p. 1 

# PICK-UPDATE : 3/15/200 7 BO X O F 

# 50_ Ste p 2 : FO R ASR C INTERNA L US E ONL Y 

### (PAR TB o

fB )


# EP ADOCKE TID : 102RQ-R N 1 ) 102RQ-RN-5-1 6 3 ) 102RQ-RN-5-1 8 5 ) 102RQ-RN-5-2 0 7 ) 102RQ-RN-5-2 2 9 ) 102RQ-RN-5-2 4 11 ) 102RQ-RN-5-2 6 13 ) 102RQ-RN-5-2 8 15 ) 102RQ-RN-5-3 0 17 ) 102RQ-RN-6- 1 19 ) 102RQ-RN-6- 3 21 ) 102RQ-RN-6- 5 23 ) 102RQ-RN-6- 7 25 ) 102RQ-RN-6- 9 27 ) 102RQ-RN-6-1 1 29 ) 102RQ-RN-6-1 3 31 ) 102RQ-RN-6-1 5 33 ) 102RQ-RN-6-1 7 35 ) 102RQ-RN-6-1 9 37 ) 102RQ-RN-6-2 1 39 ) 102RQ-RN-6-2 3 Ste p 3 : FO R ASR C INTERNA L US E ONL Y CD : OA : / 

# 2 ) 102RQ-RN-5-1 7 4 ) 102RQ-RN-5-1 9 6 ) 102RQ-RN-5-2 1 8 ) (102RQ-RN-5-23" ) 10 ) 102RQ-RN-5-2 5 12 ) 102RQ-RN-5-2 7 14) 102RQ-RN-5-2 9 16 ) 102RQ-RN-5-3 2 18 ) 102RQ-RN-6- 2 20 ) 102RQ-RN-6- 4 22 ) 102RQ-RN-6- 6 24 ) 102RQ-RN-6- 8 26 ) 102RQ-RN-6-1 0 28 ) 102RQ-RN-6-1 2 30 ) 102RQ-RN-6-1 4 32 ) 102RQ-RN-6-1 6 34 ) 102RQ-RN-6-1 8 36 ) 102RQ-RN-6-2 0 38 ) 102RQ-RN-6-2 2 40 ) 102RQ-RN-6-2 4 Ste p 1 : FO R ASR

C INTERNA L US E ONL Y^ 7 Are ther e more document s fo r thi s Docke t i n anothe r box ? *YE S //N O *Fil l ou t Continuatio n Shee t an d go t o Ste p 2 Interna l SFUN D Bo

x Numbe r _3 6 O F _28 3 Initials/Date : LD S / 3-15-200 7P. 2 

# i^m-M-5-m WORKBOO K O F ATMOSPHERI C DISPERSIO N

ESTIMATE S

H

/ 

# U.S . ENVIRONMENTA L PROTECTIO N AGENC Y

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# WORKBOO K

O F ATMOSPHERI

C DISPERSIONESTIMATE S

D . BRUC E TURNE R Ai rResource s Fiel d Researc h Office , Environmenta l Scienc e Service s Administratio n V "



### ENVIRONMENTA L PROTECTIO N AGENC Y Office o f Ai rProgram s Research Triangl e Park, Nort h Carolina

Revise d 197

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y " Th e AP serie s o f report s i s issue d b yth e Environmenta l Protectio n Agenc yt o repor t th e result s o f scientifi c an d engineering studies , an d informatio n o f genera l interes t i n th e fiel d o f ai r pollution . Informatio n presente d i n thi s serie s include s coverag e o f intramura l activitie s involving ai r pollutio n researc h an d contro l technolog y an d o f cooperativ e program s an d studie s conducte d i n conjunctio n wit h stat e an

d loca l agencies , researc h institutes , an d industria l organizations . Copie s o f A P report s ar e availabl e fre e o f charg e - a s supplie s permi t - fromth e Offic e o f Technica l Informatio n an d Publications , Offic e o f Ai r Programs , Environmenta l Protectio n Agency , Researc h Triangl e Park , Nort h Carolin a 27711 , o r fromth e Superintenden t o f Documents . )

6t h printin g January197 3 Offic e o f Ai r Program s Publicatio n No . AP-2 6

Fo rsal e b y tb e Superintenden tof Document* . U.S . Governmen tPrintin g Office , Washington , D.C . 20*0 3 - Pric e 11.0 0 Stoc kNumbe rWB-OO U 

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### PREFAC E Thi s workbook

present s som

e computational technique s currentl y use db y scientist s workin g wit

hatmospheri c dispersio nproblems . Becaus e th e basi c working equation s ar e general , thei r

applicatio nto specifi c problem s usuall y require s specia l car e andjudgment ; suc hconsideration s ar e illustrate db y 26 exampl e problems . Thi s workboo k i s intende da s a

n ai dt o meteorologist s andai r pollutio nscientist s wh o ar e require dto estimat e atmospheri c concentration s o

f contaminant s fro

mvariou s type s o

f sources . I t

i s no t intende da s acom

plet e do-it-yoursel f

manua l fo r atmospheri c dispersio nestimates ; al l o f th e numerou s compli
cation s tha t

aris e inmakin

g bes t estimate s o

f dispersio ncanno t

b e s o easil y resolved . Awarenes s o

f th e possibl e complexitie s ca nenabl e th e use r t o appreciat e th e validit y o f hi s "firs t approximations " an dt o realiz e whe nth e service s o

f aprofessiona l ai r

pollutio nmete orologis t ar e required . Sinc e th e initia l publicatio no f thi s workbook , ai r

pollutio nmeteorologist s affiliate d withth e Environmental Protectio nAgency hav e turne dt o usin g th e methodo f Brigg s t o determin e plum

e ris e inmost

case s rather

thanusin g th e plume-ris e equatio no f Hollanda s se t fort h i nChapter

4 . Th e reader

i s directe dto : Briggs , Gar

y A . 1971 : "Some Recen t Analyse s o

f Plume Ris e Observations. " In : Proceeding s o

f th e SecondInternationa l CleanAi r Congress . Academi c Press , Ne w York, N . Y . p

p 102 9 -103 2 an dmodifiedb

y Briggs , Gar

y A . 1972 : "Discussion , Chimne y Plume s i nNeutra l an dStabl e Surroundings. " Atmospheri c Environment , 6:507-510 .

/ V M *

v* . .-•*"•;.•, •.'',-'.'",v'iifc.'..v.-JS'- - i»^r; , -'!' i i ,j*::-''V^j?i-V; - ;P. 6

ACKNOWLEDGMENT S Th e autho r

wishe s t o expres s hi s appreciatio nt o Rober t A . McCormick , Pau l A . Humphrey , an dothe r member s o

f th e Fiel dResearc hOffic e for thei r helpfu l dis
cussion s an dreview ; t o Jea nJ . Schueneman , Chief , Criteri aan dStandard s Develop
ment , Nationa l Cente r

fo r Ai r Pollutio nControl , wh o suggeste dthi s workbook ; t o Phylli s Pollan dan dFran k

Schiermeier , wh o checke dth e proble msolutions ; t o Rut hUmflee t an dEdn aBeasle y for

thei r aid ; an dt o th e Nationa l Cente r fo r Ai r Pollutio nControl , Publi c Healt hService , an dAi r Resource s Laboratory , Environmenta l Scienc e Service s Administration , for

thei r support . 

# 3

r I V )

•.•U*.^g!1CONTENT S P. 7

/ ABSTRAC T vi i

Chapte r 1 . INTRODUCTIO N1 Chapte r 2 . BACKGROUN D « 3 Chapte r 3 . ESTIMATE S O FATMOSPHERI C DISPERSIO N5 Coordinat e Syste m5 Diffusio nEquation s > 5 Effect s o f Stabilit y 6 Estimatio no

f Vertica l an dHorizonta l Dispersio n_7 Evaluatio no

f Win dSpee d_7 Plot s o f Concentration s agains t Distanc e _7 Accurac y o

f Estimate s _7 Graph s for

Estimate s o

f Diffusio n_1 0 Plottin g Ground-Leve l Concentratio nIsopleth s _ 1 0 Area s Withi nIsopleth s .' . _ 1 7 Calculatio no

f Maximu mGround-Leve l Concentration s _ . 1 7 Revie w o f Assumption s . „ 1 7 Chapte r 4 . EFFECTIV EHEIGH T O FEMISSIO N3 1 Genera l Consideration s _3 1 Effectiv e Heigh t

o f Emissio nan dMaximu mConcentratio n. _3 1 Estimate s o

f Require dStac k

Height s _ 3 1 Effec t o f Evaporativ e Coolin g _3 2 Effec t o f Aerodynami c Downwas h—3 2 Chapte r 5 . SPECIA LTOPIC S 3 5 Concentration s i na nInversio nBreak-u p Fumigatio n_3 5 Plum e Trappin g _ 3 6 Concentration s a t

Groun dLeve l Compare dt o Concentration s a t th e Leve l o

f Effectiv e Stac k

Heigh t fro mElevate dCon
tinuou s Source s 3 6 Tota l Dosag e fro maFinit e Releas e 3 7 Crosswind-Integrate dConcentratio n3 7 Estimatio no

f Concentration s for

Samplin g Time s Longe r tha naFe w Minute s 3 7 Estimatio no

f Seasona l o r

Annua l Averag e Concentration s a t aRecepto r

fro maSingl e Pollutan t Sourc e 3 8 Meteorologica l Condition s Associate dwit hMaximu m Ground-Leve l Concentration s 3 8 Concentration s a t

aRecepto r

Poin t fro mSevera l Source s ... _3 9 Are aSource s _3 9 Topograph y _4 0 Lin e Source s _4 0 Instantaneou s Source s 4 1 Chapte r 6 . RELATIO NT O OTHE RDIFFUSIO NEQUATION S 4 3 Chapte r 7 . EXAMPL EPROBLEM S 4 5 Appendices : '. 5 7

1 —Abbreviation s an dSymbol s - 5 9 2 — Characteristic s o

f th e Gaussia nDistributio n_ 6 1 3 —Solution s t o Exponential s 6 5 4 — Constants , Conversio nEquations , Conversio nTable s _6 9

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Chapte r1 —INTRODUCTIO N NOTE : SE

EPREFAC ET

O TH ESIXT H PRINTIN

GO NPAG Eiii . Durin g recen t

year s method s o

f estimatin g at mospheri c dispersio nhav e undergon e considerabl e revision , primaril y du e t o result s o f experimenta l y measurements . I nmos t dispersio nproblem s th e relevan tatmospheri c laye r i s tha t neares t th e ground , varyin g i nthicknes s fro msevera l hundre d t o afe w thousan dmeters . Variation s i nbot h therma l an dmechanica l turbulenc e an di nwin d velocit y ar e greates t

i nth e laye r

incontac t

wit h th e surface . Turhulenc e induced . b_

_buoyancy_iorce s i nth e atmospher e i s closel y relate dt o th e vertica l 60 0 temperatur e structure . Whe ntemperatur e decrease s wit hheigh t

a t arat e highe r

tha n5.4° Fpe r

100 0 f t (J' C P^ r ir ' Q meters) , th e atmospher e i s i nun stabl e equilibriu man dvertica l motion s ar e en hanced . Whe ntemperatur e decrease s a t alowe r rat e o r increase s wit hheigh t

(inversion) , vertica l motion s ar e dampe do r

reduced . Example s o

f typ ical variation s i ntemperatur e an dwin dspee dwith heigh t for daytim e an dnighttim e condition s ar e illustrate di nFigur e 1-1 .

50 0 - 400 - E 300 - 200 - 100
-10 ] 2 - 3 4 5 6 7 8 9 1 0 1 1 1 2 0 I

TEMPERATURE , °

C 2345678 9 1 0 1 1 WIN D SPEED , m/sec Figur e 1-1 . Example s o f variatio n o f temperatur e an d win d spee d wit h heigh t (afte rSmith , 1963) .



# r Th e transfe r o f momentu mupwar do r down
ward_i n th e atmospher e i s als o relate dt o stability : whe nth e atmospher e i s unstable, , usuall y i nth e daytime , upwar dmotion s transfe r th e momentu m• "deficiency " du e t o edd y frictio nlosse s nea r th e earth' s surfac e throug harelativel y dee p layer , causin g th e win dspee dt o increas e mor e slowl y wit hheigh t

tha na t nigh t (excep t i nth e lowes t

few
meters) . I nadditio nt o therma l turbulence , rough
nes s element s o nth e groun dengende r mechanica l turbulence , whic haffect s bot hth e dispersio no f materia l i nth e atmospher e an dth e win dprofil e (variatio no

f win dwit hheight) . Example s o f thes e effect s o nth e resultin g win dprofil e ar e show ni n Figur e 1-2 . J A s win dspee dincreases , th e effluen t fro ma continuou s sourc e i s introduce dint o agreater*vol- . um e o f ai r pe r uni t tim e interval . I nadditio nt o thi s dilutio nb y win dspeed , th e spreadin g o f th e materia l (norma l t o th e mea ndirectio no f trans port ) b y turbulenc e i s amajo r facto r i nth e dis
persio nprocess . Th e procedure s presente dher e t o estimat e at mospheri c dispersio nar e applicabl e whe nmea nwind * spee dan ddirectio ncanb e determined . J.u t meas urement s o

f turbulence " suc haa tht*standar dde
viatio no f win ddirectio nfluctuations, art*not-avail
able . If suc hmeasurement s ar e a t hand , technique s suc ha s thos e outline db y Pasquil l (1961 ) ar e likel y t o giv e mor e accurat e results . Th e diffusio nparam -

- ' «f«*« . '^"ft.-!-"''." - '" * 

### '-fk'3^"'^' ; • - . iJ^fi^JT' 7P. 9

eters ; pi______te

dher e ar e mos t

applicabl e t o ground
leve l <n r Brow-leve l release s (fro mth e surfac e t o abou t • > metes]), , althoug hthe y ar e commonl y applie da t .gha r dictation s withou t

ful l experiment s olida
tion. . It t i s assume dtha t

stabilit y i s th e sam e throag$_a__

t th e diffusin g layer , an dn o turbulen t transfe r occur s through layer s o f dissimila r

stabilit y characteristics . Becaus e mea nvalue s fo r win ddirec
tion s __s__ l speed s ar e required , neithe r th e variatio n o f win dspee dno r

th e variatio no

f win ddirectio n wit hfi___^_t

J nth e mixin g laye r

ar e take nint o ac count . TTiai

s usuall y i s no t

aproble mi nneutra l o r unstaftf e {eg. , daytime ) situations , bu t ca ncaus e oyeg^^taBBation s o

f downwin dconcentration s i n stabil e ramditions. 

## REFERENCE S Davenport , A . G. , 1963 : Th e relationshi p o f win d structur e t o win dloading . Presente da t Int . Conf . o nTh e Win dEffect s o nBuilding s an d Structures , 26-2 8 Jun e 63 , Natl . Physica l Lab- , oratory , Teddington , Middlesex , Eng . Pasquill , F. , 1961 : Th e estimatio no f th e dispersio n o f win dborn e material . Meteoro LMag . 90, 1063 , 33-49 . Smith , M . E. , 1963 : Th e us e an dmisus e o f th e at mosphere , 1 5 pp. , Brookhave nLectur e Series , No . 24 , 1 3 Fe b 63 , BN L78 4 (T-298 ) Brook
have nNationa l Laboratory . ^

6 GD©n — URBA N ARE A SUBURB S LEVE L COUNTR Y

)

0 . 

### Figur e 1-2 . Example s ofvariatio n ofwin d wit h heigh t ove rdifferen t size roughnes s element s (figure s ar e percentage s ofgradien t wind) ; (fro m Davenport , 1963) .



# r 

# J ATMOSPHERIC DISPERSIO NESTIMATE S

•- -*, . .... . ,*v * St-'ttfri- '/ P.1 0
Chapte r 2 —BACKGROUN D Fo r anumbe r

o f year s estimate s o

f concentra tion s wer e calculate deithe r fro mth e equation s o

f Sutto n(1932 ) wit hth e atmospheri c dispersio n parameter s Cr

, C „ an dn , o r

fro mth e equation s o

f Bosanque t

(1936 ) wit hth e dispersio nparameter s p an dq . Ha y an dPasquil l (1957 ) hav e presente dexperi
menta l evidenc e tha t

th e vertica l distributio no f spreadin g particle s fro ma nelevate dpoin t i s re late dt o th e standar ddeviatio no f th e win deleva
tio nangle , a K

, a t th e poin t

o f release . Crame r

(1957) , derive dadiffusio nequatio nincorporatin g standar d deviation s o

f Gaussia ndistributions : g . for th e distributio no

f .material , in.ihg

j>liime_..acrQSSJfflind . in_th e horizontal , an d<r , for th e vertica l distributio n Qjjnateria l i ntjhejpjume. " (Se e "Appendi x 2 for prop ertie s o f Gaussia ndistributions. ) Thes e statistic s wer e relate dt o th e standar ddeviation s o f azimut h angle,YT A 7 an delevatio nangle , (oi? t calculate dfro m win dmeasurement s mad e wi__ f abi-directiona l win dvan e (bivane) . Value s for diffusio nparam eter s base do nfielddiffusio ntest s wer e suggeste d b y Cramer , e t

al . (1958 ) (an dals o i nCrame r 1959 a an d1959b) . Ha y an dPasquil l (1959 ) als o pre sente dametho dfor

derivin g th e sprea do

f pollut
ant s fro mrecord s o

f win dfluctuation. Pasquil l (1961 ) ha s furthe r

propose dametho dfo r esti
matin g diffusio nwhe nsuc hdetaile dwin ddat aar e no t available . Thi s metho dexpresse s th e heigh t an dangula r

sprea do f adiffusin g plum e i nterm s o f mor e commonl y observe dweathe r parameters . Sug
geste dcurve s o

f heigh t an dangula r

sprea da s a functio no

f distanc e downwin dwer e give nfor sev era l "stability " classes . Giffor d(.1.961 ) converte d Pasquill' s yalue_L_of__ahgula r sprea dan d_iei%h

t int o standar d..deviation sjof. . plume_^ijcentratiqrL.di5tri
butjon , vy and_a K

Pasquill' s method , wit h.Gifford' s • conversio n incorporated , i s use di nthis.workFoo k " (se e Chapter, 3 ) fbTHiffusior T estimates . Advantage s o

f thi s syste mar e tha t

(1 ) onl y tw o dispersio nparameter s ar e require dan d(2 ) result s o f mos t diffusio nexperiment s ar e no w bein g re porte di nterm s o

f th e standar ddeviation s o f plum e spread . Mor e fielddispersio nexperiment s ar e bein g conducte dan dwil l b e conducte dunde r condition s o f varyin g surfac e roughnes s an datmospheri c sta bility . If th e dispersio nparameter s fro maspecifi c experimen t

ar e considere dt o b e mor e representativ e tha nthos e suggeste di nthi s workbook , th e param ete r value s ca nb e use dwit hth e equation s give n here . REFERENCE S Bosanquet , C . H. , an dJ . L . Pearson , 1936 : Th e sprea do f smok e an dgase s fro mchimneys . Trans . Farada y Soc , 32, 1249-1263 . Cramer , H . E. , 1957 : A practica l metho dfor esti
matin g th e dispersio no f atmospheri c contami
nants . Proc . 1s t

Natl . Conf

. o nAppl . Meteorol . Amer . Meterol . Soc . Cramer , H . E. , F . A . Record , an dH . C . Vaughan , 1958 : Th e stud y o

f th e diffusio no

f gase s o r aerosol s i nth e lower

atmosphere . Fina l Repor t Contrac t A F19(604)-105 8 Mass . Inst , o f Tech. , Dept . o f Meteorol . Cramer , H . E. , 1959a : A brie f surve y o

f th e mete orologica l aspect s o

f atmospheri c pollution . Bull . Amer . Meteorol . Soc , 40, 4 , 165-171 . Cramer , H . E. , 1959b : Engineerin g estimate s o f atmospheri c dispersa l capacity . Amer . Ind . Hyg . Assoc . J. , 20, 3 , 183-189 . Gifford , F . A. , 1961 : Use s o f routin e meteorologica l observation s for

estimatin g atmospheri c disper
sion . Nuclea r

Safety , 2 , 4 , 47-51 . Hay , J . S. , an dF . Pasquill , 1957 : Diffusio nfro ma fixedsourc e a t

aheigh t

o f afe w hundre dfee t i nth e atmosphere . J . Flui dMech. , 2 , 299-310 . Hay , J . S. , an dF . Pasquill , 1959 : Diffusio nfro ma continuou s sourc e i nrelatio nt o th e spectru m an dscal e o

f turbulence , p p 345-36 5 i nAtmospheric Diffusion and

Air Pollution, edite db y F . N . Frenkie l an dP . A . Sheppard , Advance s i nGeophysics , 6, Ne w York , Academi c Press , 47 1 pp . Pasquill , F. , 1961 : Th e estimatio no f th e dispersio n o f windborn e material . Meteorol . Mag. , 90, 1063, 33-49 . Sutton , 0 . G. , 1932 : A theor y o f edd y diffusio ni n th e atmosphere . Proc . Roy . Soc , A , 135, 143
- 165 .

Backgroun d

^r»W* - *•-.;•;•&'£» • * vSSET -P.1 1 Chapte r 3 —ESTIMATE S O FATMOSPHERI C DISPERSIO N 

# r

/ - .

( Thi s chapte r outline s th e basi c procedure s t o b e use di nmakin g dispersio nestimate s a s sug geste db y Pasquil l (1961 ) an dmodifie db y Giffor d (1961) . COORDINAT ESYSTEM j \I nth e syste mconsidere dher e thejKigv n ifi„a t i j jyoundJeve l a t

o r beneat h„th e .point._o f

emission , ' \ wit hth e x-axis"extendin g horizontall y i n the~direc
tio no f th e mea nwind . Th e y-axi s i s i nth e hori
zonta l plan e perpendicula r t o th e x-axis , an dth e z-axi s extend s vertically . Th e plum e travel s alon g o r paralle l t o th e x-axis . Figur e 3- 1 illustrate s th e coordinat e system . DIFFUSIO NEQUATION S Th e concentration , x , o f ?a^2L_L§£2_£J s__E5#i " cle_sJessJhan_a,bautJffi.jnQte a t x,y, z fro macontinuou s sourc e wit ha neffectiv e emissio n height , H , i s give nb y equatio n3.1 . Th e notatio n use dt o depic t

thi s concentratio ni s x (x,y,z;H) . H i s th e heigh t

o f th e plum e centerlin e whe ni t become s essentiall y level , an di s th e su mo f th e physica l stac k

height , h , an dth e plum e rise, AH . Th e followin g assumption s ar e made : th e plum e sprea dha s aGaussia ndistributio n(se e Appendi x 2 ) i nbot hth e horizonta l an dvertica l planes , wit h standar ddeviation s o

f plum e concentratio ndistri
butio ni nth e horizonta l an dvertica l o f o > an dor, , respectively ; th e mea nwin dspee daffectin g th e plum e i s u ; th e unifor memissio nrat e o f pollutant s i S Q ; an d tota j refWtir. l " * +h ° plnm o + _V____plgrp a t .th e earth.'? ; surface , j.e. , ther e i s n o depositio n o r reactio na t

th e surfac e (se e proble m9) . %*.' x (x,y,z;H ) Q
ex p z-fH 

# I'M •)•] ! 2ir<x T oy U z- H 

## ° _ 

# M-M^Y] r ] + < 

# * p

# [ - i

2 (3.1) . *Note : ex p —a/ b = e - » / b wher e e i s th e bas e ofnatura l logarithm s an d i s approximatel yequa l t o 2.7183 .

,-y,Z )
(x,-y,0 )

Figure 3-1 . Coordinat e syste m showin g Gaussia n distribution s i n th e horizonta l an d vertical . Estimate s
----i_____3_r : ' ;P.1 2

An y consisten t

se t o f unit s ma y b e used . Th e mos t commo n is : X ( g m~ 3 ) or , fo r

radioactivit y (curie s m~ 3 ) i " Q (gsec -1 ) o r

(curie s sec -1 ) ' / u (msec -1 ) Y <r } , o z, H,x,y , an dz (m ) Thi s equatio ni s th e sam e a s equatio n(8.35 ) p . 29 3 o f Sutto n(1953 ) whe na' s ar e substitute dfo r Sut
ton' s parameter s throug hequation s lik e (8.27 ) p . 286 . Fo r evaluation s o

f th e exponential s foun di n Eq . (3.1 ) an dthos e tha t follow , se e Appendi x 3 . \i s amea nover

th e sam e tim e interva l a s th e tim e interva l fo r

whic hth e o' s an du ar e representative . Th e value s o

f bot hJJ V an da_ar e evaluate di n term s o f th e downvyinddistance , x . Eq . (3.1 ) i s vali dwher e diffusio ni nth e direc
tio no f th e plum e trave l ca_TL.b e neglected , tha t

is , n^_iig_i§i2____n . the_xjJireciipn . • > , Thi s ma y b e assume di f th e releas e i s continuou s : ' o r i f th e duratio no

f releas e i s equa l t o o r

greate r i,tha n th e trave l tim e (x/u ) fro mth e sourc e t o th e locatio no

f interest . Y

< •'',,...,, , - ;->-o~---

- *£"*• • -' : Fo r concentration s calculate da t groun dlevel , i.e. , z = 0 , (se e proble m3 ) th e equatio nsimplifie s 

### to: x (x,y,0;H ) = Q T O y <7 , U ex p 

# -[-i(-^r ] [-M-i-Y] (3.2 ) Wher e th e concentratio ni s t o b e calculate d alon g th e centerlin e o

f th e plum e ( y = 0) , (se e problem-2 ) furthe r

simplificatio nresults : x (x,0.Q:H ) = - Q ex p 

# [-Mm

VyOzU I_

i \Or J > 1(3.3 ) Fo r aground-leve l sourc e wit hn o effectiv e plum e ris e ( H = 0) , (se e proble m1) :

Q rr o- y o - U(3.4 ) x(x,0,0;0 ) = EFFECT S O FSTABILIT Y Th e value s o

f ayan da zvar y wit hth e turbulen t structur e o

f th e atmosphere , heigh t abov e th e sur face, surfac e roughness , samplin g tim e ove r whic h th e concentratio ni s t o b e estimated , win dspeed , an ddistanc e fro mth e source . Fo r th e paramete r value s give nhere , th e samplin g tim e i s assume dt o b e abou t 1 0 minutes , th e heigh t t o b e th e lowes t severa l hundre dmeter s o f th e atmosphere , an d

. surfac e t o b e relativel y ope ncountry . Th e bulen t structur e o

f th e atmospher e an dwin d .ee dar e considere di nth e stabilit y classe s pre sented , an dth e effec t o f distanc e fro mth e sourc e i s considere di nth e graph s determinin g th e paramete r values . Value s for

o y an do , ar e estimate dfro mth e stabilit y o

f th e atmosphere , whic hi s i ntur nesti
mate dfromth e win dspee da t aheigh t

o f abou t 1 0 meter s and , durin g th e day , th e incomin g solar radiatio nor , durin g th e night , th e clou dcove r (Pas
quill , 1961) . Stability < categorie s .(i n si x classes ) ar e given_JnJX'ablL-___l'. ' Clas s " A i s th e mos t

un stable , clas $ Fth e mp^f

, ptflhli T clas s rnr^iriWfiH

j liftrft. *" " "'"refer s t o th e perio dfro m1 hou r befor e sunse t t o 1 hou r

afte r sunrise . Not e tha t

th e neutra l class , D , ca nb e assume dfor overcas t

condition s durin g da y o r

night , regardles s o

f win dspeed . Tabl e 3- 1 KE YT O STABILIT YCATEGORIE S Surfac e Win d Spee d (a t 1 0 m) , m sec - 1 < 2 2- 3 3- 5 5- 6 > 6 Da y Incomin g Sola rRadiatio n Stron g A A- B B C C Moderat e A- B B BC C- D D Sligh t B C C D D Nigh t Thinl yOvercast o r 2=4/ 8 Lo wClou d E D D D -=3/ 8

