U.S. ENVIRONMENTAL PROTECTION AGENCY
       Annapolis Field Office
      Annapolis Science Center
     Annapolis, Maryland  21401
         TECHNICAL PAPERS
            Volume  20

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                          Table of Contents


                             Volume 20
            A Digital  Technique for Calculating  and Plotting
            Dissolved  Oxygen  Deficits
            A River-Mile Indexing System for  Computer Application
            in Storing and Retrieving Data      (unavailable)
            Oxygen Relationships in Streams,  Methodology to  be
             Applied when Determining the Capacity of a  Stream
            to Assimilate Organic Wastes - October 1964
            Estimating Diffusion Characteristics  of Tidal  Waters
            May 1965
            Use of Rhodamine B Dye as a  Tracer  in  Streams  of the
            Susquehanna River Basin - April  1965
 6          An In-Situ Benthic Respirometer - December 1965
 7          A Study of Tidal  Dispersion in the Potomac  River  -
            February 1966
 8          A Mathematical  Model  for the Potomac River -  What  it
            has done and what it  can do - December 1966
            A Discussion and Tabulation of Diffusion Coefficients
            for Tidal  Waters Computed as a Function of Velocity -
            February 1967
10          Evaluation of Coliform Contribution by Pleasure  Boats
            July 1966

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                            PUBLICATIONS

                U.S.  ENVIRONMENTAL PROTECTION AGENCY
                             REGION III
                       ANNAPOLIS FIELD OFFICE*


                              VOLUME 1
                          Technical  Reports

 5         A Technical  Assessment of Current Water Quality
           Conditions and Factors Affecting Water Quality in
           the Upper Potomac Estuary

 6         Sanitary Bacteriology of  the Upper Potomac Estuary

 7         The Potomac  Estuary Mathematical Model

 9         Nutrients in the Potomac  River Basin

11         Optimal  Release Sequences for Water Quality Control
           in Multiple Reservoir Systems

                              VOLUME 2
                          Technical  Reports

13         Mine Drainage in the North Branch Potomac River Basin

15         Nutrients in the Upper Potomac River Basin

17         Upper Potomac River Basin Water Quality Assessment

                              VOLUME  3
                          Technical  Reports

19         Potomac-Piscataway Dye Release and Wastewater
           Assimilation Studies

21         LNEPLT

23         XYPLOT

25         PLOT3D

     * Formerly CB-SRBP, U.S. Department of Health, Education,
       and Welfare; CFS-FWPCA, and CTSL-FWQA,  Middle Atlantic
       Region, U.S. Department of the Interior

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                             VOLUME 3   (continued)

                         Technical Reports


27         Water Quality and Wastewater Loadings - Upper Potomac
           Estuary during 1969


                             VOLUME 4
                         Technical Reports


29         Step Backward Regression

31         Relative Contributions of Nutrients to the Potomac
           River Basin from Various Sources

33         Mathematical Model Studies of Water Quality in the
           Potomac Estuary

35         Water Resource - Water Supply Study of the Potomac
           Estuary

                             VOLUME 5
                         Technical Reports


37         Nutrient Transport and Dissolved Oxygen Budget
           Studies in the Potomac Estuary

39         Preliminary Analyses of the Wastewater and Assimilation
           Capacities of the Anacostia Tidal River System

41         Current Water Quality Conditions and Investigations
           in the Upper Potomac River Tidal System

43         Physical Data of the Potomac River Tidal System
           Including Mathematical Model Segmentation

45         Nutrient Management in the Potomac Estuary


                             VOLUME 6

                         Technical Reports


47         Chesapeake Bay Nutrient Input Study

49         Heavy Metals Analyses of  Bottom Sediment in the
           Potomac River Estuary

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                                  VOLUME  6  (continued)

                              Technical  Reports

     51          A System of Mathematical Models for Water Quality
                Management

     52         Numerical Method for Groundwater Hydraulics

     53         Upper Potomac Estuary Eutrophication Control
                Requirements

     54         AUT0-QUAL Modelling System

Supplement      AUT0-QUAL Modelling System:  Modification for
   to 54        Non-Point Source Loadings

                                  VOLUME  7
                              Technical Reports

     55         Water Quality Conditions in the Chesapeake Bay System

     56         Nutrient Enrichment and Control Requirements in the
                Upper Chesapeake Bay

     57         The Potomac River Estuary in the Washington
                Metropolitan Area - A History of its Water Quality
                Problems and their Solution

                                  VOLUME  8
                              Technical Reports

     58         Application of AUT0-QUAL Modelling System to the
                Patuxent River Basin

     59         Distribution of Metals in Baltimore Harbor Sediments

     60         Summary and Conclusions - Nutrient Transport and
                Accountability in the Lower Susquehanna River Basin

                                  VOLUME  9
                                 Data Reports

                Water Quality Survey, James River and Selected
                Tributaries - October 1969

                Water Quality Survey in the North Branch Potomac River
                between Cumberland and Luke, Maryland - August 1967

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                            VOLUME 9   (continued)

                           Data Reports


           Investigation of Water Quality in Chesapeake Bay and
           Tributaries at Aberdeen Proving Ground, Department
           of the Army, Aberdeen, Maryland - October-December 1967

           Biological Survey of the Upper Potomac River and
           Selected Tributaries - 1966-1968

           Water Quality Survey of the  Eastern Shore Chesapeake
           Bay, Wicomico River, Pocomoke River, Nanticoke River,
           Marshall Creek, Bunting Branch, and Chincoteague Bay -
           Summer 1967

           Head of Bay Study - Water Quality Survey of Northeast
           River, Elk River, C & D Canal, Bohemia River, Sassafras
           River and Upper Chesapeake Bay - Summer 1968 - Head ot
           Bay Tributaries

           Water Quality Survey of the  Potomac Estuary - 1967

           Water Quality Survey of the  Potomac Estuary - 1968

           Wastewater Treatment Plant Nutrient Survey - 1966-1967

           Cooperative Bacteriological  Study - Upper Chesapeake Bay
           Dredging Spoil  Disposal - Cruise Report Mo. 11

                            VOLUME 10

                            Data Reports

 9         Water Quality Survey of the  Potomac Estuary - 1965-1966

10         Water Quality Survey of the  Annapolis Metro Area - 1967

11         Nutrient  Data on  Sediment Samples of the Potomac Estuary
           1966-1968

12         1969 Head  of  the  Bay Tributaries

13         Water Quality Survey of  the  Chesapeake  Bay  in the
           Vicinity  of  Sandy Point  - 1968

14         Water Quality  Survey  of  the  Chesapeake  Bay  in the
           Vicinity  of Sandy Point  - 1969

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                             VOLUME 10(continued)

                           Data Reports

15         Water Quality Survey of the  Patuxent River -  1967

16         Water Quality Survey of the  Patuxent River -  1968

17         Water Quality Survey of the  Patuxent River -  1969

18         Water Quality of the Potomac Estuary Transects,
           Intensive and Southeast Water Laboratory Cooperative
           Study - 1969

19         Water Quality Survey of the  Potomac Estuary Phosphate
           Tracer Study - 1969

                             VOLUME 11
                            Data Reports

20         Water Quality of the Potomac Estuary Transport Study
           1969-1970

21         Water Quality Survey of the Piscataway Creek Watershed
           1968-1970

22         Water Quality Survey of the Chesapeake Bay in the
           Vicinity of Sandy Point - 1970

23         Water Quality Survey of the Head of the Chesapeake Bay
           Maryland Tributaries - 1970-1971

24         Water Quality Survey of the Upper Chesapeake Bay
           1969-1971

25         Water Quality of the Potomac Estuary Consolidated
           Survey - 1970

26         Water Quality of the Potomac Estuary Dissolved Oxygen
           Budget Studies - 1970

27         Potomac Estuary Wastewater Treatment Plants Survey
           1970

28         Water Quality Survey of the Potomac Estuary Embayments
           and Transects - 1970

29         Water Quality of the Upper Potomac Estuary Enforcement
           Survey - 1970

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   30


   31


   32
   33
   34
Appendix
  to 1
Appendix
  to 2
    3


    4
                  VOLUME 11  (continued)
                 Data Reports

Water Quality of the Potomac Estuary - Gilbert Swamp
and Allen's Fresh and Gunston Cove - 1970

Survey Results of the Chesapeake Bay Input Study -
1969-1970

Upper Chesapeake Bay Water Quality Studies - Bush River,
Spesutie Narrows and Swan Creek, C & D Canal, Chester
River, Severn River, Gunpowder, Middle and Bird Rivers -
1968-1971

Special Water Quality Surveys of the Potomac River Basin
Anacostia Estuary, Wicomico.River, St. Clement and
Breton Bays, Occoquan Bay - 1970-1971

Water Quality Survey of the Patuxent River - 1970

                  VOLUME 12

               Working Documents

Biological Survey of the Susquehanna River and its
Tributaries between Danville, Pennsylvania and
Conowingo, Maryland

Tabulation of Bottom Organisms Observed at Sampling
Stations during the Biological Survey between Danville,
Pennsylvania and Conowingo, Maryland - November 1966

Biological Survey of the Susquehanna River and its
Tributaries between Cooperstown, New York and
Northumberland, Pennsylvnaia - January 1967

Tabulation of Bottom Organisms Observed at Sampling
Stations during the Biological Survey between Cooperstown,
New York and Northumberland, Pennsylvania - November 1966

                  VOLUME 13
               Working Documents

Water Quality and Pollution Control Study, Mine Drainage
Chesapeake Bay-Delaware River Basins - July 1967

Biological Survey of Rock Creek (from Rockville, Maryland
to the  Potomac River)  October 1966

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                             VOLUME   13   (continued)

                          Working  Documents

 5         Summary of Water Quality  and  Waste  Outfalls,  Rock  Creek
           in Montgomery County, Maryland and  the  District  of
           Columbia - December 1966

 6         Water Pollution Survey  -  Back River 1965  -  February  1967

 7         Efficiency Study of the District  of Columbia  Water
           Pollution Control  Plant - February  1967

                             VOLUME   14

                          Working  Documents

 8         Water Quality and Pollution Control  Study - Susquehanna
           River Basin from Northumberland to  West Pittson
           (Including the Lackawanna River Basin)  March 1967

 9         Water Quality and Pollution Control  Study,  Juniata
           River Basin - March 1967

10         Water Quality and Pollution Control  Study,  Rappahannock
           River Basin - March 1967

11         Water Quality and Pollution Control  Study,  Susquehanna
           River Basin from Lake Otsego, New York, to  Lake  Lackawanna
           River Confluence, Pennsylvania -  April  1967

                             VOLUME  15
                          Working Documents

12         Water Quality and Pollution Control  Study,  York River
           Basin - April 1967

13         Water Quality and Pollution Control  Study,  West Branch,
           Susquehanna River Basin - April  1967

14         Water Quality and Pollution Control  Study,  James River
           Basin - June 1967 .

15         Water Quality and Pollution Control  Study,  Patuxent  River
           Basin - May 1967

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                             VOLUME 16

                          Working Documents

16         Water Quality and Pollution Control  Study,  Susquehanna
           River Basin from Northumberland, Pennsylvania,  to
           Havre de Grace, Maryland - July 1967

17         Water Quality and Pollution Control  Study,  Potomac
           River Basin - June 1967

18         Immediate Water Pollution Control  Needs, Central  Western
           Shore of Chesapeake Bay Area (Magothy, Severn,  South,  and
           West River Drainage Areas)  July 1967

19         Immediate Water Pollution Control  Needs, Northwest
           Chesapeake Bay Area (Patapsco to Susquehanna Drainage
           Basins in Maryland) August 1967

20         Immediate Water Pollution Control  Needs - The Eastern
           Shore of Delaware, Maryland and Virginia - September 1967

                             VOLUME 17
                           Working Documents

21         Biological Surveys of the Upper James River Basin
           Covington, Clifton Forge, Big Island, Lynchburg, and
           Piney River Areas - January 1968

22         Biological Survey of Antietam Creek and some of its
           Tributaries from Waynesboro, Pennsylvania to Antietam,
           Maryland - Potomac River Basin - February 1968

