Streeter & Phelps, 1925

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UNITED STATES PUBLIC HEALTH SERVICE-PUBLIC REALTH BULLETIN No. 146

FEBRUARY, 925

A STUDY OF THE POLLUTION ANDNATURAL PURIFICATION OF

THE OHIO RIVER111. FACTORS CONCERNED IN THE PHENOMENA OFOXIDATION AND REAERATION

BYH.W. TREETER, anitary Engineer,and EARLE B.PHELPS, onsultant,

U.S.Public Health Service

PREPARED BY DIRECTION OF THE SURGEON GENERAL

Reprinted by U.S. Department of Health, Education,& elfarePUBLIC AEALTB SERVICE

1958


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CONTENTSPage

LIST OF TABLESTableNO1 Aver age resul ts, by months, of l aboratory determnati ons of di ssol ved oxygen at var i ous sampl i ng stati ons in the Ohi o Ri ver andtr i butari es, together w t h col l ateral data . . . . . . . . . . . . . . . . . . . . . . .2 Factors in resul tant oxygen f ormul a (1) obtai ned f r om data inTabl e No. 1---------------------_--------_----_----------------3. Deri ved val ues of Kz at 20C. ( f r omTabl e No. 2) - - - _ _ _ _ _ - - - - - - - _4. Reduct i on i n oxygen demand bet ween Ohi o Ri ver stati ons Nos.475and 455,as observed and as corrected to a uni f orm basis of t i meequival ent to 24 hours and t emper ature 20C _ _ - _ _ _ _ _ - _ _ _ - _ _ _ _ _5. Aver age rates of reaerat i on, in parts per ml l i on of di ssol ved oxygen,per mle of ri ver l ength, observed in desi gnated stretches of theOhi o Ri ver dur i ng specif i ed mont hs of 1914 and 1915 _ _ _ _ _ _ _ _ _ _ _6.Rel ati on between the reaerati on coeffi cient (IC.), the mean depth(H)of the st r eamabove ext r eme l ow mater, and t he vel oci ty offlow (V), n certai n stretches of the Ohi o Ri ver _ _ _ _ _ _ _ _ _ _ _ _ _ _ _7 Val ues of *c and n in rel ati on KF= or vari ous stretchesHZof the Ohi o River-__-_______-_______________________-----------8. I ncrease i n mean vel oci ty of f l ow in cert ai n Ohi o Ri ver str etches,i n rel ati on to increase i n gage height _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _9. Rel ati on betmen mean i ncrease i n vel oci ty of f l owf or gi ven i ncreaseof gage hei ght in cert ai n Ohi o Ri ver str etches and correspondi ngval ues of n i n reaerati on f ormul a (K2H=eVn)_ _ _ _ _ _ _ _ _ _ _ _ _ _ _10. Val ues of i rregul ari ty factor for gi ven Ohi o Ri ver str et ches-- - - - -11. Rel ati ons between val ue of c i n reaerati on f ormul a (&H=cV*)and l owwater sl ope for two general t ypes of stretches of Ohi oRi ver - - - - - - - - _ - - - - _ - - - _ - - - - - - - - - - - - - - - - - - - - - - - - - _- - - - - - - - - - - - -

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12. Cal cul ated val ues of reaerati on coeff i ci ent in speci f i ed st retches oft he Ohi o Ri ver under di ff erent vel oci ty-of - f l owcondi t i ons- - - - - - - - -13. Mean depths (H) f Ohi o Ri ver above ext r eme l ow wat er i n certai nstretches corr espondi ng to gi ven vel ociti es of f l ow _ _ _ _ _ _ _ _ _ _ _ _ _ _14. Compar i son of t he observed di ssol ved oxygen content of the Ohi oRi ver at var i ous sampl i ng stati ons w t h correspondi ng val ues cal cu-l ated by t he use of f ormul ae (l), (7), nd (S) . . . . . . . . . . . . . . . . . . .15. Compar i son of cal cul ated m t h observed di ssol ved oxygen resul ts atspeci f i ed poi nts i n Tha mes Ri ver basi n, Connecti cut

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FigureNo.LIST OF FIGURES

PageA. Ma p of Ohi o Ri ver , show ng l ocati on of sampl i ng stati ons-- - -- - -- --1 Rel ati on between oxygen demand and t i me at 20 C _ _ _ _ _ _ _ _ _ _ - - - - _ _2. Rel ati on of val ues of deoxygenat i on coeff i cient (Kl)t vari ous t em3 Pl ot of D bdi n' s curve w t h oxygen val ues converted to ter ms of4 Fundament al f actors i nvol ved in di ssol ved oxygen changes i n st r eam5 Progressi ve change in di ssol ved oxygen bel ow an assumed poi nt ofpollution___-______---------_--_-____----____-----_--_-__------6-a. Ef f ects of known i ncrement s of di l uti on or pol l uti on in progessi vesati sfacti on of oxygen demand i n a tream. . . . . . . . . . . . . . . . . . . . . .6-b. Met hod of obtai ni ng hypothet i cal val ue of (L.) by averagi ng obser-vat i ons t aken at Stat i ons (A) and ( B) and br i ngi ng t hemto ac ommon basi s f or compar i son at Stati on ( B) _ _ - _ _ _ _ _ _ _ _ - - - _ - - _ -7. Rel ati on of val ues of reaerati on coeff i ci ent (Ka)t var i ous t emper a-tures to its val ue at 20 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - - - -8. Rel ati on between monthl y aver age vel ocit i es of f low in three typi calstretches of the Ohi o Ri ver and corr espondi ng val ues of t he reaera-ti on coeff i cient (KZ)ei ght ed by t he square of the st r eamdept h

(H)______---____-___________-____----___--_---------_--__-_-_9. Mean vel oci ti es of f l ow in certai n str etches of the Ohi o Ri ver cor-respondi ug to var i ous val ues of (H)_ _ - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _10. Rel ati on bet ween val ues of (n) n reaerati on f ormul a (KJ3?=cVn)and i nf l uence of i ncreasi ng ri ver st age upon vel oci ty of f l ow- - - - - _11. Rel ati on between l ow- wat er sl ope and val ues of (c) in reaerati onf ormul a ( 2H =cV") accordi ng to r oughness of channel - - - _- __- .12. Val ues o f - r e a ~ r ~ ~ i i o ~ e e ~ ~ ~ c ~ ~ - i ~ t ~ e t c h e sf Ohi oRi ver correspondi ng to var i ous actual mean vel oci ti es of f l ow infeet per second--_-___-_--_______________________-__---_--__--_13. Est i mated progressi ve changes in di ssol ved oxygen content of Ohi oRi ver under aver age reaerat i on condi t i ons prevai l i ng bel ow Pi tts-bur gh under l ow- wat erstages and s ummer t emperatures, assum ngdi f ferent i n ti al degrees of oxygen demand ( L a ) and oxygen sat u-rati on defi ci t (D.)-----_-------_---__-_---____________-------__14. Est i mated progressi ve changes in di ssol ved oxygen content of Ohi oRi ver under average reaerati on condi t i ons prevai l i ng bel ow Ci n-ci nnat i under l ow- wat er stages and s ummer t emperatures, assumi ng di f ferent i n ti al degrees of oxygen demand (La) nd oxygensaturat i on defi ci t (D.)--_---__-__--_______________________----_

peratbres to i ts val ue at 20"saturat i on

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UNITED STATES PUBLIC HEALTH SERVICE

PUBLIC HEALTH BULLETIN No. 146FEBRUARY, 925

A STUDY OF THE POLLUTION ANDNATURAL PURIFICATION OF

THE OHIO RIVER111. FACTORS CONCERNED IN THE PHENOMENA OFOXIDATION AND REAERATION

BYEl. W. TREETER, anitary Engineer, nd EARLE B. PHELPS, onsultant,

U. S. Public Health Service

PRE PARE D BY DIRECTION OF THE SURGEON GENERAL

Reprinted by U.S. Department of Health, Education,& elfarePUBLIC HEALTH SERVICE


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CONTENTS

LIST OF TABLESTableNo.1. Average resul ts, by mout hs, of l aboratory determnati ons of di s-sol ved oxygen at var i ous sampl i ng stati ons in the Ohi o Ri ver andtr i butari es, together w t h col l ateral dat a_ _ _ - - - _ - - - - _ - _ _ _ _ - - _ _ _ _ _2. Fact ors i n resul tant osygen f ormul a (1) obtai ned f r om dat a i nTabl e No. l--_--_--_--_------------________________------------3 Deri ved val ues of Kz at 20" C ( f r omTabl e No. 2) _ - _ - _ _ _ _ _ _ _ _ _ _ _ _ _4 Reduct i on i n oxygen demand bet ween Ohi o Ri ver st at i ons Nos. 475and 488, as observed and as corrected to a uni f orm basi s of t i meequi val ent to 24 hours and t emper ature 20" C _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _5. Average rates of reaerat i on, in part s per ml l i on of di ssol ved oxygen,per ml e of ri ver l ength, observed in desi gnated st retches of t he

Ohi o Ri ver dur i ng specif i ed mont hs of 1914 and 1915 _ _ _ _ _ _ _ _ _ _ _6. Rel ati on between t he reaerati on coeff i cient (9,)the mean dept h(H) , f t he st r eamabove ext r eme l ow water , and the vel oci ty off l ow (V), n certai n st retches of the Ohi o Ri ver _ _ _ _ _ _ _ _ _ _ _ _ _ _ _7. Val ues of 'I c " and ''n " i n relati on K,= .v" f or var i ous stretches

of the Ohi o River_--_---_---_-___----__--_-------_-_----~----~-8. I ncrease in me5n vel oci ty of fl ow i n cert ai n Ohi o Ri ver Stretches,in rel at i on to i ncrease in gage hei ght _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _9. Rel ati on betwen mean i ncrease in vel oci ty of f l owf or gi ven i ncreaseof gage hei ght i n certai n Ohi o Ri ver str etches and cor respondi ngval ues of " n " i n reaerat i on f ormul a (K2H' =eVn)_ _ _ _ _ _ _ _ _ _ _ _ _ _ _10.Values of " rregul ari ty " actor f or gi ven Ohi o Ri ver str et ches-- - - - -11. Rel ati ons between val ue of " c " in reaerati on f ormul a ( 2Hg=cVn)and l owwater sl ope f or two general t ypes of stretches of Ohi oRi v e r _ - - - - - - - - - - - - - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - - - - - - ~- - - - ~~- - - - - -( 11)

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IvPage12. Cal cul ated val ues of reaerati on coeff i cient in specif i ed stretches ofthe Ohi o Ri ver under di ff erent vel oci ty-of- f l owcondi t i ons__- - - - - - -13. Mean depths (H)f Ohi o Ri ver above ext r eme l owwater in certai nstretches correspondi ng to gi ven vel ociti es of f l ow_ _ _ _ _ _ _ _ _ _ _ _ _ _ _14. Compar i son of t he observed di ssol ved oxygen content of the Ohi oRi ver at var i ous sampl i ng stati ons w t h corr espondi ng val ues cal cu-

l ated by t he use of f ormul ae (l), ('i), and (5) . . . . . . . . . . . . . . . . . . .15. Compar i son of cal cul ated w t h observed di ssol ved oxygen resul ts atspeci f i ed poi nts in Tha mes Ri ver basi n, Connect i cutLIST OF FIGURES

FigureNOA. Map of Ohi o Ri ver , show ng l ocati on of sampl i ng stati ons-- -- - -- - -_1 Rel ati on between oxygen demand and t i me at 20"C _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _2 Rel ati on of val ues of deoxygenat i on coeff i cient (Kl)t vari ous t emperatures to i ts val ue at 20" C3. Pl ot of D bdi n' s curve w t h oxygen val ues convert ed to t er ms ofsaturat i on deficit_---_---_-__-____------__--_____--________----4 Fundament al f actors i nvol ved in di ssol ved oxygen changes i n st r eam5 Progressi ve change in di ssol ved oxygen bel ow an assumed poi nt ofpol l ut i on _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ - - - _ _ - _ _ - - - -S a . Ef fects of known i ncrement s of di l uti on or pol l uti on in progessi vesat i sfact i on of oxygen demand i n a st r eam_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -6-b. Met hod of obtai ni ng hypothet i cal val ue of ( L a ) by averagi ng obser-vat i ons t aken at Stat i ons (A) and ( B) and bri ngi ng t hemto ac ommon basi s for compari son at Stat i on (B) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -7. Rel ati on of val ues of reaerati on coeff i cient (Kz)t var i ous tempera-tures to its val ue at 20" C _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ - - _ _ _ - - _ _ _ -8. Rel at i on between monthl y average vel ocit i es of f l ow i n three typi calstretches Qf t he Ohi o Ri ver and corr espondi ng val ues of t he reaera-ti on coeff i cient (K1)ei ght ed by t he squar e of the st ream depth(H)--___------_______________-_-_--__---___-____-__--_------9. Mean vel ociti es of f low in cert ai n stretches of the Ohi o Ri ver cor-r espondi ng to var i ous val ues of ( H) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _10. Rel ati on bet ween val ues of (n) i n reaerat i on f ormul a ( I Z2HZ=cVn)and i nf l uence of i ncreasi ng ri ver st age upon vel ocit y of f l ow__ - __ -

