 09 

6.3649 

E 1 / 

3.8«42 

F 14 

2.Z478 

E U 

1.5270 

E 00 

1,0000 

E 00 

2.1523 

E 14 

6.7259 

E 06 

1.6815 

E 12 

U S FLUID 

OU'ICF 

2.957 4 

F-05 

2,9573 

E-02 

1.8047 

E OO 

1,0444 

E-03 

'.095 0 

E-15 

4,646 2 

E-15 

1,0000 

E 00 

3,125 0 

E-08 

7.8125 

E-03 

U S QUART 

U S GALLON 

9.4.3 5 

E 02 

3,7854 

F-03 

9,4613 

E 0 * 

3,78. 3 

E 00 

5.7750 

E 07 

2.310 0 

E 02 

3.342 0 

E 04 

1.3168 

E - o i 

2,2704 

E-07 

9,0817 

E-13 

1.4868 

E-07 

5.9472 

E-13 

3.200 0 

E 07 

1.2800 

E 02 

1,0000 

E 00 

4,000 0 

E-06 

2,500 0 

E 05 

1,0000 

E 00 

TO CONVFRT A VA|UF FROM A GIVEN U'U I TO A 

ANO BENFATH THE DESIRED UNIT. NOTf. MAT 

DESIRE1) UNIT, MULTIPLY THE GIVEN VALUE «Y THE FACTOR OPPOSITE THE GIVEN UNITS 

E-XX MEANS 10 TO THE -XX POWER. 

\ ^ 
fe: 

fV 

> 

a 

a 

& 

x 

CONVERSION FACTORS - MASS 

DESIRED UNITS GRAM 

GIVEN UNITS 

GRAM 

MICROGRAM 

KILOGRAM 

METRIC TON 

SHORT TON 

LONG TON 

GRAIN 

OUNCE 

(AVDP) 

LB (AvDP) 

MICROGRAM KILOGRAM METRIC TON SHORT TON LONG TON GRAIN OUNCE LB (AVDP) 

(AVDP) 

1,0000 

E 00 

1,0000 

E-06 

1,0000 

E 03 

1,0000 

E 06 

9.0718 

E 05 

1.0160 

E 06 

6,4799 

E-02 

2.8349 

E 01 

4,5359 

E 02 

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 

4.3339 

E 08 

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-Ol 

1.0000 

E-06 

1.0000 

E-12 

1.0000 

E-03 

1.0000 

E 00 

9.0718 

E-Ol 

1.0160 

E 00 

6.4799 

E-08 

2.8349 

E-03 

4.5359 

E-04 

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 

9.8421 

E-07 

9.8421 

E-13 

9.8421 

E-04 

9,8421 

E-Ol 

8,9286 

E-Ol 

1,0000 

E 00 

6,3775 

E-08 

2,7902 

E-05 

4,4643 

E-04 

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 

3,5274 

E-02 

3,5274 

£.08 

3,5274 

E 01 

3.5274 

£ 04 

3.2000 

E 04 

3.5840 

E 04 

2,2857 

E-03 

1,0000 

E 00 

1,6000 

*E 01 

2,2046 

E-03 

2.2046 

E-09 

2.2046 

E 00 

2.2046 

E 03 

2,0000 

E 03 

2,2400 

E 03 

1,4286 

E-04 

o,«-500 

E-02 

1,0000 

E 00 

.-JT'' I 

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. 