23         Biological Survey of the Monocacy River and Tributaries
           from Gettysburg, Pennsylvania, to Maryland Rt. 28 Bridge
           Potomac River Basin - January 1968

24         Water Quality Survey of Chesapeake Bay in the Vicinity of
           Annapolis, Maryland - Summer 1967

25         Mine Drainage Pollution of the North Branch of Potomac
           River - Interim Report - August 1968

26         Water Quality Survey in the Shenandoah River of the
           Potomac River Basin - June 1967

27         Water Quality Survey in the James and Maury Rivers
           Glasgow, Virginia - September 1967

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                             VOLUME  17   (continued)

                           Working Documents

28         Selected Biological  Surveys in the James River Basin,
           Gillie Creek in the Richmond  Area, Appomattox River
           in the Petersburg Area, Bailey Creek from Fort Lee
           to Hopewell  - April  1968

                             VOLUME  18
                           Working Documents

29         Biological  Survey of the Upper and Middle Patuxent
           River and some of its Tributaries - from Maryland
           Route 97 Bridge near Roxbury Mills to the Maryland
           Route 4 Bridge near Wayson's Corner, Maryland -
           Chesapeake Drainage Basin - June 1968

30         Rock Creek Watershed - A Water Quality Study Report
           March 1969

31         The Patuxent River - Water Quality Management -
           Technical Evaluation - September 1969

                             VOLUME 19
                          Working Documents

           Tabulation, Community and Source Facility Water Data
           Maryland Portion, Chesapeake Drainage Area - October 1964

           Waste Disposal Practices at Federal  Installations
           Patuxent River Basin - October 1964

           Waste Disposal Practices at Federal  Installations
           Potomac River Basin below Washington, D.C.- November 1964

           Waste Disposal Practices at Federal  Installations
           Chesapeake Bay Area of Maryland Excluding Potomac
           and Patuxent River Basins - January  1965

           The Potomac Estuary - Statistics and Projections -
           February 1968

           Patuxent River - Cross Sections and  Mass Travel
           Velocities - July 1968

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                            VOLUME  19 (continued)

                         Working Documents

          Wastewater Inventory - Potomac River Basin -
          December 1968

          Wastewater Inventory - Upper Potomac River Basin -
          October 1968

                            VOLUME 20
                         Technical Papers-

 1         A  Digital Technique for Calculating and Plotting
          Dissolved Oxygen Deficits

 2         A  River-Mile  Indexing System for Computer Application
          in Storing and Retrieving Data      (unavailable)

 3         Oxygen  Relationships in Streams, Methodology to be
          Applied when  Determining the Capacity of a Stream to
          Assimilate Organic Wastes - October 1964

 4         Estimating Diffusion Characteristics of Tidal Waters -
          May  1965

 5         Use  of  Rhodamine B Dye as a Tracer in Streams of the
          Susquehanna River Basin - April 1965

 6         An In-Situ Benthic Respirometer - December 1965

 7         A  Study of Tidal Dispersion in the Potomac River
          February  1966

 8         A  Mathematical Model for the Potomac River - what it
          has  done  and  what it can do - December 1966

 9         A  Discussion  and Tabulation of Diffusion Coefficients
          for  Tidal Waters Computed as a Function of Velocity
          February  1967

10         Evaluation of Coliform  Contribution by Pleasure Boats
          July 1966

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                            VOLUME  21
                         Technical Papers

11        A Steady State Segmented Estuary Model

12        Simulation of Chloride Concentrations in the
          Potomac Estuary - March 1968

13        Optimal Release Sequences for Water Quality
          Control in Multiple-Reservoir Systems - 1968

                            VOLUME  22
                         Technical  Papers

          Summary Report - Pollution of Back River - January 1964

          Summary of Water Quality - Potomac River Basin in
          Maryland - October 1965

          The Role of Mathematical  Models in the Potomac River
          Basin Water Quality Management Program - December 1967

          Use of Mathematical Models as Aids to Decision Making
          in Water Quality Control  - February 1968

          Piscataway Creek Watershed - A Water Quality Study
          Report - August 1968

                            VOLUME  23
                        Ocean Dumping Surveys

          Environmental Survey of an Interim Ocean Dumpsite,
          Middle Atlantic Bight - September 1973

          Environmental Survey of Two Interim  Dumpsites,
          Middle Atlantic Bight - January 1974

          Environmental Survey of Two Interim Dumpsites
          Middle Atlantic Bight - Supplemental Report -
          October 1974

          Effects of Ocean Disposal Activities on Mid-
          continental Shelf Environment off Delaware
          and Maryland - January 1975

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                            VOLUME 24

                           1976 Annual
Technical
Report 61

Technical
Report 62
Current Nutrient Assessment - Upper Potomac Estuary
Current Assessment Paper No. 1

Evaluation of Western Branch Wastewater Treatment
Plant Expansion - Phases I and II

Situation Report - Potomac River

Sediment Studies in Back River Estuary, Baltimore,
Maryland

Distribution of Metals in Elizabeth River Sediments
A Water Quality Modelling Study of the Delaware
Estuary

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                       TABLE OF CONTENTS



                                                           Page



       List of Figures



   I.  Introduction	    1



  II.  Oxygen Sag Equation	    1



 III.  Main Program and Subroutines .	    2



  IV.  Preparation of Data	    5



   V.  Data Output  .	  .    8



  VI.  Cost Data  .	    9



 VII.  Conclusions  	 ......   10



VIII.  Acknowledgments	   10

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                        LIST OF FIGURES



Figure 1  Simplified flow chart showing operations
            performed by the program

Figure 2  Main program for the oxygen sag equation

Figure 3  Subroutine MAP - used by the main program

Figure 4  Subroutine WRTTTEM - used by subroutine MAP

Figure 5  Data package format for Set No. 1

Figure 6  Data output and graph for Set No. 1

Figure 7  Data output and graph for Set No. 2

Figure 8  Data output and graph for Set No. 3

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I .
        A package program for vise on the IBM 7090 computer is

presented for obtaining a numerical solution of the classical

Street er-Phelps oxygen sag equation.  Oxygen deficits are com-

puted for each desired time and plotted as a function of time.

        In general, no knowledge on the reader's part is assumed

with regard to computers or the program presented.  Certain

terminology having general use will be discussed in order to

clarify the presentation; however, the step-by-step instructions

should enable engineers and scientists to obtain correct results

without a thorough knowledge of computer terminology.

II.  Oxygen Sag Equation

        In 1925 Streeter-Phelps^ ' formulated the oxygen sag

equation which describes the changes in dissolved oxygen content
of a stream following the introduction of an oxygen demanding
organic waste.  The mathematical formulation describes the net

rate of change in the oxygen deficit (D) at any time (t) and is

expressed as a first order differential equation:

                     = %L - K2D                   Equation (l)
                  dt
where K,L represents the increase in the deficit at a rate which

is assumed to be proportional to the oxygen demand of the waste.

The second term of the equation, namely -^D, represents the

rate of reaeration expressed in terms of the oxygen saturation

deficit .

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        On integrating Equation (l) the dissolved oxygen content

of the water may be obtained as the deficit below saturation at

any time.  The integrated form is then:
                       Jf T      —K t     K +
                  D = —!_S— (e~ 1  - e" 2 ) + Dae "*"  Equation (2)
                      K2 ~ Kl
where:  Da = Initial dissolved oxygen saturation deficit (mg/l)

        D  = Oxygen deficit, after time (t) (mg/l)

        La = Ultimate biochemical oxygen demand (mg/l)

        KI = Empirical deoxygenation rate constant

        KŁ = Empirical reaeration rate constant

        t  = Elapsed time in days

        e  = Base of naperian or natural logarithms and is equal
             to 2.71828


        The numerical solution to the above form requires that

knowledge of the reaeration and deoxygenation rate constants

together with the ultimate biochemical oxygen demand and initial

oxygen deficit be known.  Once these values are in hand, we may

solve for the oxygen deficits at any desired time.
   o  Main Program and Subroutines

        In order to visualize the flow of data and functions of

the program, Figure 1 is presented showing a simplified flow

chart of the various operations performed „  The input informa-

tion is seen to consist, of K^, KŁ, La, Da, and T-j_ values where

i = 1 to N.  The program computes the corresponding D^ value
                                                     jSSfc
or each t± value for a  given K^, Kg, La, and D&.  The computed

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                           START
                            i
                      READ IN ! K|,K2
                       L,Q,Da and  Tj
                      values i = !  to N
                        COMPUTES :
                       (e~kiti-e"k2t«)-l-Da
                         i = I to N
                             i
                          PRINTS
                        Dj,t; values
                         i s I  to N
                          GRAPHS
                     DJ as  a function of t;
                          i= I  to N
SIMPLIFIED  FLOW  CHART  SHOWING  OPERATIONS
         PERFORMED  BY  THE  PROGRAM
                                               FIGURE  I

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tj[ and DJ> values for each set of input data are printed and



graphed.  After the first set of data has been computed, control



returns to the beginning of the program and new values for %,



K2, La, Da, and t^'s are read in.  This process continues until



the last set of data has been computed and printed.



        The program presented here has been written in what is



termed FORTRAN.  Every type of computer is designed to respond



to a special code, called a "machine language."  The instructions



telling the computer what steps to perform to solve a problem



must be given to the computer in its own language.  The FORTRAN



program makes it unnecessary for the programer to learn the more



complicated machine language.  The word FORTRAN, derived from



formula translation, is a method of programing using language



similar to familiar usage.  The FORTRAN program is then assembled



by the computer in proper form for machine interpretation.



        The main program for calculating dissolved oxygen deficits



and plotting the deficits as a function of time is shown in Figure



2..  In all, there are eighteen FORTRAN statements, exclusive of



the XEQ, LABEL, and END card.  Each statement is punched on a



separate IBM card.  At times it may be necessary to change three



cards in the main program depending on the data input, plus the



input and output tape unit numbers.  In order to obtain an under-



standing of when these changes should be made, a sample case



will be discussed here.  First, let us consider Card No. 3; the

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FORTRAN statement appears as DIMENSION TIME (25), FIVE (25).



This instructs the computer to assign 25 storage locations for



each variable TIME and FIVE,  The FIVE written here is actual



storage assigned for the D^ values.  If more than 25 TIME values



are to be used in calculating the dissolved oxygen deficits, it



will be necessary to change both TIME (25) and FIVE (25) to read



the number of TIME values desired.  Let N represent the number



of TIME values; then the statement in general form may be written



DIMENSION TIME (N), FIVE (N).  If the number N of desired TIME



values is less than or equal to 25, no change to the statement



is necessary.



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the input and output tape unit numbers used by the computing



center.  In preparing these cards, it is necessary to request



the input and output tape unit numbers from the center where



the program will be run.  In general, the computing center will



usually obtain the tape unit numbers; however, it is advisable



to instruct them of the input-output numbers.



        Card No, 4> appearing with the statement IT = 5, specifies



that the input data tape unit number is 5.  Similarly, KT = 6



on Card No. 5 specifies that the output tape unit number is 6.



        Figure "± shows one of the three subroutines used by the



main program.  Again, each statement appearing is punched on a



separate IBM card.  This subroutine is designed to aid in the

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plotting of dissolved oxygen deficits as a function of time and



is called into use by the main, program by the statement appear-



ing on Card No0 19=  Figure 4  is the second subroutine that is



used by the first to write out the computed data.  The other sub-



routine is not shown here because of its existence on tape or



card deck at the computing center.  This type of subroutine is



termed a library routine and is designed to perform calculations



on the exponential function,,



        In punching the main program and subroutine on IBM cards,



it is advisable to punch the main program on cards of a different



color than the subroutine cards.  This practice insures rapid



identification when changes are to be made to the main program.



Prior to actually running the program, a request to the keypunch



operator for verification of the information punched on the cards



is desirable.






IV „  Preparation of Data



        A sample case is shown in Table I of the input data.



Here it is desired to compute and plot the dissolved oxygen



deficits for three sets of data, each with a different initial



oxygen deficit (Da) and ultimate biochemical oxygen demand (La).