Clou d F E D D Th e neutra l class , D , shoul d be assumed to rovercast condition s durin g da yo rnigh t "Strong " incomin g solar radiatio ncorrespond s t o asolar altitud e greate r

tha n60 ° wit hclear

skies ; "slight " insolatio ncorrespond s t o asolar altitud e fro m15 ° t o 35 c wit hclea r skies . Tabl e 170 , Sola r Altitud e an dAzimuth , i nth e Smithsonia nMete orological Table s (list , 1951 ) ca nb e use di ndeter
minin g th e solar

altitude . Cloudines s wil l decreas e incomin g solar

radiatio nan dshoul db e considere d alon g wit hsola r

altitud e i ndeterminin g sola r radia
tion . Incomin g radiatio ntha t woul db e stron g wit hclea r

skie s ca nb e expecte dt o b e reduce dt o moderat e wit hbroke n( % t o % clou dcover ) mid
dl e cloud s an dt o sligh t wit hbroke nlo w clouds . A nobjectiv e syste mo

f classifyin g stabilit y fro m hourl y meteorologica l observation s base do nth e abov e metho dha s bee nsuggeste d(Turner , 1961) . Thes e method s wil l giv e represeqfotiy e indica
- J I S o f i^flhility . rarer

.npp n rnnntt y n r

r^ra l arpaa , J tion s hu t «r y |P_ B rplighl o f

n r nr h ? " „ rf y e Thi s differ
- i enc e i s du e primaril y t o th e influenc e o f th e city' s large r surfac e roughnes s an dhea t islan deffect s upo nth e stabilit y regim e ove r urba nareas . Th e greates t differenc e occur s o ncal mclear nights ; o n suc hnight s condition s ove r rura l area s ar e ver y stable , bu t

ove r urba narea s the y ar e slightl y un stabl e o r nea r neutra l t o aheigh t

severa l time s th e averag e buildin g height , wit hastabl e laye r abov e (Duckwort han dSandberg , 1954 ; DeManais , 1961) . " ^

' )



# J

. - r.2sBte:.y..--. ;*!?iSS*__5 . ATMOSPHERI C DISPERSION ESTIMATE S •>#5& YP.1 3

Som e preliminar y result s o f adispersio nexperi
men t i nSt . Loui s (Pooler , 1965 ) showe dtha t th e dispersio nove r

th e cit y durij_g_J__e*daytime-behave d somewha t

lik e type s B an dCi_for_pne_night experi
men t o , varied''with ' distanc e betwee ntype s D and-E. ; ESTIMATIO NO FVERTICA LAN D HORIZONTA LDISPERSIO N Havin g determine dth e stabilit y clas s fro m Tabl e 3-1 , on e ca nevaluat e th e estimate s o f o r an d o , a s afunctio no

f downwin ddistanc e fro mth e source , x , usin g Figure s 3- 2 an d3-3 . Thes e value s o f o v an drr,. ar e representativ e for asamplin g tim e o f abou t 1 0 minutes . Fo r

estimatio no

f concentra tion s for longe r tim e period s se e Chapte r 5 . Figure s 3- 2 an d3- 3 appl y strictl y onl y t o ope nleve l countr y an dprobabh.^_underestimat e the . jlume__dispei__io n potential.Jrb mlo.w.-Jevel.sources-_Q_built;.up_areas . Althoug hth e vertica l sprea dma y b e les s tha nth e value s for

clas s Fwit hver y ligh t wind s o naclea r night , quantitativ e estimate s o f concentration s ar e nearl y impossibl e for

thi s condition . Wit hver y ligh t wind s o naclea r

nigh t for ground-leve l source s fre e o f topographi c influences , frequen t shift s i nwin d directio nusuall y occu r

whic hserv e t o sprea dth e plum e horizontally . Fo r elevate dsource s unde r thes e extremel y stabl e situations , significan t con centration s usuall y d o no t reac hgroun dleve l unti l th e stabilit y changes . A stabl e laye r

existin g abov e a nunstabl e laye r wil l hav e th e effec t

o f restrictin g th e vertica l diff u sion . Th e dispersio ncomputatio nca nb e modifie d for thi s situatio nb y considerin g th e heigh t o f t h bas e o f th e stabl e layer , L . A t aheigh t

2.1 5 o

L abov e th e plum e centerlin e th e concentratio ni s one tent hth e plum e centerlin e concentratio na t th e sam e distance . Whe none-tent hth e plum e centerlin e concentratio nextend s t o th e stabl e layer , a t heigh t L , i t i s reasonabl e t o assum e tha t th e distributio n start s bein g affecte db y th e "lid. " Th e followin g metho di s suggeste dt o tak e car e o f thi s situation . Allo w o

_t o increas e wit hdistanc e t o avalu e o f L/2.1 5 o r

0.4 7 L . A t

thi s distanc e x_ , th e plum e i s assume dt o hav e aGaussia ndistributio ni nth e vertical . Assum e tha t

b y th e tim e th e plum e travel s twic e thi s far , 2 x_ , th e plum e ha s becom e uniforml y distribute dbetwee nth e earth' s surfac e an dth e heigh t L , i.e. , concentratio ndoe s no t var y wit h heigh t (se e Figur e 3-4) . Fo r

th e distance s greate r tha n2 xi „ th e concentratio nfo r an y heigh t

betwee n th e groun dan dLca nb e calculate dfrom : X (x,y,z;H ) =—= •

Q 

# (*)' ] \/2? rO y L u ex p 

# 1- + (3.5 ) 

### i (se e proble m6) . Not e tha t Eq . (3.5 ) assume s nor ma l o r Gaussia ndistributio no f th e plum e only i n th e horizonta l plane . Th e sam e resul t ca nb e ob
taine dfro mth e followin g equatio nwher e o.

_i s a n effectiv e dispersio nparamete r becaus e \/2* r

L= 2.506 6 Lan d0. 8 * L—2.5 1 L .
x(x,y,z;H ) = — ^ — - [ ex p 1—(-^—^) = 1 T O y O l L U |

_I

\ (Ty j

J (3.6 ) fo r an y z fro m0 t o L fo r x > 2„ L ; x f, i s wher e o . Th e valu e o

f o_ „ = 0. 8 L 0.4 7 L

fro man y z fro m0 t o L for x > 2 x L ; x r . i s wher e <r, — 0.4 7 L EVALUATIO NO FWIN D SPEE D Fo r th e win dspeed , u , amea nthroug hth e ver tica l exten t

o f th e plum e shoul db e used . Thi s woul db e fro mth e heigh t H —2 o . throug hH -+ - 2 o z . O f course , i

f 2 o . i s greate r

tha nH the nth e win dca nb e average dfro mth e groun dt o H -j
- 2 o z . However , th e "surfac e wind " valu e ma y b e al l tha t i s available . Th e surfac e win di s mos t applicabl e t o surfac e o r

low-leve l emissions , especiall y unde r stabl e conditions . PLOT S O FCONCENTRATION S AGAINS T DISTANC E T o ^'"^ggffin." TM i"gjffh + *"* " adiffusio nprob
le mi t i s ofte ndesirabl e t o plo t centerlin e concen tration s agains t

distanc e downwind . A convenien t procedur e i s t o determin e th e ground-leve l center lin e concentration s fo r

anumbe r

o f downwin ddis
tance s an dplo t

thes e value s o nlog-lo g grap hpaper . B y connectin g th e points , on e ma y estimat e con centration s for

intermediat e downwin ddistance s (se e proble m6) . ACCURACY O FESTIMATE S Becaus e o

f amultitud e o

f scientifi c an dtechni
ca l limitation s th e diffusio ncomputatio nmetho d presente di nthi s manua l ma y provid e best estimates bu t no t infallibl e predictions . I nth e unstabl e an d stabl e cases , severalfol derror s i nestimat e o f o , ca noccu r

for th e longe r

trave l distances . I n som e case s th e o , ma y b e expecte dt o b e correc t withi n a facto r o f 2 , however . Thes e are : (1 ) al l stabilitie s for distanc e o

f trave l ou t

t o afe w hundre dmeters ; (2 ) neutra l t o moderatel y unstabl e condition s for distance s ou t

t o afew kilometers ; an d(3 ) unstabl e condition s i nth e lowe r

100 0 meter s o

f th e atmos pher e wit hamarke dinversio nabov e for distance s ou t t o 1 0 k mo r

more . Uncertaintie s i nth e esti
mate s o f o y ar e i ngenera l les s tha nthos e o f o, . Th e ground-leve l centerlin e concentration s for thes e Estimate s //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.; ' •;'-' « .-.-:.*••'..-,;. • "- . .-• * . sP.1 4

7 yWiVt. ' /Y-/ , ';»'-<.' J ''>'. ; " •/ . / . "ir *sAMj>llfiil>

T/r'-tC Or /i&OuT

10 W-Ji/Tif >000 r .„_„p_j|j^l{.:li&^ ^

• » •& " .f e 7 6 V 1 DISTANC E DOWNWIND , km Figur e 3-2 . Horizonta l dispersio n coefficien t a s a functio n o f downwin d distanc e fro m th e source . 

# j

ATMOSPHERI C DISPERSIO N ESTIMATE S

- *..- •-Y-y.jii'y;;;^. ^P.1 5 Ss}x>< ..«;_•.

_A : SN t-t*~ m .mi /,.-••'.c /

H->\;I~.

1,00 0 s3 = ;n i v; :;,^M_ll__|p 5r ^ 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 ! .I r -1 " . V

I .T I i.lTrHY.'.ill."-"-- ! "JffLJ. I j:r'::i~:~l~.llll- L 

### 3ES E 

# Egg5=§^i p J_^I - 

### p_^-_^..^..._^r:::-:::j::::::_[::^-.jz ; 

### pf : 

### } :

2 3 - S 5 - - 7 -*-f\ *
- J W' £fc 7 _-?l ( DISTANC E DOWNWIND- , k m 10 0 Figur e 3-3 . Vertica l dispersio n coefficien t a s a functio n o

f downwin d distanc e fro m the . source . Estimate s 339-90 1 O - 8 9 - J

__ h vW^tc'WjKyt'ty^l. " :. *~ •.•m^yrm -, ^mig-*%-m W *mJ^^^~x.^.r>v^.^fi,.m....*:P.1 6

y~

Figure 3-4 . Variation s i n concentratio n i n th e vertica l beneat h a mor e stabl e layer . : >

/ thre e case s (wher e o . ca nb e expecte dt o b e withi n afacto r o f 2 ) shoul db e correc t

withi nafacto r

o f 3 , includin g error s i n_- } - an du . Th e relativ e confidenc e i nth e o! s (i ndecreasin g order ) i s indicate db y th e heav y line s an ddashe dline s i nFigure s 3- 2 an d3-3 . Estimate s o

f H , th e effectiv e heigh t

o f th e plume , ma y b e i nerro r

becaus e o

f uncertaintie s i nth e esti
matio no f AH , th e plum e rise . Also , for problem s tha t requir e estimate s o

f concentratio na t

aspecifi c point , th e difficult

y o f determinin g th e mea nwin d ove r agive ntim e interva l an dconsequentl y th e locatio no

f th e x-axi s ca ncaus e considerabl e un certainty . GRAPH S FO RESTIMATE S O FDIFFUSIO N T o avoi drepetitiou s computations , Figur e 3- 5 (A throug hF ) give s relativ e ground-leve l concen tration s time s win dspee d( \u Q ) agains t down
win ddistance s for

variou s effectiv e height s o f emis
sio nan dlimit s t o th e vertica l mixin g for eac hsta bility clas s ( 1 figure for eac hstability) . Computa
- "->n s wer e mad e fro mEq . (3.3) , (3.4) , an d(3.5) . timate s o f actua l concentration s ma y b e deter
nine db y multiplyin g ordinat e value s b y Q/u . 10

-'.»*k ; .-£••-- . -.-4i-jB$itU? , PLOTTIN GGROUND-LEVEL CONCENTRATIO NISOPLETH S Ofte non e wishe s t o determin e th e location s wher e concentration s equa l o r excee dagive nmag nitude . First , th e axia l positio no f th e plum e mus t b e determine db y th e mea nwin ddirection . Fo r plottin g isopleth s o

f ground-leve l concentrations , th e relationshi p betwee nground-leve l centerlin e concentration s an dground-leve l off-axi s concentra tion s ca nb e used : x (x,y,0;H ) x(x,0,0;H ) = ex p 

# l-H*.* ! (3.7 ) Th e y coordinat e o

f aparticula r

isoplet hfro mth e x-axi s ca nb e determine da t eac hdownwin ddis
tance , x . Suppos e tha t on e wishe s t o kno w th e off-axi s distanc e t o th e 10~ ag_m~3 isoplet ha t a nx o f 60 0 m , unde r

stability*?ypeB7wher e th e ground
leve l centerlin e concentratio na t thi s distanc e i s 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 0.34 5 

# •-

O / «. c s i c l ATMOSPHERI C DISPERSIO NESTIMATE S > i ' t Y .P.1 7

X H T %

1 0 " ,'.!I.U'-r. l ,.!.,- l jiV.'-„'-,!.T.' 1 - !'..'.!'.....'*! < ?.'. . • ' .'"! " - .x. -. u__.- yx/,\-.-,,. ..-••- . n?rar;ti_itm!r.i_s^ ^

.•••.EgjgpigEr ] saf§_* M :-Ty-imm ".!]—-*i!__T!.J I \\!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 i l w;_a.)?tfiffilUPii§ffi ^

fn f If r f^-^- v *sa . ___ ; i:::_.:::!:__i:_i:::::.::Lti 'n—frtT^;"'' : : " Y-- : ; ::: f ^"-H ^ *a»iiJ I ::i:V:#a_! _
: |- : ••:..=!• . i i

10 '

E O

10" S -33 =

IO 10 "

10 0 DISTANCE.. . Figur e 3-5A. xu/ Q wit h distanc e fo r variou s heights o

femissio n (H) an d limits t o vertica l dispersio n (L) , A stability . Estimate s *2ggjg*Y ; . . - -._._- . _ t • ; 

# m(,

IOO " .

/ DISTANCE , k m Figur e 3-5B . vu Q wit h distanc e fo rvariou s height s o f emissio n (H) an d limit s t o vertica l dispersio n (U , B stability . 1 2 ATMOSPHERI C DISPERSIO N ESTIMATE S 

## *m& :i^Slfc ; -'.L&»yP.1 9



### •" '

10 0 ( DISTANCE . k >

Figure 3-5C . xu/ Q wit h distanc e fo r variou s height s o f emissio n (H ) an d limit s t o vertica l dispersio n (L) , C stability . Estimate s

•.•^.rm^mm.. - - - - vija^i^ . . ^.yti& r y... ••.:.P.2 0



### f~



## £~

( 

## liuiyillliffllliii'illi g

DISTANCE , k

m igur e 3-5D . ,v

u Q wit h distanc e fo rvariou s height s of emissio n (H ) an d limit s t o vertica l dispersio n (L) , D stability . J 1 4 

## <mmx- £$$#£;•:.•- ATMOSPHERI C DISPERSIO N ESTIMATE S ___^--P.2 1

( IO O DISTANCE , k

m Figur e 3-5E . xu/ Q wit h distanc e fo r variou s height s o femissio n (H ) an d limit s t o vertica l dispersio n (L) , E stability . Estimate s 1 5
j^i^Viis.f-rJ- -

# r 7-t ry

DISTANCE , km 

# }

gur e 3-5F . xu/ Q wit h distanc e fo r variou s height s ofemissio n (H ) an d limit s t o vertica l dispersio n (L) , F stability . 

# V)
1 6 ATMOSPHERI C DISPERSIO N ESTIMATE S .\.:.'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.2 3 

# r~-&



# r B__on

mTTaiH e A- 1 (Appendi x 3 ) whe nex p 

# -Mi)'] 0.34 5 Fman mffigpse 3-2 , fo r

stabilit y B an dx = ,6p0 m , o y = S_ LT__H_sefor

e y = (1.46 ) (92 ) =Q34 . meters . Tina s i s ti&ff

i distanc e o

f th e IO - 3 isopletiTfro mth e S-O___ Ea ma adownwin ddistanc e o

f 60 0 meters . als o b e determine dfrom : F— 

## [ 2 

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

X (x,y,0;H ) (3.8 ) TTBB Epassio n correspondin g t o th e downwin ddis
axi s distanc e ca n the nb e plotted . AffibH r < & _Q_i___be

r o f point s hav e bee nplotted , th e aaiiimenntarfiiD

n isoplet hma y b e draw n(se e problem s ffi a_n_ l 2S; . - Figure s 3- 6 an d3- 7 giv e ground-leve l TforgjrJV'tffl" * «s £jru/ Q for

variou s stabilitie s for

source s a t H = 0 an dH = 100 meters . Fo r example , t o HcwaBt e iflb e 10~ 3 g m" 3 isoplet hresultin g fro ma g3imiai____r__sw_

i sourc e o

f 2 0 g sec" 1 unde r

B stabilit y <nn_«____i_a_)

s wit hwin dspee d2 msec" 1 , on e mus t festtdaEttemnsiae th e correspondin g valu e o f \u/ Q sinc e __n_ s fe t_J_ £quantit y graphe di n Figur e 3-6 . xu/ Q = l©-" 1
_ _2/ ; '2 0 = 10~ 4
. Therefor e th e xu/ Q isoplet h i mFSgnin e 3-6 B havin g avalu e o f 10~ 4 m - 2 corre arf«pmi#» ! tt© ax isoplet hwit havalu e o f 10" ' g m~ 3
. ABEA S WITHI N ISOPLETH S ]F%i__te3-j . give s area s withi nisopleth s o f ground
height , th e produc t u o- y <J

_wil l no t chang e appreci
ably . Th e greate r

th e effectiv e height , th e mor e likel y i t i s tha t th e stabilit y ma y no t

b e th e sam e fro mth e groun dt o thi s height . Wit hth e longe r trave l distance s suc ha s th e point s o f maximu m concentration s for

stabl e condition s (Type s E o r F) , th e stabilit y ma y chang e befor e th e plum e travel s th e entir e distance . REVIE WO FASSUMPTION S Th e precedin g ha s bee nbase do n thes e as sumptions , whic hshoul db e clearl y understood : (i ) Continuou s emissio nfro mth e sourc e o r emissio ntime s equa l t o o r greate r tha ntrave l time s t o th e downwin dpositio nunde r considprfltion . s o that j
(iii ) Th e equatio no

f continuity : / + 3 0 l+ X Q = / / x u d y d z (3.9 )

atratio n i n term s o

f x u/ Q f° r

aground
- I fo r variou s stabilit y categorie s (Gifford' 1962 ; Hiiaaaeie r

an dGifford , 1962) . Fo r th e exa m pil e _wsAt

given , th e are ao

f th e 10~ 3 g m~ 3 isopleth ; (1©"" " mnT

- x u/ Q isopleth ) i s abou t 5 x 10 * meter 2

- ! CA1COJLATION O FMAXIMU M GEOUMM.EVE LCONCENTRATION S yfetnm e 3- 9 give s th e distanc e t o th e poin t o f nn__x_in_____

_concentration , x mnx , an dth e relativ e maxi
- __n_s

_concentration , x u/Q„„_ , a s afunctio no f e_£etit_TO £heigh t o f emissio nan dstabilit y clas s (Ma_it_B , 1965) . Thi s figure wa s prepare dfro m g_ajj__ B o f concentratio nversu s distance , a s i n Fig
ur e 3-5 LTh e maximu mconcentratio nca n b e deter
mine db y findin g x u/ Q a s afunctio no f effectiv e esssissBMH B heigh t an dstabilit y an dmultiplyin g b y Q/B LI n usin g Figur e 3-9 , th e use r mus t kee p i n min dt&a t

th e dispersio na t

highe r level s ma y diffe

r co__6M_erabl

y fro mtha t

determine db y th e <r y' s an d o_* s use dhere . A s noted , however , sinc e o > gener all y decrease s wit hheigh t an du increase s wit h **H_ Tdenote s natura l logarithms , i.e. , t o th e bas e e . i s fulfilled , i.e. , non e o f th e materia l emitte di s re move dfro mth e plum e a s i t move s downwin dan d ther e i s complet e reflectio na t th e ground . (iv ) Th e mea nwin ddirectio nspecifie s th e x-axis , an damea nwin dspee drepresentativ e o f th e diffusin g laye r

i s chosen . (v ) Excep t

wher e specificall y mentioned , th e plum e constituent s ar e distribute dnormall y i n bot h th e cross-win dan dvertica l directions . (vi ) Th e <r'

s give ni n Figure s 3- 2 an d3- 3 repre sen t tim e period s o

f abou t 1 0 minutes . REFERENCE S DeMarrais , G . A. , 1961 : Vertica l temperatur e dif
ferenc e observe dove r

a n urba narea . Bull . Amer . Meteorol . Soc , 42, 8 , 548-554 . Duckworth , F . S. , an dJ . S . Sandberg , 1954 : Th e effec t o f citie s upo nhorizonta l an dvertica l temperatur e gradients . Bul LAmer . Meteorol . Soc , 35, 5, 198-207 . Gifford , F . A. , 1961 : Us e o f routin e meteorologica l observation s for

estimatin g atmospheri c disper
sion . Nuclea r

Safety , 2, 4 , 47-51 . Gifford , F . A. , 1962 : Th e are awithi n ground-leve l dosag e isopleths . Nuclea r Safety , 4, 2, 91-92 . Estunate sP.2 4



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ington . D . C , Smithsonia nInstitution , 52 7 pp . Martin , D . O. , 1965 : Persona l communication . Pasquill . F. , 1961 : Th e estimatio nof th e dispersio n of windborn e material . Meteorol . Mag. , 90, 1063 , 33-49 . Pooler . F. , 1965 : Persona l communication . Sutton . 0 . G. . 1953 : Micrometeorology, Ne w York , McGraw-Hill . 33 3 pp . Turner , D . B. , 1961 : Relationship s betwee n24
- hou r mea nai r

qualit y measurement s an dmete orologica l factor s i nNashville , Tennessee . J . Ai r Poll . Cont . Assoc , 11, 483-489 .

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# f. GENERA LCONSIDERATION S

I nmos t problem s on e mus t

estimat e th e effec
tiv e stac k

height , H , a r

whic hth e plum e become s essentiall y level . Rarel y wil l thi s heigh t correspon d t o th e physica l heigh t

o f th e stack. , h . I

f th e plum e i s caugh t i nth e turbulen t

wak e o f th e stac k

o r o f building s i nth e vicinit y o f th e stack , th e effluent wil l b e mixe drapidl y downwar dtowar dth e groun d (aerodynami c downwash) . If th e plum e i s emitte d fre e o f thes e turbulen t

zones , anumbe r

o f emissio n factor s an dmeteorologica l factor s influenc e th e ris e o f th e plume . Th e emissio nfactor s are : velocity o f th e effluent

a t th e to p o

f th e stack , v. ; tempera tur e o f th e effluent

a t th e to p o

f th e stack , T s ; an d diamete r o f th e stac k

opening , d . Th e meteorolog
ica l factor s influencin g plum e ris e ar e win dspeed , u ; temperatur e o

f th e air , T., ; shea r

o f th e win d spee dwit hheight , d u dz ; an datmospheri c sta bility . N o theor y o nplum e ris e take s int o accoun t al l o f thes e variables ; eve ni f suc hatheor y wer e available , measurement s o f al l o f th e parameter s woui dseldo mb e available . Mos t o f th e equation s tha t hav e bee nformulate dfor computin g th e ef

fectiv e heigh t

o f emissio nar e semi-empirical . Fo r a recen t revie w o

f equation s for

effectiv e heigh t

o f emissio nse e Moses , Strom , an dCarso n(1964) . Mose s an dStro m(1961) , havin g compare dac tua l an dcalculate dplum e height s b y mean s o f si x plum e ris e equations , repor t "Ther e i s n o on e for
mul awhic hi s outstandin g i nal l respects. " Th e formula s o

f Davidson-Bryan t

(1949) , Hollan d (1953) , Bosanquet-Carey-Halto n (19.50) , an dBo sanque t (1957 ) al l giv e generall y satisfactor y re sult s i nth e tes t

situations . Th e experiment s con ducte db y Mose s an dStro minvolve dplum e ris e fro mastac k

o f les s tha n0. 5 mete r

diameter , stac k ga s exi t velocitie s les s tha n1 5 msec~ M an deffluent temperatur e no t

mor e tha n35° C highe r tha ntha t o f th e ambien t

air . Th e equatio no

f Hollan dwa s develope dwit h experimenta l dat afro mlarge r source s tha nthos e o f Mose s an dStro m(stac k diameter s from1. 7 t o 4. 3 meter s an dstac k

temperature s from8 2 t o 204 ; C) ; Holland' s equatio ni s use dinth e solutio n o f th e problem s give ni nthi s workbook . Thi s equa tio nfrequentl y underestimate s th e effectiv e heigh t o f emission ; therefor e it s us e ofte nprovide s asligh t "safety " factor . Holland' s equatio nis : AH=-^A(l. 5 + 2.68xlO-=p-^=^-d ) (4.1 ) where : A H -- = th e ris e o

f th e plum e abov e th e stack , m v. , = stac k ga s exi t velocity , msec _ : d--= * th e insid e stac k

diameter , m u -- = win dspeed , msec - 1 p = atmospheri c pressure , m b T „ « = stac k ga s temperature , ° K T . = ai r temperature , ° K an d2.6 8 x 10 - 3 i s aconstan t havin g unit s o

f mb - 1 m~ l
. Hollan d(1953 ) suggest s tha t avalu e betwee n 1. 1 an d1. 2 time s th e A H fro mth e equatio nshoul d b e use dfor

unstabl e conditions ; avalu e betwee n 0. 8 an d0. 9 time s th e A

H fro mth e equatio nshoul d b e use dfor

stabl e conditions . Sinc e th e plum e ris e fro mastac k occur s ove r som e distanc e downwind , Eq . (4.1 ) shoul dno t b e applie dwithi nth e first

fe w hundre dmeter s o

f th e stack . EFFECTIV EHEIGH T O FEMISSIO N AN D MAXIMU M CONCENTRATIO N I f th e effectiv e height s o f emissio nwer e th e sam e unde r

al l atmospheri c conditions , th e highes t ground-leve l concentration s fro magive nsourc e woul doccur , wit hth e lightes t winds . Generally , however , emissio ncondition s ar e suc htha t th e ef
fectiv e stac k

heigh t i s a ninvers e functio n o f win d spee da s indicate di nEq . (4.1) . Th e TnnYimiiT p ground-leve l concentratio noccur s a t som e inter
mediat e win dspeed , a t

whic habalanc e i s reache d betwee nth e dilutio ndu e t o win dspee dan dth e effect o f heigh t o f emission . Thi s critica l win dspee d wil l var y wit hstability . I norde r to determin e th e critica l win dspeed , th e effectiv e stac k heigh t a s a functio no

f win dspee dshoul dfirst b e determined . Th e maximu mconcentratio nfo r eac hwin dspee d an dstabilit y ca nthe nb e calculate dfro mFigur e 3- 9 a s afunctio no

f effectiv e heigh t

of emissio n an dstability . Whe nth e m_uri___u mconcentratio n a s afunctio no

f win dspee di s {dotte do nlog-lo g grap hpaper , curve s ca nb e draw nfo r eac hstabilit y class ; th e critica l win dspee dcorrespond s t o th e poin t o f highes t maximu mcomcemtratia n o nth e curv e (se e proble m14) . ESTIMATE S O FREQUIRE D STAC K HEIGHT S Estimate s o

f th e stac k

heigh t require dt o pro duc e concentration s belo w agive nvaline ma y b e mad e throug hth e us e of Figur e 3- 9 b y obtainin g solution s for

variou s win dspeeds . Us e «_ § thi s figure consider s maximu mconcentration s a t an y distanc e fromth e source . I nsom e situation s hig hconcGratraftmnis upo nth e propert y o

f th e emitte r

ar e o f littl e concern , bu t Effective Heigh t «$£&&£?, 3 1P.3 7

maximu mconcentration s beyon dth e propert3 ' lin e ar e o f th e utmos t

importance . Fo r

first approxima
- ' on s i t ca nb e assume dtha t

th e maximu mconcen itio n occur s wher e \/2".»- = H an dtha t a t thi s distanc e th e a' s ar e relate dt o th e maximu mcon centratio nby : Q

x u e x- = - 0.11 7 Q

U ,\,„ n x (4.2 ) Knowin g th e sourc e strength , Q , an dth e concen tratio nno t

t o b e exceede dxm«x

> on e ca ndetermin e th e necessar y *rr

*zfo r agive nwin dspeed . Figur e 4- 1 show s «r

r a za s afunctio no

f distanc e for

th e variou s stabilit y classes . Th e valu e o f <r T<r

_an da desig ndistance , X

d(th e distanc e beyon dwhic h\ i s les s tha nsom e pre-determine dvalue) , wil l deter
min e apoin t