<n 
CONVERSION FACTORS - FLOW 

DESIRED UNITS CU METER CU METER LITER LITER LITER CU FT CU FT CU FT CU C^l 

PER SEC PER HR PER SEC PER MIN PER HR PER SEC PER MJN PER HR PER SEC 

GIVEN UNITS 

m 

iii 

m 

> 

H 

3 OSP 

X 

n SB 

ft 

o rm 

CfPEl R 

Cfl 

m* 

O 

25 

CU 

CU 

METER 

PER SEC 

METER 

PER HR 

LITER 

PER SEC 

LITER 

PER'MIN 

LITER 

CU 

CU 

CU 

CU 

TO 

PER HR 

FT 

PER SEC 

FT 

PER MIN 

FT 

PER HR 

CM 

PER SEC 

CONVERT 

1.0000 

E 00 

2.7778 

E-04 

I.0000 

E-03 

1.6667 

E-05 

2,7779 

E-07 

2,8317 

E-02 

4,7193 

E-04 

7,8658 

E-06 

1,0000 

E-06 

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 

9.9997 

E 02 

2.7777 

E-Ol 

1.0000 

E 00 

1.6667 

E-02 

2,7778 

E-04 

2,8316 

E 01 

4,7194 

E-Ol 

7,8656 

E-03 

9,9997 

E-04 

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-Ol 

5.9998 

E-02 

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 

3,5314 

E 01 

9,8096 

E-03 

3.3315 

E-02 

5,8859 

E-04 

9,8098 

E-06 

1,0000 

E 00 

1.6667 

E-02 

2.7778 

E-04 

3.3314 

E-05 

2.1189 

E 03 

5,8857 

E-Ol 

2.1189 

E 00 

3.5315 

E-02 

5,8859 

E-04 

6,0000 

E 01 

1,0000 

E 00 

1.6667 

E-02 

2,1189 

E-03 

1,2713 

E 05 

3,5314 

E 01 

1.2714 

E 02 

'.1189 

E 00 

3.5315 

E-02 

3.6000 

E 03 

6.0000 

E 01 

1.0000 

E 00 

1.2713 

E-Ol 

1,0000 

E 06 

2.7778 

E 02 

I.OOOO 

E 03 

1,6667 

E 01 

2.7779 

E-Ol 

2,8317 

E 04 

4,7195 

E 02 

7,86*8 

E 00 

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, 
]>•'• 

m 

> 

•a 

n 

s 

w 

CONVERSION FACTORS - CONCENTRATION, DENSITY 

DESIRED UNITS GRAM P£R MG PER MICROGRAM MICROGRAM GRAIN PER OUNCE PER LB PER GRAM PER LB PER 

CU METER CU METER PER CU M PER LITER CU FT CU FT CU FT CU FT Cu METER 

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 

1.0000 

E 00 

I.OOOO 

E-03 

1.0000 

E-06 

9.9997 

E-04 

2.2883 

E 00 

l.oou 

E 03 

1.6018 

E 04 

3.5314 

E 01 

4.5359 

E 02 

1.0000 

E 03 

1.0000 

E 00 

1.0000 

E-03 

9,9997 

E-Ol 

2.2883 

E 03 

1.00U 

E 06 

1.6018 

E 07 

3.3314 

E 04 

•.5359 

E 05 

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 

1.0000 

E 03 

1.0000 

E 00 

1.0000 

E-03 

1,0000 

E 00 

2.2884 

E OS 

1.0012 

E 06 

1.6019 

E 07 

3.3315 

E 04 

4.5360 

E 05 

4,3700 

E-Ol 

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 

9.9885 

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 

3.5274 

E-02 

4.3307 

E-Ol 

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 

*.83l7 

E-02 

*.83l7 

E-05 

'.8317 

£.08 

',8316 

E>09 

6,4799 

E-02 

<.B349 

E 01 

4,3359 

£ 02 

1,0000 

£ 00 

1.2844 

E 01 

2.2046 

E-03 

2.2046 

E-06 

2,2046 

E-09 

2,2046 

E-06 

3.U449 

E-03 

2,2072 

E 00 

3,9314 

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

"Ifc. ••-ttf« 
( • 

05 

CONVERSION FACTORS - DEPOSITION RATF (SHORT TON .STAT. MILE) 

DESIRED UNITS GM PER SQ KG PER SQ MG PER SQ TON PER SQ OZ PER SQ LB PER GM PER SQ MG PER SQ 

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 

# • ^ - 4:: ' 

m-

"'?p 

GM PER SO 

M PER MO 

KG PER SQ 

KM PER MO 

MG PER SQ 

CM PER MO 

TON PER SO 

MI PER MO 

OZ PER SO 

FT PER MO 

LB PER 

ACRE PERMO' 