It is assumed that % = 0,12, and K/> - 0,25 for each set.  This



is done here for reasons of simplicity; actually, K]_ and Kg nay



take on different values for each set of data0  Again, for sim-



plicity, the desired deficits here are computed for each day

-------

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from 1 to 20 days for each set,,  The time values may be given in

tenths or hundredths of a day, if desired; however, the interval

between values should remain constant„  In addition, for all

practical purposes the program is designed to accept an unlimited

and variable length number of time values from set to set.  Refer

to Figure Ł for the data setup.


                            Table I

                              Da
      Set                   Initial               Ultimate
     Number              Oxygen Deficit              BOD

       1                      0.00                   5.00
       2                      1.00                  10.00
       3                      2.00                  15.00


        To begin, the first data card will contain:

        !„  Number of time values N (In this case N = 20 for
            each set)
        20  Set Number (Set No. 1)
        3.  Values for K]_ (deoxygenation rate constant)
        4.  Value for K2 (reaeration rate constant)
        5.  Value of initial oxygen deficit (Da)
        6.  Value of ultimate biochemical oxygen demand (La)


        The second card will contain ten values of the time,

starting with 1,00 and ending with 10.000  The third data card

will start with 11.00 and end with 20.00.  This completes the

first set of data that the computer will work with,,  The second

set of data will contain the six pieces of information contained

on the first data card, only using the values that pertain to

Set No, 2.  Again, since our sample case specifies the same time

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values as the first set, the second and third cards of the second

set will be identical to the second and third cards of the first

set.  Similarly, Set No. 3 will be punched in the order specified

above.  The number of sets is unlimited, since each set is read

into memory prior to the calculations, and the second set of

data will not be read in until the completed plot of the calculat-

ed information from the first set is finished.  After the last

set of data is worked on, the program halts.

        In punching the data, the following format must be

rigidly adhered to:

        1.  The number of time values N should be punched from
            right to left, beginning in Card Column 4; i.e., if
            nine values of the time are to be used, a 9 punch
            should appear in Column 4.  If N = 20, as in our case
            here, the 0 appears in Column 4, and the 2 appears
            in Column 3.

        2.  The set number is to be punched in Column 10.  Again,
            if the set number exceeds 9, the last digit appears
            in Column 10.  Columns 5, 6, and 7 should contain
            the word SET.

        3.  The deoxygenation rate constant K^ is punched in
            Columns 19 and 20, with the decimal punch appearing
            in Column 18.  The decimal point must always appear
            in Column 18, whether the number is an integer or
            decimal.

        4.  The reaeration rate constant K2 is punched in Columns
            29 and 30, with the decimal point punched in Column
            28.  Again, the same holds regarding the decimal
            point punch as above,

        5.  Initial oxygen deficit is punched with the integer
            value in Column 3V, decimal point in Column 38, and
            tenths and hundredths in Columns 39 and 40, respec-
            tively.

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                                                              8


        6,,  The ultimate biochemical oxygen demand is punched
            in Columns 46 through 50, with decimal punch in
            Column 4#»

        The time values begin on the second data card of each

set, with the first appearing in Columns 1 through 7.  The decimal

point punch appears in Column 5,  Decimal points may be located

on each data card beginning with the second card by adding seven

columns successively; i.e., decimal point for the second time

value would be punched in Column 12, the third in Column 19,

etc., until the tenth decimal point appears in Column 68.


V.  Data Output

        Figures 6, 7_, and 8 show the output for our sample case

using three sets of input data.  First, the run identification

number indicates the output data which follows is for a specific

set number.  The input values for time are printed, together

with the computed oxygen deficits corresponding to a particular

time value.  The printed data for each set is then plotted directly.

        A graph of the oxygen sag appears with the time values

on the horizontal ordinate and oxygen deficit values along the

vertical ordinate.  The time values along the horizontal ordinate

appear in floating point form where E 00 represents the exponent

to which 10 is raised.  In conversion to decimal form, it is

necessary to multiply the number preceding the E by 10 to the

appropriate power.

-------

-------
              I  I I  I  I
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                                                   t-  UJ  OOOOOOOOOOOOOOOOOOOOO.
                                                   Z  X  OOOOOOOOOOOQOOOOOOOO— i,  ., .
                                                   uj  —  *	K  Value
           I <  I  I I  I  I I  t  I  I I  I  I I  I
          oooooooooooooooooooo
          ooooooooooooouoooooo
                                                                                              Set number
                                                                                              Number of time voluet
                   TIME (DAYS)
            DATA    OUTPUT  AND   GRAPH    FOR   SET   NUMBER
                                                                                              FIGURE   6

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  o


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   -  - - - -   --   - —   -  -->«oh.h.«o<
                              i O r B r-


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                                                                                                  , Value
                                                    *-   UJ  OOOOOOOOQOOOOOOOOOOOfM

                                                    z   x  oooooooooooooooooooo-*«  Value


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                                                                                                 '
           I  I I  I  I I  I  I I I  .1  I I I  I  I I
          oooooooooooooooooooo
                                      * Set number


                                      at
                                      (/I


                                      °Number of time values
                    TIME (DAYS)
            DATA   OUTPUT  AND   GRAPH   FOR    SET    NUMBER   2
                                                                                              FIGURE   7

-------

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                                                                                             Ultimate  BOO
                                                                                             |nit|a| QQ Deficit
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         oooooooooooooooooooo


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         oooooooooooooooooooo
                                                                                              K  Value
                                                                                             Set number
                                                                                             Number of time values
                  TIME (DAYS)
           DATA   OUTPUT   AND   GRAPH   FOR   SET    NUMBER
                                                                                             FIGURE   6

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-------
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                                                 M   t
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                                                                                         »o i.>t, i n/\ n*ji :.
                                                                                         -« • Initial 00 Deficit
                                                                                           .  K0 Value
                                                                                          o   2
                                                 I-  111  O OO O O O O O O OO OOOOO OO O O fM
                                                 z  z  oooooooooooooooooooo — K  Value
          I  I  I I I  I I  I  I I  I  I I  I  I I  I  I I  I
          ooooooooooooo ooooooo
                                                                                             S«t number
                                                                                           2Number of time values
                   TIME (DAYS)
           DATA   OUTPUT   AND   GRAPH   FOR   SET    NUMBER   2
                                                                                           FIGURE   7

-------

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                                                                                           .  . .  . __  -  ., ,.
                                                                                           Initial DO  Deficit
                                                                                         ~ K« Value
                                                                                         o  ^
                                                      OOOOOOOOOOOOOOOOOOOOfM
                                                      OOOOOOOOOOOOOOOOOOOO-^K  Value
                                              O  ^   ^(Mrt*tA^4<
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o o o o o o o <


oooooooooooooooooooo
                   f4(**iA
-------

-------
        The vertical ordinate is developed by taking the largest



value of the computed oxygen deficit and letting it be represented



by the alphabetic character K, with the smallest computed oxygen



deficit represented by the character A.  The range of values for



the deficit then becomes K-A.  The alphabetic characters from A



through K are assigned floating point values, as shown above



each graph.






„1.  Cost Data



        For actual production runs, using the IBM 7090, the



machine rental rates vary from approximately $360 per hour to



$500 per hour.  The rental time required to run the cases shown



in Figures 6_, 7_, and 8 amounted to less than one minute, or



approximately $6 for a minimum machine rental,,  Since costs and



methods of charging vary from one computer installation to the



next, it is advisable to determine if a minimum rental charge



exists.  In other words, certain installations may require a



minimum of five or ten minute charge regardless of actual machine



time.  In this case, it would be advisable to run many sets of



data at one time or search for another installation.  Since



computer rates vary, it is usually advisable to shop; however,



this should be justified by the rate differential, as the admin-



istrative time cost involved should not exceed the monies saved



by procuring a lower rate computer charge.  In addition, the



procurement of a computer close to the technical personnel using

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                                                             10


the machine will produce a savings far in excess of the differ-

ential between low and high computer rentals.


VII,  Conclusions

        The program package has been shown to consist of four

separate card decks, namely:

        1.  Main Program Deck
        20  Subroutine Deck Map
        3,  Subroutine Deck Writtem
        4,  Data Input Deck

        Assuming the program will be re-run at the same comput-

ing center, no changes need be made in the symbolic decks.

Hence, to conserve computing time, we may replace (l), (2), and

(3) by the corresponding binary decks,  (These are machine

language programs which are compiled by the FQRTHAN program

during the first run„)


VIII.  Acknowledgments

        The authors wish to express their appreciation to Mr0

Emanuel Mehr, Consulting Computer Mathematician, New York

University, and to Mr. P, O'Hara, Mathematician, National Bureau

of Standards, Washington, D. C., for their cooperation in develop-

ing this technique.

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PURPOSE

This manual has been compiled to facilitate water resources
studies by providing a readily available source of information
covering methodology and some of the concepts used to estimate
oxygen relationships in a stream.  There are many fine technical
writings, journals, and books covering oxygen relationships in
a stream; however, a need has developed to have some of the
methodology and analysis techniques available in a reference
manual.  It is hoped this manual can fill the need.
ACKNOWLEDGMENTS

The preparation of this manual was greatly facilitated by the
use of information from the following sources and the assistance
of the following individuals:

        T. A. Wastler - Public Health Service

        R. L. O'Connell - Public Health Service

        J. E. McLean - Public Health Service

        Eckenfelder & O'Connor - "Biological Waste and
          Treatment," Pergamon Press, 196l

        Fair & Geyer - "Water Supply and Waste-Water
          Disposal," Wiley & Sons, Inc., 195H

        E. C. Tsivoglou - "Natural Self-Purification
          of a Polluted Stream," (RATSEC Training
          Course Manual), Public Health Service

        Phelps - "Stream Sanitation," Wiley & Sons,
          Inc.,

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                           TABLE OF CONTENTS

                                                               Page

    I.  Introduction ....................     1

   II.  Dissolved Oxygen Relationships in a Stream .....     1

  III.  Biochemical Demand (BOD) ..............     3

   IV.  Deoxygenation Rate Constant (K, or k )  .......     5

    V.  Determination of Deoxygenation Rate Constant
  VII.  Reaeration
                                                                 8
   VI .   Determination of Stream K  Rate  ..........    11
 VIII.  Reaeration Coefficient - K  (base e) or k?
          (base 10)  ....... ....... 7 .....    15

   IX.  Oxygen Sag Equation  ................    IT

    X.  Uses of Oxygen Sag Equation  ............    19

   XI.  Stream Assimilation Capacity ............    22

 TABLES

    I.  Expected Values for the Deoxygenation Rate (K, and
          k ) for Streams vith Varying Degrees of Pollution      7

   II.  Typical Values of the Self -Purification Factor
          "f"  .......................    19

FIGURES

    1.  Saturation D. 0. Concentrations vs. Temperature
          and Pressure ...................    2k

    2.  BOD Exertion vs. Time  ...............    25

    3.  Per Cent BOD Removed vs. Time and K  (k )  .....    26
                                            / rri^prj \
    U.  Temperature Correction Factor (l.OUT  ~   )  for
          K  (k) and K  (k)  ...............    2?

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                     TABLE OF CONTENTS (Continued)



FIGURES                                                        Page



    5.  Daily Difference Determination ...........     28



        5a.  BOD Exerted vs. Time  .............     28



        5b.  Log BOD Difference vs. Time ..........     29



    6.  Oxygen Balance Profile - Stream BOD (pounds) vs.

          Stream Miles ...................     30



    7.  Stream Reaeration Reaction - D. 0.  Concentration

          vs. Time .....................     31
    8.  Temperature Correction Factor (1.017      )  for
        lOa.  D  = 1.0 mg/1
               a
                                                                32
    9.  Graph of the Typical Oxygen Sag - D.  0.  Concentra-

          tion vs .  Time  ..................     33



   10.  Graphical Solution of the Oxygen Sag  Equation  ...     3^
        lOb.  D  =2.0 mg/1  ................     35
               a


        lOc.  D  = 3.0 mg/1  ................     36
               €1


   11.  Log L  (mg/l) vs. Temperature  ...........     37
             ŁL


   12.  Allowable Stream BOD Loading (pounds) vs.

          Temperature and Flow ...............     38



EXAMPLES



    I.  Daily Difference Method  ..............      8



   II.  Graphical Solution of the Assimilative Capacity

          Problem by Method 2a ...............     20



  III.  Use of the Graphical Method to Determine Minimum

          D. 0. Concentrations Following the Introduction

          of a Waste Into a Stream .............     20



   IV.  A Procedure for Developing Assimilative Capacity

          Curves ......................     22

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 I,  Introduction

 The availability of water of suitable quality has determined the
 location of most past and present civilizations.   Therefore, it
 must be concluded that future population and economic growth will
 rely heavily upon the availability of water.