11. Rel ati on between l ow- wat er sl ope and val ues of (c) in reaerati onf ormul a ( zHz=eV" ) accordi ng to roughness of channel _- - - _- __.12. Val ues of reaerati on coeffi cient (Kz)n certai n stretches of Ohi oRi ver correspondi ng to var i ous actual mea n vel ociti es of fl ow i nfeet per second--_--_______-_-__---_--_____-_______------____--13. Est i mated progressi ve changes i n di ssol ved oxygen content of Ohi oRi ver under average reaerati on condi t i ons prevai l i ng bel ow Pi tt s-bur gh under l ow- wat erstages and s ummer temperatures, assum ngdi f f erent in ti al degrees of oxygen demand (La) and oxygen satu-rati on defi ci t (D.)___-____-_-_-_____-----______---_____-__--___14. Est i mated progressi ve changes in di ssol ved oxygen content of Ohi oRi ver under aver age reaerati on condi t i ons prevai l i ng bel ow C n-ci nnat i under l ow- wat er stages and s ummer t emperatures, assumi ng di f ferent i n ti al degrees of oxygen demand (La) nd oxygensaturat i on defi ci t ( Da ) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

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F A W R S CONCERNED IN TH E PHENOMENA OF OXIDA*TION AND REAERATIONINTRODUCTION

The studi es presented in thi s report wer e made by t he Uni tedStates Publ i c Heal t h Servi ce duri ng the year s 1914 and 1915 as par tof a comprehensi ve survey of t he pol l ut i on and natural puri f i cati onof the Ohi o Ri ver , conduct ed under the supervi si on of Sur g. WHFrost. The scope and purposes of thi s survey as a whol e are out -l i ned in a previ ous publ i cati on: to whi ch r ef erence is made for adetai l ed descri pt i on of the Ohi o Ri ver , summar i es of its sources ofpol l ut i on, and measur ements of di scharge and vel oci ty, also forpresentat i on and di scussi on of the resul ts of bacteri ol oai cal exam -nati ons and chemcal anal yses other t han those deal i ng wth observa-ti ons on di ssol ved oxygen. These latter observat i ons, whi ch arepresented in the previ ous publ i cat i on onl y in the f or mof a basics ummar y w thout di scussi on, are regarded as bei ng suffi ci entl y di s-t i ncti ve in thei r si gni f i cance and in t he character of anal ysi s requi redto j usti fy thei r separate t reat ment in thi s suppl ement ary report .I n the caseof ast r eaml i ke t he Ohi o Ri ver , mpor t ant not onl y fori ts si ze and navi gabi l i ty but al so because i t is the sol e avai l abl e sourceof water suppl y for a l arge and gr owi ng popul at i on, permssi bl el imts of i ts pol l ut i on are gi ven in bacteri ol ogi cal rather t han chem-cal t erms; that is, t hey are f i xed by the permssi bl e l oad of bacteri alpol l ut i on whi ch may be pl aced upon the ri ver wth referenceto watersuppl i es rather t han by consi derat i ons i nvol vi ng t he exhaust i on oft he oxygen suppl y and physi cal nui sance. Neverthel ess, the possi -b l i ti es exi sti ng f or at l east a part i al depl et i on of the re, erve oxygensuppl y of t he ri ver, under condi t i ons of pol l ut i on al ready approach-inga cri ti cal stagefrom a bacteri al st andpoi nt in cert ai n zones, coul dhardl y be negl ected in any consi derat i on of the general probl emAn except i onal oppor t uni t y was presented, moreover, for a st udyof t he oxygen status of t he ri ver, and especial l y of its pur i ccat i oncapaci ty f r oman oxygen standpoi nt , in vi ew of t he avai l abi l i ty ofextensi ve col l ateral dat a rel ati ve to ri ver t emperat ure, di scharge,

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lBIanusmipt submitted June, 1924.'8.Study of the Pollution and Natural Purification of the Ohio River.aOp. dt., able No. 51, pp. 124-128.

11. Report onSurveYE and Laboratory Studies,Public Health Bulletin No. 143, Washington, 1924.


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2and t i mes of f l ow bet ween the var i ous sampl i ng stati ons, col l ectedin connect i on wth the investi gati on.T he general vi ewpoi nt of the studi es here descri bed was i nf l uencedto a l arge extent by t he newer concept i on of st r eampuri f i cati onwhi ch has resul ted f r omthe mar ked advances that have t aken pl acedur i ng recent years in the appl i cat i on of bacteri ol ogy and of physi caland bi ol ogi cal chemst ry to sani tary sci ence. Fi rst i n i mpor t ancehave been di scoveri es rel ati ve to t he general i ty of l aws governi ngthe death ratss of bacteri a, whi ch have emphasi zed the progressi vechmact er of t he compl ex bi ochemcal reacti ons concerned in streampnri f i cat i on, and hence t he cont rol l i ng i nf l uence exerted by the t i mefactor in such phenomena. O al most equal si gni f i cance has beent he evol ut i on of a newer bi ochemst ry of sewage and sewage-pol -l uted waters, wher ei n t he ol der set wage chemst ry, deal i ng w thni t rogen in i ts var i ous f or ms, has been l argel y repl aced, in pr ob-lems nvol vi ng the stabi l i ty of organi c matt er s of sewage ori gi n, bybi ochem cal met hods of st udy permt t i ng a di rect measur ement oft he oxi dat i on reacti ons mor e di rectl y rel ated to organi c stabi l i za-f i on processes. As exampl es of these met hods may be cited theI rel ati ve stabi l i ty and bi ochemcal oxygen demand tests, whi chare famliar to everyone who has f ol l owed the l i terature of sewagedur i ng recent years. Fi nal l y, t he great val ue of moder n physi calchemstry as an ai d in i nterpret i ng and appl yi ng to st r eamcondi-$i ons t he resul ts of bi ochemcal met hods of st udy shoul d be noted.Previ ous to the f oregoi ng devel opment s, studi es of t he sel f - pur i -f i cati onof st r eams had necessari l y been, in the mai n, empi r i cal ; thatis, t hey had compri sed the determnati on and recordi ng of actualcondi t i ons measur ed in anal yti cal t erms, w t hout any at t empt tof ormul ate resul ts in t erms of general pri ncipl es. Such a procedureis val uabl e as a matt er of hi stori cal record rel ati ve to B gi ven st r eamor l ocal condi t i on, but unf or tunatel y i t fails to gi ve data havi ngpos-sibi l i ti es of mor e general appl i cat i on. I n some cases general i zati onssuch as have been att empted f r omdata of thi s character have re-sul ted in ser i ous msconcept i ons of the rel ati ve i mpor t ance of di l u-t i on as a factor in the oxi dati on of wast e matt ers in st reams, ascompar ed wth that of reaerat i on, whi ch is of ten of f ar greatersi gni f i cance. A si mpl e exampl e wll i l l ustrate thi s poi nt.Accept ed st andards for a saf e di l ut i on rati o, based on certai nst r eamcondi t i ons, especial l y in Massachuset t s, are f r oma mni mumof3.5 to a maxi mumof 6.0second- f eet of normal unpol l ut ed st r eamwat er per t housand of popul ati on cont r i but i nwsewage.The sewage of the D stri ct of Col umbi a has in s ummer a total bi o-chemcal oxygen demand equi val ent to 112gr ams per capi ta dai l y,or about 300 parts per ml l i on when corrected to a nor mal sewage

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3r oughl y 0. 15 second- f eet per t housand of popul at i on. These oxygendemand val ues, whi ch agree very closel y wth the f i gure, 100 gr amsper capi ta dai l y, gi ven by Pearse4 as a resul t of studi es of Chi cagosewage, may be t aken as bei ng fai rl y representat i ve for normaldomest i c sewage.Dur i ng the summer per i od, J une 1 to Oct ober 15, 1914, the meandi scharge of the Ohi o Ri ver at a poi nt i mmedi atel y bel ow Ci nci nnat irepresented a00w of 5.1 second- f eet per t housand of urban popul a-ti on in t he watershed above thi s poi nt , at whi ch poi nt t he averagedi ssol ved oxygen content observed was 57part s per ml l i on, or 68Fer cent saturati on. Ass um ng the nor mal summer oxygen contentof a theoreti cal l y unpol l uted Ohi o Ri ver t o be at the mean s ummersaturati on val ue, 82 part s per ml l i on, the draf t i mposed upon thenor mal di ssol ved oxygen content ob the ri ver to sati sfy the oxygendemand of the ur ban sewage al one woul d be represented, in thi scase, by t he di f f erence between 8.2and 5.7 parts, or 2.5 parts permllion. On thi s basis, the requi red di l ut i on, in t he absence of re-aerat i on, woul d be 300: 2.5, or 120: 1, amount i ng to a st reamflow of18.5 second- f eet per t housand of popul at i on. Si nce the f l ow wasactual l y but 5.1 second- f eet per t housand, i t woul d appear t hatdi l ut i on al one was r esponsi bl e f or about one-quart er, and r eaerat i onfor near l y three- quarters, f the total puri f i cati on of the ri ver t aki ngpl ace LI Po the poi nt in questi on. Wth a permssi bl e oxygen contentof t heOhi o Ri ver at this poi nt l ower t han the appr oxi matel y 70percent saturaki on f i gure observed dur i ngthe s ummer of 1914, hestreamf l owactual l y requi red woul d be reduced by even mor e than a propor -ti onate amount , as the relati ve quanti t i es of di ssol ved oxygen sup-pl i ed by r eaerat i on woul d be greater wth l ower saturahi on val ues inthe ri ver.The f oregoi ng exampl e not onl y i l l ustrates the great i mpor t anceof reaerat i on in the puri f i cati on of r unni ng st reams, but al so em-phasi zes the fal l acy of dependi ng sol el y upon mer e di l uti on as ameasur e of the oxi dati on of wast es di scharged i nto, l ow ng bodi esof water. An at t empt to appl y di l ut i on rati os, der i ved from ri vershavi ng great reaerat i on capaci t i es, to sl uggi sh st reams l i ke theChi cago drai nage canal , woul d unquest i onabl y l ead to seri ous error,as has been bor ne out by exper i ence wth a number of sl uggi sh canal s,whi ch have gi ven ri se to of fensi ve condi t i ons, hough not excessi vel ypol l uted f r oma st andpoi nt of ordi nary di l ut i on cri teri a.The devel opment of a better under st andi ng of the rel at i ons be-tween di l ut i on and reaerati on as f actors in streampuri f i cati on, andin fact our moder n concept i on of the overwhel m ng i mpor t ance ofdi ssol ved oxygen in det erm ni ng the power of natural bodi es ofwater to di gest and oxi di ze organi c pol l ut i ng mat ters, owes muc h to


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4the pi oneer wor k i n sewage bi o- chemst rycarri ed out by the Frank-l ands, McGowan, Lett s, Di bdi n, Adeney and thei r coworkers inEngl and, and to adaptati ons and modi f i cati ons of thei r met hods ofst udy by vari ous workers i n the Uni ted States, notabl y Bl ack andPhel ps, Hoover , Lederer , and Theri aul t. Whi l e no extended bi bl i og-raphy of the studi es above noted wll be presented in connect i onwth the present paper, a number of references coveri ng certai nspeci fi c poi nts wll be gi ven in the l ater text.Wth the ai d of the newer bi o-chemstry of sewage and of thequanti tati ve vi ew of the oxygen rel ati ons i n pol l uted st r eams whi chi t permts, i t has been possibl e to formul ate and test empi ri cal l y ageneral theory of st reampuri fi cati on f r o man oxygen standpoi nt ,usi ng for th s purpose thedata obtai ned in connecti onwth the Ohi oRi ver studi es. Before proceedi ng wth a presentati on and anal ysisof these data, t wll cl ari fy the subsequent di scussi on to outl i ne thi sunderl yi ng theory.