o nthi s grap hyieldin g astabilit y clas s o r poin t betwee nclasses . Th e a. for thi s stabilit y (o r poin t betwee nstabilities ) ca nthe nb e deter
mine dfro mFigur e 3-3 . Th e require deffectiv e stac k heigh t fo r thi s win dspee dca nthe nb e approxi
mate db y H = y ^ CT- (se e proble m15) . Sinc e Eq . (4.2 ) i s a napproximation , th e resultin g heigh t shoul db e use dwit hEq . (3.3 ) t o ensur e tha t th e maximu mconcentratio ni s sufficientl y low . If enoug hi s know nabou t th e propose dsourc e t o allo w us e o

f a nequatio nfor

effectiv e heigh t

o f emission , th e relatio nbetwee nA H an du ca nb e determined . Th e physica l stac k heigh t require da t th e win dspee dfo r

whic hH wa s determine di s H —

. . Th e sam e procedure , startin g wit hth e deter
natio no f o? a,, mus t

b e use dwit hothe r

win d speed s t o determin e th e maximu mrequire dphysica l stac k heigh t (se e proble m16) . EFFEC T O FEVAPORATIV ECOOLIN G Whe n effluent

gase s ar e washe dt o absor b cer tai nconstituent s prio r

t o emission , th e gase s ar e coole d- an dbecom e saturate dwit hwate r vapor . Upo nreleas e o

f th e gase s fro mth e absorptio ntower , furthe r coolin g du e t o contac t wit hcol dsurface s o f ductwor k

o r stac k i s likely . Thi s coolin g cause s condensatio no

f wate r droplet s i nth e ga s stream . Upo nreleas e o

f th e gase s fro mth e stack , th e wate r droplet s evaporate , withdrawin g th e laten t hea t o f vaporizatio nfro mth e ai r an dcoolin g th e plume . Th e resultin g negativ e buoyanc y reduce s th e effec
tiv e stac k

heigh t (Scorer , 1959) . EFFEC T O FAERODYNAMI C DOWNWAS H Th e influenc e o

f mechanica l turbulenc e aroun d abuildin g o r

stac k ca nsignificantl y alte r th e ef
fectiv e stac k

height . Thi s i s especiall y tru e wit h hi? hwinds , whe nth e beneficial effec t o f hig hstack
- ""> s velocit y i s a t

aminimu man dth e plum e i s tte dnearl y horizontally . Th e regio no f disturbe d / surround s a nisolate dbuilding , generall y t o a t leas t twic e it s heigh t

an dextend s downwin d5 t o 1 0 time s it s height . Buildin g th e stac k 2. 5 time s th e heigh t o f th e highes t

buildin g adjacen t

t o th e stac k usuall y overcome s th e effect s o f buildin g turbulenc e (Hawkin s an dNonhebel , 1955) . Ensurin g tha t th e exi t velocity o

f th e stac k

ga s i s mor e tha n1. 5 time s th e win dspee dwil l usuall y preven t downwas hi n th e wak e o

f th e stack . Mos t

o f th e knowledg e abou t th e turbulen t

wake s aroun dstack s an dbuilding s ha s bee ngaine dthroug hwin dtunne l studie s (Sher
loc k an dLesher , 1954 ; Strom , 1955-1956 ; Strom , e t al , 1957 ; an dHalitsky , 1962) . B y us e o f model s o f buildin g shape s an dstacks , on e ma y determin e th e win dspeed s require dt o caus e downwas hfo r variou s win ddirections . Wit hawin dtunne l th e meteorologica l variable s mos t easil y accounte dfor ar e win dspee dan dwin ddirectio n(b y rotatio no f th e mode l withi nth e tunnel) . Th e emissio nfactor s tha t ma y b e considere dar e th e siz e an dshap e o f th e plan t building ; th e shape , height , an ddiamete r o f th e stack ; th e amoun t

o f emission ; an dth e stack
ga s velocity . Throug hwin dtunne l studies , th e critica l win d speed s tha t

wil l caus e downwas hfro mvariou s di
rection s ca nb e determine dfor agive nse t

o f plan t factors . Th e averag e numbe r o f hour s o f downwas h pe r yea r canthe nb e calculate db y determinin g th e frequenc y o

f win dspeed s greate r

tha nth e critica l speed s for

eac hdirectio n(Sherloc k an dLesher , 1954 ) i f climatologica l dat arepresentativ e o f th e sit e ar e available . Maximu mdownwas habou t arectangula r

struc tur e occur s whe nth e directio no f th e win di s a t

a n* angl e o f 4 5 degree s fro mth e majo r axi s o f th e struc - ;•_

_i > ture ; minimu mdownwas hoccur s wit hwin dflow 7 ^ paralle l t o th e majo r

axi s o f th e structur e (Sherloc k 3 an dLesher , 1954) . Halitsk y (1961 . 1963 ) ha s show ntha t th e efflu
en t fro mflushopening s o nflat roof s frequentl y flows i nadirectio nopposit e t o tha t o f th e fre e atmospheri c wind , owin g t o counter-flo w alon g th e roof i nth e turbulen t

wak e abov e th e building . I n additio nt o th e effec t

o f aerodj-nami c downwas h upo nth e releas e o

f ai r pollutant s fro mstack s an d buildings , on e mus t

als o conside r

th e effect s o

f aero dynami c downwas hwhe nexposin g meteorologica l instrument s nea r

o r upo nbuildings . Mtri

Mil*
ittme wi« o 

# r ii.; . Wher e th e pollutio ni s emitte dfro maven t o r openin g o nabuildin g an di s immediatel y influ
ence db y th e turbulen t wak e o f th e building , th e pollutio ni s rapidl y distribute dwithi nthi s turbu
len t wake . T o accoun t

for mixin g i nth e turbulen t wake , on e ma y assum e binorma l distribution s of concentration s a t

th e source , wit hhorizonta l an d vertica l standar ddeviation s o f <r,. „ an da**. Th e standar ddeviation s ar e relate dt o th e widt han d heigh t o f th e building , for

example , lettin g 4. 3 o ro equa l th e widt ho

f th e buildin g an d2.1 5 <*„ . equa l tauum f_« .

) 32

^ - ATMOSPHERI C DISPERSIO NESTIMATE Sio* r S~ li;_l_l!;;! l l|'.!!_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 ^

IO O Distonc t Downwind , k m Figur e 4-1 . Th e produc t o f<r,<r , a s a functio n o fdownwin d distanc e fro m th e source . Effectiv e Heigh t iS&U. . • :=_*_=r - .^ASr&C- V •-.-.IHSSQ'S E • • 3 3( • th e he-igfai . Value s othe r tha n4. 3 an d2.1 5 ca nb e ••sed. . \6y__ej

_ thes e value s ar e use d97'/' , o f th e dis
- •jautita n i s include dwithi nthes e limit?- . Virtua l -stantee s x, - an dx z ca nb e foun dsuc h:_u.c a t x y , <r y== • ai*,, smd

a t x„ , <x_ , ••= a z „. Thes e x' s wil l diffe r wit hstaMity . Equation s applicabl e t o poin t source s ca ntrten i b e used , determinin g <? , a s afunctio no

f x -f
- x; „ ffiiaiido,as afunctio no f x + x t . REFERENCE S BosarrqpEefc , C . H. , W . F . Carey , an dE . M . Halton , 1955S : Dus t

fro mchimne y stacks . Proc . Inst . Mesab . Eng. , 162, 355-367 . Bosaraqpiet , C . H. , 1957 : Th e ris e o f aho t wast e ga s plniraiE . J . Inst . Fuel , 30, 197 , 322-328 . Dav i in ® € H F. , 1949 : Th e dispersio nan dspread
a£ gase s an ddus t

fromchimneys . Trans . o nInd . Wastes , 14thAnn . Meeting , Ind . Found . Amer. , 38-55 . Halitsfcy , J. , 1961 : Win dtunne l mode l tes t o f ex hau_E t ga s recirculatio na t

th e NI H Clinica l Censter . Tech . Rep . No . 785.1 , Ne w York Univ . Halits&gF, , J- , 1962 : Diffusio no f vente dga s aroun d buiMimgs . J . Ai r

Poll . Cont . Assoc , 12, 2 , 74-80 . Halits&y. , J. , 1963 : Ga s diffusio nnea r buildings , thjffisneiica

l concept s an dwin dtunne l mode l ex pemmmemt

s wit hprismati c buildin g shapes . Geo
pbigfflica l Science s Lab . Rep . No . 63-3 . Ne w

. Yom k Univ . Hawkins , J . E. , an dG . Nonhebel , 1955 : Chimney s an dth e dispersa l o

f smoke . J . Inst . Fuel , 28, 530-546 . Holland , J . Z. , 1953 : A meteorologica l surve y o f th e Oa k Ridg e area . 554-55 9 Atomi c Energ y Comm. , Repor t

ORO-99 , Washington , D.C , 58 4 pp . Moses , H. , an dG . H . Strom , 1961 : A compariso n o f observe dplum e rise s wit hvalue s obtaine d fro mwell-know nformulas . J . Ai r Poll . Cont . Assoc. , 11, 10 , 455-466 . Moses , H. , G . H . Strom , an dJ . E . Carson , 1964 : Effect s o f meteorologica l an dengineerin g fac
tor s o nstac k

plum e rise . Nuclea r

Safety , 6, 1 , 1-19 . Scorer , R . S. , 1959 : Th e behavio r o f plumes . Int . J . Ai r Poll. , 1, 198-220 . Sherlock , R . H. , an dE . J . Lesher , 1954 : Rol e o f chimne y desig ni ndispersio no f wast e gases . Ai r Repair , 4, 2, 1-10 . Strom , G . H. , 1955-1956 : Win dtunne l scal e mode l studie s o f ai r pollutio nfro mindustria l plants . Ind . Wastes , Sept . - Oct . 1955 , Nov . - Dec . 1955 , an dJan . - Feb . 1956 . Strom , G . H. , M . Hackman , an dE . J . Kaplin , 1957 : Atmospheri c dispersa l o f industria l stac k

gase s determine db y concentratio nmeasurement s i n scal e mode l win dtunne l experiments . J . Ai r Poll . Cont . Assoc , 7 , 3 , 198-203 . )

) 3 4 ATMOSPHERI C DISPERSIO N ESTIMATE S

S*/."'. ' ' -i6?

iP.4 0

y Chapte r 5 —SPECIA LTOPIC S CONCENTRATION S I NA NINVERSIO N BREAK-U PFUMIGATIO N A surface-base dinversio nma y b e eliminate db y th e upwar dtransfe r of sensibl e hea t

fro mth e groun dsurfac e whe ntha t surfac e i s warme r

tha n th e overlyin g air . Thi s situatio noccur s whe nth e groun di s bein g warme db y sola r radiatio no r

whe n ai r flows fro macol dt o arelativel y war msurface . I neithe r

situatio npollutant s previousl y emitte d abov e th e surfac e int o th e stabl e laye r wil l b e mixe d verticall y whe nthe y ar e reache db y th e therma l eddies , an dground-leve l concentration s ca nincrease . Thi s process , calle d"fumigation " wa s describe db y Kewso nan dGil l (1944 ) an dHewso n(1945) . Equa tion s fo r estimatin g concentration s wit hthes e con dition s hav e bee ngive n b y Hollan d(1953) , Hew so n(1955) , Giffor d(1960a) , Bierl y an dHewso n (1962) , an dPoole r

(1965) . T o estimat e ground-leve l concentration s unde r inversio nbreak-u p fumigations , on e assume s tha t th e plum e wa s initiall y emitte dint o astabl e layer . Therefore , a*, an dCT. characteristi c of stabl e condi
tion s mus t

b e selecte dfo r

th e particula r

distanc e o f concern . A nequatio n fo r th e ground-leve l con centratio nwhe nth e inversio nha s bee neliminate d t o aheigh t

h s is : X F(x,y,0;H ) = Q 

# 1 ex p (—0. 5 p- ) d p

V2J Tor

y Fu h i 

# exp 

# [--H^r ] (5.1 ) wher e p - H an d&-J- Fi s discusse dbelow . Value s fo r

th e integra l i n bracket s ca nb e foun di n mos t statistica l tables . Fo r example , se e page s 273
- 276 , Buringto n(1953) . Thi s facto r account s fo r th e portio nof

th e plum e tha t

i s mixe ddownward . I f th e inversio n i s eliminate du p t o th e effectiv e stac k height , hal f

of th e plum e i s presume dt o b e mixe ddownward , th e othe r hal f remainin g i nth e stabl e ai r

above . Eq . (5.1 ) ca nb e approximate d whe nth e fumigatio nconcentratio ni s nea r it s maximu mby : ' ,. . X r (x,y,0;H ) Q T T - ex p

V 2J T U ' 0>F ' h i h , —H -f

- 2 a , = h+ A H + 2 a ,



# I2 U. F

# JJ

(5.2 ) (5.3 ) A difficult y i s encountere di nestimatin g area sonabl e valu e fo r

th e horizonta l dispersio nsinc e i n mixin g th e stabl e plum e throug havertica l dept h som e additiona l horizonta l spreadin g occur s (se e proble m12) . If

thi s spreadin g i s ignore dan dth e <r Tfo r stabl e condition s used , th e probabl e resul t woul db e estimate dconcentration s highe r tha nac tua l concentrations . Or , usin g a napproximatio n suggeste db y Bierl y an dHewso n(1962 ) tha t th e edg e of th e plum e spread s outwar dwit ha nangl e of 15 s , th e <Ty

Ffo r th e inversio nbreak-u p fumigatio n equal s th e CT, fo r

stabl e condition s plu s one-eight h th e effectiv e heigh t

of emission . Th e origi nof thi s concep t ca nb e see ni nFigur e 5- 1 an dth e followin g equation , wher e th e edg e of th e plum e i s th e poin t a t whic hth e concentratio nfall s t o 1/1 0 tha t a t th e centerlin e (a t

adistanc e o

f 2.1 5 a, fro mth e plum e center) . <TyT 2.1 5 CT T(stable ) + H ta n15 °
o y(stable ) 2.1 5

H / 8 (5.4 ) A Gaussia ndistributio ni nth e horizonta l i s as sumed . 20 - BOUNDAR YO F STABL E PLUM E

2.1 5 » y '(FUMIGATION ) 

### Figure5-1 . Diagra

m showin gassume d height , hi an d ? 7 

### durin gfumigation , fo rus e i n equatio n(52) . Eq . (5.4 ) shoul dno t

b e applie dnea r

th e stack , fo r if th e inversio nha s bee neliminate dt o aheigh t sufficien t t o includ e th e entir e plume , th e emissio n i s takin g plac e unde r

unstabl e no t

stabl e conditions . Therefore , th e neares t downwin ddistanc e t o b e considere dfo r

a nestimat e o f

fumigatio nconcen tration s mus t

b e grea t

enough , base do nth e tim e require dt o eliminat e th e inversion , tha t thi s por tio nof th e plum e wa s initiall y emitte dint o stabl e air . Thi s distanc e i s x = ut m , wher e u i s th e mea n Specia l Topic s 35

\«*-*.m*rr'$) r rM,yP.4 1

win di n th e stabl e laye r an dt„ , i s th e tim e require d r-J-o eliminat e th e inversio nfro mh , th e physica l igh t o f th e stac k

t o h ( (Eq . 5.3) . t mi s dependen t

upo nbot hth e strengt ho f th e inversio nan dth e rat e o f heatin g a t

th e surface . Poole r (1965 ) ha s derive da n expressio nfo r esti
matin g thi s time :

P a c p 8 0 8 z (h , 

# .- « m R8 z V1 " "'

\ 2 J

(5.5 ) wher e tn , = tim e require dfor th e mixin g laye r

t o develo p fro mth e to p o

f th e stac k

t o th e to p o f th e plume , se c P „ = ambien t

ai r density , g m - 3 c p = specifi c hea t

o f ai r a t constan t pressure , ca l g" 1 °K- ' R= ne t rat e o f sensibl e heatin g o

f a n ai r colum nb y solar

radiation , ca l m - 2 sec - 1 -r - = vertica l potentia l temperatur e gradient ,

8 T 5 K m - 1 ~ —

r r (th e adiabati c laps e rate ) S

z h i = heigh t

o f bas e o f th e inversio nsufficien t t o b e abov e th e plume , m h= physica l heigh t

o f th e stack , m Not e tha t

h t — hi s th e thicknes s o

f th e laye r

t o b e ••atedan d[ —^—- ) i s th e averag e heigh t o f th e yer . Althoug hRdepend s o n season , an dclou d cove r an dvarie s continuousl y wit htime , Poole r ha s use davalu e o

f 6 7 ca l m - 2 sec - 1 a s a n averag e fo r .fumigation . Hewso n(1945 ) als o suggeste dametho do f esti
matin g th e tim e require dt o eliminat e a n inversio n t o aheigh t

z b y us e o

f a n equatio no

f Taylor' s (1915 , p . 8) :

z 2 (5.6 ) t = where : 4 K

t = tim e require dt o eliminat e th e inver
sio nt o heigh t

z , se c z = heigh t

t o whic hth e inversio nha s bee n eliminated , m K = edd y diffusivity for

heat , m 2 sec - 1 Rewritin g t o compar e wit hEq . (5.5) ,

h, = —h 2 t » — 4 K (5.7 )

/ Hewso n(1945 ) ha s suggeste davalu e o f 3 m 2 sec _ i for K . ^LIJiMETRAPPIN G Plum e trappin g occur s whe nth e plum e i s vappe dbetwee nth e groun dsurfac e an dastabl e 3 6 laye r aloft . Bierl y an dHewso n(1962 ) hav e sug geste dth e us e o

f a n equatio ntha t

account s fo r

th e multipl e edd y reflection s fro mbot hth e groun dan d th e stabl e layer : X (x,0,z;H ) —
ex p Q 2j rU <j ya. 

# \-M-^-Y\ . 

# —[--M^y ] + N= J N— 1 

# [---H-V"- )

ex p 

# -M

-*- ex p — 

### + ex p — 

### z + H—

<<- . 

### 2 N L'

' z —H - f

2 NL <T , 

### z + H + 2 NL 

# r 1 / Z - H + 2NL \* 

# -H' + H 

# : 2NL 

# y]H > wher e Li s th e heigh t

o f th e stabl e laye r

an dJ —

3 o r 4 i s sufficien t

t o includ e th e importan t reflec
tions . A goo dapproximatio no f thi s length y equa tio nca n b e mad e b y assumin g n o effec t o f th e stabl e laye r unti l <r

_= 0.4 7 L(se e Chapte r 3) . I t i s as sume dtha t

a t thi s distance , x_, th e stabl e laye r begin s t o affec t

th e vertica l distributio ns o tha t a t th e downwin ddistance , 2 x_, unifor mvertica l mix
in g ha s take nplac e an dth e followin g equatio nca n b e used : X (x,y,z;H ) Q

V2J T o y Lu ex p 

# [-MiY] (5.9 ) 

# t Fo r distance s betwee nx Lan d2 x_th e bes t approxi
matio nt o th e ground-leve l centerlin e concentratio n i s tha t rea dfro mastraigh t

lin e draw nbetwee nth e concentration s fo r

point s X Lan d2 x_

, o n alog-lo g plo t o f ground-leve l centerlin e concentratio na s a functio no

f distance. . 

### CONCENTRATION S A T GROUN D LEVE L COMPARE D T O CONCENTRATION S A T TH E LEVE L O F EFFECTIV

E STAC K HEIGH T FRO M ELEVATE D CONTINUOU S SOURCE S Ther e ar e severa l interestin g relationship s be
twee ngrrnnntl-lpvpl rnnr-Pntxatinn aan dr-oncentra tion s a t th e leve l o

f th e plung e rpntg.rline . On e o f ATMOSPHERI C DISPERSIO N ESTIMATE S )

y

•~ : f-t-. 'MX^^S^l^i^^^^^i^i^i^^i^^ , .P.4 2 

# w

/

/ 

# 6<

i s a t th e distanc e o

f maximu mconcentratio n a t th e ground . A s aroug happroximatio nth e maxi
- ___Q__ n grrmnH-jpyp l rnnpqn^rntin n OCCUr S a tth e dis tanc e where ! CT. = —j= H . fThi s approximatio n i s muc hbette r

for unstabl e condition s tha nfor stabl e conditions . Wit hthi s approximation , th e rati o o f (concentratio na t

plum e centerlin e t o tha t a t th e groun dis : X (* , 0,H ) X (x.0,0 ) 

# * [ 1. 0 + ex p 1 /2 H 

### 2 V <*z 

## •)• ] ^ x



### 1 0 ex p [1. 0 + exp 

# 4-(-?•) ' ^

•0.5(2V2) 2 ] ex p —0. 5 (v'2) " (1. 0 + 0.0182 ) 0.36 8 

# if 1.3 8 Thi s calculatio nindicate s tha t a t th e distanc e | o f maximu mground-leve l concentratio nth e concen su s tratio na t

plum e centerlin e i s greate r b y abou t >one-third . I t i s als o o

f interes t t o determin e th e relation
shi p betwee n<r z an dH suc htha t

th e concentratio n a t ground-leve l a t

agive ndistanc e fro mth e sourc e i s th e sam e a s th e concentratio na t plum e level . Thi s conditio nshoul doccu r where : Th e valu e H/CT , = 1.1 0 satisfie s thi s expression , whic hca nb e writte na s <*

_= 0.9 1 H (se e proble m 10) . TOTA LDOSAG

EFRO M A FINIT ERELEAS E Th e tota l dosage , whic hi s th e integratio no f concentratio nove r

th e tim e o

f passag e o

f aplum e o r puff , ca nb e obtaine dfrom : D T(x,y,0;H ) = Q . iray <r , U ex p 

# -I-H*)* ] l-M-i)] (5.10 ) wher e D T= tota l dosage , g se c m~ 3 an dQ T= tota l release , g Th e CT'S shoul db e representativ e o f th e time : perio dove r

whic hth e releas e take s place , an dcar e shoul db e take nt o conside r th e x-axi s alon g th e trajector y o r

pat ho f th e plum e o r

puf f travel . Larg e error s ca neasil y occu r i f th e pat hi s no t

know n accurately . Th e estimat e o f thi s patf e 5 s usuall y in
creasingl y difficul t

wit hshorte r

releas e femes. D

_ ca nals o b e give ni ncuri e se c m _ Jif Q

_i s i mmmies . CROSSWIND-INTEGRATE D CONCENTRATIO N Th e ground-leve l crosswind-infepgyrattw dconcen tratio ni s ofte no

f interest . Fa r

a. <rain______i_n__

. ele
vate dsourc e thi s concentratio ni s dettB__mi__s_ l fro m Eq . (3.2 ) integrate dwit hrespec t to y _rao_

_"* • t o + v (Gifford1960a ) giving : Xcw i 2 Q ex p 

# I-H*)* ] fill ) \/2W j u I ndiffusio nexperiment s th e wind-integrate dconcentratio ni s ©ite mde&_______ie

d a t particula r

.downwin ddistance s firearma. <_3_fi__w_t_ d lin e o r ar c o f samplin g measuronenit s _i___d_

__at t thi s distance . Whe nth e sourc e strength , Q, , an dantcrag e win dspeed , u , ar e known , v_ca nb e «°«im"_Hihwf Pin
directl y eve nthoug hn o me__sure______i_ s wane i___.d

e i nth e vertical . I

f an y o f th e trace r

os ! reactio no r

deposition , th e result-Di g w_imam estimate s wil l no t

represen t

th e vattika l «lli»*jiiwr!ii«

w (se e proble m18) . ESTIMATIO NO FCONCENTRAT_©_<S FO X SAMPLIN GTIME S LONGERTHA NA FE WMINUTE S Concentration s directl y doinnri_a_

_fama t wmir e decreas e wit hsamplin g tim e nsaini y Hwjmwf t o f a . large r cydu e t o increase dmeande r of f mmdg___mrtion . Stewart , Gale , an dCrook s (1958 $ uteyu_.ta l tha t thi s decreas e i nconcRntrati"* * *«mu__»

__^r.jgfrfr , prugg rla wnrifh ...th ac^ffiplm g rim_» ffiirr.EpmiTQHnC T period s fro mabou t

3 minute s to abcnri

t __a_ f aa aboar. Crame r (1959 ) indicate s tha t

tin s ______

_punter'la w applie s for

samplin g time s fro m3 <»gg«»«f as © 1 0 minutes . Bot ho

f thes e studie s WEB S Erase da mob
servation s take nnea r

th e heigh t

of f mefease . GilSim . (1960b ) indicate s tha t

ratio s o f pea_ k to mea n con centration s ar e muc hhighe r tha nttftms

e gjwen i b y th e abov e powe r

la w wher e ofasE_^3tt_____

s of fasaaceatration s ar e mad e a t

height s canBdeoabl y <___5ere__ t fro mth e heigh t

o f releas e o r

co___a__ffi_a_bJ

y _,a___o.e d fro mth e plum e axis . H e als o muffin**** : fltafc for increasin g distance s fro ma nrf_aEa__eri______aro&_.tlte ratio s o f pea k t o averag e OHM-«i-__,lt__»-__ . gftaearve d a t groun dlevel approac hunity , Scggg r iiSHfeis. ) an d Singer , e t

al . (1963 ) sho w tfia t

_______ _<_ f pea k to mea nconcentration s depen dals o a mth e s____nf__t

y o f th e atmospher e an dth e type of f tanisrintt&ad

. th e plum e i s passin g over . Nanhdb d((11960 ) reports tha t Mead e deduce darelatio nbeftawae ac___a___c£e

d concentration s a t

groun dlev dam i tf__e rampfing tim e fro m" astud y o

f publishe d<_&__

_ am . l___a__ l an d vertica l diffusio ncoefficient s mstead y winds. " Thes e relation s ar e show ni nTaM e 5-H . Specia l Topic s 37

*»-—•*-• •P.4 3

y

Im2. Fo r

elevate dsource s maximu m"instantaneous" concentration s occu r

wit hunstabl e condition s whe nportion s o

f th e plum e tha t

hav e undergon e littl e dispersio nar e brough t t o th e ground . Thes e occu r

clos e t o th e poin t

o f emissio n(o n th e orde r o f 1 t o 3 stac k

heights) . Thes e con centration s ar e usuall y o f littl e genera l interes t becaus e o

f thei r ver y shor t

duration ; the y cannot b e estimate dfro mth e materia l presente di n thi s workbook . 3 . Fo r elevate dsource s maximu mconcentration s for tim e period s o

f afe w minute s occu r

wit h unstabl e conditions ; althoug hth e concentra tion s fluctuat e considerabl y unde r thes e condi
tions , th e concentration s average dove r afe w minute s ar e stil l hig hcompare dt o thos e foun d unde r othe r conditions . Th e distanc e o f thi s maximu mconcentratio noccur s nea r th e stac k (fro m1 t o 5 stac k

height s downwind ) an dth e concentratio ndrop s of

f rapidl y downwin dwit h increasin g distance . 4 . Fo r elevate dsource s maximu mconcentration s for tim e period s o

f abou t hal f a nhou r ca noccu r wit hfumigatio ncondition s whe na nunstabl e laye r increase s verticall y t o mi x downwar da plum e previousl y discharge dwithi nastabl e layer . Wit hsmal l -iH , th e fumigatio nca noccu r clos e t o th e sourc e bu t

wil l b e o f relativel y shor t duration . Fo r

larg e ^H , th e fumigatio nwil l occu r som e distanc e fro mth e stac k (perhap s 3 0 t o 4 0 km) , bu t

ca npersis t

for alonge r

tim e interval . Concentration s considerabl y lowe r tha n thos e associate dwit hfumigations , bu t o f sig
nificanc e ca noccu r

wit hneutra l o r

unstabl e condition s whe nth e dispersio nupwar di s se verel y limite db y th e existenc e o f amor e stabl e laye r abov e th e plume , for

example , a ninversion . 5 . Unde r

stabl e condition s th e maximu mconcen tration s a t

ground-leve l fro melevate dsource s ar e les s tha nthos e occurrin g unde r unstabl e condition s an doccu r

a t greate r distance s fro m th e source . However , th e differenc e betwee n maximu mground-leve l concentration s fo r stabl e an dunstabl e condition s i s onl y afacto r o f 2 fo r effectiv e height s o

f 2 5 meter s an dafacto r o f 5 for H o f 7 5 m . Becaus e th e maximu m occur s a t greate r distances , concentration s tha t ar e belo w th e maximu mbu t stil l significan t

ca n occu r ove r larg e areas . Thi s become s increas
ingl y significan t

i f emission s ar e comin g fro m mor e tha non e source . CONCENTRATION S A T A RECEPTO RPOIN T FRO M SEVERALSOURCE S Sometimes , especiall y for multipl e sources , i t

i s convenien t

t o conside r

th e recepto r

a s bein g a t

th e origi no f th e diffusio ncoordinat e system . Th e source-recepto r geometr y ca nthe nb e worke dou t merel y b y drawin g o r

visualizin g a nx-axi s oriente d upwin dfro mth e recepto r an ddeterminin g th e crosswin ddistance s o

f eac hsourc e i nrelatio nt o thi s x-axis . A s pointe dou t

b y Gifford(1959) , th e con centratio na t

(0 , 0 , 0 ) fro masourc e a t (x , y , H ) o nacoordinat e syste mwit hth e x-axi s oriente dup win di s th e sam e a s th e concentratio na t (x , y , 0 ) fro masourc e a t

(0 , 0 , H ) o nacoordniat e syste m wit hth e x-axi s downwin d(Figur e 5-2) . Th e tota l concentratio ni s the ngive nb y summin g th e indi
vidua l contribution s fro meac hsourc e (se e proble m 20) . SOURC E ...H ) urwiN O

RECEPTO R 10.0.0 )

DOWNWIN D (x.y.O ) Figur e 5-2 . Compariso n o fsource-oriente d an d receptor oriente d coordinat e systems . I t i s ofte ndifficult

t o determin e th e atmos pheri c condition s o

f win ddirection , win dspeed , an d stabilit y tha t

wil l resul t

i nth e maximu mcombine d concentration s fro mtw o o r mor e sources ; drawin g isopleth s o

f concentratio nfo r

variou s win dspeed s an dstabilitie s an dorientin g thes e accordin g t o win ddirectio ni s on e approach . AREA SOURCE S I ndealin g wit hdiffusio no f ai r pollutant s i n area s havin g larg e number s o f sources , e.g. , a s i n urba nareas , ther e ma y b e to o man y source s o f mos t atmospheri c contaminant s t o conside r eac hsourc e Specia l Topic s

; '»?i______

' c%Bgftv;fe^ n «* .P.4 4

Tabl e 5- 1 VARIATIO N O F CALCULATE D CONCENTRATIO N

WIT H SAMPLIN G TIM E Samplin g Tim e Rati o o f Calculate d Concentratio n t o 3-minut e Concentratio n 3 minutes 1 5 minutes 1 hou r 3 hour s 2 4 hour s .. . 1.0

0 0.8 2 0.6 1 0.5 1 0.3 6 Thi s tabl e indicate s apowe r relatio nwit htime : Xot_t~2 17
. Not e tha t

thes e estimate s wer e base d upo npublishe ddispersio ncoefficient s rathe r tha n upo nsamplin g results . Informatio ni nth e refer
ence s cite dindicate s tha t effect s o

f samplin g tim e ar e exceedingl y complex . If i t i s necessar y t o esti
mat e concentration s fro masingl e sourc e for th e tim e interval s greate r

tha nafe

w minutes , th e bes t estimat e apparentl y ca nb e obtaine dfrom :



### x » »(*) ' (5.12 )
( wher e x*i s th e desire dconcentratio nestimat e for th e samplin g time,vt^ ; x

_i s th e concentratio nesti
mat e fo r th e shorte r

samplin g time , t k , (probabl y -' " ou t 1 0 minutes) : an dp shoul db e betwee n0.1 7 i 0.2 . Eq . (5.12 ) probabl y woul db e applie d .ios t appropriatel y t o samplin g time s les s tha n2 hour s (se e proble m19) .