 To insure maximum utilization of water resources, many variables
 must be considered, as maximum utilization requires water quality
 to be suitable for multi-purpose uses-  Multi-purpose uses include
 water supply, recreation, support of fish and aquatic life, plus
 waste assimilation and transport.  To maintain water quality suit-
 able for these beneficial uses requires development of specific
 water quality objectives; and these objectives or criteria must
 be basically concerned with the introduction, elimination, or
 control of waste materials in the water.

 A principal problem in the analysis or evaluation of water
 resources is the coincidence of adverse natural stream conditions
 with periods of maximum water use.  Normally, summer and early
 fall months are the most critical periods for water quality and
 quantity, because of high temperatures, low flows, and maximum
 water use.  Prior to the formulation of specific  water management
 programs, it is necessary to have some knowledge  of the physical,
 chemical, and biological characteristics of available water
 resources, especially surface waters.

 This presentation will set forth some of the available methods
 for analyzing and evaluating effects of biologically degradable
 organic wastes on stream quality.  The indicator  of water quality
 used throughout this manual is the dissolved oxygen content
 (D.O.), while the measure used for expressing organic pollution
 in the following discussions and calculations is  the bio-chemical
 oxygen demand (BOD).  In presenting the following methodology,
 it is assumed that there are multiple stream uses, including
 waste assimilation and transport, and that a minimum quality
 objective is to be maintained.
II.   Dissolved Oxygen Relationships In A Stream

 Aerobic stabilization of organic matter within a stream environ-
 ment results in utilization of oxygen dissolved in the water.
 Oxygen is generally available or becomes available from the
 following five sources:

       1.  Dissolved oxygen within the stream,

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      2.  Oxygen transfer to the water from the atmosphere
          (stream aeration or reaeration),
      3.  Dissolved oxygen within the waste,
      k.  Oxygen produced by stream flora (algae),
      5-  Chemical reduction of compounds (e.g., nitrites and
          nitrates, 2NO  + 2N02 + Og

Where relatively high nutrient concentrations, long periods of
sunlight, and low turbidity exist, stream flora may cause con-
siderable fluctuations in dissolved oxygen and BOD levels.  When
significant algal populations exist, oxygen concentrations
usually exhibit diurnal fluctuations; higher D.O. concentrations
during periods of sunlight and lower concentrations at night.
Stream flora utilize oxygen continuously in respiration; however,
at night, or on overcast days, a lack of sunlight may cause the
respiration rate (rate of oxygen use) to exceed the rate of
oxygen production from photosynthesis.  When this condition
occurs, the flora can exert a considerable oxygen demand causing
the large diurnal fluctuations. Upon death, algae can be respon-
sible for a major BOD loading in the stream.  Although nutrient
concentrations are becoming major problems in more and more areas,
the effects of nutrient balance and resulting flora on a stream's
oxygen balance are considered beyond the scope of this presenta-
tion; therefore, have been omitted.

The measurement of the D.O. concentration in a laboratory sample
is a reasonably accurate determination; however, it must be
recognized that a stream is a dynamic system.  It is unrealistic
to consider a single D.O. measurement as representative of a
stream under all conditions, because of variations in flow,
temperature, waste load, and other independent variables.

The quantity of oxygen required to stabilize a given amount of
oxygen material is relatively constant.  Approximately the same
number of pounds of oxygen are required to stabilize an organic
waste at 30° as would be required at 5°C.  However, because of
the effect of temperature on biological metabolic rates, the
time required for stabilization of a waste is greatly increased
when temperatures are lowered.

Oxygen, as it occurs in a stream, is measured as a concentration,
milligrams per liter (mg/l).  To convert concentration to mass
flow rate (pounds/day) requires the following calculation:

      Ibs oxygen/day = (mg/l D.O.) x (MGD stream flow) x (8.31* Ibs/gal)

                            or since 1 MGD =1.55 cfs

      Ibs oxygen/day = (mg/l) x (cfs stream flow) x (5-38 Ibs/cfs)

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  This calculation gives the total mass flow rate of oxygen dis-
  solved in the stream, for a particular location and time of
  sampling.  When a D.O. objective has been established for the
  stream, the dissolved oxygen in the stream available for oxida-
  tion of organic materials would be:

  0  available (mg/l) = present stream D.O. (mg/l) - stream D.O.
  objective (mg/l)

  This calculation shows that in many cases only a portion of the
  total D.O. in a stream may be utilized for oxidation, as the
  stream D.O. objective (minimum allowable D.O.) may represent the
  greater portion of the stream D.O.

  Maximum dissolved oxygen concentrations in water (saturation D.
  0's.) are dependent upon temperature, as illustrated by Figure
  ]L.   Engineering calculations to determine stream waste assimila-
  tion capacities-^-  are dependent upon the amount of oxygen avail-
  able and the rate of oxygen utilization.  Both of these variables
  are temperature dependent.  Figure !_ gives oxygen solubility in
  water in degrees Centigrade and degrees Fahrenheit for the usual
  range of temperatures.  Since less oxygen may be dissolved in a
  stream at warm temperatures, the amount of D.O. available for
  oxidation of wastes is also decreased.  When periods of warm
  stream temperatures and low stream discharges coincide, primarily
  during the summer and fall, the critical conditions for waste
  assimilative capacity occur.
III.  Biochemical Demand (BOD)

  BOD is a laboratory measurement of the amount of oxygen that is
  required or utilized in the stabilization of an organic waste.
  A graphical representation of a typical curve of BOD exertion vs
  time is shown in Figure 2_.  Figure 2_ shows that there are two
  stages of BOD exertion; the first (carbonaceous) stage is satis-
  fied in approximately 20 days; then the second (nitrogenous)
  stage exerts its oxygen demand.  In most engineering calculations,
  the carbonaceous BOD is the measurement used; therefore, all
  references to BOD in this report refer to the carbonaceous BOD.
  It is significant to note that BOD results may show considerable
  fluctuations, primarily because the BOD test is based upon the
  functioning of a biological system which tends to be quite vari-
  able.  Averaging values over a period of time increases relia-
  bility of the results; however, even the averaged values should
  not be considered absolute, regardless of the type of sampling
  and/or laboratory technique employed.
  ^-   Assimilative Capacity - the ability of a system to absorb a
      change (waste)  without destroying the prior uses of the system.

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BOD measurements to determine oxygen utilization are usually
carried out over a 5-day period at a temperature of 20°C; hence,
the reporting terminology "5-day BOD."  Complete stabilization
of a waste normally requires a much longer period than 20 days;
hovever, the ultimate BOD (oxygen required to completely stabi-
lize the carbonaceous BOD) can be calculated from the 5-day value.
The deoxygenation of wastes (rate of BOD exertion) through the
first stage reaction is generally approximated by a first order
equation.  The rate of reaction is directly proportional to the
amount of organic material present.  This reaction is represented
mathematically by the differential equation:

                             Q- K r
                             dt - KLL

        K  = reaction rate constant
         LI

        L  = amount of BOD remaining


        — = rate of BOD utilization
        dt

On integration this becomes:
               —K i*
       L  = L e  1   and represents first stage curve, Figure 2.
             ŁL                                                """"

       L  = BOD remaining

       L  = ultimate BOD of the waste
        a

       K  = deoxygenation rate constant (Base "e")^

       t  = elapsed time

~           T    _  —ft-T t   T  / -1    —"1 "k \
Or:    y  = L  - L e  1  = L  (1-e  1)
             a    a         a

       y  = amount of BOD utilized

       L  = ultimate BOD of the waste
        a

       K  = deoxygenation rate constant (Base "e")

       t  = elapsed time

Reaction rates in the above equations are expressed in terms of
Base "e;" however, they may also be expressed to the Base "10."
-^-   Convention indicates K  be used for Base "e" notation and
    k  be used for Base "10" notation.

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 Considerable care must be exercised to insure the proper base
 is being used.  Base "e" figures may be converted to Base "10"
 figures in the following manner:

         Kx (Base "e") = k± (Base "10") (2.3)

 To calculate the ultimate BOD value for a waste from the 5-day
 BOD, the following relationships are used:


         Tnt. n.   RnT1 ,T } _  Y (5-day)	5-day BOD (100)
         Ultimate J30D (L ) = —*	^ t A\ =	
                        a    1 - e  1O;   # BOD satisfied in 5 days

 The per cent BOD satisfied in 5 days is dependent upon tempera-
 ture and the bio-degradability of the waste.  Figure 3_ indicates
 the proportion of BOD removed in a given time period with a
 specified reaction rate constant.  When laboratory data on a
 given waste or stream are not available, 5-day BOD removal is
 usually taken as 68 - 83 per cent which, from Figure _3_, indicates
 K  to be 2.3 - 3.^5-  The above discussion was centered on 5-day
 BOD values, but any time period can be taken to use in approxi-
 mating the ultimate BOD; however, the 5-day values give more
 consistent results than the BOD values for shorter time intervals.

 In addition to providing more consistent values for the ultimate
 BOD, the 5-day BOD is utilized to reduce the time lag between
 the sample collection and laboratory results; to reduce incubator
 space requirements in the laboratory;  and to allow comparison of
 results by the selection of standard conditions.  These factors
 are extremely important when volume sampling is being done.
IV.   Deoxygenation Rate Constant (K,  or k )
 The deoxygenation rate constant is generally defined as the rate
 of oxygen utilization by a waste material, within a particular
 environment.   Characteristics which influence the rate constant
 are as follows:—

         a..  Turbulence - The speed of many chemical reactions
             is increased by turbulence.   The same effect is
             expected on biochemical reactions because of the
             greater opportunity that is  afforded for contact
             between the organic matter and the biological
             population.
 —   Eckenfelder and O'Connor,  "Biological Waste Treatment,"
     Pergamon Press, 196l.

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t> •  Biological growth on the stream bed - A biological
    population attached to the stream bed, particularly
    in shallow, turbulent waters containing rocks, will
    greatly increase the reaction rate.  This biological
    growth would be similar to that found in a trickling
    filter at a waste treatment facility.

c.  Immediate chemical demand - Some wastes contain chem-
    ical substances or end products of anaerobic decompo-
    sition which exert an immediate chemical demand.   Upon
    reaching a stream, these wastes have an almost instan-
    taneous uptake of D.O. and reach stability by chemical
    rather than biological processes.

    NOTE:  Significant amounts of immediate chemical
           demand can be separated out when determining
           the biological reaction rate constant.  This
           demand is measured as the BOD exerted in the
           first few minutes; a period too short to
           allow biological activity to become signifi-
           cant, and is shown when plotting BOD exerted
           vs time.

d.  Nutrients - Nutrients (nitrogen, phosphorus, and per-
    haps other substances) are necessary for the support
    of stream flora and fauna (plant and animal life).
    Lack of nutrients (fertilizer) restrains the growth
    of biological organisms responsible for the oxida-
    tion processes.  If a waste of the receiving stream
    is deficient in nutrients, oxidation will proceed
    at a much slower rate than in a laboratory when a
    standard BOD dilution water is used.

e.  Lag in oxidation processes - If an insufficient bio-
    logical population is present in a stream and/or
    waste, some interval of time will pass before normal
    oxidation occurs.  The lag is the time required to
    build up an adequate population.

f.  Dilution or waste concentration - Large volumes of
    water dilute waste discharges which, in turn, reduce
    the opportunity for contact between the organic
    material and the biological population.  If waste
    concentration is very low, the reaction rate will
    be considerably reduced.