THEORETICAL DISCUSSIONThe capaci ty of a streamto recei ve and oxidi ze sewage dependsupon its oxygen resources. The condi ti on of a pol l uted streamatany t i me is the resul t of a balance between these resources and thedemand made upon t hemby the organi c pol l uti ng matter carr i edbyt he stream Thi s demand, bei ng the resul t of a sl ow bi o- chemcalreacti on, s, i n the absence of new pol l uti on, a progressivel y decreas-i ng one, and as the resources of the st r eamare composed in part of acont i nuous i nfl ux of oxygen f r o mthe atmosphere, the state of bal -ance whi ch determnes the moment ar y condi ti on of the stream isconstantl y changi ng. There are, therefore, t wo pri mary phases ofthe probl emnamel y, the actual , moment ar y condi t i on, and thedi recti on and extent of the exi sti ng changes, whi ch i ndi cate thefuture condi ti on. Fresh sewage, or exampl e, may contai nsome di s-sol ved oxygen, and, measured upon the oxygen scal e of nui sance,may be in the samemoment ar y condi ti on as a streamwhi ch has aboutcompl eted the work of oxi di zi ng organi c pol l uti on and contai ns thesame amount of resi dual di ssol ved oxygen. The di recti on of change,however , s enti rely di fferent and determnes the di sti ncti on betweenthet wo cases. The oxygen resources are comparabl e to the assets ofa balance sheet; the oxygen demand to the l i ab l iti es. The condi ti onof a strong sewage contai ni ng oxygen i s comparabl e, in f i nanci alterms, to one of moment ar y sol vency, wth avai l abl e cash, but wthexcessive obl i gati ons maturi ng on the mor r ow. A comprehensi vetheory of sel f-puri f i cati on must therefore deal wth the oxygendemand as wel as wth the oxygen resources, and must consi der therelati on of thevari ous factors of t i me, temperature and other physi -

i


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5cal condi t i ons to the rates of change of these t wo f undament al qdan-tities.

THE OXYGEN DEMAXD UPON A STREAMChanges in the di ssol ved oxygen content of a streamare inti-mat el y associ ated wth bi ochemcal changes. They are broughtabout pr i mar i l y by the oxi dat i on of organi c matt er di scharged i ntost r eams as soi l was h and as wastes. I n the presence of a suppl y ofoxygen, together wth cert ai n oxi di zi ng bacteri a and oxi di zabl e or-gani c matt er, progressi ve oxi dat i on and stabi l i zing of the organi cmat t er wll t ake pl ace.It has been s hown that , under exper i ment al condi t i ons appr oxi -mat i ng those prevai l i ng in a st r enm cont ai ni ng reserve di ssol vedoxygen, thi s reacti on is an order l y and consi stent one, proceedi ng ata measurabl e rate and accordi ng to the f ol l ow ng defi ni te l aw:The rate of biochemical oxidation of organic matter is propor-tional to the remaining concentrtu%m of unoxidiaed su6stance, eas-

ured in ferms of oxidizability.Thi s l aw, whi ch happens to be si ml ar to that whi ch def i nes thecourse of a monomol ecul ar reacti on: ma y be stated in i ts di f ferenti alf or mthus :

whi ch may be i ntegrated to the form-L'logr=Kt

L' bei ng t he i ni ti al and L t he h a 1 oxi di zabi l i ty, or oxygen demandof t he or gani c substance, in t erms of oxygen; t bei ng the el apsedt i me and K a constant coeffi ci ent, def i ni ng the rate at whi ch t he re-acti on proceeds. The val ue of IS: depends upon t he characher oforgani c matt er and upon the temperature.It wll be assumed for t he present that this rel at i on hol ds al sounder actual st reamcondi t i ons. Evi dence support i ng thi s assump-ti on wll be presented l ater in t he text (p. 40).Def i ni ng t he oxygen demand as t he total r emai ni ng oxi di zabi l i tyof t he subst ance present at any t i me, the l aw states that in equal1 Phelps, Earle B., Biochemistry of Sewage, VI I I , Int. Cong. Appl. Chem., XXVI , 251.'This state ment should be qualified to the extent of noting that little definite knowl-edge exista as to whether the law stated holds for periods of time longer than about 20

days. Experimental data bearing on this point are, in fact, somew hat meager for periodslonger than 10 days, though for shorter periods the most reliable evidence has beenconflrmatory.'The similarity of this law to that of monomolecular chemical reactions is probablyclue to the biochemical nature cd the phenomenon. If the reaction were strictly chemicalit woul d thearetically be more likely to follow the law of bimolecular reactions, as thetwo reacting substances, oxygen an d oxidizable organic matter, are both present inlimited amounts .

1

i

i


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6peri ods of t i me an equal proport i on of the remai ni ng oxygen de-mand wll be sati sfi ed. That i s , i f 20per cent of the in tial oxygendemand be satisfi ed in the first 24 hours, 20 per cent of the remai n-i ng demand wll be satisfi ed in the second 24 hours, and so on.(See fig 1 f or graphi cal i l l ustrati on.) Si nce the oxygen demand,as actual l y determned in the l aboratory, is gi ven in t erms of

di ssol ved oxygen, the rate of sati sfacti on of the demand, whi ch isdenoted by the te rm( -) is equi val ent to therate of oxygen de-pl eti on. If the di ssol ved oxygen content be expressed in t erms of

d L

saturati on defici t (Dl),ts rate of depl eti on is ($$)nd the fol lowi ng rel ati on therefore holds

- - =-L dDl =KLdt dtThe nature of the substances f ound in city sewage and the num-ber and ki nds of bacteri a present have been f ound to be sufficientl y


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7constant under var i ous condi t i ons to gi ve a fai rl y constant val ue of Kfor th s reacti on at a const ant t emperature. I ts val ue at 20 C,the t i me bei ng expressed in days, was det erm ned by Phel ps by t hemethyl ene bl ue reacti on f or t he sewage of Boston, 4 and l ater bydi rect determnati on of t he oxygen demand of t he sewage of Was h-i ngt on; and al so comput ed f r om resul ts obtai ned by Lederer 5 atChi cago in a compari son of t he di l uti on and sal tpeter i ncubati onmethods, usi ng methyl ene bl ue. F r om a l these data, val ues of Kin t he above equati on of approxi matel y 0.1were obtai ned or de-ri ved. Lat er wor k by Lederer and col l aborators6 has i ndi catedsome vari at i on of val ue of K f or di f ferent sewages, t hough thesedi f ferences are not str i ki ng. Val ues of the constant f or di f ferentorgani c i ndustri al wastes appear t o var y mor e, doubt l ess becauseof t he w del y var yi ng character of t he organi c matt er present insuch wastes, t hough the resul ts of recent studi es by Ther i aul t ? i ndi -cate that when tests are caref ul l y control l ed val ues of the const antsi ml ar to those for sewage are obtai ned for a wi de cl ass of i ndustr i alwastes. Val ues f or pol l uted ri ver water shoul d not vary great l yf r omthose for average sewage, si nce a maj or part of the oxi di zabl eorgani c mat t er present in such wat er has ts ori gi n in sewage. *For any part i cul ar sewage or si ml ar waste the val ue of t hevel oci ty const ant K s a f uncti on of the t emperature. The t empera-ture rel ati on has been f ound empi r i cal l y to be def i ned by t hef ormul a: _-E dTf-T)in whi ch (T' ) and (T)are the tlvo t emperatures, (K) and (K)t he correspondi ng val ues of t he vel oci ty const ant of t he reacti on,and 0 he t her mal coef f i ci ent, constant f or t he reacti on, whi ch ma ybe determ ned exper i mental l y.

The val ue of the t her mal coeff i ci ent 0 has been det erm ned exper i -ment al l y at Ci nci nnat i in connect i on wth the present studi es andal so by Phel ps in connecti on wth studi es at Bost on and at the' Phel ps, Earl e B. ,U. S. Geol. Sur vey, W.S Paper No. 229, Washi ngt on, 1909.sLederer , A, Jour. Inf. Ds . , Yol.XIY, 914, 482.eLeder er, A.,Am our. Pub]. Heal t h, Vol. V, 1015, p. 384.?Publ i c Heal t h Report s, Repri nt No 594 (19201,U. S. Publ i c Heal t h Servi ce, Wash-ington, D CZLater studies of t he val ue of K, mad e on waters of t he Chi cago drai nage canal , t haupper Illinois Ri ver, and t he Ohi o Ri ver at Ci nci nnati , have gi ven resul ts cl osel y COD-f i rm ng thi s st atement . Th e stuai es on Ohi o Ri ver water , whi ch wer e in progress att he t i me of fi nal revi si on of th s t ext , have i nvol ved probabl y t he most el aborate andrarcfull y contr ol l ed seri es of tests t hus far made of the f orm and const ant s of t he 031-dat i on cur ve, empl oyi ng three separate t emper atur es of i ncubati on, So C. , 20" C. and30" C For peri ods of t i me up to about 30 dags these curves have been f ound to f ol l owcl osel y t he l aw st ated on page 6, and thei r (K) al ues at 20" C to agree w t hi n from.5 to 10 per cent w t h the ral ue, 0.1, empl oyed iu connecti on w t h the present t est.


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Hygi eni c Laboratory at Washi ngt on. These val ues are gi ven bel owas f ol l ows:1. Cincinnati M i l l Creek water) : Val uo of eTemperature range,10 C.to 20" C _ _ - _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _.0524Temperature range,20 C. o 37.5 C _ _ _ _ _ _ _ _ _ - _ _ _ _ _ - _ _ _ _ _ - _ - .0504

Temperature range, 20" C. to 37.5" C _ _ _ _ _ _ _ _ _ _ - __ - _ _ - _ _ _ _ _ - .0415Temperature range,15" C.to 24.5 C . . . . . . . . . . . . . . . . . . . . . . . - - 1.0441Temperature range, 24.5" C.to 37" C _ _ _ _ _ _ _ - _ _ _ _ _ - _ _ _ _ _ - _ - - - -1.01

2. Boston (sewage, ethylene blue method) :3. Hygienic Laboratory (nitrate method) :

Average, excluding value marked (*) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .For t he pur pose of t he present di scussi on we wll adopt t he meand u e of 1.047, obtai ned f r om the data gi ven in th s tabl e, af terel i mnat i ng t he vd ue of 1.01, vhi ch is obvi ousl y out of har monywth t he others. The vari at i on in t he val ue of (K) t di ff erent t emperatures, as def i ned by a val ue OP 0 equal to 1.047is i l l nstratedin Fi gur e No. 2, by the l i ne show ng t he rel ati on of IC val ues atvar i ous t emper atures to i ts val ue at 20" C. Conversi on of t he KTal ues f r om one t emper ature to another may be readi l y made by

=leans of a si ml ar chart .a s stated on page 7 ( f ootnote S), f urther studi es of the t emperat ure rel ati ons of ( R) for Ohi o Ri ver water at Ci nci nnat i ,Qhi o, were in progress at the Ci nci nnat i l aboratory of t he Publ i cHeal t h Servi ce at t he t i me of f i nal revi si on of the present text. F r omt he resul ts of these studi es avai l abl e up to that time, i t appearedChat val ues of t he t her mal correcti on f actor 0 woul d be obtai nedagreei ng cl osel y wth t he mean Tval ne, 1.047, s above der i ved, assumi ng the experi mcntal val ues of (IC) at the di f ferent i ncubat i on t emperatt i res to be comput ed in t. he same manner as in t he present case.T he met hod of comput at i on t hus f ol l owed has consi sted of cal cu-l at i ng, f or t he oxi dati on curve obtai ned at each respecti ve i ncubati ont emperature, t he percent age of t he 20- day oxygen demand at thatt emperature r emai ni ngat successi ve i nterval s of t i me up to 20 days.These val ues, when pl otted as ordi nates agai nst i ncubati on t i mes,using seml ogar i t hmc paper , def i ne a strai ght l i ne havi ng a sl opeequal to (IC. Thi s procedure carr i es an assumpt i on that, for allpract i cal purposes, the oxygen demand sati sfi ed in 20 days is equi v-al ent to t he total avai l abl e oxygen demand (wth a val ue of K at20 C. equal to 01 it i s actual l y 99 per cent of t he tota). Thi sassumpt i on is substanti al l y correct f or t emperatures of 20" C. andupwar ds, but becomes l ess so as the t emper ature is di m ni shed bel ow20C., i nce at t he l ower t emperatures thetim r9qui red f or t he satis-f acti on of a l arge proport i on of t he total oxygen demand i s l ongert han at 20 degrees. Whe n t he studi es descri bed in the present textmeTe made, no basi s exi sted f or ext rapol at i ng oxido ' on curves

1.047


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9beyond a t i me of 20 days at any t emperature; hence, the coeffi cient(K) whether uncorr ectedat 20" C or corrected to its equi val ents atother temperatures, can hardl y be regarded as being wel l def i nedfor any peri od of t i me exceedi ng20 days. Thi s l i mti ng ti me, how-ever, usual l y is l ong enough for ordi nary purposes of cal cul ati on.