Fo r asourc e tha t

emit s a t aconstan t

rat e fro m hou r t o hou r an dda y t o day , estimate s o f seasona l o r annua l averag e concentration s ca nb e mad e fo r an y distanc e i nan y directio ni f stabilit y win d"rose " dat aar e availabl e for

th e perio dunde r

study . A win dros e give s th e frequenc y o f occurrenc e for eac hwin ddirectio n(usuall y t o 1 6 points ) an dwin d spee dclas s ( 9 classe s i nstandar dWeathe r Burea u use ) fo r th e perio dunde r

consideratio n(fro m1 mont ht o 1 0 years) . A stabilit y win dros e give s th e sam e typ e of

informatio nfo r

eac hstabilit y class . I f th e win ddirection s ar e take nt o 1 6 point s an d i t i s assume dtha t

th e win ddirection s withi neac h secto r ar e distribute drandoml y ove r aperio do

f a mont ho r

aseason , i t

ca nfurthe r

b e assume dtha t th e effluen t

i s uniforml y distribute di nth e hori
- 'ta l withi nth e secto r

(Holland , 1953 , p . 540) .

. appropriat e equatio nfor averag e concentratio n the neither : Q 2T TX exp V 2 , a , U( w f 

# 2o3 

# M--H-^y ] [-MZY]

OrU X (5.13 ) o r 

# •°m 2.5 5 Q L u x (5.14 ) dependin g upo nwhethe r astabl e laye r

alof t i s af
fectin g th e distribution . Th e estimatio no

f x for aparticula r

directio n an ddownwin ddistanc e ca nb e accomplishe db y choosin g arepresentativ e win dspee dfo r eac hspee d clas s an dsolvin g th e appropriat e equatio n(5.1 3 o r 5.14 ) for al l win dspee dclasse s an dstabilities . Not e tha t aSS Wwin daffect s arecepto r t o th e NN E o f asource . On e obtain s th e averag e concentratio n for agive ndirectio nan ddistanc e b y summin g al l th e concentration s an dweightin g eac hon e accord
in g t o it s frequenc y for

th e particula r

stabilit y an d win dspee dclass . If

desired , adifferen t

effectiv e heigh t o f emissio nca nb e use dfor variou s win d speeds . Th e averag e concentratio nca nb e expresse d by : X(x.© ) = 2 Q f (G.S.N ) N) V2ir<r

l S " * ^ ex p 

# [--HS wher e f (e , S , N ) i s th e frequenc y durin g th e perio d o f interes t tha t th e win di s fro mth e direc
tio ne , for

th e stabilit y condition , S , an d win dspee dclas s N . <J.S i s th e vertica l dispersio nparamete r evaluate d a t th e distanc e x fo r

th e stabilit y conditio nS . u. v i s th e representativ e win dspee dfor clas s N . H ui s th e effectiv e heigh t o f releas e fo r

th e win d spee dUx . • Wher e stabilit y win dros e informatio ncanno t b e obtained , afirst-order

approximatio nma y b e mad e o f seasona l o r

annua l averag e concentration s b y 1 usin g th e appropriat e win dros e i nth e sam e man ner , an dassumin g th e neutra l stabilit y class , D , j l only . METEOROLOGICA LCONDITION S ASSOCIATE D WIT H MAXIMU M GROUND-LEVELCONCENTRATION S 1 . Fo r ground-leve l source s maximu mconcentra tion s occu r

wit hstabl e conditions . 3 8 ATMOSPHERI C DISPERSIO NESTIMATE S

•..-Z#ta$y. ;^$%e».--, .~-.&$ji&3 pindividually . Ofte na napproximatio nca nb e mad e

b y combinin g al l o

f th e emission s i nagive nare a ^~- n dtreatin g thi s are aa s asourc e havin g a ninitia l jrizonta l standar ddeviation , o } „. A virtua l dis
ance , x „ ca nthe nb e foun dtha t wil l giv e thi s standar ddeviation . Thi s i s jus t th e distanc e tha t «sH-»3fie_ dth e appropriat e valu e for <r y fro mFigur e (^-^JValues o

f xy wil l var y wit hstability . The n equation s fo r

poin t source s ma y b e used , determin
in g o T a s afunctio no

f x - f x„ asligh t

variatio no

f th e suggestio nb y Hollan d(1953) . Thi s procedur e treat s th e are asourc e a s across-win dlin e sourc e wit hanorma l distribution , afairl y goo dapproxi
matio nfo r

th e distributio nacros s a nare asource . Th e initia l standar ddeviatio nfor asquar e are a sourc e ca nb e approximate db y • a,„ : __: s/Jjft, "1 ^ s i s th e lengt ho

f asid e o f th e are a(se e problem * If th e emission s withi na nare aar e fro mvaryin g effectiv e stac k

heights , th e variatio nma y b e ap proximate db y usin g aa_i; ; Thu s H woul db e th e mean effectiv e heigh t

o f releas e an do zn th e standar d deviatio n o

f th e initia l vertica l distributio no f sources . A virtua l distance , x_ , ca nb e found , an d poin t sourc e equation s use dfor estimatin g concen trations , determinin g o

_a s afunctio no

f x -f
- x_. 

### TOPOGRAPH Y Unde r condition s o

f irregula r

topograph y th e .ec t ajjplicatio n o

f astandar ddispersio nequatio n J S ofte ninvalid . I nsom e situation s th e bes t on e ma y foe abl e t o d o withou t th e benefi t

o f in situ experiment s i s t o estimat e th e uppe r limi t o f th e oonceoatration s likel y t o occur . Fa r example , t o calculat e concentration s o na hillsid e downwin dfro man dfacin g th e sourc e an d a t abomf e th e effectiv e sourc e height , th e equatio n for ccHttcentration s a t

ground-leve l fro maground
ileve l siw_rce (Eq . 3.4 ) wil l yiel dth e highes t ex pected ! concentrations . Thi s woul dclosel y approxi
mat e tibe situatio nunde r stabl e conditions , whe n th e pafatan t

plum e woul db e mos t likel y t o en counte r th e hillside . Unde r

unstabl e condition s th e flo w as amor e likel y t o rise ove r

th e hil l (se e proble m 21). . downslop e flow whe nth e recepto r i s a t a lowe r eDeratio n tha nth e source , alikel y assumptio n

_ s thad t th e flow parallel s th e slope ; i.e. , n o allow
anc e n s mad e fo r

th e differenc e betwee nground
leve l iteration s a t

th e sourc e an da t

th e receptor . Wimx astee p ridg e o r

bluf f restrict s th e hori
zontal ! dispersion , th e flo w i s likel y t o b e paralle l -t o sucfl aabluff . A nassumptio no

f complet e reflec
K o n af t th e bluff

, simila r t o edd y reflectio na t

th e ' wm i fro ma nelevate dsource , i s i norder . Thi s .ay % e accomplishe db y using : x(x,y,0;H ) Q iro y o, U ex p 

# l-Mi-Y]

•+ • ex p 

# [--H-W]) H 

# (-s-rl l (5.16 ) B i s th e distanc e fro mth e x-axi s t o th e restrict
in g bluff , an dth e positiv e y axi s i s define dt o b e i n th e directio no

f th e bluff

. Th e restrictio no

f horizonta l dispersio nb y valle y side s is . somewha t

analogou s t o restrictio n o f th e vertica l dispersio nb y astabl e laye r aloft . Whe n th e oy become s grea t

enough , th e concentration s ca nb e assume dt o b e unifor macros s th e widt ho f th e valle y an dth e concentratio ncalculate daccord
in g t o th e followin g equation , wher e i nthi s cas e Y i s th e widt ho

f th e valley . 

## 2 Q f

1 f H v i * ~ V2;«r.Y u P

## L2 U J J (5.17 ) UN ESOURCE S Concentration s downwin do f acontinuousl y emittin g infinit e lin e source , whe nth e win ddirec
tio ni s norma l t o th e line , ca nb e expresse db y rewritin g equatio n(12 ) p . 15 4 o f Sutto n(1932) : x (x,y,0;H ) = —==

2 q yjltro, u ex p 

# l-MSY] (5.18 ) Her e qi s th e sourc e strengt hpe r uni t distance , for example , g sec - 1 m~ 1
. Not e tha t th e horizonta l dispersio nparameter , o s, doe s no t appea r i n thi s equation , sinc e i t

i s assume dtha t

latera l dispersio n fro mon e segmen t

o f th e lin e i s compensate db y dis
persio ni nth e opposit e directio nfro madjacen t segments . Als o y doe s no t appear , sinc e concentra tio na t agive nx i s th e sam e fo r an y valu e o

f y (se e problerrf

? §3) ) Concentration s fro minfinit e lin e source s whe n th e win di s no t

perpendicula r

t o th e lin e ca nb e approximated . I f

th e singl e betwee nth e win ddirec
tio nan dlin e sourc e i s 0 , th e equatio nfo r concen tratio ndownwin do

f th e lin e sourc e is : x <x,y,0;H ) si n 0 

# v!.o-_

u exp 

# [~1r(£ ) J

(5.19 ) Thi s equatio nshoul dno t b e use dwher e 0 i s les s tha n45 c . 

# 3

m fjjft**:r^t,^r ATMOSPHERI C DISPERSIO N ESTIMATE S

«£%!" •P.4 6

Whe nestimatin g concentration s fro mfinit e lin e sources , on e mus t

accoun t fo r "edg e effects " cause d b y th e en do

f th e lin e source . Thes e effect s wil l o f cours e exten dt o greate r cross-win ddistance s a s th e distanc e fro mth e sourc e increases . Fo r concen tration s fro mafinite lin e sourc e oriente dcross wind , defin e th e x-axi s i n th e directio no f th e mea n win dan dpassin g throug hth e recepto r o f interest . Th e limit s o

f th e lin e sourc e ca n b e define da s ex tendin g fro my , t o y . wher e y , i s les s tha ny 2 . Th e equatio nfor

concentratio n(fro mSutton' s (1932 ) equatio n(11) , p . 154) , is : x (x,0,0;H ) 

# v^l u ex 

# p[—H^r ) j

.—-• ex p (—0. 5 p 2 ) d p \'2TX (5.20 ) wher e p , 

# V P s = 

# ~ Th e valu e o

f th e integra l ca n b e determine dfro m tabulation s give ni n mos t statistica l table s (fo r

ex ample , se e Burringto n(1953) , pp . 273-276 ; als o se e proble m24) . INSTANTANEOU S SOURCE S Thu s fa r w e hav e considere donl y source s tha t wer e emittin g continuousl y o r fo r tim e period s equa l t o o r greate r tha nth e trave l time s fro mth e sourc e t o th e poin t

o f interest . Case s of

instantaneou s re lease , a s fro ma n explosion , o r short-ter mrelease s o nth e orde r

o f seconds , ar e ofte no

f practica l con cern . T o determin e concentration s a t an y positio n downwind , on e mus t

conside r

th e tim e interva l afte r th e tim e o

f releas e an ddiffusio ni n th e down
win ddirectio na s wel l a s latera l an dvertica l diffu
sion . O f considerabl e importance , bu t ver y difficult , i s th e determinatio no

f th e pat ho r

trajector y o

f th e "puff. " Thi s i s mos t importan t

i f concentra tion s ar e t o b e determine da t specifi c points . Deter minin g th e trajector y i s o f les s importanc e i

f knowl
edg e o f th e magnitud e o

f th e concentration s fo r particula r

downwin ddistance s o r trave l time s i s require dwithou t

th e nee dt o kno w exactl y a t wha t point s thes e concentration s occur . Rewritin g Sut
ton' s (1932 ) equatio n(13) , p . 155 , result s i n a n equatio ntha t

ma y b e use dfo r

estimate s o

f concen tratio ndownwin dfro mareleas e fro mheight , H : X (x,y,0;H ) = . 2 . , Q Tex p (27. ) ' - «. „ Oy O t 

# (^) , 

# 1-I--K40, 

# 1 ex p ^__(__ j J ^^ ^ (Th e numerica l valu e o

f (2w) 3 '' i s 15.75. ) 

# [- 4 Th e symbol s hav e th e usua l meaning , wit hth e

importan t

exception s tha t

Q Trepresent s th e total mass o f th e releas e an dth e a' s ar e not thos e eval
uate dwit hrespec t

t o th e dispersio nof

acontinuou s sourc e a t

afixedpoin t

i n space . I nEq . (5_21 ) th e a' s refe r t o dispersio nsta tistic s followin g th e motio no f th e expandin g puff . Th e o x i s th e standar ddeviatio no f th e concentra tio ndistributio ni n th e puf f i n th e downwin ddirec
tion , an dt

i s th e time afte r

release . Not e tha t ther e i s n o dilutio ni n th e downwin ddirectio nb y win dspeed . Th e spee do f th e win dmainl y serve s t o giv e th e downwin dpositio no f th e cente r

o f th e puff , a s show nb y examinatio no f th e exponentia l involvin g o*-. Win dspee dma y influenc e th e dis
persio nindirectl y becaus e th e dispersio nparameter s cr_ , oy, an do x

ma y b e function s o f

win dspeed . Th e <Tj,' s an do z 's fo r

a n instantaneou s sourc e ar e les s tha n thos e fo r

afe w minute s give ni n Figur e 3- 2 an d 3-3 . Slad e (1965 ) ha s suggeste dvalue s fo r a«r T an do t fo r quasi-instantaneou s sources . Thes e ar e give ni n Tabl e 5-2 . Th e proble mremain s t o mak e bes t estimate s o f

<J_. Muc hles s i s know no f diffu
sio ni n th e downwin ddirectio ntha ni s know no f latera l an dvertica l dispersion . I n genera l on e shoul d expec t th e a, valu e t o b e abou t th e sam e a s o> . Initia l dimension s o f

th e puff

, i.e. , fro ma n explo
sion , ma y b e approximate db y finding avirtua l distanc e t o giv e th e appropriat e initia l standar d deviatio nfo r

eac hdirection . The naywil l b e deter
mine da s afunctio no f x -f
- x„ a. a s afunctio no f x - f x „ an dor

, a s afunctio no f

x -f
- x, . Tabl e 5- 2 ESTIMATIO

N O FDISPERSIO

NPARAMETER

S FO R QUASI-INSTANTANEOU

S SOURCE S (FRO M SLADE , 1965 )
Unstable Neutra l Ver y Stabl e X = "x 1 0 4 1. 3 10 0 m o t 1 5 3. 8 0.7 5 x = 4 k

m Oy o. 300 220 12 0 5 0 3 5 7 

## REFERENCE S Bierly , E . W. , an dE . W . Hewson , 1962 : Som e restrictiv e meteorologica l condition s t o b e con sidere di n th e desig no

f stacks . J . AppLMete orol. , 1, 3 , 383-390 . Burington , R . S. , 1953 : Handboo k o f Mathematica l Table s an dFormulas . Sandusky , Ohio , Hand
boo k Publishers , 29 6 pp . Cramer , H . E. , 1959 : Engineerin g estimate s o f atmospheri c dispersa l capacity . Amer . Ind . Hyg . Assoc . J. , 20, 3 , 183-189 . Specia l Topic s 1M-M 1 O - 6 9 - 4 4 1*** Gifford , F . A. , 1959 : Computatio no f pollutio n ^

_fro msevera l sources . Int . J . Ai r Poll. , 2 , 109
- 110 . iiord , F . A. , 1960a : Atmospheri c dispersio ncal
culation s usin g th e generalize dGaussia nplum e model . Nuclea r

Safety , 2 , 2 , 56-59 , 67-68 . Gifford , F . A. , 1960b : Pea k t o averag e concentra tio nratio s accordin g t o afluctuating plum e dis
persio nmodel . Int . J . Ai r Poll. , 3, 4 , 253-260 . Hewson , E . W. , an dG . C . Gill , 1944 : Meteorolog
ica l investigation s i nColumbi aRive r Valle y nea r Trail , B . C , p p 23-22 8 i nRepor t submitte d t o th e Trai l Smelte r

Arbitra l Tribuna l b y R . S . Dea nan dR . E . Swain , Bur . o f Mine s Bul l 453 , Washington , Govt . Print . Off. , 30 4 pp . Hewson , E . W. , 1945 : Th e meteorologica l contro l o f atmospheri c pollutio nb y heav y industry . Quart . J . R . Meteorol . Soc , *72 , 266-282 . Hewson , E . W. , 1955 : Stac k height s require dt o minimiz e groun dconcentrations . Trans . ASM E 77, 1163-1172 . Holland , J . Z. , 1953 : A meteorologica l surve y o f th e Oak Ridg e area , p . 540 . Atomi c Energ y Comm. , Repor t

ORO-99 , Washington , D . C , 58 4 pp . Nonhebel , G. , 1960 : Recommendation s o nheight s fo r ne w industria l chimneys . J . Inst . Fuel , 33, 479-513 . Pooler , F. , 1965 : Potentia l dispersio no f plume s fro mlarg e powe r

plants . PH S Publ . No . 999 - AP-16 , 1965 . 1 3 pp . Singer , I . A. , 1961 : Th e relatio nbetwee npea k an d mea nconcentrations . J . Ai r Poll . Cont . Assoc , 11, 336-341 . Singer , I . A. , K . Imai , an dR . G . De l Campos , 1963 : Pea k t o mea npollutan t

concentratio nratio s fo r variou s terrai nan dvegetatio ncover . J . Ai r Poll . Cont . Assoc , 13, 40-42 . Slade , D . H. , 1965 : Dispersio nestimate s fro mpol
lutan t release s o

f afew second s t o 8 hour s i n duration . Unpublishe dWeathe r Burea u Report . Aug . 1965 . Stewart , N . G. , H . J . Gale , an dR . N . Crooks , 1958 : Th e atmospheri c diffusio no f gase s discharge d fro mth e chimne y o

f th e Harwel l Reacto r

BEPO . Int . J . Ai r

Poll. , 1, 87-102 . Sutton , O . G. , 1932 : th e atmosphere . 135, 143-165 . A theor y o f edd y diffusio ni n Proc . Roy . Soc . London , A , Taylor , G . I. , 1915 : Edd y motio ni nth e atmos phere . Phi LTrans . Roy . Soc , A , 215, 1-26 . 

# 3

....rXttiir*il*m.- L *»VJ«WR- ; ATMOSPHERI C DISPERSIO N ESTIMATE SP.4 8

('••- Chapte r 6 —RELATIO N T O OTHE RDIFFUSIO N EQUATION S Mos t othe r widel y use ddiffusio nequation s ar e varian t form s o f th e one s presente dhere . Wit hre spec t t o ground-leve l concentration s fro ma nele
vate dsourc e (Eq . 3.2) : 

### exp 

# [--r(^") = 

# ] (3.2 ) Othe r well-know nequation s ca nb e compared : Bosanque t

an dPearso n(1936) :

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

\'2TT p qx - u ex p 

# (*)'•]-[-£ 1 [ - (6.1 ) wher e p an dqar e dimensionles s diffusio ncoeffi
cients . Sutto n(1947) : X (x,y,0:H ) =

H = 2 Q W v V> * u ex p [ x- _ n 

# ( * 

# + ^) ] (6.2 ) wher e ni s adimensionles s constan t an dC, an dC , ar e diffusio ncoefficient s i nm"' 2
. Calde r (1952) : x (x.y,0;H ) Q u 

# ( * + 

# ») ] 2 k
- av.. ; x ex p I kv, x wher e a= — - ,

vr (6.3 ) th e rati o o

f horizonta l edd y velocit y t o vertica l edd y velocity , k i s vo nKarman' s co n stan t approximatel y equa l t o 0.4 , an dv x= wher e z „ i s aroughnes s parameter , m . 

## I n A z « NOTE : Calde r wrot e th e equatio n for th e con centratio na t

(x , y , z ) fro maground-leve l source . Fo r Eq . (6.3 ) i t

i s assume dtha t

th e concentratio n a t groun dleve l fro ma nelevate dsourc e i s th e sam e a s th e concentrato na t a nelevate dpoin t

fro ma ground-leve l source . Tabl e 6- 1 list s th e expression s use di nthes e equation s tha t

ar e equivalen t

t o o yan do z(con
tinuou s source ) i nthi s paper . Tabl e 6- 1 EXPRESSION S EQUIVALEN TT O o y AN D o , I N VARIOU S DIFFUSIO N EQUATIONS . Equatio n Bosanque t an d Pearso n Sutto n ^

_c_ Calde r vT a u Oy q x 2- n x2

* v * x a .



### vTp x i 2 " n 

## v r c 

## < * 2 V ' l k v xx u REFERENCE S Bosanquet , C . H. , an dJ . L . Pearson , 1936 : Th e sprea do f smok e an dgase s fro mchimneys . Trans . Farada y Soc , 32, 1249-1263 . Calder , K . L. , 1952 : Som e recen t Britis hwork

o n th e proble mo

f diffusio ni nth e lower atmos phere , 787-79 2 i nAir

Pollution, Proc . U . S . Tech . Conf

. Ai r Poll. , Ne w York , McGraw-Hill , 84 7 pp . Sutton , O . G. , 1947 : Th e proble mo f diffusio ni n th e lowe r atmosphere . Quart . J . Roy . Me t Soc , 73, 257-281 .

Othe r Equation s 4 3

-•-••^? , *'^:.T.^~?^^ ^ •"i-v-r'Z- Tr*V*/"V ,.* >P.4 9 Chapte r 7 —EXAMPL EPROBLEM S 

# 7 Th e follow__q£2£^exampl e problem s an dthei r solution s illustrat e th e applicatio no f mos t o f th e technique s an dequation s presente di nthi s work
book . PROBLE M 1 : I t

i s estimate dtha t

aburnin g dum p emit s 3 g sec - 1 o f oxide s o

f nitrogen . Wha t i s th e concentratio no

f oxide s o f nitrogen , average dove r

approximatel y 1 0 minutes , fro m thi s sourc e directl y downwin da t adistanc e o

f 3 k mo na novercas t

nigh t wit hwin dspee do

f 7 msec -1 ? Assum e thi s dum p t o b e apoin t ground-leve l sourc e wit hn o effectiv e rise. SOLUTION : Overcas t condition s wit hawin d spee dof . 7 _ asec - 1 indicat e tha t

stabilit y clas s D i s mos t applicabl e (Statement , botto mo f Tabl e 3-1) . Fo r

x = 3 k man dstabilit y D , a, = 19 0 m fro mFigur e 3- 2 an da z= 6 5 mfro mFigur e 3- 3 Eq . (3.4 ) fo r

estimatio no

f concentration s di
rectl y downwin d( y = 0 ) fro maground-leve l sourc e i s applicable :

Q 3 • y y y 

# 7 (x,0,0;0 )

1. 1 a

ra- o zU - 19 0 (65 ) 7 j
( x 10~ s g m3 o f oxide s o f nitrogen . PROBLE M 2 : I t

i s estimate dtha t

8 0 g sec - 1 o

f sulfu r dioxid e i s bein g emitte dfro mapetroleu m refiner y fro ma naverag e effectiv e heigh t o f 6 0 meters . A t

080 0 o na novercas t

winte r mornin g wit hth e surfac e win d6 msec -1 , wha t i s th e ground-leve l concentratio ndirectl y downwin d fro mth e refiner y a t

adistanc e o

f 50 0 meters ? SOLUTION : Fo r

overcas t conditions , D clas s sta bilit y applies
- Wit hD stabilit y a t x —50 0 m , o, = 3 6 m , «r

, = 18. 5 m . Usin g Eq . (3.3) : Q __. _T 1 /

H Al l bu t th e exponentia l involvin g y ha s bee n foun di nth e precedin g problem . Therefore : X (500 , 50,0 ; 60 ) = 3. 3 x IO - 5 ex p [—0. 5 (50/36)- ]

—3.3x10
- (0.381 ) / = 1. 3 x IO" 5 g m - 3 o

f SO
PROBLE M 4 : A powe r plan t burn s 1 0 ton s pe r hou r o f coa l containin g 3 percen t sulfur ; th e effluent i s release dfro masingl e stack . O na sunn y summe r

afternoo nth e win da t

1 0 meter s abov e groun di s 4 msec - 1 fro mth e northeast . 

# [ Th e mornin g radiosond e take na t anearb y Weathe r Burea u statio nha s indicate dtha t a fronta l inversio nalof

t will limi t

th e vertica l mixin g t o 150 0 meters . Th e 1200-mete r win di s fro m30 ° a t

5 msec -1
. Th e effectiv e heigh t o f emissio ni s 15 0 meters . Fro mFigur e 3-9 , wha t i s th e distanc e t o the . maximu mground-leve l concentratio nan dwha t i s th e concentratio na t thi s point ? SOLUTION : T o determin e th e sourc e strength , th e amoun t

o f sulfu r burne dis : 1 0 ton s hr - 1 x 200 0 l b ton - 1 x 0.0 3 sulfu r = 60 0 l b sulfu r

hr -1
. Sulfu r ha s amolecular

weigh t o f 3 2 an dcom bine s wit h0 , wit hamolecula r weigh t o f 32 ; therefor e for

ever y mas s uni t

o f sulfu r burned , ther e resul t

tw o mas s unit s o

f SO, .