GM PER SO 

FT PER MO 

MG PER SO 

IN PER MO 

1,0000 

E 00 

1,0000 

E-03 

1.0000 

E 01 

3.5026 

E-Ol 

3,0919 

E 02 

1.1208 

E-Ol 

1,0764 

E 01 

1.5500 

E 00 

1.0000 

E 03 

I.oooo 

E 00 

1.0000 

E 04 

3.3026 

E 02 

3.0515 

E 05 

1.1208 

E 02 

1.0764 

E 04 

1.5500 

E 03 

1.0000 

E-Ol 

1.0000 

E-04 

1.0000 

E 00 

3.3026 

E-02 

3.0515 

E 01 

1.1208 

E-02 

1,0764 

E 00 

1.5500 

E-Ol 

2.8550 

E 00 

2.8530 

E-03 

2.8550 

E 01 

1.0000 

E 00 

8.7120 

E 02 

3.2000 

E-Ol 

3.0T31 

E 01 

4.4252 

E 00 

3.2771 

E-03 

3.2771 

£.06 

3.2771 

E-02 

1.1478 

E-03 

1,0000 

E 00 

3,6731 

E-04 

3.3274 

E-02 

5.0795 

E-03 

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 

9.2903 

E-02 

9.2903 

E-05 

9.2903 

E-Ol 

3.2541 

£.02 

2,8349 

E 01 

1,0413 

E.02 

1,0000 

E 00 

1,4400 

E.01 

6,4516 

E-Ol 

6,4516 

E-04 

6,4516 

E 00 

2,2598 

E-Ol 

1.9687 

E 02 

7,2313 

E-02 

6,9444 

E 00 

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. 

Cfl 

TJ 

00 
•-• 

$'<• • 

> 

•a 

A 

B 

eu 

sr 

•iv 

i 

CONVERSION FACTORS - PRESSURE 

DESIRED UNITS MILLIBAR BAR 

GIVEN UNITS 

MILLIBAR 

BAR 

ATMOSPHERE 

DYNES 

PER SO CM 

KG 

PER SO CM 

LBS 

PER SQ IN 

MM MERCURY 

IN MERCURY 

ATMOSPHERE DYNES KG LBS MM MERCURY IN MERCURY 

PER SQ CM PER SQ CM PER SQ IN 

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 

3.3864 

E 01 

1,0000 

E-03 

1.0000 

E 00 

1.0133 

E 00 

1.0000 

E-06 

9,8066 

E-Ol 

*,8947 

E-02 

1.3332 

E-03 

3.3864 

E-02 

9.8692 

E-04 

9.8692 

E-Ol 

1.0000 

E 00 

9.8692 

E-07 

9.6784 

E-Ol 

6.8046 

E-02 

1.3158 

E-03 

3,3421 

E-02 

1.0000 

E OS 

1.0000 

E 06 

1.0133 

E 06 

1.0000 

E 00 

9.8066 

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 

E-02 

1.3595 

E-03 

3.4332 

£-02 

1.4504 

E-02 

1.4504 

E 01 

1.4696 

E 01 

1.450* 

E-05 

1.4223 

E 01 

1.0000 

E 00 

1.9337 

E-02 

4.9115 

E-Ol 

7.5006 

E-Ol 

7.5006 

E 02 

7.6000 

E 02 

7,5006 

£.04 

7.3536 

£ 02 

5,1715 

E 01 

1.0000 

E 00 

2.5400 

E 01 

2.9530 

E-02 

2.9330 

E 01 

2.9921 

E 01 

*.93S0 

E-09 

..8999 

E 01 

2,0360 

E 00 

4.9370 

E-02 

1.0000 

E 00 

T__.Ci?2V§?I * y.L!.!«FR2!_

 A GIVE N UN, T T 0 A WSIRE D UNIT » MULTIPLY THE GIVEN VALUE B Y THE FACTOR OPPOSITE THE GIVEN UNITS 

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

00 
•p 

• w ' 

9 

r-'t'*. 

O 

Cfl 

a 

0 

M 

Cfl 

•B w 

S3 

CA i 

H 

> 

3 

CONVERSION FACTORS - TIME 

DESIRED UNITS SECOND 

GIVEN UNITS 

SECOND 

MINUTE 

HOUR 

WEEK 

MONTH (28) 

MONTH (30) 

MONTH (31) 

YEAR (365) 

YEAR (366) 

MINUTE HOUR WEEK MONTH (28) MONTH (30) MONTH (31) YEAR (365) YEAR (366) 

1,0000 

E 00 

1,6667 

E-02 

2,7778 

E-04 

1.6334 

E-06 

4,1336 

E-07 

3.8580 

E-07 

3.7336 

E-07 

3,1710 

E-08 

3.1623 

E-08 

6,0000 

E 01 

1,0000 

E 00 

1.6667 

E-02 

9.9206 

E-05 

2.4802 

E-05 

2.3148 

E-03 

2.2401 

E-05 

1.9026 

E-06 

1.8974 

E-06 

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 

6.0480 

E 05 

1.0080 

E 04 

1.6800 

E 02 

1.0000 

E 00 

2.3000 

E-Ol 

2.3333 

E-Ol 

2.2381 

E-Ol 

1.9178 

E-02 

1.9126 

E-02 

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 

2.3920 

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-Ol 

8.2192 

E-02 

8.1967 

E-02 

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 

3.1536 

E 07 

9,2560 

E 05 

8,7600 

E OS 

9.2143 

E 01 

1.3036 

E 01 

1.2167 

E 01 

1,1774 

*E 01 

1,0000 

E 00 

9,9727 

E-Ol 

3,1622 

E 07 

5.2704 

E 05 

8,7840 

E OS 

5,2286 

E 01 

1,3071 

E 01 

1.2200 

E 01 

1.1806 

E 01 

1.0027 

E 00 

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. 