THE OXYGEN RESOURCES OF A STREAMUnpol l uted mater tends to hold i n sol uti on the max i mdmamount:of oxygen whi ch i t is capabl e of contai ni ng at the exi sti ng t empera-ture and part i al oxygen pressure of the atmosphere. Thi s is theso-cal l ed saturati on val ue and ranges at nor mal sea l evel baromet>r i cpressure f r omapproxi matel y 14mg. per l iter at j ust above f reezi ngto about 7.6mg. per liter at 30 C.I n pol l uted st reams the draft i mposed upon the di ssol ved oxygeemsuppl y by the progressi ve sati sfacti on of the oxygen demand reduces*The ctual saturation value dependa upon the partial solution pressure of oxygea imthe owrlyiag atmosphere, and is directly proportional to the percentage of oxygm in theovezlylng gas. Far normal atmoepherie air, the solution prmsure, and therefore the

a n - sa+n,.atinn valna ip o,,.,,.nrimmtnln -.xn4iNh a+- -mi-- -a+ - - ----I-*-- -L- -


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12in whi ch-D=t he requi red average concent rati on of di ssol ved oxygen ex-

B=t he uni f orm y di stri buted i ni ti al concent rat i on expressed ine=2.718.

pressed in per cent of saturati on, aft er t i me, t.t he same uni ts.

t=t he el apsed t i me si nce concent rati on (R) exi sted.L z t he i near dept h of t he col umn.a=t he di f fusi on coeffi ci ent, a const ant f or pure water, and a gi venThi s equat i on appl i es pri mar i l y to qui escent mater, but i t hasal ready been i ndi cated t hat t he eff ect of m xi ng is vi rtual l y todecreasethe ef fecti ve depth t hrough whi ch di f fusi on acts, so t hat the apFl 'i ca-t i on to t urbul ent waters i s permssi bl e, the depth t ermbei ng t heni ndetermnate.For the purposes of t he present di scussi on i t is desi red todet erm nethe rate of sol ut i on of oxygen under any stated condi t i ons. Thi s rateis der i vabl e f r omt he equat i on of condi t i on by di f ferenti ati on wi L hrespect to a vari abl e t i me. The actual operat i on need not be per -f or med, f or i t i s obvi ous that t he resul t wll be a compl ex expressi on

cont ai ni ng t he factor (1 -&,he i ni ti al saturat i on defi ci t, t oget herwth a compl ex t i me f uncti on. The rate of sol ut i on, theref ore, ispropor t i onal , among other thi ngs, to t he ini ti al saturat i on defi ci t, andt he proport i onal i ty factor i s itself a t i me functi on-i . e. , i t vari eswth t he ti me. At zero tim-i. e, at t he start- the rate is stri ctl ypropor t i onal to t he defi ci t.I n any st r eamhavi ng suff i ci ent t urbul ence to make reaerati on areal f actor in sel f -puri f i cati on, there i s suff i ci ent m xi ng tu br kgabout a fai rl y uni f orm condi t i on t hr oughout the 1-erti cal cross-secti on, so that at no t i me is t here mater i al vert i cal strati fi ca ' on.Such a condi t i onmay be r egarded as bei ng made up of shor t per i odsof qui escence f ol l owedby compl ete mxi ng, so that t he final di ssol vedoxygen val ue at t he end of any short per i od of qui escmce becomest h e initial,uni f orm y di str i buted vdue at the begi nni ng of the nextpcri od. Si nce the rate of sol ut i onat t he begi nni ng of any peri od isstri-ctlypropor t i onal to t he defi ci t at t hat t i me, t f ol l ovs that underthe assumed condi t i ons-and these are approxi matel y the condi t i onsmt w th- the rate of sol ut i on is proport i onal to t he exi sti ng satura-t i on defi ci t. Thi s is t he l aw of the vel oci ty of sol ut i on of sol i ds inwater , der i ved exper i ment al l yby Noyes and Whi tney. 14

gas ( oxygen) at const ant t emperature.

h

A * .-=-A W h 3 f - m ~ R.. Zeit f. ohvsik. Chem..23, 1897, p. 689.


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13The physi cs of reaerat i on phenomena have been. studi ed exten-si vel y by Adeney l5 and hi s coworkers , who have devel oped the fol-l ow ng f ormul a expressi ng the rate of reaerat i on of qui escent col -umns of wat er:

w=(100 m) (1 - e-p(8/v)t)where-w=amount of gas di ssol ved, expressed as percent age of saturat i on.w=ni ti al concentrati on.f=coeffi ci ent of escape of gas f r omthe l i qui d per unt of meaand vol ume.v=vol ume of l i qui d.a=area of surf ace.t =t i me of exposure.If thi s f ormul a be di f ferenti ated wth respect t o t i me (t) , i tbecomes-

whence t he rate of reaerat i on (g)s shown to be di rectl y pro-port i onal to the saturat i on defi ci t (100-w). It i s thus apparentthat whet her r eaerat i on be vi ewed as a phenomenon of di f fusi on orone of st r eam ng, bot h theori es l ead to t he same concl usi on asi egards t he f undament al i mpor t ance of the l aw of sol ut i on in deter-m ni ng t he rate of progressi on of t he reacti on.An exper i ment al conf i rmati onof thi s l amas appl i ed to t he sol u-t i on of atmospheri c oxygen by wat er was obt ai ned by D bdi n*6roma seri es of about 150 tests made in connect i on wth experi ment s onthe condi t i on of t he water in t he Ri ver Tl i ames, i n Engl and. H eexposed deaerated wat er in open vessel s f or per i ods of t i me rang-i ng f r o m 1 to 96 hour s, det erm ni ng t he di ssol ved oxygen at i n-t ermedi ate interval s. The resul ts obtai ned wer e pl ot ted in thef o r m of a curve, whi ch has been reproduced in LZ di ff erent f or min Fi gur e No. 3, t he ordi nates bei ng saturat i on defi ci t val ues pl ot-ted on a l ogar i t hmc scal e and t he absci ssae, correspondi ng timesf r omt he start i ng poi nt. I t is noted that t he pl otted observati onsl ie al most exactl y al ong a str ai ght li ne. Denot i ng the tim as ( t)and t he saturat i on def i ci t as (D)me have, t hen, that-

l og D ==-(c t +d)=Adeney, W E.Adeney, W E.,and Becker, H.G. Philosophical Ma gazine , vol. 38, 1919, pp. 317-338.Adeney, W E.,Leonard, A S. C., nd Richardson, A. Sci. Proc. Dub. Roy. Sac., vol.leMbdin, W. .. The Purification of Sewage and Water, 8d. ed., 1903, pp. 283-284

Sei. Proc. Royal Dublin SOC., 914.Philosophical Magazine, YO]. 42,1921, pp. 87-96.17, 922, pp. 19-28.

(Diaeram 91.


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14

U~G.o.0.5 t l PLOT OF VIBDIN'S CURVE WITH OXYGEN VALUESCONVERTEP TO TERM5 OF SATURATION DEFICIT

Notc;Curve taken from Dibdin's "Purification ofa6 Water and %wage': Viaqram 5,pp204-285.Formula:G-KPOA

0.3

0.2

0 IO 20 30 40 50 60 70 80 SOVALUE OF t - 7 - 1 ~ ~NHOURS FROM NITI L POINT'


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15t he const ant (c) bei ng t he slope. of the l i ne and (d) bei ng the i n-tercept on the (D) axi s. D f f erent i at i ng thi s equat i on wth re-

dDSi nce x)ef i nes t he rate of sol ut i on of oxygen in h ~ sfsaturat i on defi ci t, i t i s apparent t hat thi s rake is di rectl y pr opor-ti onal to the saturati on defi ci t (D) whi ch is in accordance w t ht. he general l aw of sol ut i on above stated.F r o m what has been previ ousl y st ated regardi ng t he rel at i on ofmechani cal mxi ng to di f f usi on and streamng as agenci es in t hereaerati on of f l ow ng bodi es of water, it natural l y f ol l ows t hat re-aerati on of st reams, whi l e condi t i oned pr i mar i l y by the rate of sol u-t i on of oxygen at t he water surf ace, is modi f i ed by t hose f actorswhi ch aff ect t he rapi di ty and thor oughness wth whi ch t he oxygen,once di ssol ved, is di str i buted t hroughout its depth. Thus i t wasf ound by Fai r 1? that at a gi ven saturat i on defi ci t val ue, t he rate ofreaerati on of a qui escent body of wat er is great l y accel erated merel yby t he mxi ng resul t i ng f r om i nduced wave acti on. I n Shef f i el d,Engl and, an acti vated sl udge pl ant f or sewage t reat ment has r e-cent l y been devel oped in whi ch the hi gh rate of aerat i on requi redf or oxi dat i on of the sewage is obtai ned enti rel y by a mechani calmxi ng devi ce. Exampl es of thi s ki nd, whi ch are numer ous, s howconcl usi vel y t he great i nf l uence exerted upon t he rate of reaerat i onof f l ow ng bodi es of water by those f orces of mxi ng and convect i onwhi ch ma y be s ummed up under t he ter mturbul ence. I n run-ni ng st reams the t urbul ence factor is hi ghl y vari abl e and pr oducescorrespondi ngl y var i ed effects upon reaerati on rates. I n a gi venst r eamstretch and under a gi ven condi t i on of f l ow where tke tur bu-l ence r emai ns fai rl y constant , t he rate of reaerat i on i s a di rectf unct i on of , and shoul d be closel y proport i onal to, t ho prevai l i ngoxygen saturat i on defi ci t. Under condi t i ons f ound in st reams, here-f ore, t he operati on of the l aw of sol uti on is f undament al , and vari a-t i ons in the rate of sol ut i on are gover ned l argel y by t hose physi calcharacteri sti cs of a gi ven st reamwhi ch cause di f ferent degrees ofturbul ence.

THE OXYGEN BALANCE I N A STRI$AMThe t wo opposi ng reacti ons, deoxygenat i on and r eaerat i on, t endal ways to come to a condi t i on of t emporary equi l i bri um If t hewater be nearl y oxygen- satur ated, and hi ghl y pol l uted, t here is aIDiseussion of paper by R. H. Gould, The area of water surface as a controllingfactor in the condition of polluted harbor waters, Trans. Am. SOC.C. E., ol. 85, 1922,

pp. 728-731.