X (x,0,0;H ) = , = • Or, 0 Z U ex p 

# i-um 8 0 ex p (—0. 5 (60/18.5) 2 ] Q

*3 6 (18.5 ) 6 = 6.3 7 x IO - 3 ex p [—0. 5 (3.24) 2 ] Th e exponentia l i s solve dusin g Tabl e A- 1 (Ap
pendi x 3) . = 6.3 7 x IO - 3 (5.2 5 x IO -3 ) # 0 . J* « X —3. 3 x KT 5 g m - s o

f SO . 6 4 (molecula r weigh t o f SO. ) 3 2 (molecula r

weigh t o f sulfur ) 60 0 l b hr - 1 (453. 6 g lb -1 ) X ^^j,,^—^360 0 se c hr - 1 ^15\g^et~'

o f SO . O nasunn y summe r

afternoo n th e shoul db e strong . Fro mTabl e 3-1 , latio nan d4 msec - 1 wind s yiel dcla i Fro mFigur e 3-9 , th e dista m insolatio n n g inso
tability.. / e Doint o f apget o maximu mconcentratio ni s (junio r class- B st a
PROBLE M 3 : Unde r th e condition s o

f proble m 2 , wha t i s th e concentratio na t th e sam e dis
tanc e downwin dbu t

a t adistanc e 5 0 meter s fro mth e x-axis ? Tha t

is : x (500 , 50 , 0 ; 60 ) = - ? SOLUTION : Usin g Eq . (3.2) :

Q bilit y an deffectiv e heigh t o f 15 0 meters . Fro m Figur e 3- 3 a t

thi s distanc e o z= 11 0 m . Thi s i s -^ao ^ muc k

^ es s tha n [o.^PET^Therefore , a t thi s dis
- • ^ ' tance , th e limi t

o t mixin g o

f 150 0 meter s wil l not ^ affec t th e grourt^-lfYfil r.nri%ar,h " %i TM n Fro m Figur e 3-9 , th e maximu mx u / Q f° r B s l an dthi s effectiv e heigh t o f 15 0 m_s_77If

x 10~_ , Xoi " 

### x « 

## J L

u 7. 5 x 10 - ax 15 1 tonjx-' r 

# < ! t 

# ^ H 

# > — 7^r^[-T\i) j j -*•«no-.*-<_so ; 

# v PROBLE M 5 : Fo r

th e powe r

plan t i nproble m4 , a t wha t distanc e doe s th e maximu mground
Exampl e Problem s 4 5

.'fcT»*^ ' —»._.._•'. « • 'mm.mi-'iiijyiji^mif**-... ''--"'
- * —*-Y^-*-*i-* ? «»' » »*•"•*»•*

_T-*"r *P.5 0

levd l aorrceratratio n occu r an dwha t

i s thi s con cenii_Qi_bn

_an a novercas t

da y wit hwin dspee d 4 nnsenr 1 ? JLUUltimSf

c O na novercas t

da y th e stabilit y claasff i moii- i b e D . Fro mFigur e 3- 9 fo r D sta bilitbyanril H of

15 0 m , th e distanc e t o th e poin t of f _n_Es_j_n___

_ground-leve l concentratio ni s 5. 6 krm . and l tfo e maximu m\u/Q i s 3. 0 x 10—. XmOKK " x IO -1 1 x 15 1

= IL H _ _IO - 4 g m~ : i 

# X J PRO__ffl___»f

i @zFo r

th e condition s give ni nprob
le m4k. aHaaa

w agrap ho

f ground-leve l centerlin e sulffin r diarsad e concentratio nwit hdistanc e fro m 10GDm_atei_

5 to 10 0 km . Us e log-lo g grap hpaper . SOLUJHMHSf

c Th e fronta l inversio nlimit s th e mix
in g ttoIL = 150 0 meters . Th e distanc e a t whic h o z= <_Lffi71

_= 70 5 mi s x w ^ = 5. 5 km . A t dis
ta__a__£l_e_si_h__

n this , Eq . (3^ ) i s use dt o calcu
lat e (gamtmr

n illations : ( ; s ; Q

—ff,. <r z U ex p 

# [-nm Ai t (fiBE_a____ e equa l t o o r

greate r tha n2 x L , whic h is , 11 1 Ifam

, Mq. <f3.5Li s used :

Q X <&0lftS_» —7== _

V 2- ff

r Lu Soik___iiiEi_- B in r th e equation s ar e give ni nTabl e 7-I LHHna s -calue s o

f concentratio nar e plotte d agaiinst t aiBSitanc e i nFigur e 7-1 .

2 xo~'

io- '

io—s . 

## j _..:;_

_=!. : '. . 1 'i'lim * ! •• ' .; ; " "Z~ . *.'.'. '. '. •'. ] I II I 

### ,-,.--=:•.! : .T.i_-j.| r i - l I-TY^I M T; ! ;TT j 

# • : 

# l \4W% x.i-^r-zsm. X i 7 V • 1 • • " ! ' • 

## 1 1 1 \. i ; 

## .in . ;-_ . _ : : : jff

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

1 r i '^^"S : ! • ::# : • : : i f | : : ":|::::': : 

### i | t ~~ H t .11 . . . ll 11 i-^^ . "."'" . •>"-.":• : { .; _ 

# xx :: 

# xISfi
..TT." * ~ T~T ~

i' .. . : r

_•_*""ZT_T.T : "rrtruJZJ" .

—-t—:—=—f-—!—i--

J i i: ' • l , 1 • ! ^-----—- • —T-r f 

## |i
- _ —rr^r j

: ; | i• • MM : ; i o DOWNWIN D DISTANCE , k m 10 0 f -.re s KL . ©smcentratio n a s a functio n o

f downwin d distanc e (Proble m 6) . Tabl e 7- 1 CALCULATIO N O F CONCENTRATION S FO R VARIOU S DISTANCE S (PROBLE M 6 ) 

# a - X , u , k mmsec - 1 Oy,

m o z . 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 5 2 8 3 12 9 15 7 29 5 42 5 72 0 30 5 1 85 

## iif i 230 36 5 70 5 5.0 2.9 4 1.7 7 1.3 S 0.6 5 0.4 1 0.2 1 3.73 x 10
- 1.33 xlO - 4 0.20 9 0.39 7 **/ 0.81 0 0.91 9 0.97 8 2.9x10
-

3.8x10
- 2.3x10- * 

## (lirxTcR 1.4x10
- 7. 1 x 10 - 6 2.1xlO- » * . U , ff y , k m m sec - 1 m 11. 0 4. 5 130 0 3 0 4. 5 300 0 10 0 , '4. 5 820 0 L , m J5D D 150 0 150 0 Xg nr- 3 6.9 X 10
- 3.0x10
- 1. 1 x 10
- \VEQBLEM

7 : Fo r

th e condition s give ni nprob
le m4 , dra w agrap ho

f ground-leve l concentra tio nversu s crosswinddistanc e a t adownwin d distanc e o

f 1 km . SOLUTION : Fro mproble m4 th e ground-leve l centerlin e concentratio na t 1 k mi s 2. 8 x 10

— g m— . T o determin e th e concentration s a t dis
tance s y fro mth e x-axis , th e ground-leve l cen terlin e concentratio nmus t b e multiplie db y th e facto r ex p 

# I-*(*. 1 <r v= 15 7 meter s q * Y—I kTM
- Value s for

thi s computatio nar e give ni nTabl e 7-2 . Tabl e 7- 2 DETERMINATIO N O F CROSSWIN D CONCENTRATION S (PROBLE M 7 ) y . m 

# •i-[-MiY]

*TM ±10 0 ±20 0 ±30 0 ±40 0 ±50 0 0.6

4 1.2 7 1.9 1 2.5 5 3.1 8 0.81 5

0.44 6 0.16 1 3.87x10
- 6.37x10
- 2JxlO
1. 3 x 10- * 4.5x10
- 1.1x10
- 1.8x10
- Thes e concentration s ar e plotte d i n Figur e 7-2 . PROBLE M 8 : Fo r

th e condition s give ni nprob
le m4 , determin e th e positio no f th e 10

— g m — groun dleve l isopleth , an ddetermin e it s area . SOLUTION : Fro mth e solutio nt o proble m6 , th e grap h(Figur e 7-1 ) show s tha t th e IO - 5 g m - isoplet hintersect s th e x-axi s a t approximatel y x = 35 0 meter s an dx = 8. 6 kilometers . ^

4 C ATMOSPHERI C DISPERSIO N ESTIMATE SP.5J L

y \ — i r e 3-10"*^ -

t a e * *2«I0~** — 5 ! i 3 ! 1 

# " T i I i

r^mm^r -40 0 1

-20 0 1

\ _ ! ) '20 0 1

MO O -

-

-

CROSSWIN D DISTANC E ly) , m Figure 7-2 . Concentratio n as a functio n o f crosswin d

distanc e (Proble m 7) . Th e value s necessar y t o determin e th e isoplet h hal f widths , y , ar e give ni nTabl e 7-3 . Tabl e 7- 3
k m 0. 5 0. 8 1. 0 2. 0 3.0 4. 0 5.0 6.0 7. 0 8.0 ffy,

m 8 3 12 9 15 7 29 5 42 5 54 0 67 0 78 0 89 0 98 0 DETERMINATIO

NO FISOPLET H WIDTH S (PROBLE M 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 ) 0.26 3 4.35x10" = 3.5 3 x 10-= 7.14x10
- 1.4 2 xlO - ' 0.25 0 0.41 7 0.55 6 0.71 4 0.90 9 Hi Or

1.6 4 2.5 0 2.5 9 2.3 0 1.9 8 1.6 7 1.32 1.0 8 0.8 2 0.4 4 y . m 136 32 3 

## 4oj p 67 9 84 2 90 2 88 4 84 2 730 43 2 Th e orientatio no

f th e x-axi s wil l b e towar d 22 5 • clos e t o th e source , curvin g mor e towar d 210 ° t o 215 ° azimut ha t greate r distance s be
caus e o f th e chang e o

f win ddirectio nwit h height . Th e isoplet hi s show ni nFigur e 7-3 . Sinc e th e isoplet happroximate s a nellipse , th e are amay.b e estimate db y r a b wher e ai s th e semimajo r

axi s an db i s th e semimino r axis . 860 0 —35 0 2 = 412 5 m b = 90 2 A (m 2 ) = - (4125 ) (902 ) = 11. 7 x 10 " m or A = 11. 7 km
SOU&C E \-fT,firi*l*r



### V R Figur e 7-3 . Locatio n o

fth e IO" 5 g m~ 3 plet h (Proble m 8) . ground-leve l isoROBLE M 9 : Fo r

th e condition s give ni nproble m 4 , determin e th e profil e o ^ concentratio nwit h heigh t fromgroun dlevel^tQ 1 z = 45 0 meter s a t x = 1 km , y = 0 meters , an ddra w agrap ho f concentratio nagains t

heigh t abov e ground . SOLUTION : Eq . (3.1 ) i s use dt o solv e thi s prob
lem . Th e exponentia l involvin g y i s equa l t o 1 . A t x = 1 km , ff

y = • 15 7 m, o

_ = 11 0 m . (Fro m proble m4) . 2.ff?ff, u - 2.157 1 qi0) 4 ° 3.5 ^ g^ 3 Value s for

th e estimatio no

f x(z ) ar e give ni n Tabl e 7-4 . PROBLE M 10 : Fo r

th e condition s give ni n prob
le m4 , determin e th e distanc e a t whic hth e ground-leve l centerlin e concentratio n equal s tb e centerlin e concentratio na t 15 0 meter s abov e ground . Verif

y b y computatio no

f x (*t0,0 ) an dx(x,0,15O) . SOLUTION : Th e distanc e a t whic hconcentra tion s a t th e groun dan dat-jahnnf . heigh t ar e equa l shoul doccu r

wher e (a? = 0.9 1 H

_ Chapte r 5) . Fo r B stabilit y an dH =="T5 0 m , «r , = 0.9 1 (150 ) = 13 6 moccur s a t xj=^ 1- 2 km . A t thi s distanc e o y= 18 1 m . Exampl e Problem s 47 

### ^^^^^j^ffi,-,^^ ^ '•^•m*^ „ ' MpBi YI'I Y_ ' rT^i ' _'

# r Tabl e 7- 4 DETERMINATIO N O F CONCENTRATION S FO R VARIOU S HEIGHT S (PROBLE M 9 ) f . g

z- H -e» p 

# [-K^']^-[-+(^) 1 c. + t. XU) . g m - ' 0-1.3 6 30—1.0 9 60—0.8 2 90—0.5 5 120—0.2 7 15 0 0.0 18 0 0.2 7 21 0 0.5 5 24 0 0.8 2 27 0 1.0 9 30 0 1.3 6 33 0 1.6 4 36 0 1.9 1 39 0 2.1 8 42 0 2.4 5 45 0 2.7 3 0.39 7 v 0.55 2 0.71 4 0.860 0.964 1. 0 0.96 4 0.860 0.71 4 0.552 0.397 026 1 0.16 1 0.0929 0.049 7 0.024 1 1.3

6 1.6 4 1.91 2.1 8 2.4 5 2.7 3 3.00 3.2 7 3.54 3.82 4.0 9 4.3 6 4.64 4.9 1 5.1 8 5.4 5 0.397 " 0.26 1 0.16 1 0.092 9 0.049 7 0.024 1 1.1 1 x IO - 2 4.7 7 xIO - 3 1.9 0 x10~

3 6.7 8 xIO - 4 2.33 x10" * 7.4 5 xIO - 5 2.11x10- ' 5.82x10- ° 1.4 9 xIO - 6 3.5 5 x10~ T 0.79 4 0.81 3 0.87 5 0.95 3 1.014 1.02 4 0.97 5 0.86 5 0.71 6 0.55 3 0.39 7 0.26 1 0.16 1 0.09 3 0.05 0 0.02 4 2.78xl0-« y 2.85x10- * y 3.06x10- * J 3.34x10" * 3.55x10- * v 3.58 x10- * 3.4 1 x10" * 3.0 3 xIO - ' 2.5 1 x10" * 1.94x10- * 1.3 9 x10" * 9.14x10- " 5.6 4 x10- " 3.2 6 xIO"8 1.75xlO~ s 8.4 0 xIO - 8 

### / T These value

s ar e plotte d i n Figur

e 74 . 50 0
40 0 —

._ - 30 0
20 0 — IO O 4.8 8 x IO - * ex p [
—\_ (1.10) 2 ] 4.8 8 x IO - * (0.546 ) 2. 7 x 10" * g m - s 

# H> 

# -[--H-ifr)' ] ^ 151.,. . 2 * 18 1 (136 ) 4
ex p

48 -18 1 (136 ) 4 

# ^ ° C H ) 

# '°f tl \

v. - V V 

# [-M&Y]]

—2.4 4 x 10" * j 1.

0 + ex p [ |
- (2.21) 2 

### 1 J

- —2.4 4 x IO - * (1. 0 + 8.7 0 x IO -2 )

—2.44X10 - * (1.087 )

—2. 7 x IO - * g m - 3 PROBLE M 11 : Fo rth e powe rplan ti n proble m 4 , wha twil l th e maximu m ground-leve l concentra tio n b e beneat h th e plum e centerlin e an d a t wha tdistanc e wil l i toccu ro n aclea rnigh twit h win d spee d 4 m sec -1 ? SOLUTION : A clea rnigh twit h win d spee d 4 m sec - 1 indicate s E stabilit y conditions . Fro m Fig ur e 3-9 , th e maximu m concentratio n shoul d occu ra tadistanc e o f 1 3 km , an d th e maximu m xu/ Q i s 1. 7 x IO - 5 Xm» x ' X " Q Q 1. 7 x IO - 6 x 15 1 u 4 6. 4 x IO - 5 g m - s o f

SO .

OUT * 10

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

CONCENTRATION , g m- l Figure-74 . Concentratio n a s a functio n o

f height (Prob

lem 9) . fck

%--{\<.*\ Verifying : 

# ( 

# —- s s 

# —-[- w PROBLE M 12 : Fo rth e situatio n i n proble m 11 , wha twoul d th e fumigatio n concentratio n b e th e nex tmornin g a tthi s poin t( x —1 3 km ) whe n superadiabati claps e rate s exten d t o includ e mos to f th e plum e an d i ti s assume d tha twin d spee d an d directio n remai n unchanged ? SOLUTION : Th e concentratio n durin g fumiga tio n condition s i s give n b y Eq . (5.2 ) wit h th e exponentia l involvin g y equa l t o 1 . i n thi s prob lem . Q X F 

# (x^m - V^i rU ffyF h i Fo rth e stabl e conditions , which wer e assume d t o b e clas s E , a tx = 1 3 km , o r= 52 0 m., an d ff, = 9 0 m . Usin g Eq . (5.3 ) t o solv e fo rhi : h , = H - f

2 ff. —15 0 + 2 (90 ) = 33 0 m . From th e horizonta l spreadin g suggeste d b y Eq . (5.4) : ATMOSPHERI

C DISPERSIO

N ESTIMATES )

m.t$titfem%r7r.£..:~r>~ mmmmmm'**-* i-mien.- nam I- ,, :. ;, ;•_. • .»'_-ck.--.::- . -.-••;v w *3ff<; ^ .:.:x.u..,m-.;!8i(.«S&&^*^ : *^&f'- W^Sf

m PU . -JW * •• - .••.'-.ilpw-.^.j^g':. : 

## 'Mms^^m,P.5 3

(:. •*• • —ff y (stable ) + H/ 8 —52 0 4
- 1 9 = 53 9 15 1 ^ . 4 (539 ) 33 0 = 8.5xlO- s gnr 3 ofSO _ Mates tha t

th e fumigatio nconcentration s unde r ttfcese condition s ar e abou t 1. 3 time s th e maxi
- ___n_ aground-leve l concentration s tha t occurre d Umamg th e nigh t

(proble m11) . H*i_p(___ft.HT__

r 13 : A nai r

samplin g statio ni s locate d a i a mazimut ho

f 203 ° fro macemen t

plan t a t a alE'HHto.Miif f o f 150 0 meters . Th e cemen t plan t re lease s fine particulate s (les s tha n1 5 micron s dfianaeter) a t

th e rat e o

f 75 0 pound s pe r

hou r firtnnma30-mete r

stack . Wha t

i s th e contributio n _3m__

_th e cemen t

plan t t o th e tota l suspende d paatiicailat e concentratio na t th e samplin g sta - _a_a

_whe nth e win di s fro m30 ° a t 3 msec - 1 o n acfleo r da y i nth e lat e fal l a t

1600 ? SOIOTTON : Fo r

thi s seaso nan dtim e o

f da y th e C daa s stabilit y shoul dapply . Sinc e th e sam plin g statio ni s of

f th e plum e axis , th e x an dy distance s ca nb e calculated :

x = 150 0 co s 7 ° y —150 0 si n7 ° Tli e sourc e strengt his : 148 9 18 3 Q —75 0 l b hr
- x 0.12 6 -MJE 94. 5 g sec - 1 A t thi s distance , 148 9 m , fo r stabilit y C , o, = 15 0 m , «r

_= 87 . Th e contributio nt o th e concen tratio nca nb e calculate dfro mEq . (3.2) : X (*_F,0-,H ) - Q

IT Oy ff, U ex p es p 

# l-M&Y] 1-M-iY]

94. 5
ex p 15 0 (87 ) 3

3 0 ex p 

# [-* •OS-)' ] H (•$•)•

] —0. 5 94. 5 ex p [—0. 5 (1.22) 3 ] 1.2 3 x IO 3 ex p [—0. 5 (0.345) 3 J -=7.6 8 x 10- * (0.475 ) (0.943 )

—3. 4 x 10" * g m" » PROfiLE M 14 : A propose dsourc e i s t o emi t 7 2 g seer 1 o f SO
- fro mastac k

3 0 meter s hig hwit h adiamete r

of 1. 5 meters . Th e effluent gase s ar e emitte da t

atemperatur e o

f 250° F(394°K ) wit ha nexi t

velocit y o

f 1 3 msec -1
. Plo t

o nlog
lo g pape r

agrap ho

f maximu mground-leve l concentratio na s afunctio no f win dspee dfo r stabilit y classe s B an dD . Determin e th e crit
ica l win dspee dfor

thes e stabilities , i.e. , th e win dspee dtha t

result s i nth e highes t

concen trations . Assum e tha t

th e desig natmospheri c pressur e i s 97 0 m b an dth e desig n ambien t ai r temperatur e i s 20° C (293°K) . SOLUTION : Usin g heigh t equation : Holland' s effectiv e stac k AH . v. d u 

# [ 1. 5 + 2.6 8 x IO - 8 

### nJ__l_L_.i l

__ . 1 3 ( u L 5 ) j 1. 5 -f

- 2.6 8 x IO - 3 (970 ) 39 4 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 Th e effectiv e stac k

height s fo r

variou s win d speed s an dstabilitie s ar e summarize di nTabl e 7-5 . Tabl e 7- 5 EFFECTIV

ESTAC K HEIGHT S (PROBLE M 14 )

u , msec - 1 0. 5 1. 0 1. 5 2 3 5 7 1 0 2 0 Clas s 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 Clas s B

1.1 5 AH , m 112. 2 56. 1 37. 5 28. 1 18.7 I U 8. 0 h+ 1.1 5 _\H

, m UU 86. 1 67. 5 58. 1 48. 7 AU 38. 0

B y us e o f th e appropriat e height , H , th e maxi
mu mconcentratio nfor eac hwin dspee dan d stabilit y ca nb e determine dby . obtainin g th e Exampl e Problem s
R P UWI.U>H_JII. ; i *maximu mxu/ Q a s afunctio n of H an dstabilit y fro mFigur e 3- 9 an dmultiplyin g b y th e appro priat e Q/u . Th e computation s ar e s'crn larize d i n Tabl e 7-6 , an dplotte di n Figur e 7-5 .

0. 5 2 3 4 5 7 WIN D SPEED , m ite- ' 1 0 2 0 Figur e 7-5 . Table 7- 6 Maximu m concentratio n as a functio n o f

win d spee d (Proble m 14) . MAXIMU M CONCENTRATIO N A S A FUNCTIO N O F WIN D SPEE D (PROBLE M 14 ) 

# f Stability Clas s B

D u

, msec - 1 0. 5 1. 0 1. 5 2 3 5 7 0. 5 1. 0 1. 5 2 3 5 7 1 0 2 0 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 14 4 7 2 4 8 3 6 2 4 14. 4 10. 3 14 4 7 2 4 8 3 6 2 4 14. 4 10. 3 7.2 3. 6 Xmwt

* g nr s 1.15x10- ' 1.4 4 x IO" 3 1.49xl0~ 3< < - 1.48 xlO" 3 1.37 x IO" 3 1.12xl0- s 8.96x10" * 6.3 4 x 10" * 1.0 2 x IO" 3 1.1 9 xlO" 3 1.26xl0- 3 < - 1.2 2 xlO" 3 1.0 5 xlO" 3 8.45x10- * 6.77x10
- 3.96x10- *

Y _ T h e win dspeed s tha t giv e th e highes t

maximu m concentration s fo r

eac hstabilit y are , fro mFig
ur e 7-5 : B 1.5 , D 2.0 . PROBLE M 15 : A propose dpul p processin g plan t i s expecte dt o emi t

y_to n pe r

da y o f hydroge n sulfid e fro masingl e stack . Th e compan y prop ert y extend s aminimu mo f 150 0 meter s fro m th e propose dlocation . Th e neares t recepto r i s asmal l tow no f 50 0 inhabitant s 170 0 meter s northeas t

o f th e plant . Plan t

manager s hav e decide dtha t

i t i s desirabl e t o maintai n concentration s belo w 2 0 pp b (part s pe r billio n b y volume) , o r

approximatel y 2. 9 x IO - 0 g m - \ fo r an y perio dgreate r

tha n3 0 minutes . Win d directio nfrequencie s indicat e tha t wind s blo w fro mth e propose dlocatio ntowar dthi s tow n betwee n1 0 an d1 5 pe r cen t o f th e time . Wha t heigh t stac k shoul db e erected ? I t i s assume d tha t adesig nwin dspee do f 2 msec - 1 wil l b e sufficient , sinc e th e effectiv e stac k ris e wil l b e quit e grea t

wit hwind s les s tha n2 msec -1
. Othe r tha nthi s stipulation , assum e tha t th e physica l stac k

heigh t an deffectiv e stac k

heigh t ar e th e same , t o incorporat e asligh t safet y factor . SOLUTION : Th e sourc e strengt his : O 100 0 l b day 1 x 453. 6 g l b - 1 y "°" 86,40 0 se c day - 1 FromEq . (4.2) : 0.11 7 Q 0.11 7 (5.25 ) 5.2 5 g sec "

Oy O . Xou 1.0 6 x 10 * m 2 (2. 9 x 10" s ) 2 A t adesig n distanc e o

f 150 0 meter s (th e limi t o f compan y property) , o s o t « —1.0 6 x 10 * give s apoin t fro mFigur e 4- 1 abou t 0. 2 fro mQas s C t o Clas s O alon g th e lin e x = —150 0 m . Fro m Figur e 3-3 , o z= 8 0 fo r thi s stability . H = \/2~o z= 11 3 meter s PROBLE M 16 : I n proble m1 5 assum e tha t th e stac k diamete r

i s t o b e 8 ft , th e temperatur e o f th e effluen

t 250 ° F , an dth e stac k ga s velocit y 4 5 f t sec -1
. Fro mHolland' s equatio n fo r effec
tiv e stac k

heigh t an dth e metho duse di n prob
le m15 , determin e th e physica l stac k heigh t require dt o satisf

y th e condition s i n proble m15 . I n estimatin g AH , us e T . = 68° Fan dp = 92 0 mb . SOLUTION : Firs t

determin e th e relatio n betwee n AH an du fro mHolland' s equation . v R—4 5 f t sec - 1 = 13. 7 msec - 1 d— 8 f t — i 2.4 4 m T . —250° F—12 1 ° C —394° K T . = - 68° F—20° C = - 293° K p = 92 0 m b v.d . A H u 1. 5 + 2.6 8 x 10~ 3 p T,—T . T . 13. 7 (2.44 ) u 394-29 3 1. 5 + 2.6 8 x IO" 3 (920 ) 39 4 (2.44 ) ^

) 5 0

•?&-.;•. ATMOSPHERI C DISPERSIO NESTIMATE S

B M - '-'• —P.5 5



# r :

(



# CAH 33. 4 u 33. 4 u 10 2 u [1.5 + (2.46 ) 0.25 6 (2.44) ] (1. 5 + 1.54 )
Th e relatio nbetwee no

> o zan du is : 0.11 7 Q 0.11 7 (5.25 ) 2.1 2 x 10 * OyO Z X d " 2. 9 x IO" 5 u u Th e require dcomputation s usin g Figur e 4- 1 ar e summarize di nTabl e 7-7 : Tabl e 7- 7 REQUIRE D PHYSICA L STAC KHEIGH TA S A FUNCTIO N O F WIN D SPEE D (PROBLE M 16 )
u . AH , t nsec - 1 m 0. 5 1. 0 1. 5 2 0 2 5 3. 0 5. 0 7. 0 10.0 15.0 20 4 10 2 6 8 5 1 4 1 3 4 2 0 1 5 1 0 7 Oy O v m 2 4.2 4 x 10 * 2.1 2 x 10 * 1.4 1 x 10 * 1.0 6 x 10 * 8.4 8 x 10 3 7.0 6 xlO 3 4.2 4 x10 s 3.0 3 x IO 3 2.1 2 x IO

3 1.4 1 x IO 1 Stability t o

Giv e o v <y t a t 150 0 m 0.9 , fro mAt o B 0. 6 fro mB t o C 0.9 fro mB t o C 0. 2 fro mC t o D 0. 4 fro mC t o D 0. 6 fro mC t o 0 D 0. 5 fro mD t o E E 0.5 fro mEt o F Oz' m 19 0 12 0 9 6 76 6 4 5 6 4 2 34 2 8 2 3 H 

### Lr° V 2o v m 26 9 17 0 13 6 10 8 9 1 79 6 0 4 8 4 0 3 3 h= H'-AH , m 6 5 6 8 68 5 7 5 0 45 4 0 3 3 30 2 6 Th e require dphysica

l heigh t i s 6 8 meters . PROBLE M 17 : A dispersio nstud y i s bein g mad e ove r relativel y ope nterrai nwit hfluorescent particle s whos e siz e yield s 1. 8 x IO 1 0 particle s pe r gra mo f tracer . Samplin g i s b y membran e filters throug hwhic h9 x IO - 3 m 3 o f ai r i s draw n eac hminute . A stud y involvin g a1-hour release , whic hca nb e considere dfro mground-level , i s t o tak e plac e durin g condition s forecas t t o b e slightl y unstabl e wit hwind s 5 msec -1
. I t i s desirabl e t o obtai naparticl e coun t o f a t leas t 2 0 particle s upo nmembran e filters locate da t ground-leve l 2. 0 k mfromth e plum e centerlin e o nth e samplin g ar c 8 k mfro mth e source . Wha t shoul dth e tota l releas e be , i ngrams , fo r thi s run ? SOLUTION : Th e tota l dosag e a t th e sample r

i s determine db y th e tota l sampl e i ngram s divide d b y th e samplin g rate : D T( g se c m" 3 ) 2 0 particle s