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   Other factors which must be considered when trying to establish
   the deoxygenation rate in a stream include flocculation and
   sedimentation, scour, and volatilization.  Although these
   factors do not affect the actual reaction rate, they can result
   in the misinterpretation of field measurements.  Flocculation
   and sedimentation, as well as volatilization, give results
   which indicate marked decreases in BOD.  This would indicate
   that the rate of removal of organic material in the stream is
   much higher than actually exists.  However, organic sediment
   will exert its BOD at a later date.  Scour can indicate a low
   reaction rate, because sediments within the area may be brought
   into suspension, indicating little BOD exertion, although con-
   siderable oxidation may have taken place.

   The deoxygenation rate varies significantly and directly with
   temperature.  The variation is a result of increased biological
   activity at higher temperatures, and limited or reduced activity
   at lower temperatures.  The generally accepted relationship
   between the reaction rate constant and temperature is as follows:
                                                     (T—20)
           K  % any temperature T = K  @ 20°C x 1.0^7

           Where T = stream temperature in °C

                                                       (T—20)
   Figure h_ shows numerical values of the factor, 1.0^7      ,
   plotted over the normal range of temperatures.  The base temper-
   ature of 20°C is used, since this agrees with the laboratory
   incubation temperature at which the reaction rates are normally
   evaluated.

   Expected values for the deoxygenation rate constant are given in
   the table below:

                               TABLE I

      Stream Characteristics           KI (base e)       k  (base 10)


Heavily polluted streams               0.23  -0.69      0.1  -0.3
                                      generally O.Ul    generally 0.17

Streams not subject to immediate
  pollution                            0.19  - 0.36      0.08 - 0.15

Streams with small pollution loads     0.12  - 0.23      0.05-0.10

Sludge deposits (does not consider
  waste loads in the stream above
  the sludge deposit)                  0.023-0.19      0.01-0.08

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V.  Determination of Deoxygenation Rate Constant (K )


Given BOD-time series data from laboratory analyses, there are
several methods of obtaining the reaction rate of the incubated
sample.  Each method gives approximately the same result; there-
fore, the simplest method has been selected for presentation
here.  It must be realized that reaction rates calculated from
laboratory observations are not necessarily the same as those
in the stream.  The biological environment of a dynamic system,
such as a stream, cannot be duplicated in the laboratory.

    Example I

        Daily Difference Method

        The following results were obtained from a short-term
analysis of a sample by determining the BOD exerted each day
for a period of 7 days.  It is not necessary to make the BOD
determinations at the time intervals indicated, but the time
of observation must be carefully noted and the data plotted
accordingly.

        Step 1.  Laboratory Results

        t (days)                   y (BOD exerted) mg/1

           0                               0
           1                               0.7
           2                               l.U
           3                               1.6
           4                               1.7
           5                               1.9
           6                               2.2
           7                               2.3

        Step 2.  Graphic Plot

        Plot the laboratory data on arithmetic graph paper as
shown in Figure 5a.

        Step 3.  Curve Fitting

        Fit a smooth curve through the plotted points (Figure
5a).   From this smooth curve, take BOD exerted values (y) for
the corresponding times (t).   This procedure adjusts or averages
the BOD readings.

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                                        Adjusted Values
        t (days)                        y (BOD exerted)

           0                                 0
           1                                 O.T2
           2                                 1.25
           3                                 1.55
           h                                 1.80
           5                                 2.00
           6                                 2.20
           7                                 2.35

        Step k.  Daily Differences

        Using the adjusted BOD values, calculate the differences
over equal increments of time.  A daily period is generally
satisfactory and most frequently used.

Time Interval         BOD Difference         Plotting Position
   (days )  	(mg/l)	(used in Step 5)
0-1
1-2
2-3
3-U
M
5-6
6-7
0.72
0.53
0.30
0.25
0.20
0.20
0.15
1/2
1 1/2
2 1/2
3 1/2
It 1/2
5 1/2
6 1/2
        Step 5.

        Plot the incremental data on semi-log paper, with time
on the linear scale and the BOD differences on the log scale,
as shown in Figure 5b.  Values are usually plotted at the mid-
point of the time interval.

        Step 6.

        Draw a line of best fit through the points, extending
the line to time zero.  The plotted values may not exhibit a
straight line relationship beyond t = U, or t = 5, indicating
nitrification is beginning.

        Step 7.

        Using the incremental values of BOD at selected times
to get the maximum time interval having good correlation with
the curve, in this case t = 0 and t = U to eliminate the portion
affected by nitrification, make the following calculation:

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                                                             10
        BOD/day g t = h = 0.195 = n ?r
        BOD/ day § t = 0   0.75
        This indicates that after ^ days, 26% of the BOD remains
to be oxidized, and that 7W of the ultimate (First Stage) BOD
has been stabilized.

        Step 8.

        From Figure 3_, using t = k, and y = 26$, the laboratory
K  is determined to be approximately 0.32 @ 20°C (the laboratory
incubation temperature).

        Figure J3 is an expedient over using the following equa-
tions to calculate the deoxygenation rate constant.
       K  = 1/t In    r-   NOTE:  Ay figures are ordinates of
        1          Ay              Figure 5b.
    b° Kl   - - -   -  NOTE:  Ay figures are ordinates
                t or AO                  „ _ .      ,-T
                                        of Figure 5b_.

        Step 9-

        The ultimate BOD of this sample may be calculated as follows:

        § t = k, Jh% of the BOD has been oxidized; from Figure
5a, the BOD exerted @ t = k is 1.6 mg/1.

        Therefore:

        7W of the ultimate BOD (L ) = 1.6 mg/1
                                  cL

        0.72 L  =1.6 mg/1
        The ultimate BOD can also be calculated from the following
relationships :
    a.  L  -
         a   ,     -K,t
             1 - e  1
        yt = BOD exerted after time t (from Figure 5a)

        K  = deoxygenation rate constant calculated above

        t  = elapsed time

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     b.  L  = yt
                                                              11

                   Ayo
          a   J  Ayo - Ayt

         yt = BOD exerted after time "t" (from Figure 5 a)

         Ayo = ordinate @ time zero, Figure 5b_.

         Ayt = ordinate § time "t," Figure 5b.


VI.  Determination of Stream K  Rate


 A combination of field measurements and the laboratory (bottle)
 K  rate is used to calculate the deoxygenation rate of a stream
 reach.  This determination requires stream BOD values for at
 least two sampling stations downstream from a waste discharge.
 The stations should be a reasonable time of flow apart, and
 theremust not be another source of waste entering the reach.
 The magnitude of the waste is determined by locating a sampling
 point above as well as below the point of introduction of the
 waste.  Any tributaries entering between the sampling points must
 be considered; however, sampling points should be selected to
 avoid this situation when at all possible.

         Derivation

         1.  It has previously been shown that the BOD-time curve
 is logarithmic (Figure 2).  The curve is expressed mathematically
 as follows:
                   -K t                -K t
         L  = L  (e    ) or L.  = LQ (10  ^ )
          U    cl             O    cL
                                    f
         L  = BOD (mg/l) remaining after time "t"
          \j
         K  = deoxygenation rate, Base e

         t  = time interval (days)

         L  = ultimate first
          fi.

         2.  By taking the In (log) of both sides of the equation,
 it is possible to obtain a straight line relationship simplify-
 ing the calculation of K .
                   -K t

         Lt ' La 
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                                                             12
        3.  Assuming data is available for two sampling stations,
B and C, with flow time "t" "between stations; In La_ is the
natural logarithm of the ultimate BOD at point "B."  Likewise,
In Lap is the natural logarithm of the ultimate BOD at point "C."

        Therefore, given time zero at point B:
        L  = L
         a    aB

        L  = L

              Sc   ^
        -K.t = In (•—)   (from Step 2)
          X        i_i
                    a
        K. =    in     ) =   in ()
         It     LaB    t     L&B

        U.  Using the ultimate BOD values at points A and B, plus
the time of flow between the points , K  can be estimated a direct
calculation.

A graphical solution for the determination of the stream K
utilizes the same equation; however, the graph itself may indicate
many characteristics of the stream, waste, and environment.  The
graphical approach is of greatest value when points of signifi-
cant waste discharge are known or suspected.  The graph provides
a method for estimating waste strengths, reaches where sedimenta-
tion may be occurring, and the deoxygenation rate.  This technique
is usually referred to as the Oxygen Balance Calculation.

        Procedure for Constructing Figure 6:

        Step 1.

        Using K  values computed from long-term BOD's in the
laboratory, adjust the stream 5-day BOD's (as determined in the
laboratory at 20°C) to ultimate BOD's.

        Step 2.

        Determine stream flows for the days of sampling.

        Step 3.

        Convert ultimate BOD's from mg/1 to pounds BOD/day in the
stream.

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                                                             13
        Step h.

        Plot a BOD profile of the stream.  The must useful plot
is log BOD pounds/day vs time of flow; however, this is only
practical when the flow rate is approximately uniform over the
stream reach during the sampling period.  With variable flows,
a plot of log BOD vs stream mile is more practical.  Figure j5
shows log, BOD's plotted against stream miles and points A, D, E,
H, I, L, and M represent measured values of stream BOD.  Points
B1, C1, F', G', JT, and K' represent values or points located by
extrapolation.

        Step 5-

        Beginning with the first two plotted points downstream
from a waste discharge, use the following procedure:

        a.   Draw a straight line between the first two points
            below the waste discharge, points D and E.  For
            more accurate results, there should not be any
            significant waste or flow contribution between
            points D and E.

        b.   Project the line fixed by points D and E to the
            point of waste discharge, point C1 and downstream
            to point F'.

        c.   Draw a line parallel to C'-D-E-F', through point A
            and extending the line to point B1.

        d.   The number of pounds of BOD represented by the
            distance between points C1 and B' indicates the
            amount of waste contribution between points A and
            D, probably contributed at point #1.

        e.   Continue for other points downstream.

The following conclusions may be reached after an analysis of
Figure 6_:

        1.   Slope of line D-E indicates the rate of BOD removal
            for the reach of stream bounded by points C1  and F1.

        2.   The interval B'-C'  indicates the amount of waste
            contributed at point #1.

        3.   The interval F'-G1  indicates the waste contributed
            at point #2.  Slope of line H-I indicates the BOD
            removal rate for the waste concentration below point
            #2.  The lesser slope indicates that the new waste

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            may be more difficult to oxidize biologically or
            contains toxic substances which inhibit biological
            activity.

        k.  The steep slope of line L-M indicates the waste
            mixture below point #3 has a very rapid reduction
            of BOD.  The probable reasons for the rapid reduc-
            tion would include:

            a.  The waste mixture below point #3 is easily bio-
                degradable.

            b.  There is a chemical oxygen demand.

            c.  Sedimentation is occurring.

            d.  Shallow, rocky stream having heavy biological
                growth on the rocks which perform like a trick-
                ling filter.


    Reaeration

Reaeration is the process of oxygen transfer from air into water
to bring the partial pressure of oxygen in the stream into equi-
librium with the partial pressure of oxygen in the atmosphere.
Absorption of oxygen in a stream occurs only at the surface layer
of water.  The water surface is readily saturated; however, com-
plete oxygenation throughout the depth of the stream depends upon
turbulence to mix the saturated surface layer with the lower levels
and expose a new surface layer to the admosphere.  Based on the
above, a swift, shallow, turbulent stream will have a much higher
oxygen uptake rate than a deep stream with laminar flow and uniform
channel characteristics.

Reaeration becomes operative when the oxygen content of water is
below the saturation level.  Reaeration proceeds as a first
order reaction, as shown in Figure 7..  The mass transfer rate for
oxygen is proportional to the reaeration rate constant (K ) and
the oxygen deficit (D).

        r  = K2D

        r  = mass transfer rate for oxygen

        K  = reaeration rate constant

        D  = oxygen deficit = (saturation D.O. - stream D.O.)