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r api d rate of w t hdr awal of oxygen and a sl owrate of r epl acement ,resul t i ng in a decrease in the avai l abl e di ssol ved oxygen. As thi sval ue decreases, t he r ate of r eoxygenati on is cor respondi ngl y i n-creased unti l i t equal s t he rate of depl et i on, at whi ch poi nt thet wo reacti ons are f or t he moment in equi l i bri um and there is nochange in t he actual oxygen content . Thi s equi l i br i um however ,is ony moment ar y, for t he decreasi ng oxygen demand of the or-gani c mat t er , resul ti ng f r om i ts o wn oxi dat i on, makes the r ateof depl et i on cor respondi ngl y l ess and permt s t he gradual recoveryof t he di ssol ved oxygen up to its ful saturati on val ue. Undercondi t i ons of cont i nuous or r epeat ed pol l ut i on, however , an equi l i b-r i um poi nt may be reached at whi ch the rate of r eoxygenat i on isexactl y equal to that of deoxygenati on, and is so mai nt ai ned. Thei mpor t ance of the reoxygenati on f actor i tsel f and of jts accurate.exper i ment al determ nati on is theref ore obvi ous. Upo n thi s val ue,under any gi ven condi t i ons, depends t he resul tant oxygen condi -ti on of the streamfor a stated degree of pol l uti on, or, conversel y,t he max i mum amount of pol l ut i on compat i bl e w t h any stated degr eeof oxygen depl et i on.P r om the pr i mary l aws of oxi dat i on of organi c matt er and ofr eoxygenat i on of a st r eam the resul tant general equati on of streamcondi t i on may now be der i ved, expressed in t erms of di ssol ved oxy-gen. The appl i cat i on of t he exper i ment al dat a to thi s equati onwllthen per m t the deri vat i on of t he var i ous constants whi ch character -i ze t he st r eam in r egard to i ts capaci ty to recei ve and di spose ofsewage pol l uti on.Accor di ng to t he ar gument whi ch has been presented, the rateof change in t he oxygen defi ci t is gover ned by t wo i ndependent re-acti ons. Fi rst , t he defi ci t i ncreases at a rate whi ch may be assumedIRto be propor t i onal to t he oxygen demand of t he organi c mat ter.Secondl y, i t decreases by reaerat i on, at a r ate di rectl y proport i onalto its own val ue. T h e t wo rates ma y be expressed in di f ferenti alf ormthus:

andin whi ch-

t =t i me of reacti on, in days.L= xygen demand of t he organi c matter. espressed in t erms ofD= xygen saturat i on defi ci t of the water , in part s per ml l i on.part s per ml l i on of oxygen.

For evidenGe supporting this assumption see later text, pp. 40 to 44. t


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17- _I- rate of deoxygenat i on, n t erms of oxygen saturat i on defi ci t.dtdD3-ate of reaerat i on, n t erms of oxygen saturat i on defi ci t.Kl coeffi ci ent def i ni ng the rate of deoxygenat i on.E2 coeffi ci ent def i ni ng the rate of reaerat i on.The net rate of change in t he oxygen def i ci t (D) t any t i me isequal to t he di f ference betwecn (or al gebrai c sum of) the two par-

ti s1 and opposi ngrates as def i ned above (see fig. No. 4) and ma y beexpr essed mathei nat i cal l y as f ol l ows:d D dD. dD,

whence-- = Idt dt +dtdt -- E, L- E2D

whi ch is a l i near di f ferenti al equati on of t he fi rst or der ( somet i mescal l ed Lei bni tz' s equat i on) havi ng t he general f orm

The i ntegrated equati on der i ved f r om thi s di f ferenki al equati ondef i nes t he actual di ssol ved oxygen content of t he water, expressed_ _ 11.. .l.IC.ZL l..l..-- -.1-----L... 1 ~ 1 - - I P . . , I


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18factors. The ful l mathemat i cal deri vat i on of t he i ntegrated equa-t i on is gi ven in Appendi x A, he resul t i ng f or mul a bei ng-

in whi ch-D =ni ti al di ssol ved oxygen saturat i on defi ci t of t he water , inDzsat urat i on defi ci t, in part s per ml l i on, af ter t i me (t) .L,=ni ti al oxygen demand of t he organi c matt er of the wat er , inK, =coef f i ci ent def i ni ng the rate of deoxygenat i on.K, =coeff i ci ent def i ni ng the rate of reaerat i on.t zel apsed t i me, in days.e=base of Naper i an or natural l ogari thm=2. ' 71828.

part s per ml l i on.

part s per ml l i on.

Co mmo n l ogari t hms may be used in obtai ni ng val ues of (K, )and (I&), in whi ch case the quant i t y (10) is substi tuted for (e).Th e quanti ti es (Da) ,D), La),nd (L)may be expressed in t ermsof ei ther par ts per ml l i on or per cent of oxygen saturat i on; butshoul d be stated i nvar i abl y in the same t erms.The t ype of curve def i ned by thi s f or mul a is i l l ustrated by curveA inFi gur e No. 5, which is based on an assumed si mpl e case wherei nthe water i s saturated wth oxygen i ni ti al l y and a l of the pol l ut i ngmat t er enters a gi ven str etch of the st ream at or above i ts upper. . 7. I


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19i n terms of the oxygen saturati on val ue, whi ch is equal to 100 percent m nus the defi ci t ( D) s gi ven by f ormul a (1). T h e curve,whi ch is typi cal of oxygen condi ti ons f requentl y observed in st reamsbel ow maj or poi nts of pol l uti on, has a di sti nct m ni mum poi nt,mher e the rates of deoxygenat i on and of reaerati on are moment ari l yequal . By di f ferenti ati ng equat i on (1) wth respect to t i me, andpl aci ng the resul ti ng expressi on equal to zero, he poi nt of m ni mumoxygen content, n t erms of t i me (t) , s thus defi ned:

It wll be noted that in equati on (2) the vari abl e oxygen defi ci t,represented by (D) n equat i on (I), is absent. I n order to obtai nits val ue, equati ons (1) and (2) may be combi ned, gi vi ng the fol-l ow ng expression :Thi s equati on c a n be cl eared of a l t erms i n (t) and the max i mumdefi ci t expressed in terms onl y of the f qur constants, but the expres-si on obtai ned is unw el dy, and i t is mor e conveni ent to sol ve first for(t) in equati on (2) and then for (D) n equat i on (3).Si ml arl y, he temperature f uncti on of thi s poi nt may be obtai nedin a singl e equati on, gi vi ng the t i me and maxi mumdefi ci t as affectedby vari ati on i n temperature, but thi s al so is i nconveni ent for prac-ti cal use, nd tha resul t is obtai ned mor e di rectl y by usi ng (K, ) nd(K, ) al ues i ndependent l y determned for the t emperahre in ques-ti on. The temperature el'ect upon the constant (K, ) as al readybeen gi ven; that for the reaerati on coeffi cient (K, )whi ch remai ns tobe determned experi mental l y, wll be di scussed l ater in connecti onwth the appl i cati on of the experi mental data to the determnat i onof that constant.The si gni f i cance of the vari ous t erms in equati on (1) is fai rl yobvi ous, except i ng t hat of the reaerati on coeffi ci ent ( C,), the mean-i ng of the deoxygenat i on constant (K, ) avi ng been previousl ydi scussed (p. 6). The reaerati on coeffi ci ent (K, ) s anal ogous to(K, ) n that i t defi nes a geometri c rate of progressi on on a t i mebasi s; for exampl e, f the val ue of (K, ) e such that 20 per cent ofthe exi sti ng saturati on deficit is sati sfi ed by reaerati on in the firstuni t of t i me, then 20 per cent of the remai ni ng defici t wll be sati s-fied in the second uni t of t i me, and so on. It di f fers f rom(Kl),however , i n not bei ng a constant for a gi ven temperature, as is true(or approxi matel y so) of (KJ It has al ready been noted that therate of reaerati on of a body of water is modi f i ed to a l arge extentby its degree of turbul ence, other thi ngs bei ng equal. I n f l ow ng


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20st reams, wher e t urbul ence undergoes w de vari at i ons accordi ng tovel oci ty of fl owcharacter, and sl opeof t he channel , and ot her physi -cal f actors, correspondi ngl y mar ked di f ferences are to be expectedin rates of reaerat i on and hence in val ues of (K, )observed in di f fer-ent stretches of the same ri ver, or evea in t he s ame st r eamstretchunder varyi ng flowcondi t i ons. On the other hand, t he reaerat i onrate shoul d be cl osel y rel ated to and governed by t hose condi t i onswhi ch i nf l uence turbul ence of fl ow; hence val ues of (K, ) as actu-al l y det erm ned in a gi ven river str etch, shoul d bear a closec rel ati onto the several measurabl e f actors of physi cal condi t i on whi ch causevaryi ng degrees of turbul ence. Wth a gi ven t ype of channel orfl owcondi t i on, val ues of the coeffi ci ent (K, ) houl d be wel def hedand characteri sti c f or that t ype or condi t i on.The practi cal si gni f i cance of the reaerat i on coeffi ci ent in probl emsof st r eampol l ut i on is theref ore t Kof ol d. Fi rst, there is t he l ocal appl i cati on, n whi ch a set of (K, ) al ues, once determ ned f or a par -ti cul ar st r eam may be uti l i zed to cal cul ate i ts capaci ty f or reaera-t i on under any assumed condi t i ons of f uture pol l uti on, usi ng f orthi s purpose t he three f ormul as that have been devel oped above. ( Seepp. 18-19.) Secondl y, here is t he mor e general appl i cat i on, wherei ncorrel at i ons of val ues of (K,)wth certai n measurabl e f actors ofphysi cal st r eamcondi t i on may be empl oyed to est i mate the reaera-t i on capaci ti es of other st r eams f or whi ch these f actors are kno wn butin whi ch no di rect measur ement s have been made of the coeffi ci ent.( See p 64.) Obvi ousl y the poi nt of depar t ure for a st udy of thi ski nd i s t he di rect measur ement of t he val ue of (K, ) n the streamThe met hods whi ch have been empl oyed in the deri vat i on of reaera-tion coeffi cients for a number of stretches of the Ohi o Ri ver wlltherefore be descri bed in some detail .Ref er r i ng no w to equat i on (l), i f t he pr obl emwere that of sol v-i ng for an unlmo~vvn xygen content (D), th a l of t he other f ac-tors l mown, he matt er woul d be one of si mpl e substi tuti on. Thi swoul d be the procedure in practi ce, t he constants bei ng gi ven and i tbei ng requi red to det ermne the resi dual di ssol ved oxygen af ter anyt i me and under ai ven or assumed condi t i ons of pol l uti on. I n experi -ment al l y measur i ng the reaerat i on coeffi ci ent (K, )however, a l ofthe other t erms, i ncl udi ng (D), ust first be det ermned. Fo r con-veni ence in ref erence, these t erms wll be li sted agai n, as fol l ows:

9

K, =the deoxygenat i on constant.L,=he i ni ti al total oxygen demand of t he st r eamwater in partsD =the i ni ti al di ssol ved oxygen content of the st r eamwater inD=t he di ssol ved oxygen content of the stream in parts per ml-

per ml l i on of oxygen.part s per ml l i on, expressed as saturat i on defi ci t.- . I . . * l ~ ,7 r . L L - :-:*:-I -+


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21k t h e t i me of f l ow in days, h o m an oxygen content of D a ) toone of (D).The det ermnat i on of (K, ) nd the t emper ature rel ati ons i nvol vedal ready have been di scussed. I n the present case val ues have beenassi gned to (HI)y correcti ng its val ue, 0.100, at 20' C. to its

var i ous equi val ents at di f ferent observed st ream temperatures,usi ng f or thi s purpose the curve shown in Fi gur e No. 2 or the cor -rect i on f or mul a gi ven on page 7, wth the thermal coeffi ci ent (@t aken as equal to 1.047. The determnat i ons of (Da)nd (D), ndof the t i me (t) in a gi ven st r eamstretch, requi re the sel ecti on of t wosampl i ng stat i ons, A and B, one l ocated at the upst r eam and theother at the downst r eamend of the stretch, and di rect observat i onof the di ssol ved oxygen content and t he water t emper at me at theset wo stati ons, together wth measur ement s or comput at i ons of themean t i me of f l owbetween themat the vari ous ri ver stages at whi chthe di ssol ved oxygen content is observed.The assi gnment of a proper val ue to the i ni ti al oxygen demand(La)however , presents an extr emel y d ffi cu t probl emowi ng l argel yto the uncertai nt i es i nvol ved in det erm ni ng, under condi t i ons f oundin natural st reams, a quant i t y whi ch may be t aken as bei ng a rep-resentati ve one f or a parti cul ar ri ver si xetch under observat i on. Itis proposed, therefore, o di scuss thi s quest i on in consi derabl e detai l .If the ri ver stretch in quest i on were enti rel y free f r omi nf l ow ngpol l ut i on or di l uti on at poi nts i nt ermedi ate bet ween t wo gi vensampl i ng stati ons, or i f the amount s and poi nt s of ent ry of suchi nf l ow wer e def i ni tel y known, the vari ous f actors concerned in theprobl em woul d be determnate and its sol ut i on woul d be compar a-ti vel y si mpl e. I n the fi rst case, t he onl y change in the initiallyobserved oxygen demand, occurr i ng bet ween the upper Stati on Aand the l ower Stat i onB, woul d be a progressi ve and orderl y decreaseclue to oxi dat i on, f ol l ow ng a course whi ch, ' f or a l practi cal pur-poses, coul d safel y be assumed to be siml ar to the l ogar i t hmc t i mef unct i on curve def l ned by l i ne A in Fi gur e No. 6a. Th e i ni ti al l yobserved oxygen demand, denoted as (LA)n the chart , thereforewoul d become t he val ue of (L,) n f ormul a (1). I n the secondcase, wher e known i ncrement s of pol l uti on or di l ut i on entered theri ver stretch at recogni zed poi nt s beLween Stati ons A and B, heposi t i on of the l ine of resi dual oxygen demand woul d be al tered ateach one of khese poi nts, as shown in Fi gur e No. 6a, but its sl ope,det hi ng the rate of oxi dat i on, woul d r emai n constant for the parti c-ul ar ri ver t emper ature condi t i on prevai l i ng. I n thi s latter i nstance,a ne w val ue of ( La ) woul d be comput ed at each poi nt of entry ofkno wn i nf l ow t he new ordi nate of the cur ve l yi ng above or belowl i ne A accordi ng to whether t he effect of the added i ncrement of