1. 8 x IO 1 0 particle s g " 6 0 se c min" 1 9 x IO" 3 m 3 min " 120 0 16. 2 x IO 7 D T= = 7.4 1 x IO - * g se c m - 3 Th e tota l dosag e islpve n i ng se c m" 3 fro m 

### D T 

### (x,y,0;0 ) -f* ex p

—U Oy O s wher e Q Ti s th e tota l releas e i ngram s Therefor e Q T- * U" * D T 

# H-fc)" ] 1-M-tY] ex p Fo r slightl y unstabl e condition s (Clas s C ) a t x = 8 km , o 7

= 69 0 m , o z= 31 0 m ; y —200 0 m , u = 5 msec - 1 Q i 5 (690 ) 31 0 (7.4 1 x IO"* ) ex p 1

_/

200 0 \"- 1 

### 2 ( , 69 0 ) J 24. 9 ex p [—0. 5 (2.90)= ] 24. 9 1.49 x IO" 2 167 0 g Q T N o correctio nha s bee nmad e fo rth e fact s tha t th e releas e i s for

1 hou r an dth e standar ddevia
tion s represen t

tim e period s o

f 3 t o 1 5 minutes . PROBLE M 18 : A releas e o f 2 k g o f fluorescent particle s i s mad e base do nth e result s o f th e computatio ni nproble m17 . Th e condition s ar e clas s C stabilit y an dwin dspee d5 msec' 1
. Th e crosswind-integrate dground-leve l dosag e alon g th e 8-kn i ar c i s determine dfro mth e sampler s alon g thi s ar c t o b e 8. 2 x IO - 1 g se c m" 2
. Wha t i s th e effectiv e o zfor

thi s run ? SOLUTION : give nby : Dcw i Th e crosswind-integrate ddosag e i s

2Q T = = ex p V 2 To t u 

# [-"(•f)' l Sinc e th e sourc e i s a t

ground-level , th e expo nentia l ha s avalu e o

f 1 . Solvin g fo r

a,: 2 Q r o z V2J T DCW I U 2 (2000 ) V27.0.82 ) 5 400 0 10.2 8 o_= 38 9 m Exampl e Problem s 

## .+_«<&&: ' ;.-*;*.;:•' . • • :••. -yif.icy-.-. :: . I '0**rii£i^--*rm '-•"

*PROBLE M 19 : A t apoin t

directl y downwin d fro maground-leve l sourc e th e 3
- t o 15-minut e concentratio ni s estimate dt o b e 3. 4 v i0~ 3 g m - 3
. Wha t

woul dyo u estimat e th e 2-hoi r con centratio nt o b e a t

thi s point , assumin g n o chang e i nstabilit y o r win dvelocity ? SOLUTION : Usin g Eq . (5.12 ) an dlettin g k —3 min , s = 2 hours , an dp = 0.2 :

\12 0 j 3. 4 x 10 " 40 u - : 3. 4 x 1Q- " 2.0 9 (3. 4 x IO" 3 )

= 1. 6 x 10~ " g in
Lettin g k

1 5 min , s = 2 hours , an dp x . ..ou r = (-^- ) °- " 3. 4 x IO" 3

(3. 4 x IO" 3 ) 0.1 7

8 °- 1 7 3. 4 x 10~ 3 1.4 2 2. 4 x IO" ' g m " Th e 2-hou r

concentratio n i s estimate dt o b e betwee n1. 6 x 10 _: : an d2. 4 x 10" " g m -= . PROBLE M 20 : Tw o source s of SO = ar e show na s point s A an dB i nFigur e 7-6 . O nasunn y summe r afternoo nth e surfac e win di s fro m60 ° a t 6 msec -1
. Sourc e A i s apowe r plan t emittin g 145 0 g sec - 1 SO . fro mtw o stack s whos e physica l heigh t i s 12 0 meter s an dwhos e AH , fro mHol
land' s equation , i s A H (m ) —53 8 (m
- sec - 1 )/ u ( msec - 1 ) . Sourc e B i s arefiner y emittin g 12 6 g sec - 1 SO . fro ma neffectiv e heigh t o f 6 0 meters . Th e win dmeasure da t 16 0 meter s o nanearb y T V towe r

i s fro m70 ° a t

8. 5 msec -1
. Assumin g tha t th e mea ndirectio nof trave l o f

bot hplume s i s 245° , an dther e ar e n o othe r source s o f

SO. , wha t i s th e concentratio n of SO . a t th e recepto r show ni nth e figure ? SOLUTION : Calculat e th e effectiv e heigh t o f Sourc e A usin g th e observe dwin dspee da t 16 0 meters . A H = 53

8 = 63. 3 8. 5 H A= 12 0 + 6 3 = 18 3 m Q A= 145 0 g sec - 1 H B = 6 0 m Q B = 12 6 g sec" 1 Fo r asunn y summe r

afternoo nwit hwin dspee d 6 msec -1 , th e stabilit y clas s t o b e expecte di s C . Th e equatio nt o b e use di s Eq . (3.2) : SOURC E A i=24. 6 k m y = «. 4 k

m

RECEPTO

R SCAIE . k m I 1 — X 0 2 4 Figur e 7-6 . Location s o f source s an d recepto r(Proble m 20) .

x(x,y,0;H ) Q ex p 

# [--H-sr i KBr) 1

—Oy OzU 

### ri / ex p Fo r Sourc e A , x = 24. 6 km , y = 8. 4 k m oy = 181 0 m , cr

» • = 112 0 m , u = 8. 5 msec - 1
r 181 0 (1120 ) 8. 5 ex p I —0. 5



# [

145 0 112 0

ex p [—0. 5 (4.64) 2 ] 5.4 2 x 10 r ex p [—0. 5 (0.164) 2 ]
= 2.6 7 x 10" 5 ) (2.1 1 x 10"' ) (0.987 ) X A—5. 6 x 10" 1 0 g m" 3 Fo r Sourc e B , x = 13. 0 km , y = 4. 0 km . o T = 105 0 m , u

_= 64 0 m , u = 7. 0 msec - 1 12 6 "N

XB= - T

T105 0 (640 ) 7 ex p ex p 

# [-*>(•&)'] 

# [-"(w)" ]

12 6 ex p [—0. 5 (3.81 )- ] 1.4 8 x IO 7 ex p [—0. 5 (0.0938) 2 ]
= 8. 5 x IO" * (7.0 4 x 10"* ) (0.996 ) Xix = 6. 0 x 10" ° g nr 3
x= X A+ X B = 0.5 6 x 10" 8 + 6. 0 x 10- » = 6. 6 x IO - 0 gm' 1 " .

. -yi}i& : ;.iri.'•... .... V^&g&VATMOSPHERI C DISPERSIO NESTIMATE SPROBLE M 21 : A stac k 1 5 meter s hig hemit s 3 g sec - 1 o f aparticula r

ai r pollutant . Th e sur roundin g terrai ni s relativel y flat excep t for a rounde dhil l abou t

3 kmt o th e northeas t

whos e cres t extend s 1 5 meter s abov e th e stac k top . Wha t i s th e highes t

3
- t o 15-minut e concentra tio no f thi s pollutan t

tha t ca nb e expecte do n th e facin g slop e o

f th e hil l o naclear

nigh t whe n th e win di s blowin g directl y fro mth e stac k towar dth e hil l a t

4 msec -1 ? Assum e tha t A H i s les s tha n1 5 m . Ho w muc hdoe s th e win d hav e t o shif

t s o tha t concentration s a t

thi s poin t dro p belo w IO" 7 g m -3 ? SOLUTION : A clear

nigh t wit h4 msec - 1 indi
cate s clas s Estability . Eq . (3.4 ) fo r ground
leve l concentration s fromaground-leve l sourc e i s mos t applicabl e (Se e Chapte r 5) . A t 3 k m for clas s E , o r

= 14 0 m, o z= 4 3 m . Q 3 * J Toy o t u w 14 0 (43 ) 4 X —3.9 7 x 10" 5 g m" 3 T o determin e th e crosswin ddistanc e fro mth e plum e centeriin e t o produc e aconcentratio no f 10~7 g m - 3 Eq . (3.8 ) i s used :


### = j 2 l n

—j 2 l n x U,0,0 )

x (x,y,0 ) 3.9 7 x IO" 5

ta nG 10~7

—(21n397)v = 140

—( 2 x 5.98 ) "Z

2 14 0 = 3.4 6 x 14 0

—48 4 m . 48 4 

# 1 (140 )

300 0 G= 9.2 ° 0.161 4 A win dshif

t o f 9.2 ° i s require dt o reduc e th e concentratio nt o IO - 7 g m -3
. , PROBLE M 22 : A ninventor y o f SO . emission s ha s bee nconducte di na nurba nare ab y squar e areas , 500 0 f

t (152 4 meters ) o naside . Th e emission s fro mon e suc hare aar e estimate dt o b e 6 g sec - 1 for

th e entir e area . Thi s squar e i s compose do

f residence s an dafe

w smal l com mercia l establishments . Wha t i s th e concentra tio nresultin g fromthi s are aa t th e cente r

o f th e adjacen t squar e t o th e nort hwhe nth e win di s blowin g fro mth e sout ho nathinl y overcas t nigh t wit hth e win da t

2. 5 msec -1 ? Th e averag e effectiv e stac k

heigh t o f thes e source s i s assume d t o b e 2 0 meters . SOLUTION : A thinl y overcas t nigh t wit hwin d spee d2. 5 msec" 1 indicate s stabilit y o f class " 13 . 

### s/lei

(I t ma y actuall y b e mor e unstable , sinc e thi s i s abuilt-u p area. ) T o allo w for th e are asource , le t o y a = 1524/4. 3 = 354 . Fo r clas s Eth e vir
tua l distance , xy = 8. 5 km . Fo r x = 1524 m , <r«=-28.5 . For x Q x

y =10,02 4 m , o y= 41 0 m . X= * IT

Oy O t 

# T ex

# p[--HTr)' ]

exp 

# [—Hw ) ] \S

>r41 0 (28.5 ) 2. 5 •=6.54xl<r s (0.783 ) = 5. 1 x 10 - 9 g m" 1 PROBLE M 23 : A nestimat e i s require do f th e tota l hydrocarbo nconcentratio n30 0 meter s downwin do

f a nexpressway a t

173 0 o na nover cas t da y wit hwin dspee d4 msec -1
. Th e ex presswa y run s north-sout han dth e win di s fro m th e west . Th e measure dtraffi c flow i s 800 0 vehicle s pe r

hou r durin g thi s rus hhour , an dth e averag e spee do

f th e vehicle s i s 4 0 mile s pe r hour . A t thi s spee dth e averag e vehicl e i s ex pecte dt o emi t

2 x 10" * g sec - 1 o

f tota l hydro
carbons . SOLUTION : Th e expresswa y ma y b e considere d a s acontinuou s infinit e lin e source . T o obtai n asourc e strengt hqi ngram s sec - 1 m _l , th e num be r o f vehicle s pe r

mete r o f highwa y mus t

b e calculate dan dmultiplied.b y th e emissio npe r vehicle . — —_ Vehicles/mete r

— Flo w (vehicle s hour" 1 ) Averag e spee d(mile s hour -1 ) 160 0 ( mmile -1 ) 40x160 0 1 ' 2 5 X 10_ 1 (vehicle s m_1 ) q—1.25 x 10" 1 (vehicle s nr 1 ) x 2 x IO" 2 ( g sec - 1 vehide -1 ) q= 2. 5 x lO-^g: sec - 1 nr 1 ) Unde r overcas t condition s wit hwin dspee d4 m sec - 1 stabilit y clas s D applies . Unde r D , a t x — 30 0 meters , o %—1 2 m . Fro mEq . (5.18) : X (300,0,0;0 ) 3 V2i rff, U 2 (2. 5 x IO" 3 ) 2.50 7 (12+ 4

—4. 2 x 10" * g nr * o

f tota l hydrocarbons . PROBLE M 24 : A lin e o f burnin g agricultura l wast e ca nb e considere dafinite lin e sourc e 15 0 mlong . I t

i s estimate dtha t

th e tota l emissio n o f organic s i s a t

arat e o f 9 0 g sec' 1
. Wha t

i s th e 3
- t o 15-minut e concentratio no f organic s a t

a distanc e o

f 40 0 mdirectl y downwin dfro mth e cente r o f th e lin e whe nth e win di s blowin g a t 3 msec" ' perpendicula r t o th e line ? Assum e Exampl e Problem s SiAiv-;- : ssssas 1
-tha t

i t i s 160 0 o nasunn y fal l afternoon . Wha t i s th e concentratio ndirectl y downwin dfro mon e ' en do f th e source ? JLUTION : Lat e afternoo na t thi s tim e o

f yea r implie s sligh t

insolation , whic hwit h3 msec - 1 wind s yield s stabilit y clas s C . Fo r C stabilit y a t x = 40 0 m , <r

y = 4 5 m , o z= 2 6 m . Q 9 0 M 15 0 15 0 Eq . (5.20 ) i s appropriate .

= 0. 6 g sec - 1 m "

x(x,0,0;0 ) = V 2 ex p (—0. 5 p 2 ) d p 

## fp . 

# 3 j '2* r a . U I 

### J 

### P . 1 

### XT*

—+1.6 7 —7 5 . R 7 y

A - = 1-67 , p 2 = = 4 5 Oy 7 5 4 5
X (400,0,0,0 ) = 2 (0.6 ) 

# f

+1 

# ' 6 7
J —1.67 \'2* \/2W26) 3 ex p (—0. 5 p 2 ) d p = 6.1 4 xlO" 3 (0.91 )
= 5. 6 x IO" 3 g m" 3 Fo r apoin t downwin do

f on e o f th e end s o

f th e line : Pi —0 , p , _y

_ Oy 15 0 4 5 +3.3 3
/ ; -3.3 3 V2T . X (400,0,0;0 ) = 6.1 4 x IO" 3 ex p (—0. 5 p = ) d p
= 6.1 4 x IO" 3 (0.4995 )
= 3. 1 x 10- r

g m" 3 PROBLE M 25 : A cor e melt-dow no f apowe r re acto r tha t ha s bee noperatin g fo r ove r ayea r occur s a t

0200 , releasin g 1. 5 x 10 ° curie s o f activit y ( 1 secon dafte r th e accident ) int o th e atmospher e o

f th e containmen t

vessel . Thi s tota l activit y ca nb e expecte dt o deca y accordin g t o ( * ) - ° =

. I t i s estimate dtha t

abou t 5. 3 x IO4 curie s o f thi s activit y i s du e t o iodine-131 , whic h ha s ahalf-lif

e o f 8.04 days . Th e reacto r

buildin g i s hemisphericall y shape dwit haradiu s o f 2 0 meters . Assum e th e lea k rat e o f th e buildin g i s 0.17 c day -1
. Th e acciden t ha s occurre do narelativel y clear nigh t wit hwin dspee d2. 5 msec -1
. Wha t i s th e concentratio ni nth e ai r 3 kilometer s directl y downwin dfro mth e sourc e a t 040 0 du e t o al l radioactiv e material ? du e t o iodine-131 ? SOLUTION : Sourc e strengt h tivit y (correcte dfor

decay ) 0.00 1 day- 1 lea k

rat e x ac Lea k rat e 8640 0 se c day - 1

—1.15 7 x IO" 8 sec" 1 Sourc e strengt ho

f al l product s Q A(curie s sec" 1 ) = 1.15 7 x 10~ 8 (1. 5 x 10 r )

—0. 2 

## [ t 

## (sec ) ] [ t o (sec ) J
= 1.74 x IO" 2 

# '(4- ) —0. 2 T o determin e deca y o

f material s wit hth e half
-

.. . .. . , , /—0.6931 \ lif e given , multipl y b y ex p I = J i c tim e nnr l T . i o Violf-lif o \ / wher e t Q i (curie s sec -1 ) —0.69 3 t L Fo r I mL= Q i = 6.1 3 x IO" 4 ex p (
- i s tim e an dLi s half-life . Sourc e strengt ho

f I 131
. 1.15 7 x 10" 8 (5. 3 x 10 4 ) ex p / —0.69 3 t

\ 6.9 5 x 10 s se c

—0.69 3 t \ 6.9 5 x 10 s ) Fo r aclear nigh t wit hwin dspee d2. 5 msec -1 , clas s Fapplies . Approximat e th e spreadin g a t th e reacto r

shel l b y 2.1 5 <x y 0 — 2.1 5 oto = th e radiu s o f th e shel l = 2 0 m<r y o — » <r. o = 9- 3 m . Th e virtua l distance s t o accoun t fo r thi s are : x y = 25 0 m , xx= 56 0 m . A t x = 300 0 m . x + x T= 325 0 m , o T

= 10 0 m . x + x , = 356 0 m , o z= 2 9 m . 0 Q X (x,0,0;0 ) = W Oy O t U = 4. 4 x 10" 5 Q » 10 0 (29 ) 2. 5 Fo r concentratio na t

0400 , 300 0 mdownwin d du e t o al l radioactivity , t = 720 0 seconds . X A= 4. 4 x 1(T S (1.7 4 x IO" 2 ) (7200)- 0

- 2 = 7.6 6 x 10" 7 (0.17 ) X A—1. 3 x 10" 7 curie s m" 3 Th e concentratio na t

0400 , 300 0 mdownwin d du e t o I 1S 1 is : X i = 4. 4 x 10~ s (6.1 3 x 10 4 ) ex D [—0.99 7 x 10
- (7200) ] ) 54

•*&r - :-&$ : • ATMOSPHERI C DISPERSIO NESTIMATE SP.5 9

= 2. 7 x IO- 1 (1.0 ) Th e deca y o f I 13 1 i s insig
nifican t for 2 hour s Xi 2. 7 x 10

_ S curie s m

~ PROBLE M 26 : A spil l estimate da t 2. 9 x IO * gram s o f unsymmetrica l dimethy l hydrazin e occur s a t 030 0 o naclear

nigh t whil e arocke t i s bein g fueled . A circula r are a6 0 meter s i n diamete r buil t aroun dth e launc hpa di s revette d int o square s 2 0 fee t

o nasid e t o confin e t o a s smal l a nare aa s possibl e an y spille dtoxi c liquids . I nthi s spil l onl y on e suc h20
- b y 20-foo t are ai s involved . A t

th e curren t

win dspee do

f 2 m sec~ ! , i t i s estimate dtha t

th e evaporatio nrat e wil l b e 110 0 g sec -1
. Th e win ddirectio ni s pre dicte dt o b e fro m310 ° = 15 ° for th e nex t hour . Tabl e 7- 8 give s th e emergenc y toleranc e limit s for UDM H vapor . Tabl e 7- 8 EMERGENC YTOLERANC E LIMIT S FO R UDM H VAPO R VERSU S EXPOSUR E TIM E Time , minute s Emergency Toleranc e Limits , g nr 3 5 1 5 30 6 0 1.

2 x IO" 1 8. 6 x 10" = 4. 9 x lOr2. 5 x IO" 5 Wha t are ashoul db e evacuated ? SOLUTION : Fro mTabl e 3-1 , th e stabilit y clas s

. i s determine dt o b e Clas s F . Thi s i s no t apoin t sourc e bu t

asmal l are asource . Allowin g 4. 3 o> o t o equa l th e widt ho

f th e wette darea , 6. 1 meter s (2 0 feet) , o y{

, = 1.4 meters . I nattemptin g t o determin e th e virtua l distance , x,- , i t i s foun dt o b e les s tha n10 0 meters , an dwil l b e approxi
mate db y 4 0 meters . Th e releas e wil l take : 2. 9 x 10 " g 1. 1 x 10 " g se c 2.6 4 x 10 : ' se c = 4 4 min . Therefor e th e concentratio nfo r a nexposur e tim e o f 1 hou r (2. 5 x 10"- ' g m~" ) i s o f mai n concern . Th e equatio nfor

calculatio no

f downwin dcon centration s i s Eq . (3.4) :

Q X (x,0,0;0 ) o f X + x v . If Oy 0 Z XX wher e o yi s afunctio n Value s o f th e parameter s an do

f x ar e give ni n Tabl e 7-9 . Tabl e 7- 9 DETERMINATIO N O F CONCENTRATIO N AS A FUNCTIO N O F DISTANC E (PROBLE M 26 ) X , k m 0. 1 0. 3 0.6 1 3 6 1 0 o z.

m 2. 3 5. 6 9. 7 14 2 7 3 7 4 7 x- rx v ,

k m 0.1 4 0.3 4 : 0.6 4 1.0 4 3.0 4 6.0 4 10.0 4 Oy

m 5. 5 12. 5 2 2 3 5 9 3 17 5 27 5 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 Thes e value s o

f x ar e graphe da s afunctio no f x i nFigur e 7-7 . Th e downwin dconcentratio n drop s belo w th e critica l valu e o f 2. 5 x 10 - 2 a t

a distanc e o

f 6. 5 km .

1. o

1 0 1X1

1 0

IT 1

- * 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 Xi '' 

### 1 ! N . -

• > ! • i ! i I ^ ;

i •1 I i I i i I ; ! • , i | | II ! 

### I 1 MM ! 

# ! i i ! Ii i

- •- : II I ' '

' I ! 

## i | i j 1 r

• i . ! • ' . I 1 l I | 1 1 ; i 

## 1 X • -V - I

,.., _ "^ . ! 

## 1 " N 

# i f |

i . y i 

## 1 0. 1 1 DISTANCE , k m 1 0 Figure 7-7 . Concentratio n ofUDM H a s a functio n ofdown win d distanc e (Proble m 26) . Calculate dwidth s withi nagive n isoplethare summarize di nTabl e 7-10 . Th e maximu mwidt ho f th e are aencompasse d b y a nisoplet hi s abou t 14 0 meter s fro

m th e downwin dposition . Sinc e th e win ddirectio ni s expecte dt o b e from310 P ± 15° , th e secto r a t a n azimut ho

f 115 ° t o 145 ° plu s a140-mete r rectan gl e o ncithe r

sid e shoul db e evacuated . Se e Figur e 7-8 . Exampl e Problem s

''••*m%tym?y •P.6 0

k m 0. 1 0. 5 1. 0 2. 0 3.0 4. 0 5. 0 6. 0 Tabl e 7-1 0 DETERMINATIO N O F WIDTH S ISOPLETH S (PROBLE M 26 ) X + X y , k m 0.1 4 0.5 4 1.04 2.0 4 3.0 4 4.0 4 5.0 4 6.0 4 <r y . n i 5.5 19 35 6 6 9 3 12 0 14 9 17 5 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- ; ! 2.2 7 x10" - 6.9 4 x 10" - 1.9 2 x IO" 1 3.5 7 x IO" 1 5.2 0 x IO" 1 7.1 4 x IO" 1 9.2 6 x IO" 1 WITHI

N
y Oy 3.5 5 2.7 5 2.3 1 1.8 2 1.4 4 1.1 4 0.8 2 0.3 9 y .

I B 2 0 5 2 8 0 12 0 13 4 13 7 12 2 6 8

SCALE , k m

ITIIITIIII I ' I : M 5 * Figur e 7-S LPossibl e position s o f th e 2. 5 xIO"" 2 g m~ s isqpfet h an d th e evacuatio n are a (Proble m 26) .
( : - .

5 6

• .^-v^^'fW-VwJ'* , ATMOSPHERI C DISPERSIO N ESTIMATE S •a?** ? "•#£-.• -P.6 1



### APPENDICE S



## C":

139-90 1 O - 6 9 - I •".-•TSgS J

--^ssSLy?. ..JW&tii-Appendi x 1 : ABBREVIATION S AND . SYMBOL S

Abbreviation s ca l calori e g gra m ' K degree s Kelvi n mmete r m b milliba r se c secon d Symbol s arati o of

horizonta l edd y velocit y t o vertical ; edd y velocit y c, , specifi c hea t

a t constan t

pressur e C , Sutto nhorizonta l dispersio nparamete r C

_Sutto nvertica l dispersio n paramete r dinsid e stac k

diamete r

a t stac k to p D T(x,y,0;H ) Tota l dosag e e 2.71S3 , th e bas e of natura l logarithm s f (0,S,N ) frequenc y of win ddirectio nfo r

agiven
stabilit y an dwin dspee dclas s hphysica l stac k

heigh t hi heigh t

o f th e bas e of

a ninversio n H effectiv e heigh t

of emissio n H „ effectiv e heigh t

of emissio nfo r

aparticula r win dspee d k vo nKarman' s constant , approximatel y equa l t o 0. 4 edd y diffusivit y K L

n N P

/ Q

Q r R s S t k tw o uses : 1 . th e heigh t of a nai r laye r tha t i s relativel y stabl e compare dt o th e laye r beneat hit : ali d 2 . th e half-lif

e of aradioactiv e materia l Sutton' s exponen t a ninde x fo r

win dspee dclas s thre e uses : 1 . Bosanquet' s horizonta l disper
sio nparamete r 2 . atmospheri c pressur e 3 . adumm y variabl e i nth e equa tio nfo r aGaussia ndistribution . tw o uses : 1 . Bosanquet' s vertica l dispersio n

paramete r 2 . emissio nrat e pe r

lengt ho f

alin e sourc e emissio nrat e of

asourc e tota l emissio n durin g a nentir e releas e ne t rat e of sensibl e heatin g o f

a nai r colum n b y sola r radiatio n th e lengt ho f

th e edg e of

asquar e are asourc e a ninde x fo r

stabilit y ashor t tim e perio d tm T . T . u . U N V 7 V * V , w ' X

X i . X x X y x, , y z z. . S O 

## sT A H

P A

" A

OK

o*i.. Oy Oyl |
Ozl. Or,, tim e require dfor
- th e mixin g laye r t o develop * fro mth e to p of

th e stac k

t o th e top ; of

th e plum e atim e perio d ambien t ai r temperatur e stac k ga s temperature - a t

stac k to p win dspee d amea nwin dspee dfo r th e win dspee dclass . N~ „ horizonta l edd y vefoeit y stac k ga s velocit y a t

th e stac k

to p avelocit y use db y Calde r vertica l edd y velocit y distanc e downwin di n th e directio no f the. 1 mea nwin d desig ndistance , aparticula r downwin ddis
tanc e used, fo r

desig n purpose s th e distanc e a t

whic h<r

x = 0.47 L avirtua l distanc e s o tha t <* „ (x_ ) equal s th e ini
tia l standar ddeviation , ir x„ avirtua l distanc e s o tha t _•, . (x v ) equal s th e ini
tia l standar ddeviation , _•.,. „ avirtua l distanc e so . tha t o v (x_ ) equal s th e ini
tia l standar ddeviation , o,.„ crosswin ddistanc e heigh t abov e groun dleve l roughnes s paramete r th e rat e of

: chang e of

potentia l temperatur e wit hheigh t th e ris e o

f th e plume , centerlin e abov e th e stack : to p tw o uses : 1 . wind'direction-azimut ho r secto r 2 . potentia l temperatur e 3.141 6 ambien t ai r densit y th e standar ddeviatio nof . azimut h(win ddirec
tion ) a s determine dfro mawin dvan e o r bi
directiona l van e th e standar ddeviatio nof win delevatio nangl e a s determine dfro mabi-directiona l van e th e standar ddeviatio ni nth e downwin ddirec
tio no f apuf f concentratio n distributio n a ninitia l downwin dstandar ddeviatio n th e standar ddeviatio ni nth e crosswin ddirec
tio no f th e plum e concentratio ndistributio n "w" 1 ^'- * a ninitia l crosswin dstandar ddeviatio n th e standar ddeviatio ni nth e vertica l of th e plum e concentratio ndistributio n- ...;.*«...'•«•* , a neffectiv e o zequa l t o 0: 8 L a n initia l vertica l standar ddeviatio n th e vertica l standar ddeviatio nof th e plum e concentratio na t

aparticula r

downwin ddis
tanc e fo r th e stability , S . Appendi x 1

.'w4^i^Bfr.'«i-"i*£- - •.•a^f^f.iir*-P.6 3

p th e angl e betwee nth e win ddirectio nan da lin e sourc e concentratio n V1 ;YV Icrosswind-integrate dconcentratio n ,\-< i aground-leve l concentratio nfo r desig npur pose s Xi
- inversio nbreak-u p fumigatio nconcentratio n Xk concentratio nmeasure dove r asamplin g time , t k Xiiin s maximu mground-leve l centerlin e concentra tio nwit hrespec t

t o downwin ddistanc e X K concentratio nmeasure dove r asamplin g time , t . y £— relativ e concentratio n |L
- relativ e concentration . normalize dfo r win d " spee d X (x,y,z;H ) concentratio na t th e poin t

(x , y , z ) fro ma nelevate dsourc e wit heffectiv e height , H . X (x,e ) th e long-ter maverag e concentratio na t

distanc e x , for

adirectio n0 fro masource .