K..y 
C:)fi\<._sir:. F.' .o''s - r-\-.i... 

iXSlaF, . J"iT _ AA r T 

_TVfcN I If. T r. 

rfATT 

11 <•. T ) 

K II OWAT-1 

<lN|T) 

MF5*WAT T 

(INT ) 

C*l (INT) 

PER

 r,EC 

BTU 

PER "Ufi 

BTu 

PER nR 

JOULES ABS 

PER SEC 

WATT (A.T5) 

ELECT. 

HORSEPOWER 

A M T 

( I •-; T I 

•" 1.1 

I,, jr. on 

F .3 

l.COOO 

E 06 

4.1.7 * 

F TO 

i ,T>HH 

F 0 1 

2.931 3 

E-1 1 

9.9ad l 

E-O l 

9.9QH 1 

F-0 1 

7.458 6 

F 02 

K 11 O'-'A' r 

(I'l l 1 

L - 0 < 

l.OOUO 

E OM 

1 .OO'i . 

t o< 

4.1_' 6 

_-0 . 

1,75MB 

E-0 2 

2,"31. 3 

E - 0 . 

<c.99Hl 

E-O i 

-..<>9H1 

i>O i 

7.45* . 

E-O l 

.FC.n. AT r 

I 1 M T 1 

l.O'KJO 

E-0 6 

1,000 . 

F-0 3 

1.000 0 

F :>. 

4.1« 7 . 

F-0 6 

1.7.3 3 

F-0 5 

2.931 3 

F-117 

9.998 1 

F-0 7 

9.993 1 

E-0 7 

7.4*>86 

E-0 4 

CAI. < I 'IT j 

t'F.R SfC 

2 . 3 »nn 

E-' U 

2,'ina n 

fc' " 2 

2.3•< .0 

E «>5 

l.:i')o o 

F. *»••) 

4 . 2'IOO 

E MO 

7,o;)o n 

E-i ? 

2.3'W 5 

2.3H7 5 

E-O l 

1.7H1 1 

E " 2 

iiTU 

PER 

5.6.5 7 

E-0 2 

5,685 7 

E 0 1 

5 . 6 .57 

E 04 

«i,38l O 

E-O l 

1.000 0 

E 0 0 

1,666 7 

E-0 2 

5,684 6 

E-0 2 

5.684 6 

E-0 2 

4,240 7 

E 0 1 

BTU 

MJM P1R 

3.411 4 

E 0 0 

3.411 4 

E 03 

3.411 4 

E 0 6 

1.428 6 

E 0 1 

6,noo o 

E 0 1 

1.000 0 

E 0 0 

3.410 8 

E 0 0 

3.41Q 8 

E 00 

2.544 4 

E 0 3 

JOULES ABS WATT (ABS) ELECT. 

PER SEC HORSEPOWER 

1,3407 

E-03 

1.000 2 

F 0 0 

1.000 2 

£ 03 

1.000 2 

E 0 6 

4.188 4 

E 0 0 

1.759 1 

E 0 1 

2.931 9 

E-O l 

1.000 0 

E 0 0 

I.OOOO 

E 0 0 

7.460 0 

E 02 

1.000 2 

E 0 0 

1.000 2 

E 0 3 

1,000 2 

E 0 6 

4.188 4 

E 0 0 

1.759 1 

E 0 1 

2.931 9 

E-O l 

1.000 0 

E 0 0 

1.000 0 

E 0 0 

7.460 0 

E 0 2 

1.3407 

E 00 

1,3407 

E 03 

5,6143 

E-03 

2,3581 

E-02 

3.9301 

E-04 

1,3405 

E-03 

1.3405 

E-03 

1.0000 

E 00 

TO CQNvrRT A \/A|UF FROM fl _tvtN U'U 1 TJ A DESTRF^ JNlT, MULTIPLY THE GIVEN VALUE »Y THE FACTOR OPPOSITE THE GIVEN UNITS 