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24tity (LIB) n the chart, representi ng the max i mum amount of di s-turbance whi ch coul d possi bl y account for the di vergence observedin a gi ven case. The use of ei ther (LA)r (LB)s a basi s for (L)represents, therefore, the t wo most ext r eme assumpti ons possibl e re-gardi ng the amount of i ntermedi ate di sturbance. I n the one case,the deri ved val ue of (La)videntl y moul d be too l ow and in theother t oo hi gh.Met hod (3) represents a comprom se between the t wo al ternati veprocedures descri bed under met hod (2), he pri mary assumpti onherei nvol ved bei ng that the total amount of di sturbance between St.+-ti ons A and B is equal to an amount whi ch, i f concentrated at a

3.% rs.No.6bm - CHhRT 5WWING METHOD OFC9lAINING HYPOTHCTICALVALUE OF (14) Y AY EW IN G OB5ERVATION5 TAKCN ATI. 5TA TIO NS @)ANV (B)AND BROUCKT TO A COMMON m515FOR COMPARIWN AT STATION(0>

poi nt i mmedi atel y bel ow Stati on A, woul d account for exactl y one-hal f the observed di vergence between (LB)and (L'*) at Stat i on B.The effect of ths assumpti on i s i l l ustrated in Fi gure No. 6bby lincC, he val ue (L,) bei ng an ar i thmet i cal mean of (LB)and (L'*),r IL', +L,e%2,=It wi l l be noted that t he total amount of oxygen demand sati sfi edbetween Stati ons A and B al ong l i ne C i s equal to the ari thmeti calmean of the total amount s sati sfi ed, respecti vel y, along l i nes andB; hat i s:


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25Met hod (3) thus i nvol ves a f urther assumpt i on that the totalamount of oxygen demand sati sfi ed between Stati ons A and B isequal to the mean of the amounts whi ch woul d be sati sfi ed under themax i mum and m ni mumpossi bl e condi ti ons of di sturbance, respec-ti vel y. I n the absence of any specifi c data as to the actual amountor di stri buti on of such di sturbance, an assumpti on of thi s naturewoul d appear to be a f ar mor e reasonabl e one than those whi ch arei nvol ved in met hods (1) and (2). The cal cul ati on af (La)y th smet hod is si mpl e, i t s val ue bei ng gi ven, in t erms of the observedquanti ti es (LA)nd (LB),y the rel ati on:

The met hods above descri bed have reference sol el y to the deri va-ti on of a val ue of (La)or substi tuti on i nto f ormul a (1) whi ch, twll be recal l ed, is based on a pri mary assumpti on of an in tial oxy-gen demand, subsequent l y undi st urbed in its orderl y rate of decreaset hrough oxi dat i on. It may be argued that procedures b a d on suchan assumpti on can hardl y be appl i ed, ogi cal l y, to condi t i ons of nat-ural st seams i n that they fail to take di rect account of the manner inwhi ch the di sturbi ng i nf l uences causi ng a deviati on of (L)r om(L*)re di stri buted al ong the streamI mh- een wo gi ven observati onstati ons. A content i on of thi s ki nd unquesti onabl y is sound theo-reti cal l y, but when an at tempt is made to devel op a procedure basedon some defini te pr i mary assumpti on as to the di stri buti on of di s-turbi ng influences al ong a stream t wo dfficu ties present themsel ves. Fi rst is a questi on as to the ki nd of di stri buti on whi ch shal lbe assumed in a gi ven case, wth l i ttle or no i nf ormati on avai l abl eon whi ch to base a parti cul ar assumpti on. Second is the obvi ousfact that f or each di fferent assui npti on made a new and character -istic equati onof the t ype of f ormul a (1) must be devel oped, start i ngwth a new di fferenti al equat i on of condi t i on, and undergoi ng thevari ous steps of i ntegrat i on siml ar to those outl i ned in Appendi xA wth respect to f ormul a (1).The mathei nnt i cal compl exi t i es whi ch such a procedure i nvol vesare vel1 i l l ustrated by the exampl e, gi ven in Appendi x B, of thederi vati on of a new resul tant oxygen f ormul a based on the mostel ementary assumpti on possibl e regardi ng di str i buted di sturbance,namel y, a uni f ormdi stri buti on of i nf l ow al ong the st reambetweenStati ons A and E.D=the symbol s empl oyed bei ng the sameas n f ormul a (1) except that(LA)nd (LB)epresent the obserred oxygen demand at Stat i ons-iand respecti vel y.

The equat i on thus deri ved is as follows:ICz(KzK,) 1- F x F -E,[Xz(l --I Fl t) (~-L,e-Kat)-~l(Lb-Lae-=lt)- Dae- K2t


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26Efforts to devel op other f or mul aeof the same type, based on otherassumpt i ons as to t he di stri buti on of i nf l ow have l ed to i ntegratedequati ons even mor e compl ex t han the one above stated. For pur -poses of practi cal appl i cat i on such f or mul ae are so compl i cated asto be vi rt ual l y unwor kabl e in most cases. I n t he absence of speci f i c

i nf ormati on as to t he manner in whi ch di sturbi ng inf l uence may bedi str i buted in a gi ven i nstance, the use of a part i cul ar f ormul a,based on a si ngl e arbi trari l y assumed di stri but i on, moul d be hazar d-ous,moreover, in vi ewof t he ext r eme vari abi l i ty and hi gh degree ofuncertai nty wth whi ch such di str i buti ons occur in natural st reams.Wth t he admt t ed theoreti cal advant ages of these procedures overthe mor e si mpl e one embodi ed in f ormul a (1) thei r pract i cal di sad-vant ages are of such a natur e as to r ender thei r use i nadvi sabl e f orpurposes of wor ki ng cal cul ati ons.For use in connect i on wth the anal yses of t he Ohi o Ri ver dat a,to be di scussed in t he text whi ch f ol l ows, the procedure fi nal lyadopted as bei ng t he most sui tabl e f or t he purpose at hand was theempl oyment of f or mul a (I), der i vi ng val ues of (La)y averagi ngthose of (LB) nd (L,e-K t), as descr i bed under met hod (3) onpages23-24. By this comparati vel y si mpl e procedure val ues of (L,)wer e cal cul ated f r omthe base dat a gi ven in TabI e No. 1 f or eachstretch of t he ri ver f or whi ch observat i ons wer e avai l abl e.An nspecti on of f or mul a (1) i ndi cates that a di rect soluti onof i tfor the val ue of t he reaerati on coeffi ci ent (K, ) nvol ves mat hemat i caldi ff i cul ti es, i nce thi s t erm appear s both as a coeffi ci ent and as anexponent . Whi l e i t is possi bl e that a conveni ent sol ut i on of thi sequati on by means of a nomogr aphi c char t mght be devi sed, a f ai rl ysi mpl e met hod in practi ce has consi sted of t he i ndi rect procedureof assum ng val ues of (I&), sol vi ng for t he corr espondi ng ( D)val ues; pl ott i ng these on cross- secti on paper wth (K, ) al ues asordi nates and (D) al ues as absci ssae, and f r om a smoot h cur vedr awn t hrough the poi nts, sel ecti ng the val ue of (K2)orr espond-i ng to t heknown (D) al ue. The substi tuti on of the val ue of (K,),t hus obt ai ned, i nto f or mul a (1) wll i nsure that t he proper f i gurehas been chosen f r omthe pl ot, t hus checki ng the wor k. This met hodof procedur e i s comparat i vel y si mpl e in rout i ne wor k i f t he so- cal l ed" og- l og" sl i de rul e is used, permt t i ng the conveni ent sol uti on ofpower f uncti ons. It is rarel y necessary to obtai n mor e t han threepoi nts on the smoot h curve to obtai n the i nterpol ated val ue of (K, )sought .Empl oyi ng t he foregoi ng met hod, val ues of t he reaerat i on co-effi ci ent ma y be readi l y comput ed for any ri ver stretch or any con-di ti on of fl ow or season for whi ch the necessary l aboratory andhydrometr i c data are avai l abl e. F r om cal cul at i ons of thi s ki nd asa+ n-F (K valiitw will be obt ai ned for each Dart i cul ar r i ver stretch


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27studi ed, t he val ues varyi ng accor d*mgto t he di f f erent condi t i ons oft emper ature and f lowencount ered dur i ng the per i od of observat i ons.The coeffi ci ents t hus obti ti ned, represent i ng in each case the co-i nci dent st r eam condi t i ons, are modi f i ed by t hree maj or f actors,namel y, t emperature, st r eamdept h, and t urbul ence. The t emper a-ture i nf l uence is, stri ctl y speaki ng, a compound one, dependi ng uponthe resul tant effect of t emper ature vari at i ons upon the rats of sol u-ti on of oxygen at the wat er surf ace and upon i ts vel oci ty of di f-f usi on in t he l ower strata. These two i nf l uences are opposed toeach other in t he sense t hat t he rate of sol uti on di mni shes wth ris-i ng t emperatur e, whi l e t he rate of di f fusi on i ncreases.The effect of t emper ature vari at i ons upon t he rate of oxygensol ut i on at the sur f ace is gover ned by the rel ati ve amount s of satura-t i on defi ci t represented by a part i cul ar di ssol ved oxygen contentwhen r ef erred to saturati on val ues at di f ferent t emperatures. I f ,f or exampl e, the oxygen cont ent be 5 parts per mll ion, i ts satura-t i on defi ci t at 20" C. s 4.2 parts and at 30" C. s 26 part s, t he rel a-ti ve rates of sol ut i on at the t wo t emperatures. bei ng de he d by theproport i on 4.226 Whe r e the oxygen content i s expressed, how-ever, in t erms of saturat i on defi ci t, as i s the case in f ormul as (1)and (3), thi s t emper ature relat i on is t aken account of automat i cal l y,and t he di f fusi on rel at i onshi p is t he gover ni ng i nf l uence.I n thei r K e w Yor k Har bor studi es, Bl ack and Phel psZ1 deri vedexper i ment al l y a curve showi ng the effects of t emper ature var i a-t i ons upon r ates of di f fusi on of atmospheri c oxygen in water. I nFi gur e No. 7 hi s curve, sl i ghtl y modi f i ed f or t emperat ures below10" C. , s r eproduced in such a way as to s how relat i ve ratesof di f fusi on at var i ous t emperatur es wth reference to t he rateof 20" C. F r om thi s cur ve it appear s that the rate of di f fusi onat 20' C is doubl ed at a temper ature of about 27.2 C, rebl edat 31.4" C. , and hal ved at 10.6" C It is evi dent t hat t he. t emperature of t he water, even wthi n r anges ordi nar i l y observed inst reams, exerts a great i nf l uenceupon the rate of di f fusi on of oxygenin wat er and hence upon t he rate of reaerat i on of st reams. Bymeans of a cur ve si ml ar to that of Fi gur e No. 7, al ues of thereaerati on coeffi ci ents as det erm ned at var i ous prevai l i ng st r eamt emper atures ma y be r educed to equi val ent val ues at a st andardt emper ature of 20" C bef ore compar i ng t hem wth reference toother st r eamcondi t i ons.The nf l uence of st r eamdept h upon t he rate of reaerat i on is con-trol l ed in part by t he relat i on of depth to vol ume of flow ( whi ch,jn t urn, governs the concent rat i on, n the st r eam of oxygen der i ved=Black, Col. W. bf., and Phelpha, E. B., The Discharge of Scnvage into Nenv TorkHarbor. Report made to the Board of Estimate and Apportionment, Ncrr Tork C'itp,

1911.