# J 6 0 ATMOSPHERI C DISPERSIO NESTIMATE S

*_^w"£^-*. - •- • w.V . .•*.. . .•;5^«jsijiiy-..i. . ..^yU^.y^Y'y^hr -''-.:* - ! ^"^.yffiy ^P.6 4

Appendi x 2 : CHARACTERISTIC S O FTH E

GAUSSIA

NDISTRIBUTIO N Th e Gaussia no r

norma l distributio nca nb e de
picte db y th e bellshape dcurv e show ni nFigur e A-1 . Th e equatio nfor

th e ordinat e valu e o

f thi s curv e is : 

### y = J - ex

p 

### fL (

*— ~* ) 

### 1 V2r . [

2 1 6

) \ (A.1 ) Figur e A- 2 give s th e ordinat e valu e a t an y distanc e fro mth e cente r

o f th e distributio n(whic hoccur s a t x) . Thi s informatio ni s als o give ni nTabl e A-1 . Figur e A- 3 give s th e are aunde r th e Gaussia ncurv e fro m—"*

• t o aparticula r

valu e o f p wher e p = Thi s are ai s foun dfro mEq . (A.2) : Are a(
- ex p (—0. 5 p- ) d p 

# ^ t0P) 

# =J _~fe- (A.2 ) Figur e A- 4 give s th e are aunde r th e Gaussia n curv e fro m— p t o -j-p . Thi s ca nb e foun dfro mEq . (A.3) : Are a(— p t o +p ) = ex p (—0. 5 p 2 ) d p 

# i- P v 

# " (A.3 )

(

Figur e A-1 . Th e Gaussia n distributio n curve .

Appendi x 2 6 1

iffo U pJtZ&$J~^jfik-f** ?;•' .!••&•^-VyM*^^"fty » .-**- . &*•£<[£

# r 1. 0 9 8 7 6 5 4

0. 1 9 8 7 6 5 4 3

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: - : i,,- '

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:•.! . ' : Xil:. : .•••i:_ i

- • •:•• . : • j •• :

.:• ( - - y: : \':-- zv\y .-.



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-':• 

### :i; i ;y ;

:;: : :_ • ;: - •H H 

# v : TT : H : : ' . j

:. ~ ::: : :- . _i__ n p

:r-- • : - :

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: TM ::* : ^ C :— tH : : « TLf rrrr r r i lu : "~ " r ::r. i:i ; i:c : •;*: H: . £ H

= S 

## -fi t
ni l :^ : :r-.z iS '•P- !•: : I:: i ni . Uj 4 IX

U jw i -]'•'• M iz2- 

## z& \: : A :_ • nii := : ... . i|*= j 

# i *r H 

# p "t-
- i^ r "* r ;!: : if = *2 z

- r fl { v.i ; •H : 7ZZZ ::= = 3 tn i y< rr ; F H 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 1 2 1. 4 1. 6 1. 8 2. 0 2. 2 2. 4 2. 6 2. 8 3. 0 3. 2 3. 4 3. 6 3. 8 4. 0

Figur e A-2 . Ordinat e value s of the.Gaussia n distribution .



### f 

# j
ATMOSPHERI C DISPERSIO N ESTIMATE S

•••iM0.0 1 0. 1 0. 5 1 2 5 1 0 2 0 4 0 6 0 8 0 9 0 9 5 9 8 9 9 99. 8 99.9 9 / : P -4=

_.< p (-0. 5 p 3 ) li p Figur e A-3 . Are a unde rth e Gaussia n distributio n curv e fro m —< * t o p .

Appendi x 2 

### H*P^r " 3i p W*.% •' . - . .,'._rT , L ' • ' \__

_^c.- ' 6 3P.6 7

/ ' 99. 8 99.9 9

/ ••-'-• • Figure A-4 . Area unde rth e Gaussia n distributio n curve betwee n — p an d -fp .

6 4 ATMOSPHERI C DISPERSIO N ESTIMATE S

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

# *§i f .=__=_« . *___ _P.6 8 Vpp.-mlix 3 : SOLUTIO.N S T O EXPONENTIAL S Expression s o

f th e for mex p [—0. 5 A : ] wher e A i s H o-

7 . o r y/oy frequentl y mus t

b e evaluated . Tabl e A- 1 give s B a s afunctio no f A wher e B = ex p [—0. 5 A"] . Th e sig nan ddigit s t o th e righ t o f th e Ear e t o b e considere da s a nexponen t o f 10 . Fo r example , i

f A i s 3.51 , B i s give na s 2.H E— 0 3 whic hmean s 2.1 1 x IO" 3

/ Appendi x 3 6 5

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m N^-^N * mN^a o tfM^0*-o

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G C ATMOSPHERI C DISPERSIO N ESTIMATE S

«**T,*ns*:;..-i . -v*TM.i££ij*4.'?i-^- , sr'v- " -<t--*-1iwVi^f,'^* ^ • ^ % /;..^ > »ii, ,ji»..^J^l. V -» >^ " .

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1 V " ! jAppen

O . t*.

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$.0 0 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 7.0 C 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.0 0 B.1 C 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.O O

B 3.M E 2.2S E 1.34 C 7.9S t **. 6 H E 2.70 c 1.55 c 8.R1 E *.9. E 2.7K. E 1.52 t 8.3. E 4.50 E <!.41 E 1.291 . 6.6QE 3.4QE 1.7a_ - 9.10E - * . 5 .t - 2.20E - 1.13E 5454E 2.68E 1.29E 6.10E 2.87E 1.3*E - 6.15E 7.R0E 1.27E 5.66E - *.51E - . 6

- 6

- 6

- 7

- 7

- 7

- 7

- . . 8

- .

. 8

- 9

- 9

- 9

- 9 1 0 1 0 1 0 1 1 1 1 1 1 1 1 •1 2 1 2 .1 2
•1 3 •1 3 •1 3 •1 4 •1 4
•1 4 •1 5 1 5 1.10E-1 5 *.77E - 2.0.E - •1 6
•1 6 8.71E-1 7 3.67E - •1 7 1.53E-1 7 6.31E-1 8 <.58E 1.04E 4.1BE l.64t - 6.50E - *.53E - 9.72E i.TOf . 1.40E 5.2.E - •1 8 •1 8 •1 9 1 9 2 0 2 0 •2 1 2 1 2 1 2 2 0,. H J.55 E ?.U F 1.28 . 7.54 E 4.M F 2.56 E 1.47 F 3.32 E ".6P E 2.60 F 1.43 E 7.P2 F 4.23 F 2.26 E 1.20 E 6.27E 3.25E 1.67F 8 . . o_ - 4.23E - 2.14E - 1.05E 5.15E - <!.49E 1.19E 5.66E 2.66E 1 .2<.E 5.69E 2.59E I.iIt5.22E 2.31E - 1.01E 4.38E - - 6

- 6

- 6

- 7

- 7

- 7

- 7

- 8

- 8

- 8

- 8

- 9

- 9

- 9

- 9
•1 0 •1 0 •1 0 1 1 1 1 1 1 1 1 •1 2 1 2 •1 2
•1 3 1 3 •1 3 •1 4 •1 4 1 * 1 5 1 5 1 5 •1 6 1.B8E-1 6 '.99E-1 7 3.36E-1 7 1.40E - •1 7 9.77E-1 8 2.36E - 9.52E 3.R1E 1.51E 5.92E - •1 8 •1 9 •1 9 1 9 2 0 *.30E-*0 . 8.83E 3.36E 1.27E 4.73E . •4 1 •2 1 •2 1 • 2 2 I

'>.ri 2 3.37 E 2.01 E 1.21 c 7.11 E 4.1P . 2.4? c 1.39 £ 7.8H E 4.41 E 2.45 . 1.35 E 7.3. E 3.97 t 2.12 E 1.12 . 5.8«c - 3.0SE 1.5.E 7.94E 4.00E 1.99E abl o /

- I S

- 6

- . •7

- 7

- 7

- 7

- R

- . - .

- R

- T

- 9

- 9

- 9 •1 0 •1 0 -1 0 •1 1 •1 1 •1 1 9.B1E-1 2 4.79E 2.32E - •1 2 •1 2 1.11E-1 2 5.25E 2.46E - •1 3 •1 3 l.HE-1 3 5.26E - •l o 2.39E- U 1.08E 4.81E 2.13E 9.30E - •1 4 •1 5 1 5 •1 6 4.03E-1 6 1.73E 7.33E - •1 6 •1 7 3.09E-1 7 1.28E-1 7 5.2.E - •1 9 2.15E-1 8 B.69E 3.47E 1.37E 5.31E 2.09E 8.02E 3,OBE LISE - 4.2A_ - •1 9 •1 9 •1 9 •2 0
•2 0 •2 1 •2 1 •2 1 2 2 V I (con t

0.0 3 J.21 E 1.93 E 1.15 E h . 7 . E 1.96 E 2.29 E 1.31 E '.42 E *.16 E 2.31 E 1.27 E 6.92 E 1.73 E 1.99 E 1.05 E nuii d

- 6

- 6

- 6

- 7

- 7

- 7

- 7

- B

- 8

- 8

- 8

- 9

- 9

- 9

- 9 5.50E-1 0 2.R5E . 1.46E 7.42E 3.73E 1.86E 9.14E 4.46E Z.15E . 1.03E . 4.87E - 2.28E - •1 0

1 0 •1 1 1 1
•1 1 •1 2 •1 2 •1 2 •1 2 •1 3 •1 3 1.06E-1 3 4.86E - •1 4 2.21E- U 9.96E 4.44E . 1.96E - •1 5 •1 5 •1 5 H.56E-1 6 3.70E 1.59E - •1 6 •1 6 6.72E-1 7 Z.82E-1 7 1.17E-1 7 4.83E-1 8 1.97E . •1 8 '.93E-1 9 3.17E 1.25E 4.90E 1.90E - •1 9 •1 9 •2 0
•2 0 7.29E-2 1 2.77E l.O.E . 3.8RE - •2 1 ,2 1 •2 2 ) SOLUTION!

0.0 4 3.05 £ - A 1.81 E - 6 l.O. E - 6 *.<>T E - 7 J.75 E . 7 2.1' E - 7 1.24 E - 7 ?.01 E - 8 J.93 E - 8 2.18 E - 8 1.20 E - 8 6.51 E - 9 3.51 E - 9 l.BT E - 9 9.87E-1 0 5.16E-1 0 2.6'£-1 0 1.37E-1 0 6.93E-1 1 3,*PE-l l 1.7'E- U 8.51E-1 2 <|.15E-1 2 2.00E-1 2 9.55E-1 3 0.52E-1 3 2.HE-1 3 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-.2 0 1.73E-2 0 6.62E-2 1 2.51E-2 1 9,<»3E-2 2 3.51E-2 2 > T

O EXPONE N 0.0 5 2.90 E - 6 1.7<. E - 6 1.0* E - 6 6.09 E - 7 3.55, . - 7 2.05 E - 7 1.17 E - 7 6.62 E - 8 3.70 E - 8 2.0. E - 8 1.13 E - 8 6.12 . - 9 3.29 E - 9 1.75 E - 9 9.2bE-1 0 <i.83F-1 0 2.S0E-1 O 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-1 2 8.87E-1 3 <,.19E-1 3 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-1 6 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 TIAL S

0.0 6 2.76 E - 6 1.65 E - 6 9.82 E - 7 5.77 E - 7 3.36 E - 7 1.9<- E - 7 1.11 E - 7 6.25 E - 8 3 , .9 E - 8 1.94 E - 8 1.06 E - 8 5.76 E - 9 3.09 E - 9 1.65 E - 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-2 1 2.07E-2 1 7.75E-2 2 2.BBE-2 2 0.0 7 0.0 8

2.62 E - 6 2.49 E - 6 1.57 E - 6 .49 E - 6 9.32 E - 7 8.84 E - 7 5.47 E - 7 3.18 E - 7 1.83 E - 7 1.05 E - 7 < 5.90 E - 8 ! 3.29 E - 8 : 1.82 E - 8 9.98 E - 9 < 5.41 E - 9 '• 2.91 E - 9 ; 1.55 E - 9 8.13E-1 0 *.2<>E-1 0 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.Ol E - 7 1.73 E - 7 J.87 E - 8 >.57 E - 8 >.11 E . 8 1.72 E - 8 >.39 E - 9 >.09 E - 9 ?.73 E - 9 l.«5 E - 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-1 3 M9E-1 * I.28E-1 * l.*9E-l * ,.66E-1 ' !.95E-1 5 .30E-1 5 1.64E-1 6 !.43E-1 * 1.03E-1 6 •.36E-1 7 1.82E.1 7 r,53E- U I.OsE-1 8 1.25E-1 8 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-2 Z 0*0 9

2.37 E - 6 1.42 E . 6 B.38 E . 7 4.91 E - 7 2.BS E . 7 1.64 E . 7 9.32 E . 8 5.25 E . 8 2.93 E . 8 I.62 E . 8 B.84 E . 9 4.78 E . 9 2.56 E . 9 1.36 E . 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-1 S 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 2P.7 1 Appendi x 4 : CONSTANTS , CONVERSIO N EQUATIONS , CONVERSIO N TABLE S Constant s e = 2.718 3

—0.367 9 a - = 3.141 6 = 0.318 3 2: r = 6.283 2 \/27 = 2.506 6 V2-

2 —0.159 2

= 0.398 9

—0.797 9 (2-yr- = 15.7 5 Conversio n Equation s an dTable s T(°C ) =5/ 9 (T(°F ) —32 ) T(°K ) =T(°C ) +273.1 6 T(°F ) = (9/5T(°C ) ) +3 2

Appendi x 4

J-'n.Hlf. m T- 6 9•

a o Y

r.- CONVERSIO N FACTORS - VELOCIT Y *

* &


### im- j . GIVE N UNIT S METER S PERSE C F T PERSE C F T PERMI N K M PERH R MKSTAT ) PE RH R KNOT S MKSTAT ) PERDA Y METER S

PE R 1,000 0 E 0 0 3.0.8 0 E-O l 9.080 0 E-0 3 2.777 8 E-O l A,470 * E-O l 5.147 9 E-O i 1,862 7 E-0 2 F T

SE C PE P 3.280 8 E 0 0 1.000 0 E 0 0 1.666 7 E-0 2 9.113 4 E-O l 1.466 7 E 0 0 1.688 9 E 0 0 6.111 1 E-0 2 F T

SE C PE R MI N 1.968 9 E 0 2 6.000 0 E 0 1 1.000 0 E 0 0 5.468 1 E 0 1 8.800 0 E 0 1 1.013 4 E 0 2 3.666 7 E 0 0 K

M PE R H R 3.600 0 E 0 0 1.097 3 E 0 0 1.828 8 E-0 2 1.000 0 E 0 0 1.609 3 E 0 0 1.853 2 E 0 0 6.709 6 E-0 2 MKSTAT )

PE R H R 2,236 9 E 0 0 6.818 2 E-O l 1.136 4 E-0 2 6.213 7 E-O l 1.000 0 E 0 0 1.151 6 E 0 0 4.166 7 E-0 2 KNOTS

1.942 5 E 0 0 5.920 9 E-O l 9.868 1 E-0 3 5,395 9 E-O l 8.683 9 E-O l 1.000 0 E 0 0 3.618 3 E-0 2 MKSTAT )

PE R DA Y 5.368 6 E 0 1 1.636 4 E 0 1 2.727 3 E-O l 1.491 3 E 0 1 2.400 0 E 0 1 2,763 7 E 0 1 1,000 0 E 0 0 T O CONVER T A

VALU E FRO

M A GIVE N UNI T TO A

DESIRE D UNIT , MULTIPL YTH E GIVE N VALU E BYTH E FACTO ROPPOSIT E TH E GIVEN UNIT S AN O BENEAT H TH E DESIRE D UNIT . NOT E THAT E-X XMEAN S 1 0 T O TH E -X XPOWER .

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li. s • •

O •9 ti a c u CONVERSIO NFACTOR S - EMISSIO NRATE S

DESIRE D UNIT S GRAM S GRAM S K G K G LB S LB S LB S TON S TON S PE R SE C PE R MI NPE R HOU R PE RDA Y PE R MI NPE R HOU R PE R DA * PE R HOU R PE R DA Y GIVE NUNIT S

•Mu 

# m

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# te GRAM S

PERSE C GRAM S PERMI N K G PERHOU

R K G PERDA

Y LB S PERMI N LB S PE RHOU R LB S PEROA

Y TON S PERHOU

R TON S PE RDA Y 1.000 0

E 0 0 1,666 7 E-0 2 2,777 8 E-O l 1.137 4 E-0 2 7,559 9 E 0 0 1.260 0 E-O l 5.249 9 E-0 3 2.520 0 E 0 2 1.050 0 E 0 1 6.000 0

E 0 1 1.000 0 E 0 0 1.666 7 E 0 1 6.944 4 E-O l 4.535< j E 0 2 T.559 9 E 0 0 3.149 9 E-O l 1.312 0 E 0 4 6.299 9 E 0 2 3.600 0

E 0 0 6.000 0 E-0 2 1.000 0 E 0 0 4,166 7 E-0 2 2.721 6 E 0 1 4.533 9 E-O l 1.890 0 E-0 2 9.071 8 E 0 2 3.779 9 E 0 1 8,640 0

E 0 1 1.440 0 E 0 0 2.400 0 E 0 1 

### I.ooo o E 0 0 6.931 7 E 0 2 1.088 6 E 0 1 4.333 9 E-0 1 2.177 2 E 0 4 9.071 8 E 0 2 1,322 8

E-O l 2,204 6 E-0 3 3,674 4 E-0 2 1.531 0 E-0 3 1.000 0 E 0 0 1.666 7 E-0 2 6,944 4 E-0 4 3,333 3 E 0 1 1.388 9 E 0 0 7.936 6

E 0 0 1.322 8 E-O l 2.204 6 E 0 0 9.185 9 E-0 2 6.000 0 E 0 1 1.000 0 E 0 0 4,166 7 E-0 2 2.000 0 E 0 3 8.333 3 E 0 1 1.904 8

E 0 2 3.174 7 E 0 0 9,291 1 E 0 1 2.204 6 E 0 0 1.440 0 E 0 3 2.400 0 E 0 1 1,000 0 E 0 0 4,800 0 E 0 4 2,000 0 E 0 3 3.968 3

E-0 3 6.613 9 E-0 5 1.102 3 E-0 3 4,393 0 E-0 5 3,000 0 E-0 2 9.000 0 E-0 4 2,083 3 E-0 5 1,000 0 E 0 0 4.166 7 E-0 2 9,924 0

E-0 2 1.387 3 E-0 3 2,649 3 E-0 2 1.102 3 E-0 3 7.200 0 E-O l 1,200 0 E-0 2 9,000 0 E-0 4 2,400 0 E 0 1 1,000 0 E 0 0 T O CONVER T AVALU E FRO M AGIVE NUNI T T O ADESIRE D UNIT , MULTIPL Y TH E 6IVE NVALU E B YTH E FACTO ROPPOSIT E TH E GIVE N UNIT S AN O BENEAT H TH E DESIRE D UNIT , NOT E THA T E-X X MEAN S 1 0 T O TH E -X X POWER ,

? >*:• •• • $

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## o c/ 1 " B X a S B r* 

## o CONVERSIO N FACTOR S - LENGT H DESIRE D UNIT S METE RC M GIVE N UNIT S METE R C M
MICRO N
KILOMETE R
INCH
FOO T
YAR D MILECSTAT ) MilEjNAUT ) MICRO N KILOMETE RINCH FOO T YARD MRE(STAT ) MILE(NAUT ) 1.000 0 E 0 0 1.000 0 E-0 2 1,000 0 E-0 6 1,000 0 E 0 3 2.540 0 E-0 2 3,048 0 E-O l 9,144 0 E-O l 1.609 3 E 0 3 1.833 2 E 0 3 I.OOO

O E 0 2 I.OOOO E 0 0 1.000 0 E-0 4 1.000 0 E 0 3 2.540 0 E 0 0 3.04B 0 - E 0 1 9.144 0 E 0 1 1.609 3 E 0 9 1.853 2 E 0 5 1.000 0

E 0 6 1.000 0 E 0 4 1.000 0 E 0 0 1.000 0 E 0 9 2.540 0 E 0 4 3.048 0 E 0 5 9.144 0 E 0 5 1.609 3 E 0 9 1.853 2 E 0 9 1.000 0

E-0 3 1.000 0 E-0 5 1.000 0 E-0 9 1.000 0 E 0 0 2.940 0 E-0 5 3.048 0 E-0 4 9.144 0 E-0 4 1.609 3 E 0 0 1.853 2 E 0 0 3.937 0

E 0 1 3.937 0 E-0 ' 3,937 0 E-0 5 3,937 0 E 0 4 1,000 0 E 0 0 1.200 0 E 0 1 3.600 0 E 0 1 6.336 0 E 0 4 7,296 2 E 0 4 3.280 8

E 0 0 3.280 8 E-0 2 3.28C 8 E-0 6 3.280 8 E 0 3 8.333 3 E-0 2 1.000 0 E 0 0 3.000 0 E 0 0 9,280 0 E 0 3 6,080 2 E 0 3 1.093 6

E 0 0 1.093 6 E.0 2 1.093 6 E-0 6 1,093 6 E 0 3 2.777 8 £.0 2 3.333 3 E-O l 1.000 0 E 0 0 1.760 0 £ 0 3 2.026 7 E 0 3 6,213V

E - 4 6,213 7 £.0 6 6,213 7 E-1 0 6,213 7 E.0 1 1.978 3 E-0 9 1.893 9 £.0 4 9.681 8 E-0 4 1.000 0 E 0 0 1.151 6 E 0 0 3,395 9

E-0 4 5,395 9 E-0 6 5,393 9 E-1 0 5.395 9 E-O i 1.370 6 E-0 5 1.644 7 E-0 4 4,934 0 E-0 4 8,683 9 E-O l 1,000 0 E 0 0 T O CONVER T A

VALU E FROM

A GIVE N UNI T T O A

DESIRE D UNIT , MUUTIPL YTH E GIVE N VALU E B YTH E FACTO ROPPOSIT E TH E GIVE N UNIT S AND BENEAT H TH E DESIRE O UNIT , NOT E THAT E-XXMEAN S 1 0 T O TH E -X XPOWER ,

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M o X lb . CONVERSION FACTOR S DESIRE D UNIT S GIVE N UNIT S S O METE R
S O K M
S O C M
S O INC H
S O FOO T
S O YAR D
ACR E 5 0 STAT MIL E S O NAU T j . Mll E - AREA S Q METE R 1,000 0 E 0 0 1,000 0 E 0 6 1,000 0 E-0 4 6,451 6 E-0 4 9.290 3 E-0 2 8.361 3 E-O l 4.046 9 E 0 3 2.590 0 E 0 6 3.434 5 E 0 6 S Q K

M 1.000 0 E-0 6 1.000 0 E 0 0 1,000 0 E-1 0 6.451 6 E-1 0 9,290 3 E.0 8 8.361 3 E-0 7 4.046 9 E-0 3 2.590 0 E 0 0 '.434 5 E 0 0 S Q C

M 1.000 0 E 0 4 1.000 0 E 1 0 1.000 0 E 0 0 6.451 6 E 0 0 9.290 3 E 0 2 8.361 3 E 0 3 4.046 9 E 0 7 2.590 0 E 1 0 3.434 3 E 1 0 S Q INCH

1.350 0 E 0 3 . 1.550 0 E 0 9 1.550 0 E-O l 1.000 0 E 0 0 1.440 0 E 0 2 1.296 0 E 0 3 6.272 6 E 0 6 4.014 5 E 0 9 5.323 5 E 0 9 S Q FOO T

1,076 4 E 0 1 1,076 4 E 0 7 1,076 4 E-0 3 6,944 4 E-0 3 I.OOO O E 0 0 9,000 0 E 0 0 4,356 0 E 0 4 2.787 S E 0 7 3.696 9 E 0 7 S Q YARD

1.196 0 E 0 0 1.196 0 E 0 6 1.196 0 E-0 4 7.716 0 E-0 4 1,111 1 E-O l 1.000 0 E 0 0 4.B40 0 E 0 3 3.097 6 E 0 6 4,107 6 E 0 6 ACR E

2.471 0 £-0 4 2.471 0 E 0 2 2.471 0 £.0 8 1.594 2 E-0 7 2.295 7 E.0 5 2.066 1 E-0 4 1.000 0 E 0 0 6.400 0 E 0 2 8,486 9 E 0 2 S Q STA

T 1IL E 3.861 0 E-0 7 3.861 0 E-O l 3.861 0 E-l l 2.491 0 E-1 0 3.587 0 £.0 8 3,228 3 £.0 7 1,562 5 E-0 3 1.000 0 E 0 0 1.326 1 E 0 0 S Q NAUT

MIL E 2.911 6 E-0 7 2.911 6 E-O l 2,911 6 E-l l 1,878 5 E-1 0 2,705 0 E-0 8 2,434 5 E-0 7 1.178 3 E-0 3 7,541 1 E-O l 1,000 0 E 0 0 ISD C K2! H A THF L Dfsfo « LVr^ uni l I2_ T p E

_

»«« > ^ l T . MULTIPL YTHE GI V E N VALUE B YTHE FACTOROPPOSIT E TH E GIVEN UNIT S AI\ DBENEAT H TH E DESIRE D UNIT , NOT E THAT E-X XMEAN S 1 0 T O THE -X XPOWER ,

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### - r CONVER.IO M rACTO? s - v?LU : -l E U r SlRFi

_U-!I T S C U '*ETC P LITE " GlVE M UNIT S C U METE P I.OOO O F n o 0.999 7

E O Z C'. l INC . C U FOO T

6.102 1

. 0 4 3.531 4

E O J C u STATC u NAU Tj S FLUI D U S QUART

MIL E MIL E OUNC E *.399 1 E-1 0 1.571 1

E-1 0 3.381 4

E 0 4 1,056 7

E-0 3 U S GALLO N

2,641 7 E 0 2

» ! • LITF R

C U INC H C U FOOT C U STA T

MIL E 1.000 0 E-1 3 1,61_ 7 2.811 7 F-0 2 H.U8 Z f 0 9 l.nooo '

E O U 1.63H 7 E-0 2 2.131 6 E o r 4.161 1 E U 6.1"2 5

E 0 1 1.000 0 F0 0 1.728 0 E 0 3 2.543 6 E 1 4 3.5'U .

E-o ? 5.7X7 0 E-«' 4 1.000 0 E '' O 1.472 0 E H 2.399 2

E-1 3 3,931 5 E-1 5 6.793 6 E-1 2 1.000 0 E 0 0 1.57 U

E-1 3 2.574 6 E-1 5 4,448 8 E-1 2 6,548 6 E-O l 3,381 5

E O l 5.541 2 E-O l 9.575 1 E 0 2 1.409 4 E 1 4 1,056 7

E-0 6 1.731 6 E-0 8 2.992 2 E-0 5 4,404 5 E 0 6 2,641 8

E-O l 4,329 0 E-0 3 7,480 5 E 0 0 1.101 1 E 1 2 C U NAU T

M1L F 6,365 0 F 0 9 6.364 9

E 1 / 3.8«4 2

F 1 4 2.Z47 8

E U 1.527 0

E 0 0 1,000 0

E 0 0 2.152 3

E1 4 6.725 9

E 0 6 1.681 5

E 1 2 U S FLUI D OU'IC F 2.957 4 F-0 5 2,957 3

E-0 2 1.804 7

E O O 1,044 4

E-0 3 '.095 0

E-1 5 4,646 2

E-1 5 1,000 0

E 0 0 3,125 0

E-0 8 7.812 5

E-0 3 U S QUAR

T U S GALLO N 9.4.3 5 E 0 2 3,785 4 F-0 3 9,461 3

E 0 * 3,78. 3 E 0 0 5.775 0

E 0 7 2.310 0 E 0 2 3.342 0

E 0 4 1.316 8 E - o i 2,270 4

E-0 7 9,081 7 E-1 3 1.486 8

E-0 7 5.947 2 E-1 3 3.200 0

E 0 7 1.280 0 E 0 2 1,000 0

E 0 0 4,000 0 E-0 6 2,500 0

E 0 5 1,000 0 E 0 0 T O CONVFR TA VA|U F FRO M A GIVE N U' U I T O A AN O BENFAT H TH E DESIRE D UNIT . NOTf . MA T DESIRE 1 ) UNIT , MULTIPL YTH E GIVE N VALU E « YTH E FACTO R OPPOSIT E TH E GIVE N UNIT S E-X XMEAN S 1 0 T O TH E -X XPOWER .