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                                                                15
   Thus, higher oxygen deficits produce higher rates of oxygen trans-
   fer (r) for a given reaeration rate constant.   Temperature also
   plays an important role in reaeration, since the dissolved oxygen
   saturation values and the rate of oxygen transfer (K2) are
   temperature dependent.

VIII.  Reaeration Coefficient - K  (base e) or k  (base 10)


   The reaeration coefficient is defined as the rate constant con-
   trolling the process of reoxygenation, or rate of oxygen absorp-
   tion in a stream under given physical conditions.  Factors which
   affect K  values include: stream depth, velocity, turbulence
   (physical characteristics of the stream bed),  temperature, and
   dissolved solids such as chlorides.  Values of K? (base e)
   usually range betveen 0.1 and 12.0 per day; the lover values
   representative of deep, slow-moving rivers; and the higher
   values for shallow and/or rapid streams.

   After a stream K2 value has been determined for a particular
   temperature condition, the value can, through the use of equa-
   tions, be computed for any temperature condition.  The two most
   common empirical temperature equations are as follows:

           1.  K   = K    [l.OUT(t"20)]
                 T     20

           This is identical to the temperature correction for K
   shown in Figure h_.

           2.  K   = K    [1.01T(T"20)]
                 T     20
           Use Figure 8_.

   The amount of oxygen dissolved in a stream is  readily determined
   by laboratory analysis of stream samples; however, the amount of
   dissolved oxygen added through reaeration must be calculated.
   Several methods are available for calculating the reaeration
   coefficient, but only two will be shown here.   The first  method
   utilizes empirical relationships, such as those suggested by
   O'Connor, Velz, Churchill, and others; while the second method
   utilizes field observations to set up a "trial and error" solu-
   tion of the oxygen sag equation.

           0 ' Connor Method
                             1/2
              (base e) = -^-  — x 2k hr/day
                          H

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                                                             16
        Where K  = reaeration coefficient (day  )

              v  = stream velocity (ft/hr)

              H  = average stream depth (ft)

              D  = molecular diffusivity of oxygen in water

                   (0.81 x 15'1* ft2/hr g 20°C)

        Trial and Error Solution for K  or (k?)

        1.  The field measurements of D.O., BOD, temperature,
and time of flow.

        2.  Compute K  as discussed in Section VI.

        3.  Compute D.O. deficits at points A and B.

        h.  Assume values of K? and solve the oxygen sag equa-
tion for DB-
              K L      -Kt     -K0t         -K0t
        DB • icp\ '•     - 10    1 + V10    '

        Where D0 = oxygen deficit at point B
               D

              K  = deoxygenation coefficient

              K  = reaeration coefficient

              L  = ultimate BOD @ point A
               Ł1

              t  = time of flow "between points A and B

              D  = oxygen deficit at point A.
               /i

        5.  Plot the calculated values of D  vs the assumed
K  values.

        6.  Draw a smooth curve through the plotted points.

        T.  Using the actual (measured or observed) DB, read the
corresponding K  value from the curve.

The "trial and error" solution seldom produces good results, "but
should be considered a reference or check calculation for empirical
solutions.

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                                                             IT
 .  Oxygen Sag Equation
Introduction of an organic waste into a stream causes deoxygenation
then reaeration to be effected simultaneously.  The resultant dis-
solved oxygen concentrations plotted vs time or stream mile define
the "dissolved oxygen sag."  A plot of the D.O. profile of a stream
(D.O. vs time of flov) below a waste discharge gives a spoon-shaped
curve for which the mathematical relationships have been developed
by Streeter and Phelps.  Modification of these relationships have
been proposed by Velz, Thomas, and many others.

When using the oxygen sag equation, it must be recognized that
complex biological processes, such as waste assimilation in a
stream, are extremely difficult to express mathematically.  There-
fore, the sag equation can only approximate actual stream condi-
tions and limitations of the oxygen sag relationship must be
recognized and appreciated prior to any analysis.

The sag equation utilizes oxygen deficits to express stream D.O.
conditions.  The equation is expressed as follows:
        Base "e"
             L  K    -K t    -K_t        -K_t
        Dt = -S—i [e  I  - e  2 ] + D  e  2
             K
        Where D  = D.O. deficit (mg/1 below saturation) after
               t   time "t"
              L  = ultimate BOD within the stream at point A
              K  = deoxygenation coefficient (days  )

              K  = reaeration coefficient (days" )

              t  = elapsed time in days between point A and any
                   downstream point, point B

              D  = initial D.O. deficit at point A (mg/l)
               3,

The equation may also be expressed in terms of Base "10"


             La kl    "V     ~R2t         -V
        D  = -— - [10  X  - 10  2 ] - D  10  2
         t   k2  1                      a

In engineering practice, the maximum D.O. deficit (lowest D.O.
value, or worst D.O. condition to occur) is of major importance.
A typical oxygen sag is shown in Figure 9. which illustrates the
various terms involved.  The critical time and critical deficit
indicated in Figure 9. give the relative location and magnitude

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                                                             18


of the worst condition to be expected in the stream.  These
values are used to determine the maximum waste load that can be
discharged to a stream and yet maintain beneficial water uses;
aid in the determination of allowable uses; and provide the basis
for programming waste and/or dilution water discharges to meet
the established dissolved oxygen quality objective.

The time to the critical point (tc) is determined by differentiat-
ing the oxygen sag equation and setting the first derivative equal
to zero.

        _   K. L       -K t      -K.t         -K t
        uD    1  & r v    1  ,  v    2 i   is T*    2    A
        dt = K~^[-Kle     + K2e    ]-K2Dae     =°

The above equation simplifies to the following relationship
defining t :

          °             K
                         2
        *c = W? 10ge K7 [1 - Da
              21       1           a  1

The basic differential equation expressing these processes is:


        f • V - V

At the sag point, the deoxygenation rate equals the rate of
oxygen transfer into the stream, giving rise to the following
relationships :


        f = o = KIL - K2D

        K,L  = K0D
         1 c    2 c

        where D  = critical deficit = D
               c                       c
              L  = amount of ultimate BOD remaining after the
                   critical time t
                                  c
                      -Knt
              T    T    1 C
        since L  = L e
               C    a     -K.t
        then  K T)  = K, L e
               2 c    la
                   K,    -K.t
              D  =^Le  I C
               c   Kg  a

                                                            K2
When using the oxygen sag equation, it is convenient to let —
                                    K2                      Kl
be represented by a factor "f" (f = — ) .   The parameter "f"
                                    *1
occurs frequently and is known as the stream purification factor,

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                                                             19
providing a means of defining the combined characteristics of
stream and waste.  A stream with K  = 0.3 and K_ = 1.2 has an
"f" value of k, as does a stream with K  = 1.0 and K2 = U.O.
Higher "f" values indicate a greater capability of a stream to
assimilate organic wastes.

Temperature variations may or may not affect/the #alue of "f."
If the temperature correction factor (l.0l*7)         is used for
both K  and K  values, temperature changes do not alter the /  on°r)
purification factor.  If Kg is considered to vary by (1.017)  ~     ,
temperature changes must be considered^  Many sanitary engineers feel
the refinement offered by the (1.017)     factor is not warranted and
that the (1.0^7)     factor gives more reliable results.

Typical values of the self-purification factor have been given by
Fair and Geyer in their text.  Typical values of "f" for various
stream conditions are shown in Table II below:

 TABLE II - TYPICAL VALUES OF THE SELF-PURIFICATION FACTOR "f"

                                                     "f" Value
	Nature of Receiving Waters	§ 20°C

Small ponds and backwaters                           0.5 - 1.0

Sluggish streams, large lakes or impoundments        1.0 - 1.5

Large streams of low velocity                        1.5 - 2.0

Large streams of moderate velocity                   2.0 - 3.0
Swift streams                                        3.0 - 5.0

Rapids, waterfalls, etc.                             5.0 and up
X.  Uses of the Oxygen Sag Equation

The principal use of the sag equation is calculation of maximum
allowable organic loads that may be imposed upon a stream and
still maintain specified stream D.O. objectives.  This technique
allows optimum location of points of waste discharge, to maximize
stream utilization and maintain maximum water quality.  Three
methods are generally available for solving assimilative capacity
problems:

        1.  Manual solution of the sag equation (trial and
            error not recommended because of time required).

        2.  Graphical solution (recommended).

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                                                         20
        a.  Method published in course manual for "Water
            Quality Studies," Sanitary Engineering Center,
            Cincinnati, Ohio.  (Discussed here)

        b.  Method proposed by T. A. Wastler, Public Health
            Service, in Sewage and Industrial Wastes,
            September 1958.

    3.  Computerized solution (large scale and repetitive
        analyses).
Example II
    Graphical Solution of the Assimilative Capacity Problem
    by Method 2a;
                       f   I'1,    o c
                       f = A" iil, = 2.5
        Given:

        K  = Q.ltU @ 20°C

        K  = 1.1  § 20°C

        Stream temperature = 28°C and C  =7.92 mg/1
                                       s

        D  = 1.0 mg/1
         S.

        Minimum acceptable D.O. = U.O mg/1

        D  = C  - U.O = 7-92 - U.O = 3.92 mg/1
         c    s
Use Figure IQa for the solution, since D  =1.0 mg/1.  Figures
IQb and 10c may be used when D  = 2.0 or 3.0 mg/1, respectively.
Although field measurements do not give D  values of exactly
1.0, 2.0, or 3.0 mg/1, an interpolation of values obtained from
the tables will provide very close approximations.

Solving for the maximum allowable ultimate BOD concentration,
using Figure IQa, a value of about 17 mg/1 is obtained for L .

    Example III

        Use of the Graphical Method to Determine Minimum P.O.
        Concentrations Following the Introduction of a Waste
        Into a Stream:

        Given:

        5-day BOD of Waste = 100 mg/1

        5-day BOD of Stream = 3 mg/1

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                                                             21
        Waste Flow =(^=60 mgd = 60 mgd x 1'^dcf- = 93 cfs




        Stream Flow - Q  = 1000 cfs
                       s


        Temperature of Stream = 20°C and C  =9-17 mg/1
                                          S
D  =1.5 mg/1
 ŁL



 l
        K  @ 20°C -
                           f - 0.69 _ . 0

                           1 ~ n °^ ~ J

             20°C = 0.69




        5-day BOD of stream and waste mixture =


                        Q  (BOD ) + Q  (BOD )
                         C!     Q     \J     TJ

        5-day BOD mix = —	Q  + Q	




                      _ 1000 cfs (3 mg/1) + 93 cfs (100 mg/l)

                                1000 cfs + 93 cfs


                      = 11.25 mg/1



From Figure 3. the 5-day BOD for K  = 0.23 represents 0.68 of L  .



L  of mixture = —   /-v^— = 19-^ mg/1



From Figure lOa with D  =1.0 mg/1 and L  = 19.^ mg/1
            ———•       a                 a


D  = k.O mg/1



From Figure IQb with D& = 2.0 mg/1 and L  =19.^ mg/1



D  = 1+.25 mg/1
 c


Therefore, for D  =1.5 mg/1, the critical D.O. deficit is

approximately:


        U.25 mg/1 + U.O...mg/1 _

                  2


The stream D.O. concentration at the sag point (critical point)

equals the saturation D.O. minus the deficit.
        D-°'stream = °s " DC = 9>1T m/I " U'12 mg/1 = 5'°5 mg/1

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                                                              22
XI.  Stream Assimilation Capacity



 The most useful presentation for any reach of stream allovs

 determination of allowable BOD loadings when temperature and

 flow conditions vary.  This is best achieved using a graphical

 solution.