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28from eaerati on) and probabl y al so i n part by t he relati on of depthto the, rate of di f f usi on. It happens that both the rate of di ffusionand vol ume of f low are power functi ons of the depth, approxi mat -ing its square. A gl ance at the equi val ent of (IC) in the di f f usi onf ormul a on page 11, whi ch is gi ven by the quanti ty m)llshow, for exampl e, t hat the- ate of di f f usi on s i nversel y propor-ti onal to the square of the depth (L). As regards the vol ume offlow, t i s equal to the vel oci ty t i mes the area of f l ow the relati on

ahZ

I II

TCMPEWNZC r WATCR N 'C.

bei ng expressed by the si mpl e hydraul i c f ormul a: (Q=AV), nwhi ch (a) enotes the vol ume of f l ow (A) he area, and (V) thevel oci ty. I n most st r eams havi ng a fai rl y large ratio of w dt h todepth, t he area of flow (A) and the vel ocity (V) re each of t hemvery nearl y proport i onal to the depth (H), o thak the relati on tovol ume of f l ow may be wri tten as bei ng roughl y: (Q=cH2).heamount of reaerati on per uni t of t h e , or its rate, when measured interms of oxygen concentrat i on, shoul d be i nversel y proport i onal tothe quant i ty of mat er throughout whi ch the oxygen i s di str i buted ;


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that is, to the st r eamdi scharge (Q). r om t he rel ati on j ust s hown,thi s rate shoul d theref ore be roughl y proport i onal di rectl y to thesquare of t he depth (H)As to t he relati on between reaerat i on and t urbul ence, no wel l -def i nedtheoreti cal basi s exi sts f or j udgi ng i ts nature, t he reason be-ing that the turbul ei i ceo a st r eamis an abstr act f unct i on dependentupon and capabb of expressi on onl y in t erms of some other moreconcrete st ream characteri sti c. For a gi ven st ream t ype, somedefi ni te rel at i onshi p m ght reasonabl y be expected to exi st betweenthe turbul ence of a st r eamand its vel ocity of flow, ut i t i s evi dentthat di f ferent t ypes of st r eams shoul d reveal qui te di f ferent vel oci ty-turbul ence rel ati ons. For exampl e, in a st r eampossessi ng an even,smoot h, deep channel , wth fl at sl opes and ei ther st rai ght or gradu-al l y changi na di recti on of f l ow the effect of vel oci ty upon t ur bu-l ence is concei vabl y muc h l ess t han in a-watercourse havi ng a shal -low, rough channel , wth steep sl opes and sharp changes in di rec-ti on. Between t he t wo ext remes lie numer ous wel l - def i ned st reamtypes; and a l arge ri ver sucha3 theOhi o is l i kely to exhi bi t t hrough-out i ts course several of these types.No very def i ni te theoreti cal rel ati on exi sts bet ween t urbul ence andvel oci ty, even assumng other physi cal condi t i ons constant. I n ageneral way, turbul ence is the resul t of f ri cti onal resi stance to flow,and under uni f or mphysi cal Condi t i ons m ght be expected to be apower f unct i onof the vel oci ty of the f or m

b.

T=cVnt he constants c and n def i ni ng the st reamtype as regards the f i xedphysi cal condi t i ons, such as slope,character of bot t om dept h, shape,and di recti on of channel , etc. This subj ect can therefore be deal tT- i th nl y empi ri cal l y.

EXPERIMENTALThe quant i tat i ve wor ki ng theory of the process of oxygen st reampuri f i cati on whi ch has been devel oped and expressed in the f o r mofcert ai n al gebrai c equati ons i s capabl e of t wo di sti nct uses. Wtha l l the constants known, t makes possi bl e the comput at i on of ac-tual st r eamcondi t i ons and ma y even be empl oyed f or t he det erm-ri ati on of f ut ure condi t i ons, wth an assumed i ncrease in con-tr i buti ni popul at i on or an assumed degree of sewage puri f i cati on.I nf ormati on is l acki ng, however , concerni ng the reaerat i on or re-oxygenat i on coeffi ci ent (IC,) in the f ormul as, except i ng f r om apurel y theoreti cal standpoi nt .It is possi bl e, however , to uti l i ze these f ormul as for t he exper i -ment al det ermnati ons of thi s term by actual l y measur i ng the


33/80

mor e readi l y determnabl e present st reamcondi t i ons. T o thi s endanal yt i cal dat a have been obtai ned in t he f or mof di ssol ved oxygenand oxygen demand val ues, and t hese dat a wll be empl oyed for t hedetermnati on of t he reaerat i on coeff i ci ent. It wll t hen be possi bl eto st udy thi s coeffi ci ent in connect i on wth t he physi cal st reamcon-di t i ons whi ch affect i t and to search f or any general rel at i onshi pswhi ch woul d make t he determnat i ons of reaerat i on a matt er ofcomput at i on f or kno wn physi cal condi t i ons.It shoul d be noted that t he other dat a necessary f or the sol ut i onGI he condi t i on equati on are ei ther known or capabl e of r eady deter-mnat i on in any part i cul ar case.

PRESENTATION OF RASE DBT-4The scope af tli e observat i ons consti tut i ng the basi s of t he studyembr aced dai l y or thr i ce- weekl y det ermnat i ons of di ssol ved oxygenand bi ochemcal oxygen demand of the Ohi o Ri ver at sel ected stat i onst hr oughout its enti re l ength, f r om Pi t t sburgh to bel ow Paducal i ,

over a peri od extendi ng f r omMa y 1 to Oct ober 15, 1914, suppl e-mented by si ml ar observat i ons in a stretch of tli e ri ver extencl i ngf r omabove Ci nci nnat i to bel ow Loui svi l l e, over a peri od f r omOct o-ber 16,1914, t o Apr i l 30,1915. The data f or the l atter nai i i ed stretchthus embr aced a ful l year s cycl e of st reamcondi t i ons.The base dat a der i ved f r omthese observat i ons wer e fi rst r educedto t er ms of monthl y average figures and suni mari zed as shown inTabl e No. 1, whi ch al so i ncl udes certai n suppl ei nentary clataempl oyed i n t he anal ysi s of t he l aboratory resul ts, such as mean r i verwat er t emperatures and t i mes of f l owbet ween t he var i ous sampl i ngstati ons ( col umns 2,3, and 4). The sampl i ng stati on notat i ons asgi ven in col umn 1 requi re expl anat i on. The l ocati on of a l stati onswas ref erred to a poi nt at t he j uncti on of t he Al l egheny and Monon-gahel a Ri ver s at Pi t t sburgh, and each stat i on on t he Ohi o Ri ver wasgi ven a number corr espondi ng to i t s l ocati on in ml es bel ow the ref -erence poi nt. ( See Ma p A, how ng the l ocat i on of the var i ous sta-tions;al so Publ i c Heal t h Bul l eti nNo. 143, pp. 98- 104, for a descri p-ti on of t he stati ons. ) Thus the stati on desi gnated as Ohi o No. 23 was ocated23ml es downst r eamf r omthe ref erence poi nt. The t r i bu-tary stati ons, desi gnated by nani e, wer e l ocated in all except t wocases practi cal l y at t he tri butary mout h. The t wo except i ons weret he Al l egheny ttnd Monongahel a stati ons, whi ch wer e l ocated atdi stances of 7 and 12 ml es, respecti vel y, above thei r j uncti on atPi t t sburgh.I n the anal ysi s of t he dat a whi ch f ol l ows, 11 stretches of the ri verhave been sel ected for r eaerat i on st udy, the vari ous f actors i nvol vedin t he cal cul at i ons havi ng been transcri bed f r omTabl e No. 1 and


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31

L ~ ~ Sduri ng

arranged as shown in Tahl e No. 2. The l ast two col umns in thesetabl es contai n val ues of t he reaerati on coeffi ci ent (K, ) s det erm nedf or the actual st r eamcondi t i on by t he met hod out l i ned on pages26-27 and as converted to a st andard t emperature basi s of 20 C. ,usi ng the curve of Fi gur e 7 for the purpose. I n Tabl e No. 3is gi ven a summar y of the val ues of (K, ) hus st andardi zed andbrought together f r omTabl e No.2 for ref erence and compar i son.TABLE o. l.-Awage results, b y months, o f laboratory determinations ofdigsolved oxf/pen nd biochern4cal oxygen de ma nd at various sampling etiotis in the Ohio River and at the mouths of designated tributa,ries, ogetherwith collateral data concernzing m e a n river water temperatures and tinaesof IOZV between successive stations

MONT I I OF MAY, 914Total oxygendemand

Sampl i ng stati onPi tts-burgh

Al l egheny, No. 7 .. ___.Monongahel a, No. 12 _. ___.Ohi o, No. 3 _ . . . _ __ __ __ __ . . . .Ohio, No. 11___. . . _______. . . _Ohio, No. 19___ . ___ . _____ . __.Ohio,No. 23_ _ _ __ _ _ _. . _ _ _ __ _ _Beaver - _ __ _._ _ _ _ _._ . __Ohio,No. 29___. . . _. ______. . .Ohio, No. 65 _ . . _____ . _______Ohio,No. 7 ____. . . . ____. . . .Ohio, o. 88____. . . ______. . . .Ohio,No. 7__. . ____. . . . ____.Ohio, No. 104____. _ ____ . _ __ . _Ohio,No. 49_ . ________. _ . ___scioto___ . _ . ____. . _______ . ___Ohi o, No. 461____. . _. ______. _Litt le M am ______ . . . _______Li cki ng. . ____. . _. ___ _ _ _ _ _ -Ohi o, No. 475_ _ __ _ _. _ __ _ __ _. _Ohi o,No. 82______. _ . ______.Ohi o,No. 88 . . ______ . ______M am _ _ _ _ _ __ _ _.. . ______. _Ohi o, No. 492 . ______. . . . ____Ohi o,No. 98____. _ . ________.Ohi o, No. 611_ . ______. . _ . ____

Sta-ti onnextabove

Meonwatertern-20$c c.l ion)

pera-tureOC.' Partsmll i onFr

19.923.515. 816.015.816.017. 714.316.616.816.816.316.417.018.617.618. 819.417.17.S17.017.516.917. 618.0

.48.56.60.661.181.381.581.711.865.896.007.657.677.777.878.008.118.128.1610.1410.42

Mea n t i meoffl ow days,f rom~

.I8.08.04.Gi3.52. %.18. 15. 154.03.ll1.65.02.10.10. 13.10.02.041.98.28

.891. 141.41.971. 071. 471.361.01.25.60

.46.791.10.79.85.6498

(3) (4)

4.325.536. 44.705.207. 136.605.051.212.922.243.845.343.844.133. 14.76

Al l egheny, No. 7.. ._.. .Monongahel a,No. 12 __. _. _.Ohi o, No. _._..._......._..Ohi o, No. 11_.......__.......Ohi o, No. 3_......_...._._..Ohi o, No . 23. _. . __~._.._._.Beaver. - . .._._. ._.__. __.. _Ohio, No. 9___. ____. . __. _. __Ohi o, No. 5 ._. ..__.._.._._.Ohi o,No. 7_._...._.._.__...Ohi o, No. 88 _.. _.. ._..__._..Ohi o,No. 7____. . . . _. . . __. . _c\LI^ hT^ I

n tia di ssol ved oxygeI

. _

.-

Partser ml i on

1. i s2.093.131.091.141.33.92.66.93.46.391.03

(5)~

9. (17.219.329. 79. 109. 99.538.608.808.898.718.378.438. 268. 208.418.608. 188. 178. 148. 638.098.017.90

9. O

0.31 1.51.27 1.31.34 1.65.43 2.08.38 1.85.32 1.55.49 2.38.I8 .87.52 2.52.57 2.77.75 3.64.?ti ,2 ?