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### & x CONVERSIO N FACTOR S - MAS S DESIRE D UNIT S GRA M GIVE N UNIT S GRA M
MICROGRA

M
KILOGRA M
METRI C TO

N
SHOR T TO

N
LONGTON
GRAI N
OUNC E (AVDP ) L B (AvDP ) MICROGRA M KILOGRA

M METRI C TO

N SHOR T TO

N LON GTO N GRAI N OUNC E L B (AVDP ) (AVDP ) 1,000 0 E 0 0 1,000 0 E-0 6 1,000 0 E 0 3 1,000 0 E 0 6 9.071 8 E 0 5 1.016 0 E 0 6 6,479 9 E-0 2 2.834 9 E 0 1 4,535 9 E 0 2 1.000 0

E 0 6 1,000 0 E 0 0 1.000 0 E 0 9 1.000 0 E 1 2 9.071 8 E 1 1 1.016 0 E 1 2 6.479 9 E 0 4 2.834 9 E 0 7 4.333 9 E 0 8 1.000 0

E-0 3 1.000 0 E-0 9 1.000 0 E 0 0 1.000 0 E 0 3 9.071 8 E 0 2 1.016 0 E 0 3 6.479 9 E-0 5 2,834 9 E-0 2 4,535 9 E-O l 1.000 0

E-0 6 1.000 0 E-1 2 1.000 0 E-0 3 1.000 0 E 0 0 9.071 8 E-O l 1.016 0 E 0 0 6.479 9 E-0 8 2.834 9 E-0 3 4.535 9 E-0 4 1.102 3

E-0 6 1.102 3 E-1 2 1.102 3 E-0 3 1.102 3 E 0 0 1.000 0 E 0 0 1.120 0 E 0 0 7.142 8 E-0 8 3.125 0 E-0 5 5.000 0 E-0 4 9.842 1

E-0 7 9.842 1 E-1 3 9.842 1 E-0 4 9,842 1 E-O l 8,928 6 E-O l 1,000 0 E 0 0 6,377 5 E-0 8 2,790 2 E-0 5 4,464 3 E-0 4 1.543 2

E 0 1 1.543 2 E-0 5 1.543 2 E 0 4 1.543 2 E 0 7 1.400 0 E 0 7 1.568 0 E 0 7 1,000 0 E 0 0 4,375 0 E 0 2 7,000 0 E 0 3 3,527 4

E-0 2 3,527 4 £.0 8 3,527 4 E 0 1 3.527 4 £ 0 4 3.200 0 E 0 4 3.584 0 E 0 4 2,285 7 E-0 3 1,000 0 E 0 0 1,600 0 * E 0 1 2,204 6

E-0 3 2.204 6 E-0 9 2.204 6 E 0 0 2.204 6 E 0 3 2,000 0 E 0 3 2,240 0 E 0 3 1,428 6 E-0 4 o,«-50 0 E-0 2 1,000 0 E 0 0
.-JT' ' I T O CONVER T A VALU E FRO

M A GIVE N UNi T T O A

DESIRE D UNIT , MULTIPL YTH E GIVE N VALU E BYTH E FACTO ROPPOSIT E TH E GIVE N UNIT S AN D BENEAT H TH E DESIRE D UNIT . NOT E THAT E-XXMEAN S 1 0 T O TH E -X XPOWER .

< nCONVERSIO N FACTOR S - FLO

W DESIRE D UNIT S C UMETE RC UMETE RLITE RLITE RLITE R C U F T C U F T C U F T C U C^ l PE R SE C PE R HR PE RSE C PE RMI N PE R H R PE R SE C PE R MJ NPE R H R PE R SE C GIVE NUNIT S



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U
C U METE R PERSE C METER PERH R LITE R PERSE C LITE R PER'MI N LITE R
C U
C U
C U
C U
TO PE RH

R F T PERSE C F T PE RMI N F T PE RH R C M PERSEC CONVER T 1.000 0 E 0 0 2.777 8 E-0 4 I.000 0 E-0 3 1.666 7 E-0 5 2,777 9 E-0 7 2,831 7 E-0 2 4,719 3 E-0 4 7,865 8 E-0 6 1,000 0 E-0 6 3.600 0

E 0 3 1.000 0 E 0 0 3.600 1 E 0 0 6.000 2 E-0 2 1.000 0 E-0 3 1.019 4 E 0 2 1.699 0 E 0 0 2.831 7 E-0 2 3.600 0 E-0 3 9.999 7

E 0 2 2.777 7 E-O l 1.000 0 E 0 0 1.666 7 E-0 2 2,777 8 E-0 4 2,831 6 E 0 1 4,719 4 E-O l 7,865 6 E-0 3 9,999 7 E-0 4 5.999 8

E 0 4 1.666 6 E 0 1 6.000 0 E 0 1 1.000 0 E 0 0 1.666 7 E-0 2 1.699 0 E 0 3 2.831 6 E 0 1 4.719 4 E-O l 5.999 8 E-0 2 3.599 9

E 0 6 9,999 7 E 0 2 3.600 0 E 0 3 6,000 0 E 0 1 1.000 0 E 0 0 1,019 4 E 0 5 1,699 0 E 0 3 2.831 6 E 0 1 3,599 9 E 0 0 3,531 4

E 0 1 9,809 6 E-0 3 3.331 5 E-0 2 5,885 9 E-0 4 9,809 8 E-0 6 1,000 0 E 0 0 1.666 7 E-0 2 2.777 8 E-0 4 3.331 4 E-0 5 2.118 9

E 0 3 5,885 7 E-O l 2.118 9 E 0 0 3.531 5 E-0 2 5,885 9 E-0 4 6,000 0 E 0 1 1,000 0 E 0 0 1.666 7 E-0 2 2,118 9 E-0 3 1,271 3

E 0 5 3,531 4 E 0 1 1.271 4 E 0 2 '.118 9 E 0 0 3.531 5 E-0 2 3.600 0 E 0 3 6.000 0 E 0 1 1.000 0 E 0 0 1.271 3 E-O l 1,000 0

E 0 6 2.777 8 E 0 2 I.OOO O E 0 3 1,666 7 E 0 1 2.777 9 E-O l 2,831 7 E 0 4 4,719 5 E 0 2 7,86* 8 E 0 0 1,000 0 E 0 0 T O CONVER T A

VALU E FROM

A GIVE N UNI T T O A

DESIRE D UNIT , MULTIPL YTH E GIVE N VALU E B YTH E FACTO ROPPOSIT E TH E GIVE N UNIT S AN D BENEAT H TH E DESIRE D UNIT , NOT E THA T E-XXMEAN S 1 0 T O TH E -XXPOWER ,]>•'•



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# w CONVERSIO N FACTOR S - CONCENTRATION , DENSIT Y DESIRE D UNIT S GRA M P£ RM

GPE RMICROGRAM MICROGRAM

GRAI N

PE ROUNC E PE RL B PE RGRA M PE RL B PE R C UMETE RC UMETE RPE RC UM PE RLITE RC UF T C UF T C UF T C UF T C uMETE R GIVE N UNIT S

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& GRA

M PER CUMETE R M GPE R C UMETE R MICROGRA

M PERC UM MICROGRA

M PERLITE R GRAI N PE R CUF T OUNC E PER CUF T L B PER C UF T GRA M PER CUF T L B PER CU METE R 1.000 0 E 0 0 I.OOOO E-0 3 1.000 0 E-0 6 9.999 7 E-0 4 2.288 3 E 0 0 

### l.oo u E 0 3 1.601 8 E 0 4 3.531 4 E 0 1 4.535 9 E 0 2 1.000 0

E 0 3 1.000 0 E 0 0 1.000 0 E-0 3 9,999 7 E-O l 2.288 3 E 0 3 1.00 U E 0 6 1.601 8 E 0 7 3.331 4 E 0 4 •.535 9 E 0 5 1.000 0

E 0 6 1.000 0 E 0 3 1.000 0 E 0 0 9.999 7 E 0 2 2.288 3 E 0 6 1.001 1 E 0 9 1.601 8 E 1 0 3,531 4 E 0 7 4.535 9 E 0 8 1.000 0

E 0 3 1.000 0 E 0 0 1.000 0 E-0 3 1,000 0 E 0 0 2.288 4 E O S 1.001 2 E 0 6 1.601 9 E 0 7 3.331 5 E 0 4 4.536 0 E 0 5 4,370 0

E-O l 4.370 0 E-0 4 4,370 0 E-0 7 4,369 9 E-0 4 1,000 0 E 0 0 4,375 0 E 0 2 7,000 0 E 0 3 1,543 2 E 0 1 1.982 2 E 0 2 9.988 5

E-0 4 9.988 5 E-0 7 9.988 5 E-1 0 9.988 3 E-0 7 2.283 7 E-0 3 1.000 0 E 0 0 1.600 0 E 0 1 3.527 4 E-0 2 4.330 7 E-O l 6.242 8

E-0 5 6.242 8 E-0 8 6.242 8 E-l l 6,242 7 E-0 8 1,428 6 E-0 4 6.250 0 E-0 2 1.000 0 E 0 0 2.204 6 E-0 3 2,831 7 E-0 2 *.83l 7

E-0 2 *.83l 7 E-0 5 '.831 7 £.0 8 ',831 6 E>0 9 6,479 9 E-0 2 <.B34 9 E 0 1 4,335 9 £ 0 2 1,000 0 £ 0 0 1.284 4 E 0 1 2.204 6

E-0 3 2.204 6 E-0 6 2,204 6 E-0 9 2,204 6 E-0 6 3.U44 9 E-0 3 2,207 2 E 0 0 3,931 4 E 0 1 7.783 5 E-0 2 1.000 0 E 0 0 T O CONVER T A

VALU E FRO M

A GIVE N UNI T T O A

DESIRE D UNIT , MULTIPL YTH E GIVE N VALU E BYTH E FACTO ROPPOSIT E TH E GIVE N UNIT S AN D BENEAT H TH E OFSIRE D UNIT . NOT E THA T E-X XMEAN S 1 0 T O TH E -X XPOWER . 

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0 5

CONVERSIO N FACTOR S - DEPOSITIO N RAT F (SHOR T TON .STAT . MILE ) DESIRE D UNIT S G

M PE RS Q K

GPERS Q M

GPERS Q TON

PERS Q O Z PERS Q L B PE RG M PERS Q M

GPE RS Q M PE RM O K M PERM O C M PERM O M I PE RM

O F T PERM

O ACR E PERMO F T PERM O I N PERM O GIVE N UNIT S
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M PE RS O M PE RM O K GPE RS Q K M PE RMO M GPE RS Q C M PE RM O TON PE RS O M I PE RMO O Z PE RS O F T PE RMO L B PE R ACR E PERMO ' G M PE RS O F T PE RMO M GPERS O I N PERMO 1,000 0 E 0 0 1,000 0 E-0 3 1.000 0 E 0 1 3.502 6 E-O l 3,091 9 E 0 2 1.120 8 E-O l 1,076 4 E 0 1 1.550 0 E 0 0 1.000 0

E 0 3 I.ooo o E 0 0 1.000 0 E 0 4 3.302 6 E 0 2 3.051 5 E 0 5 1.120 8 E 0 2 1.076 4 E 0 4 1.550 0 E 0 3 1.000 0

E-O l 1.000 0 E-0 4 1.000 0 E 0 0 3.302 6 E-0 2 3.051 5 E 0 1 1.120 8 E-0 2 1,076 4 E 0 0 1.550 0 E-O l 2.855 0

E 0 0 2.853 0 E-0 3 2.855 0 E 0 1 1.000 0 E 0 0 8.712 0 E 0 2 3.200 0 E-O l 3.0T3 1 E 0 1 4.425 2 E 0 0 3.277 1

E-0 3 3.277 1 £.0 6 3.277 1 E-0 2 1.147 8 E-0 3 1,000 0 E 0 0 3,673 1 E-0 4 3.327 4 E-0 2 5.079 5 E-0 3 8.921 8

E 0 0 8,921 8 E-0 3 8.921 8 E 0 1 3,125 0 E 0 0 2.722 5 E 0 3 1,000 0 E 0 0 9,603 3 E 0 1 1.382 9 E 0 1 9.290 3

E-0 2 9.290 3 E-0 5 9.290 3 E-O l 3.254 1 £.0 2 2,834 9 E 0 1 1,041 3 E.0 2 1,000 0 E 0 0 1,440 0 E.0 1 6,451 6

E-O l 6,451 6 E-0 4 6,451 6 E 0 0 2,259 8 E-O l 1.968 7 E 0 2 7,231 3 E-0 2 6,944 4 E 0 0 1,000 0 E 0 0 T O CONVER T A

VALU E FROM

A GIVE N UNI T T O A

DESIRE D UNIT , MULTIPL YTH E GIVE N VALU E B YTH E FACTO ROPPOSIT E TH E GIVE N UNIT S AND BENEAT H TH E DESIRE D UNIT . NOT E THA T E-XXMEAN S 1 0 T O TH E -X XPOWER .

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# i CONVERSIO N FACTOR S - PRESSUR E DESIRE D UNIT S MILLIBA RBA R GIVE N UNIT S MILLIBA R
BA R
ATMOSPHER E
DYNE S PE RS O C M K G PE RS O C M LB S PE RS Q I N M M MERCUR Y
I N MERCUR Y ATMOSPHER E DYNE S K GLB S M M MERCUR YI N

MERCUR Y PE RS Q C M

PE RS Q C M

PE RS Q I N 1.000 0 E 0 0 1.000 0 E 0 3 1.013 3 E 0 3 1,000 0 E-0 3 9.806 6 E 0 2 6,894 7 E 0 1 1.333 2 E 0 0 3.386 4 E 0 1 1,000 0

E-0 3 1.000 0 E 0 0 1.013 3 E 0 0 1.000 0 E-0 6 9,806 6 E-O l *,894 7 E-0 2 1.333 2 E-0 3 3.386 4 E-0 2 9.869 2

E-0 4 9.869 2 E-O l 1.000 0 E 0 0 9.869 2 E-0 7 9.678 4 E-O l 6.804 6 E-0 2 1.315 8 E-0 3 3,342 1 E-0 2 1.000 0

E O S 1.000 0 E 0 6 1.013 3 E 0 6 1.000 0 E 0 0 9.806 6 E 0 5 6.894 7 E 0 4 1.333 2 E 0 3 3.386 4 E 0 4 1.019 7

E-0 3 1.019 7 E 0 0 1.033 2 E 0 0 1.019 7 E-0 6 1.000 0 E 0 0 7.030 7 E-0 2 1.359 5 E-0 3 3.433 2 £-0 2 1.450 4

E-0 2 1.450 4 E 0 1 1.469 6 E 0 1 1.450 * E-0 5 1.422 3 E 0 1 1.000 0 E 0 0 1.933 7 E-0 2 4.911 5 E-O l 7.500 6

E-O l 7.500 6 E 0 2 7.600 0 E 0 2 7,500 6 £.0 4 7.353 6 £ 0 2 5,171 5 E 0 1 1.000 0 E 0 0 2.540 0 E 0 1 2.953 0

E-0 2 2.933 0 E 0 1 2.992 1 E 0 1 *.93S 0 E-0 9 ..899 9 E 0 1 2,036 0 E 0 0 4.937 0 E-0 2 1.000 0 E 0 0 T__. C i?2 V §? I * y. L !.!« FR 2!

_A GIVE N

UN, T T 0 A

WSIRE D UNI T » MULTIPL YTH E GIVE N VALU E B YTH E FACTO ROPPOSIT E TH E GIVE N UNIT S AN D BENEAT H TH E OESlRE D UNIT . NOT E THA T E-X XMEAN S 1 0 T O TH E -X XPOWER .

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## 3 CONVERSIO N FACTOR S - TIM E DESIRE D UNIT S SECOND GIVE N UNIT S SECOND
MINUT E
HOUR
WEEK
MONT H (28 )
MONT H (30 )
MONT H (31 )
YEA R(365 )
YEA R(366 ) MINUT E HOU R WEE K MONT H (28 ) MONT H (30 ) MONT H (31 ) YEA R(365 ) YEA

R(366 ) 1,000 0 E 0 0 1,666 7 E-0 2 2,777 8 E-0 4 1.633 4 E-0 6 4,133 6 E-0 7 3.858 0 E-0 7 3.733 6 E-0 7 3,171 0 E-0 8 3.162 3 E-0 8 6,000 0

E 0 1 1,000 0 E 0 0 1.666 7 E-0 2 9.920 6 E-0 5 2.480 2 E-0 5 2.314 8 E-0 3 2.240 1 E-0 5 1.902 6 E-0 6 1.897 4 E-0 6 3.600 0

E 0 3 6.000 0 E 0 1 1.000 0 E 0 0 5.952 4 E-0 3 1.488 1 E-0 3 1.388 9 E-0 3 1.344 1 E-0 3 1.141 6 E-0 4 1.138 4 E-0 4 6.048 0

E 0 5 1.008 0 E 0 4 1.680 0 E 0 2 1.000 0 E 0 0 2.300 0 E-O l 2.333 3 E-O l 2.238 1 E-O l 1.917 8 E-0 2 1.912 6 E-0 2 2.419 2

E 0 6 4,032 0 E 0 4 6,720 0 E 0 2 4,000 0 E 0 0 1,000 0 E 0 0 9.333 3 E.0 1 9,032 3 E-O l 7,671 2 E-0 2 7,650 3 E-0 2 2.392 0

E 0 6 4,320 0 E 0 4 7,200 0 E 0 2 4,285 7 E 0 0 1.071 4 E 0 0 1.000 0 E 0 0 9.677 4 E-O l 8.219 2 E-0 2 8.196 7 E-0 2 2.678 4

E 0 6 4.464 0 E 0 4 7,440 0 E 0 2 4,428 6 E 0 0 1,107 1 E 0 0 1,033 3 E 0 0 1,000 0 E 0 0 8,493 2 E-0 2 8,469 9 E-0 2 3.153 6

E 0 7 9,256 0 E 0 5 8,760 0 E O S 9.214 3 E 0 1 1.303 6 E 0 1 1.216 7 E 0 1 1,177 4 * E 0 1 1,000 0 E 0 0 9,972 7 E-O l 3,162 2

E 0 7 5.270 4 E 0 5 8,784 0 E O S 5,228 6 E 0 1 1,307 1 E 0 1 1.220 0 E 0 1 1.180 6 E 0 1 1.002 7 E 0 0 1,000 0 E 0 0 TO CONVERT A

VALU E FRO M A GIVE N UNI T T

O A DESIRE D UNIT , MULTIPL YTH E GIVE N VALU E B YTH E FACTO

ROPPOSIT E TH

E GIVE N UNIT S AN D BENEAT H TH

E DESIRE D UNIT . NOT E THA T E-X XMEAN S 1 0 TO TH

E .X XPOWER .

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_A A r T _TVfc N I If . Tr . rfATT 1 1 <• . T) KI I OWAT - 1 <lN|T )
MF5*WAT T (INT ) C* l (INT ) PE R r ,E C BT U PE R "Uf i BT u PE R n R JOULE S AB S PE R SE C WAT T(A.T5 )
ELECT . HORSEPOWE R A M T ( I •- ; TI

• " 1. 1 I,, jr. on F . 3 l.COO O E 0 6 4.1.7 * F T O
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 0 2 K1 1 O'-'A ' r

(I'l l 1
L - 0 < l.OOU O E O M 1 .OO'i . t o < 4.1_' 6 _-0 . 1,75M B E-0 2 2,"31. 3 E - 0 . <c.99H l E-O i -..<>9H 1 i>O i 7.45* . E-O l .FC.n . A Tr I 1 M T1 l.O'KJ O 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-11 7 9.998 1 F-0 7 9.993 1 E-0 7 7.4*>8 6 E-0 4 CAI . < I 'I Tj t'F. R Sf C 2 . 3 »n n E-' U 2,'ina n fc' " 2 2.3• < . 0 E «> 5 l.:i')o o F . *»•• ) 4 . 2'IO O E M O 7,o;)o n E-i ? 2.3'W 5
2.3H7 5 E-O l 1.7H1 1 E " 2 iiT U PE R

5.6.5 7 E-0 2 5,685 7 E 0 1 5 . 6 .5 7 E 0 4 «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 BT U

MJ M P1 R 3.411 4 E 0 0 3.411 4 E 0 3 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 0 0 2.544 4 E 0 3 JOULE S AB S WAT T (ABS ) ELECT .

PE R SE C HORSEPOWE R 1,340 7 E-0 3 1.000 2 F 0 0 1.000 2 £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 I.OOO O E 0 0 7.460 0 E 0 2 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 1.340 7

E 0 0 1,340 7 E 0 3 5,614 3 E-0 3 2,358 1 E-0 2 3.930 1 E-0 4 1,340 5 E-0 3 1.340 5 E-0 3 1.000 0 E 0 0 TO CQNvrR T A\/A| U F FRO M fl _tvt NU' U 1 T J ADESTRF ^ JNlT , MULTIPL Y TH E GIVE NVALU E » Y TH E FACTO R OPPOSIT E TH E GIVE N UNIT S AN O BENFAT H MF . JFStRE D UNIT . NOT r . T-\M E-X X .TA'. S 1 0 TO T . _-X X POWER ,

### V in

S O 

## N

: « CONVERSIO N FACTOR S - ENERGY , WORK DESIRE D UNIT S ERGDyNE-C M GfVE N UNIT S ERG
DYNE-C M
AB S JOUL E
CA L (INT )
CA L (15 )
INT KW.H R
AB S KW-H R BT U AB S JOUL E CA L (INT ) CAL (15 ) IN T KW-H RAB S KW-H RBT U 1,000 0 E 0 0 1.000 0 E 0 0 1.000 0 E 0 7 4.186 8 E 0 7 4.185 5 E 0 7 3.600 7 E 1 3 3,600 0 E 1 3 1.055 1 E 1 0 1.000 0

E 0 0 1.000 0 E 0 0 1.000 0 E 0 7 4.186 8 E 0 7 4.185 5 E 0 7 3.600 7 E 1 3 3,600 0 E 1 3 1.055 1 E 1 0 1.000 0

E-0 7 1.000 0 E-0 7 1.000 0 E 0 0 4.186 8 E 0 0 4,185 5 E 0 0 3,600 7 E 0 6 3.600 0 E 0 6 1.055 1 E 0 3 2.388 4

E-0 8 2.388 4 E-0 8 2.388 4 E-0 1 1.000 0 E 0 0 9.996 8 E-O l 8.600 0 E 0 5 8.598 4 E 0 9 2.520 0 E 0 2 2.389 2

E-0 8 2.389 2 E-0 8 2.389 2 E-O l 1.000 3 E 0 0 1.000 0 E 0 0 8,602 7 E 0 5 8,601 1 E 0 5 2.520 8 E 0 2 ' 2,777 3

E-1 4 2,777 3 E-1 4 2.777 3 E-0 7 1.162 8 E-0 6 1.162 4 E-0 6 1.000 0 E 0 0 9.998 1 E-O l 2.930 2 E-0 4 2,777 8

E-1 4 2,777 8 E-1 4 2,777 8 E-0 7 1.163 0 E-0 6 1.162 6 E-0 6 1.000 2 E 0 0 1.000 0 E 0 0 2.930 7 E-0 4 9.478 1

E-l l 9,478 1 E-l l 9.478 1 E-0 4 3.968 3 E-0 3 3,967 1 E-0 3 3.412 8 E 0 3 3.41Z I E 0 3 1.000 0 E 0 0 T O CONVER T A

VALU E FROM

A GIVE N UNI T T O A

DESIRE D UNIT , MULTIPL YTH E GIVEN VALU E B YTH E FACTO ROPPOSIT E TH E GIVE N UNIT S AN D BENEAT H TH E DESIRE D UNIT . NOT E THA T E-X XMEAN S 1 0 T O TH E -X XPOWER .

# m • a

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CONVERSIO N FACTOR S - ENERG YPE RUNI T ARE A DESIRE D UNIT S LANGLE YCA L (15 ) BT UIN T KW-H RAB S JOULE S PE RS Q C M

PE RS O F T PE RS Q M PE RS O C M GIVE N UNIT S LANGLE Y
CA L (15 ) PE RS O C M BT U PE RS Q F T IN T KW-H R PE RS Q M AB S JOULE S PE RS O C M I.OOO O E O O 1.000 0 E 0 0 2,713 3 E-O l 8,602 9 E 0 1 2.389 2 E-O l 1,000 0

E 0 0 1.000 0 E 0 0 2.713 3 £-0 1 8.602 9 E 0 1 2.389 2 E-O l 3.685 5

E 0 0 3,685 5 E 0 0 1,000 0 E 0 0 3,170 6 E 0 2 8.805 4 E-O l 1.162 4

E-0 2 1.162 4 E-0 2 3.134 0 E-0 3 1.000 0 E 0 0 2.777 2 E-0 3 4.185 5

E 0 0 4,185 5 E 0 0 1,135 7 E 0 0 3,600 7 E 0 2 1,000 0 E 0 0 T O CONVER T A

VALU E FRO M

A GIVE N UNI T T O A

DESIRE D UNIT , MULTIPL YTH E GIVE N VALU E B YTH E FACTO ROPPOSIT E TH E GIVE N UNIT S AN O BENEAT H TH E OESIRE DUNIT . NOT E THA T E-X XMEAN S 1 0 T O TH E -X XPOWER .

a e w o o U l*••* • 0 0

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I ••••:• CONVERSIO N FACTOR S - POWE RPE RUNI T AREA (CA L AR E 1 5 DEG ) DESIRE D UNIT S CA L PE RS Q CA L PE R5 Q LANr,LE YCA L PE RS O BT UPE RS Q BT UPE RS Q AB S WAT T M PE RSE C C

M PE RMI N

PE RMI N

CM PE RDA

y F T PE RMI N

F T PE RDAYPE RS Q CM GIVE N UNIT S CA L PE RS O M PE RSE C CA L PE RS O C M PE RMI N LANGLE Y PE RMI N CA L PE RS O CM PE RDA

y BT UPE RS C F T PE RMI N BT UPE RS O F T PE RDAY AB S WAT T PE RS Q CM I.OOO O E 0 0 1.666 7 E 0 2 1.666 7 E 0 2 1,157 4 E-O l 4,522 2 E 0 1 3.140 4 E-0 2 2.389 2 E 0 3 6.000 0

E-0 3 1.000 0 E 0 0 1.000 0 E 0 0 6.944 4 E-0 4 2.713 3 E-O l 1.884 3 E-0 4 1.433 5 E 0 1 6.000 0

E-0 3 I.OOO O E 0 0 I.OOO O E 0 0 6,944 4 E-0 4 2.713 3 E-O l 1.884 3 E-0 4 1.433 3 E 0 1 8.640 0

E 0 0 1.440 0 E 0 3 1.440 0 E 0 3 1.000 0 E 0 0 3.907 2 E 0 2 2.713 3 E-O l 2.064 3 E 0 4 2.211 3

E-0 2 3.685 5 E 0 0 3,685 5 E 0 0 2,559 4 E-0 3 1,000 0 E 0 0 6,944 5 E-0 4 5,283 3 E 0 1 3,184 3

E 0 1 5,307 1 E 0 3 5.307 1 E 0 3 3,685 5 E 0 0 1.440 0 E 0 3 1.000 0 E 0 0 7,607 9 E 0 4 4.185 5

E-0 4 6,975 8 E-0 2 6,975 8 E-0 2 4,844 3 E-0 5 1.892 8 E-0 2 1.314 4 E-0 5 1,000 0 E 0 0



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.•-Sf e *o > T O CONVER T A VALU E FRO M

A GIVE N UNI T T O A

DESIRE D UNIT , MULTIPL YTH E GIVE N VALU E B YTH E FACTO ROPPOSIT E TH E GIVE N UNIT S AN D BENEAT H TH E 0ESI3E D UNIT. ' NOT E THA T E-X XMEAN S 1 0 T O TH E -XXPOWER .



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