     Example IV


         A Procedure for Developing Assimilative Capacity Curves



         Given:  D  =1.0 mg/1
                  a


                 K^ = 0.65



                 K2 = 3.9


                     3.9
                 f =  "v"- = 6  and does not vary with temperature

                               fluctuations



                 Minimum acceptable D.O. = 5.0 mg/1



         1.   Assume stream temperature = 30°C



             D.O. saturated = C  =7.63 mg/1
                               s


             DC = 7.63 mg/1 - 5.0 mg/1 = 2.63 mg/1



             From Figure 10a, L  = 21.5 mg/1
                           """"""   Q,


         2.   Assume stream temperature = 20°C



             Cs = 9-17 mg/1



             DC = 9.17 mg/1 - 5.0 mg/1 = U.17 mg/1



             From Figure IQa, L  =3^.5 mg/1
                               EL


         3.   Assume stream temperature = 10°C



             C  = 11.33 mg/1
              S


             DC = 11.33 mg/1 - 5.0 mg/1 = 6.33 mg/1



             From Figure IQa, L  =53.0 mg/1
                          ~r~-L-LL

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                                                             23
        4.  Assume stream temperature = 5 C

            C  = 12.80 mg/1
             s

            D  = 12.80 mg/1 - 5-0 mg/1 = J.BO mg/1

            From Figure IQa, L  =66.0 mg/1
                        ——-   EL

        5.  Using the values obtained in steps 1 through 4, plot
            Log L  versus temperature on semi-log paper, as
            shown in Figure 11.

        6.  Select temperatures such as 5°C, 10°C, 25°C, from
            Figure 11, and obtain the corresponding L  values.
            Construct a table to convert BOD from mg/1 to
            pounds BOD by assuming flow values.

        7.  Plot the values for pounds of BOD from the table on
            log scale versus temperature, then add constant flow
            lines, as shown in Figure 12.

The family of curves (Figure 12) developed using the preceding
steps can now be used to determine necessary flows for assimila-
tion, or maximum BOD loadings, at any temperature.  The curves
constructed in Example IV are only applicable where D  =1.0 mg/1
and the minimum acceptable D.O. is 5.0 mg/1.  Other families of
curves must be constructed for different D  values or different
                                          Q
D.O. objectives.

When making an analysis of stream assimilative capacities, the
reduced quality of the waste water returned must be considered.
For example, if 8 mg/1 is the stream D.O., stream flow is 150
cfs, water use = 40 cfs, D.O. of water (waste) returned = 2 mg/1;
then only a portion of the 150 cfs will be .available for waste
assimilation, i.e., 150 cfs - 40 cfs {  mg/^ "  . mg/JJ  Or 120
cfs available.                               mg/1

The above analyses assumed that K  and K  did not vary with fluc-
tuation in stream flows.  When there are large flow fluctuations,
K  will show significant variations, found to follow the following
relationship:

        K2 = aQb

        Q equals stream flow.

        a and b are constants evaluated from the stream cross-
        section, Q, relationship.

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                             SATURATION  D.O. CONCENTRATIONS
                           IN DISTILLED WATER  vs  TEMPERATURE
                                        AND  PRESSURE
                                     EXAMPLE
                                        GIVEN
                                             ELEVATION
                                             TEMPERATURE
                                            = 500 FT.
                                            = 20.5°C
                                             SATURATION
                                         D.O. = 8.92mg/l
626mm Hg - 5000 ft elevation
651 mm Hg - 4000 ft elevation
67?mm Hg - 3000 ft
704mm Hg - 2000 fl
732 mm Hg - I 000 ft
elevation
elevation
e levotion

-------

-------
                                                               25
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-------

-------
PERCENT  BOD  REMOVED
            VS
     TIME  AND  K (k )

-------

-------
                                                                            27
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-------

-------
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-------

-------
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-------

-------
                         TIME
C  =
D  =

Da =
V
*  =
saturation D.O. concentration  at  existing
temperature  and  pressure
observed D.O. concentration
D.O. deficit  at any  time  t, C  = C
                               9
initial  D.O.  deficit
coefficient  of reaeratjon  (sorption of
0   into  water)  base "e1
time  lapse
   GRAPH   SHOWING  STREAM
    REAERATION  REACTION
                                                   Figure 7

-------

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Figure 8

-------

-------
                                                 33
                       TIME
  Cs =  saturation D. 0.
  DQ =  initial D. 0. deficit
  Dc =  critical deficit = minimum value  D. 0.
  t  =  time  required to reach  minimum  D. 0.
GRAPH  OF A  TYPICAL
          SAG  REACTION
OXYGEN
                                              Figure 9

-------

-------
            D0= I.OOmg/1  = initial deficit
                              D.Q «7.9-5.0=2.9»g/i
                                c
0         10        20     /   30


                    La, mg/l



CRITICAL  DEFICIT, Dc  vs  POLLUTION  LOAD,LQ
                                                  Figure 10a

-------

-------
D=2.00
                        = initial deficit
                                 f =3.00,T=28°C
                                 k      *
CRITICAL  DEFICIT, D  vs  POLLUTION  LOAD,L
                                                Figure 16b

-------

-------
                                                     36
              D0s3.00jng/i  = initial  deficit
14
12
                                 D.O. =7.9-5.5=2.4nig/l
 CRITICAL DEFICIT, D   vs  POLLUTION LOAD,L
                                                    Figure lOc

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-------
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25
20         15         10

    TEMPERATURE - °C
           ALLOWABLE   BOD

LOADING  vs TEMPERATURE  8  FLOW
                                                 Figure 12

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                       TABLE OF CONTENTS




                                                           Page




INTRODUCTION ........ 	 .....   1




     Pour-Thirds Law	   2




     Random Process Analogy	,	   U




     Turbulent Pipe Flow Analogy ..... 	   5




DISCUSSION ............ 	   6




CONCLUSIONS  .......................   8




BIBLIOGRAPHY .....  	 ..... 	   9

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      ESTIMATING DIFFUSION CHARACTERISTICS OF TIDAL WATERS





I.  INTRODUCTION


                                         1 2
        The mathematical models available '  for the analyses



of pollution and other problems involving mixing in tidal waters



require a knowledge of the turbulent diffusion characteristics



of the system being studied.  These characteristics may be eval-



uated in an estuary by using external tracers such as dyes or



internal tracers which are already present, as in the case of



salinity intrusion or a recognizable continuous pollutant dis-



charge.  Similar procedures may be applied to a verified hydraulic



model of the system, where such a model exists.  However, these



methods can be expensive and time consuming.



        In cases where preliminary calculations are being made,



and general order of magnitude answers will suffice, it is most



useful to be able to make satisfactory estimates of diffusion



characteristics using readily available hydrographic information.



Furthermore, in planning dye tracer studies, it is helpful to



have some reasonable estimate of diffusion properties, to permit



better design of field activities.



        Several methods which have been proposed for estimating



a diffusion coefficient for tidal waters are described below.



In each case, it is the turbulent analog of the Fickian coeffi-



cient of molecular diffusion which is used.   This has been variously

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referred to in the literature as the coefficient of turbulent,



eddy, or longitudinal (for the one-dimensional case) dispersion,



diffusion, or mixing.





Four-Thirds Law



        It has been almost universally observed that the magni-



tude of the turbulent diffusion coefficient increases greatly



with the size of the area, or volume, containing the diffusing



substance.  This has led to the formulation of a "four-thirds



law" wherein the diffusion coefficient is proportional to the



four-thirds power of the scale of the diffusion phenonema, L.


                        3
This is quoted by Bowden  as:



        D  2,    = 0.02l*6L '3	  Eq (1)
         cm /sec


        Where L is in cm.



        For the one-dimensional estuary, the characteristic



scale (L) may be considered as the length of a tidal excursion,



or the maximum longitudinal distance a particle of water would



travel during a flooding or ebbing tide.  This length would be



given by:



        L = Vt	  Eq (2)



        L = length



        V = average tidal velocity



        t = period of time between slack waters (generally

            estimated at 6.2 hours for the Potomac Estuary)



        If a sinusoidally varying tidal current is assumed:

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        V = -V    	  Eq  (3)
            IT  max                                              Mp


        From Eq. (2)



        L   =-V   t	  Eq
         cm   ir  max


        Where: V    is in cm/sec
                max


        t is in sec



        L   = - (6.2 hrs.) (3600 sec/hr.) V
         cm   ir                            max



        L   = lH,200 V
         cm           max
        By substituting into Equation (l):



        D  2,    = 0.02U6 [1U.200 V   ]
         cm /sec                   max


                 = 0.021*6 [333,000] V
                 = 8.21 x 103 V    /3  vith V    in cm/sec —  Eq  (5)
                               max           max


        Equation (5) may be restated using units of knots for V
                                                               ITlclX


This form of the equation may be more convenient, as values for



V    in knots may be obtained from published tables for many
 max                               ^                       J

                    h
estuarial locations.



        D  2,    = 1.56 x 106 V   k/3 -----------------------  Eq  (6)
         cm /sec               max                              ^


        Where V    is in knots
               max


        Other forms of Equation (6) are as follows:
        D .2,,   =5. 2V    /0 ------------------------------  Eq (6a)
         mi /day        max                                     H v
        Where V    is in knots
               max


        D  2.    = 1.68 x 103 V       -----------------------  Eq (6b)
         ft /sec               max                              H


        Where V    is in knots
               max


        This procedure vas carried out for the Potomac River



below Washington, D. C., and the results are plotted in Figure 1^.

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Random Process Analogy



        The process of tidal mixing and dispersion has been des-



cribed by Diachishin  as a random walk type of process.  Using



probability theory, he has developed equations which resemble



solutions of the classical diffusion equation.  For this simi-



larity to be complete, it was concluded that the diffusion



coefficient must be described as follows:



        D = St-	  Eq (7)



where L is the length of each random step and n is the frequency



of steps (one per tidal cycle or 1/12.^ per hour).  Applying a



procedure similar to that above for defining the scale length,



an average step length is used which is equivalent to the tidal



excursion length, as given in Equation (k).   Combining these



expressions results in the relationship:




        Dcm2/sec ' I 
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        Coefficients for the Potomac Estuary calculated using



this equation are also shown in Figure !_.





Turbulent Pipe Flow Analogy



        Taking Taylor's expression for the longitudinal disper-



sion coefficient for turbulent flow in pipes as a starting point,



Harlemann  has developed an analogous expression for tidal waters.



In this development, it has been assumed that the required steady,



turbulent flow velocity may be approximated by the time average



of the tidal velocity over a half tidal cycle.  In addition, a



sinusoidal velocity variation has been assumed.  The resulting



expression is:
where R (ft) is the hydraulic radius for which the mean depth



is a satisfactory approximation, n is Manning's roughness coef-



ficient, and V   ( f ps )  is the maximum tidal velocity.  For the
              TOelX


Delaware Estuary, Harlemann estimated n to be 0.025.  It is also



recommended, however, that the final result be multiplied by



1«5» to account for bends and section changes, so an effective



n of 0.038 has been used in the following reduced equation:



        D  2,    =  2.92 x 103 V   R 5/6 ------------ - ---------  Eq (10)
         cm /sec               max                              H


        with V    in knots and R in feet.
              max


        In a similar manner, but employing a slightly different


                          7
set of assumptions, Bowden  derived the expression:

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                                                              6
        D  2,    = 235 V   R	  Eq (ll)
         cm /sec        max                                     ^



        With V    and R defined as above.
              max



        Results obtained using these formulas on the Potomac




Estuary are shown in Figure !_.






II.  DISCUSSION




        The first two methods described (Equations 6 and 8) pro-




duce somewhat similar results (Figure 1).  These coefficients,




in turn, differ from those obtained by the turbulent pipe flow




analogy formulas by two to three orders of magnitude.




        In order to provide a basis for comparison of the abso-




lute values obtained by these formulas, the coefficient of




diffusion was also calculated from the salinity distribution in




this portion of the estuary.  The solution to the classical dif-




fusion equation may be expressed in forward finite difference




form as:

                 Q S  2Ax

        D „           _        	  Eq


             x   x+Ax    x-Ax




        Knowledge of the longitudinal salinity distribution (S),




net advective flow (Q) and cross-sectional area (A) in the estuary




will permit solution for D.  This was carried out for relatively




steady flow conditions near 2000 cfs in the Potomac Estuary, using




chloride data provided by the District of Columbia Department of




Sanitary Engineering.

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                                                              7






        Coefficients obtained by solution of Equation (12) are




closely approximated by the "four-thirds" model and are less




than those obtained by the random process formula by a factor




of about three.  The turbulent pipe flow analogy equations, how-




ever, produce coefficients for the Potomac Estuary that are




lower by multiples of 100 to 1000 than the observed values.