PercentSatu-rati on

23.024.024.025.024.023. 423. 4_._...22. 723.723.722.60.7 "

(6)98.083.091.193.892.91.596. 892.587.690.090.988.184.986.687.085.889.92.84.284. 283. 589.82.83.382.8

_ _

......_. _. __. _0.381.452.222. 542. 702.964. 445.466. 12.i2

Satu--ati ondefi ci i(partsle mLl ion)

_. . . ____. ._._.0.381. 07.77.32.I6.261.481.02.65. ?

(7)

7.536.415.407. 297.397.297.708.017. 798.118.181.z;

0.191.39.89.63.72.85.31.771.22.98.891.181.501.311. 171. 42.98.681.541.551.601. 011. 671.611.64

24 _ _hours'i ncu-bati on Quen-tityuni ts(partsper mil-lion Xt hou-sandsecond-feet)71.516.5an.215.0192.3182.565.3340.0261.6289.5397.0367.0281.0122.220.3269.07 021. 4483.0520.0392.021.0494.0499.0521.0

MONTH OB JUNE, 914-I 87. 575. 263.387.086.684. 789. 39% 089. 494.895.688.?

9.93. 715.519.517. 414. 52.08.826.028.537.528.5


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32

Percent5atu-ati on

TABLEo. l.-Auerage results, by ,ntonths, tc.4ontilluedMONTH OF JUNE, 9144ontinued

Sat u-rati ondefi ci t(partsper mll i on)

rota1 oxygendemand

89.4Yd.696.386.277.582.377. 995.477.390.289.689.688.392.185. 390.9

Mean time offlow,days,from-

. sa.69.211.101.841.e1.83.381.96.8E.8E

.842.11.641.13..7E

o tia di ssol ved oxygen Loss_ _

Parts?rmll i on

uri ng24

Sta-ti onnextt bove

Meanwatert e mpera-ture,OC

_ _(2)

Quan-tit,yunits(partsier ml-l i on Xt hou-sandseconrl -feet)

Sampl i ng stati on 'artsil li oner

-(9)_ -2.045.002.434.764.374.423.607.284.374.613.981.94.M)1.701.263.74___ _1. O2. 092. 141.992.142.333. 111. 161.902.381.601. 511.854.371.M4.033.943.933.303.204.904.084.761.551.261.04.871.36

Pitts-w g hlion)

(3)-17.3217.5220.2420.5420.9121.3921.6421.6921.7727.8323.7841.6241.9642.3442.4042.95

(4)_ _10.09.202.72.30.37.48.25.05.086.06.9513.79.34.38.06.55

(5)7.427. 767.886.886.356.796.457. 906.487.517.387. 245.567.446. 56i.20

.421.03.50.98.90.91.741.50.90.95.82

.40.oo.35.26.77

36. 55.048.14.991.92.875. 59.098.0132.8114.5? 4.o86.821.5255.0

25. 524. 526.227. 626. 225.825.625.625.025.325. 926. 929. 426. 929.628.0

~

Ohi o, No. 349_. ____. __. _-.-Scioto. - ~. . _______ . .Ohi o, No. 61_ _ _ _ _ __ _ _ . _ _ _ _ _Li cki ng- . _ _. ___Ohi o, No. 475_ _ _ _ _ __ . _ _ _ _ _ __Ohi o, No. 82_______ . . . ___ . .Ohi o,No. 88_____. . _ . _ . ___.Mam.. . . _ __. _. ____. _. _Ohi o, No. 492 __. _. _. . __...Ohi o, No. 08 _. __. __. ___. . _Ohi o, No. 611 . . . __. _. ___. _.Ohi o, No. 04 __. ____. ___. __Cumberl and. - . - ._ -Ohi o, No. 920_-_. _. _. ___. _. .Tennessee- . . . . . .Ohi o, No. 33__. ___. . . _. _. _._ _ - _ _ IMONTH OF J UL Y, 1914

. . ____. __. _0.681.811.36.60.292. 711.731.011.00.9112.79.202.76.35.43.56.26. 147.261.zo.3214.81.45.41.06.58

7.366.584.361 . 4 67.217. 427. 507.847.867.747.496.837. 577. 706.636.006.766.626.437.707.457.087.516.287.346.476.90

2187. 178.652.84.587.885.386.788.993.593.89 289.084.289.695.685.774.983.582.377..895.592.687.895. 580.894.484.388.8

1. 021.784.001.321.041.241. 14.94.54.52.6i.921.28.71.351. 102.021.341.421.71.37.59.98.361.50.441.20.87

0.33.43.44.41I44.48

5.54.011. 510.711.512.61.47.712.615.811.610.030.33.236. 3.474.874.662.764.0113.094.4109.847.710. 140.316. 778.8_ _

Al l egheny, No. 7_ _ __ . _ _ _ __ _ _Monongahel a, No. 2_ . ____-Ohi o, No. 3__ .___ .___ . . ___. _.Ohi o, No. 11__. . _. _. __. _. . __.Ohi o, No. 9___ . _ . _ __ . _ ___. _ _Ohi o, No. 3____. . . _. _. _. . ___0.682. 493.854.454.747.459.0910.2011.2012 124.9025.1027.8628.2128.6429.2029.4629.6036.8638.0638.3853.1953.6454.0554.1154.69

~

~.64.2J.39.49.33.31.38.90

Ohi o;No. 77_. _ . ___ . _ . ___ . ___Ohi o, No. 8____. . . _____. __. _Ohi o, No. 7_______. _ . _ . _ . _ . _Ohi o, No. 04 .. _._.. .. .. .___Ohi o, No. 29___. . . _. ___. __. _Scioto. - - .__. _ _____. . _ ___ .Ohi o, No. 461__. ___. ___. _. __.Li cki ng- - _ _ _ _ __ _ _ _ _ __ _ . _Ohi o, No. 475 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Ohi o, No. 82 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Ohio. No. 488_ _ _. _ _ __ _ _. _ _ __ _

.4a.83.81.81.6E.6f1.01. 34.9E.3:. 2f.21. E. 21

~ ~Ohi o, No. 492_ _ _ _ _ __ _ _ _ _ __ . _ _Ohi o,No. 598_____ . _ _________Ohi o, No. 611_ _ __ _ __ _ __ _ _. _ _ .Ohi o, No. 619_ _ _ _ _ __ _ _ _ _ __ _ . _Ohi o, No. 904 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Cumber l and _ _ _ _ _ _ _ -Ohio, o. 920 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Tennessee. - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Ohi o; No. 933 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ I


36/80

8.256.542.716.597.095.357.738.688.778.728.327.748.297.647.435.876.916.766.828.438.428.217.316. 77.467.537.18

a&

88.27L330.272678.058.782.795.296.395. 991.388.092.386.884.967.79.077.077.297.197.093.984780.187.089.884.3

91.8

19.021.021.020.520.520.319.019.820.320.420.420.322.321.122.122.522.622.522.322.022.922.922.623.324.523.725.024.1

~ ~_ _ _ _ _ _ _ ______ . _ _1.054.116.417.357.8213.4915.8817.5419.0220.3636.1236.3439.2739.6540.1140.7240.9941.1448.8650.1450.4865.7366.1166.4866. 367.11

TABLEo. 1.-Auemge results, by months, eti:.-ContlnuedMONTH OF AUGUST. 1014

Me an timeofflowdays,trdm- Total oxygendenlanditial dissolved oxygen-3atu-ationLeflcitY m d ,lion)PWt?

-ata-tionnextibove

Meanwatertem-pera-ture00 lampling tation Percentsatu-ation

partsermillion

(4) (5) (7)23.0

,, 24.82-5.024.624 4NO4.024.224.624.424.223.925.724.826.427.226.325..825. Q25.026.027.027.127.528.0n.28.4n.

- __.1.003.735.716.597.0111.4913.8115.4716.9218.2834.8835.1239.3340.01PO.3040.4548.9850.4250.8067.5467.8868.3788.4369.00

3 8 43s.IM

_ _ _ __ .1.002.731.98.88.424.482.471.511.451.3416.62.243.n.30.a.69.29.158.071.44.3816.74.34.49.06.57

7.166.402.856.506.876.657.407.757.957.767.907.587.097.377.276.584.976.396.246.237.817.797.337.186. 287.786.957.08__

82.476.034.076.981.177.985.291.294.291.793.088.985.887.389.181.860.77.575.874.396.695.091.189.979.398.288.489.4_ _

1.522.015.531.951.601.881.28.75.49.71.50.951.181.04.891.463.201.862.002 5.41.28.72.811.64.15.91.84__-1.102.456.282. 491.993.771.38.76.44.33.38.801.04.681.171.322.871.842.021.01.26.27.531.321.681. 11.851.33

0.39.71.61.51.52.38.52.28.12.50.55.35.37.83.491.01.79.74.65.66.33.38.60.16.18.40.24.30_ _

3.17.111.09.29.46.9.96.32.711.312.47.921.23.933.03.658.453.047.952.829.333.853.a20.66.064.519.573.0-

Allegheny No. 7 ___________Monongahela o. 12 _ _ _ _ _ _ _Ohio No. 3_______ . _ _ _ _______Ohio No. 11_ _ _ __ _ _ . _ _ _ __ _ _ _Ohio No. 9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Ohio No. 3 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _1.893.452.962.482.521.852. 521.36.582.432.671.701.804 32.384.903.843.593. 153.201.601.852.91.78.871.941.171.46-

Beaver- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Ohio No. 5 _ _ _ _ _ _ _ _ _ _ _ _ _ _Ohio No. 77______. _____ . . __.Ohio No. 8 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _OhioNo. 97- __ . _________Ohio No. 04 _ _ _ _ _ -L . _ _ __ _ __OhioNo. 49- _ _ _ _ _ _ _ _ _ _ _ _suoto-__. __ _ _ _ _ _ _ _ _ _ _ _ _hio NO. 61__. ___ _ _ _ _ _ _Licking .._____________ . . _ _ _Ohio No. 475 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _OhioNo. 82 _ _ _ _ _ _ _ _ _ _ _ _ _ _Ohio No. 488_ _ _. _ _ _. _ _ __ _ __Ohio No. 92_____. _ _________Ohio No. 598 _ _ _ _ _ _ _ _ _ _ _ _ _ _Ohio No. 11.___________. . _ _Ohio 1Ohio ? ~ ~.Ohio No. 619 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Ohio No. 04_ _ _ __ _ . _ _ __ _ . _ _Cumberland--. . - .Ohio So. 920 _ __ __ _. . . _ __ . _ .Tennessee._ _. _ _ _ - . _ _OhioNo. 933.-. . . _ __ __ ._ _ _Cumberland--. . - .Ohio So. 920 _ __ __ _. . . _ __ . _ .Tennessee._ _. _ _ _ - . _ _OhioNo. 933.-. . . _ __ __ ._ _ _MONTH OF BEPTEMBER, 914 -

5.03.09.67.28.81.3.55.07.012.712.211.620.03.136.6.875.562.852.756.952.656.870.045.110.692.512.487.6

-_ __ _ _ _ _ _1.053.062 0.94.475.672. 541.511.481.3415.76.222.93.38.46.61.a.157.721.28.3415.25.38.37.05.58

0.46.55.59.44.54.08.27.23.32.58.56.53.30.79.44.73. 9.74.62.64.52.56.69.25.32.43.16.30

2.242 72.862. 142. 62.391. 311. 121.552.822.722. 581.463.842.143.554.323.593.013. 112. 522. 723.351.211. 552.09.781.46

Allegheny No. ___ . _________MonongahelaNo. 2 _ _ _ _ _ _ _ _Ohio No. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Ohio No. 1 _______. . ________OhioNo. 19. _ _ _ __ _ _ _ . _ _ _ __ _ _OhioNo.23____. _. . . __. _____Beaver.. ____ . ___ _ _ _ _ _ _ _ _ _hioNO.5__. __. ___. ____. __Ohio No. 7_ _ _ __ _ _ _ __ _ _ . _ _ _ __Ohio No. 88 ___________ . . _ __ .Ohio No. 7__.... .._._....___Ohio No. 1M . . _ _____. _____ . _Ohio No. 49--. . _. _. . __. __.Sciato . _. ___. _.__.- _ _Ohio No. _ . . _______ . ___Licking . __. __.. ___. __ _

Streeter & Phelps, 1925

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Transcript of Streeter & Phelps, 1925