ANO BENFATH MF. JFStRED UNIT. NOT r. T-\M E-XX .TA'.S 10 TO T ._ -XX POWER, 
V in 

SO 

N 

:« 

CONVERSION FACTORS - ENERGY, WORK 

DESIRED UNITS ERG DyNE-CM 

GfVEN UNITS 

ERG 

DYNE-CM 

ABS JOULE 

CAL (INT) 

CAL (15) 

INT KW.HR 

ABS KW-HR 

BTU 

ABS JOULE CAL (INT) CAL (15) INT KW-HR ABS KW-HR BTU 

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 

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 

1.0000 

E-07 

1.0000 

E-07 

1.0000 

E 00 

4.1868 

E 00 

4,1855 

E 00 

3,6007 

E 06 

3.6000 

E 06 

1.0551 

E 03 

2.3884 

E-08 

2.3884 

E-08 

2.3884 

E-01 

1.0000 

E 00 

9.9968 

E-Ol 

8.6000 

E 05 

8.5984 

E 09 

2.5200 

E 02 

2.3892 

E-08 

2.3892 

E-08 

2.3892 

E-Ol 

1.0003 

E 00 

1.0000 

E 00 

8,6027 

E 05 

8,6011 

E 05 

2.5208 

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-Ol 

2.9302 

E-04 

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 

9.4781 

E-ll 

9,4781 

E-ll 

9.4781 

E-04 

3.9683 

E-03 

3,9671 

E-03 

3.4128 

E 03 

3.41ZI 

E 03 

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. 
m 

•a 

•o 

n 

s 

a. 

CONVERSION FACTORS - ENERGY PER UNIT AREA 

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

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

GIVEN UNITS 

LANGLEY 

CAL (15) 

PER SO CM 

BTU 

PER SQ FT 

INT KW-HR 

PER SQ M 

ABS JOULES 

PER SO CM 

I.OOOO 

E OO 

1.0000 

E 00 

2,7133 

E-Ol 

8,6029 

E 01 

2.3892 

E-Ol 

1,0000 

E 00 

1.0000 

E 00 

2.7133 

£-01 

8.6029 

E 01 

2.3892 

E-Ol 

3.6855 

E 00 

3,6855 

E 00 

1,0000 

E 00 

3,1706 

E 02 

8.8054 

E-Ol 

1.1624 

E-02 

1.1624 

E-02 

3.1340 

E-03 

1.0000 

E 00 

2.7772 

E-03 

4.1855 

E 00 

4,1855 

E 00 

1,1357 

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 

ANO BENEATH THE OESIRE D UNIT . NOTE THAT E-XX MEANS 10 TO THE -XX POWER. 

ae 

w 

oo 

Ul 
*••* • 

00 

•)* • 

I ••••:• 

CONVERSION FACTORS - POWER PER UNIT AREA (CAL ARE 15 DEG) 

DESIRED UNITS CAL PER SQ CAL PER 5Q LANr,LEY CAL PER SO BTU PER SQ BTU PER SQ ABS WATT 

M PER SEC CM PER MIN PER MIN CM PER DAy FT PER MIN FT PER DAY PER SQ CM 

GIVEN UNITS 

CAL PER SO 

M PER SEC 

CAL PER SO 

CM PER MIN 

LANGLEY 

PER MIN 

CAL PER SO 

CM PER DAy 

BTU PER SC 

FT PER MIN 

BTU PER SO 

FT PER DAY 

ABS WATT 

PER SQ CM 

I.OOOO 

E 00 

1.6667 

E 02 

1.6667 

E 02 

1,1574 

E-Ol 

4,5222 

E 01 

3.1404 

E-02 

2.3892 

E 03 

6.0000 

E-03 

1.0000 

E 00 

1.0000 

E 00 

6.9444 

E-04 

2.7133 

E-Ol 

1.8843 

E-04 

1.4335 

E 01 

6.0000 

E-03 

I.OOOO 

E 00 

I.OOOO 

E 00 

6,9444 

E-04 

2.7133 

E-Ol 

1.8843 

E-04 

1.4333 

E 01 

8.6400 

E 00 

1.4400 

E 03 

1.4400 

E 03 

1.0000 

E 00 

3.9072 

E 02 

2.7133 

E-Ol 

2.0643 

E 04 

2.2113 

E-02 

3.6855 

E 00 

3,6855 

E 00 

2,5594 

E-03 

1,0000 

E 00 

6,9445 

E-04 

5,2833 

E 01 

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 

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 

m 

Cfl 

.•-Sfe *o > 

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 0ESI3ED UNIT.' NOTE THAT E-XX MEANS 10 TO THE -XX POWER. 

W