Coefficients calculated for the Patuxent Estuary ( using the




above equations, showed differences of the same order of magni-




tude as those calculated for the Potomac.




        This large discrepancy was also noted by the respective




sources from which these equations were obtained.   Harlemann




stated that the low values obtained by Equation (10) are valid




for the fresh water portions of tidal streams.  The much higher




diffusion coefficients observed in the brackish portions of




tidal waters he attributes to density effects.  The longitudinal




salinity gradient existing in estuaries is said to cause a large




scale gravitational circulation with the more saline waters




moving upstream along the bottom and downstream near the water




surface.  The over-all effect of this circulation, referred to




by Bowden as a density current, is to cause a large increase in




the observed effective diffusion coefficient.  Harlemann has




demonstrated tne validity of Equation (10) in hydraulic models,




but, apparently, not as yet in prototype estuaries.

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                                                              8
III.  CONCLUSIONS




        Both the "four-thirds law" and random process analogy-




formulas yield effective diffusion coefficients in the proper




order of magnitude for the brackish portion of the Potomac




Estuary.  Either of these formulas should provide useful ap-




proximations for other estuaries where good information on




salinity variations is not readily available.  These formulas




should be used with caution in the fresh water portion of tidal




rivers, in view of the possible important influence of salinity




gradient induced density currents on diffusion.  Prototype tracer




studies in such locations appear to be necessary to provide




reliable estimates of the appropriate diffusion coefficient.




Accumulation of experience gained by such studies will permit




evaluation of the validity of Equations (10) and (ll) for pre-




dictive purposes.

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                          BIBLIOGRAPHY
1.      Thomann, R. V., "Mathematical Model for Dissolved Oxygen,"
        JSED, ASCE, 89, Wo.  SA5, (October 1963)

2.      O'Connor, D. J., "Oxygen Balance of an Estuary," JSED,
        ASCE, 86, No. SA3, (May I960)

3.      Bowden, K. F., "The  Sea, Volume One, Section VI, Turbulence,"
        p. 819, Interscience Publishers, New York (1962)

U.      "Tidal Current Tables, Atlantic Coast of Worth America,"
        U. S. Coast and Geodetic Survey, Department of Commerce,
        U. S. Government Printing Office (1965)

5.      Diachishin, A. N., "Waste Disposal in Tidal Waters,"
        JSED, ASCE, j39, No.  SAU, (August 1963)

6.      Harlemann, D. R. F., "The Significance of Longitudinal
        Dispersion in the Analysis of Pollution in Estuaries,"
        Presented at Second  International Conference on Water
        Pollution Research,  Tokyo, Japan, (August 1963)

7.      Bowden, K. F., "The  Mixing Processes in a Tidal Estuary,"
        Advances in Water Pollution Research, Vol. 3, Pergamon
        Press, The MacMillan Co., New York (196*0

8.      Stommel, H., "Computation of Pollution in a Vertically
        Mixed Estuary," SIW, 25, 9, (September 1953)

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    10
    10
 o
 LU
 CO
 \
OJ
 2
 O
 -  ,o5
 UJ
 o
 LLl
 O
 O
 O
 co
    10
                                                                       EQ. 8  -
                                                                       EQ  12
                        	+ -
                                                                       EQ  10
                                                                       EQ. II
       13    14    15    16    17   18    19    20   21    22   23   24    25    26



               DISTANCE  BELOW KEY  BRIDGE  (THOUSANDS  OF  FEET)

    DIFFUSION   CHARACTERISTICS, POTOMAC  RIVER  ESTUARY
                                                                      FIGURE

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               USE OF RHODAMINE B DIE .45 A TRACER
           IN STREAMS OF THE SUSQUEHANNA RI?ER BASIN
PDHPOSE AND SCOPE

This paper relates the experiences of the Susquehanna Field Sta-
tical - Chesapeake Bay-Susquehanna River Basins Project - in the
use of Rhodamine B dye techniques in the stream environments of
the Susquehanna River Basin„  Particular problems encountered
in the use of fluorescent tracer techniques, and the solution
of many of these problems will be discussed„  Instruments and
equipment found most suitable for strearas in the Susquehanna
Basin are listed in Appendix I,
ACKNOWLEDGMENTS

The assistance and cooperation of the Pennsylvania Department
of Health^ U« S. Geological Survey; and Dr0 James H. Carpenterf
Chesapeake Bay Institute, is gratefully acknowledged.

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                       TABLE OF CONTENTS

                                                           Ł§ŁŁ

 I.  INTRODUCTION  .....................     1

II.  CONSIDEBATIOMS WHEN USING FLUORESCENT DYE
     TECHNIQUES „  . .  . .  . . . .  „  .  .  . „  „ „  „  .  .  .  .     1

     Heat Transfer During'  Calibration  „  . .  „ „  .  .  ,  .  .     1

     Dye Adsorption on Metal Parts of the Equipment  ,  „  .     2

     Type of Pump  „ „  . .  0 „ „ .  .  „  .  „ .  , „  .  „  „  .  „     2

     Volume of Sample Through the Fluorometer Curvette,  .     2

     Power Supply  ..,...„„......„„.....     2

     Interference Materials in the Streams   „„..„.,     3

     Effects of pH on Emission  0..<»o.u.....o     3

     Temperature   ao.<.ou.,......o..»..o     4

     Dye Loss at Power Stations „<>  o.. .«.<,.„.,.     4

     Dye Adsorption In the Stream  „  „  .  „ 0  „ .  „  .  „  „  .     4

     Metal Inhibition in the Stream  0  „  „ „  «, ,  „  „  „  .  .     4

     Limits of Dye Concentration   „  „  „  „ .  0 „  „  .  „  „  „     4

OBSERVATIONS  . «,  „ „  „ „  „ . „ .  „  „  0  0 „  „ „  .  .  „  „  ,     6

BIBLIOGRAPHY  .................  u  ....     8

APPEND;DC i  ........„„.,... o  ....  0  ..     9

APPENDIX II ......... t ..  o  ...........    10

FIGURE 1  „ „ „ 8  0 „  „ o  0 . 0 ,  „  „  „  . .                  12

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I.  INTRODUCTION

The use of Rhodamine B, or similar fluorescent, organic dyes, for
studying the physical characteristics of streams and bodies of
water has become extensive since introduction of the technique
by Carpenter-%  These dyes are primarily used for studying "time,, /
of passage" and/diffusion characteristics in estuaries , bays-^  ,
and streams^  .  The technique involves use of a substance (dye
in this case) which can be detected in very dilute concentrations
by an instrument such as a fluorometer.  The dye has physical
properties which allow it to mix and be transported as an integral
part of the water,, effectively siirrulating movement of wastes or
other materials introduced into the system,

The use of Rhodamine B dye in Susquehanna River Basin streams
brought to light several problems not encountered when using
the technique in other streams or in estuaries„  The chemical
composition, velocity, mixing, and current characteristics of
streams were found to present unusual problems for analysis.
II.  CONSIDERATIONS WHEN USING FLUORESCENT DYE

The use of fluorescent dye techniques requires consideration
and evaluation of the following factors:

        10  Instrument calibration and natural background
        20  Hydrogen ion concentration
        3 o  Temperature
        4o  Decomposition - oxidation, reduction, etc,
        5 „  Sorption
        60  Photochemical decay
        7.  Metal inhibition

Project use of Rhodamine B dye and the fluorometer produced
several specific problems and solutions.  Outlines of the
problems encountered, along vd.th the solutions found most satis-
factory, are presented below.
Heat Transfer During Calibration

The use of submersible pumps in the calibration medium proved
unsatisfactory because of gross heating of the medium from pump
operation.  The heat generated from the pump after repeated re-
circulation affected dye stability and caused fluorescence loss.
To avoid this problem, a small centrifugal pump was utilized in
the laboratory during instrument calibration.  Submersible pumps

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were quite satis fact Dry in n^M IT-A illation? where reclrcula-
tion was eliminated3
Metal parts , particularly
                               &r a:;ci bras*
                        Considerable
affinity for the  dye0
this adsorption and  s
it interferes wHt -..uliD' n4 10^ ini
tion during laboratory and. i:<,c-lc ^
pomp used during  calibration was <:-i
adsorption onto the  pump during t'i'e
A pujnp having a primarily bra^ in ..-j
                                             exhibit  a great
                                       ffleulties  arise from
                                release of dye on equipment,,  as
                                ini evaluation of dye  concentra-
                                            The small  centrifugal
                                           r-i- material,  avoiding
                                     an.
                                     l
                                       ng periods of  reoirculation«
                                      w^- -.B^d io the field;  how-
                                      the pump was  very short y  and
there was no reciroalat-ioTu  Ltitrt materials 5uch  as polyethylene
tubing and fittings were 'jt^.ilz^d both ii) the laboratory and in
the field 0
ever, contact time  of the .med a
A Little Giant Model 4-!2MB ??-utme.rsit.le pomp was unsatisfactory
for field installation because of poor lift characteristics„   A
Demming Model 2ALF4-115V,  1/3 HP submersible pump  provided the
necessary capability,,
yQjjume.,.oŁ Sample Through, ^ft EiUy

Sample volumes passing rdn rugh the Łluorometer  eurvette in excess
of about I0y gall on/'hour result In turbulent flow>, with subse-
quent light scattering aTid. lastruineiit l.i"'^tabilit.yu   Control of
flow from the pump was ai'jcosp.li.dheij by uh>e of a man.ifold with a
bleeder valve io>  grces volume »:-."-trtrcl, in series with a needle
valve for opt?nfjK  ad.fiiotmtrtf,0  Set >'.;g'ij-e 10
Power requirements  fox- the f:ield .-'tudiea were  initially supplied
by a portable  4 HP,  13 ampere5 ,1'ii volt, AC generator„   The
fluorometer requlies ar- AC power supply regulated between 105
and 130 volts  for -stable ijerieratior.o  This generator unit was
found to be of irssiifficiest eapa'r-ft,7 to prcvode power for the
1/3 HP sample  pump  ar:d !;'• maantri:«: rhft •••vistaDt voltage supply
required for the fluoxonie-* bf u

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A possible solution was the use of separate power supplies for
the pump and the fluorometer.  This would require a DC-AC convert-
er utilizing a 12 volt DC battery or generator; however, the
converters are relatively expensive„  To eliminate the converter
and second power source^ a Baker Heavy Duty 12v DC - 115v AC
generator was installed on the Ford Econovan field vehicle in
place of the standard 12 volt generator.  This unit supplies the
regulated 115 vclt AC power for the fluorometer, pump and light-
ing requirements, as well as 12 volt DC power for vehicle operation.
Interference Materials _in the_Stoeai!S

Some streams contain materials which flucresce at the same wave
length as the dye being used or within the band pass of the
emission filter.,  This is particularly true of streams receiving
pulp and paper mill wastes»  The high background contributed
from these materials in the stream mask and compromise the sensi-
tivity of the method«,  Where low concentrations of dye which
barely exceed the expected variations in background are used,, high
background becomes most problematical <,
Effects of pH on Emission

It has been stated that Rhodamine B dye appears relatively stable
over the pH range of 2 to 10; however, these limits were established
in estuaries where the buffering capacity of the water is consider-
able „  The Project found that emission is adversely affected at
each end of this pH range, as streams in the study area did not
have a large buffering capacity„  Project experiments conducted
in streams and on stream samples under laboratory conditions
reveal a loss of emission below a pH of 4 and above a pH of ?„
Emission loss does not appear quantitatively recoverable when
the pH is adjusted, i0e», from 3=5 to 4°0 or from 7^5 to ?.!„
This would indicate a reaction resulting in dye destruction,
dye conversion to a form flucreseing at a different wave length,
or formation of a non-fluorescing compound,,  An additional
problem results from the dye having different soluabiliti.es at
high and low pH«

pH is a very acute problem in the Susquehanna River Basin, and
the ranges of pH discussed above are quite commonly encountered
during passage of the dye in the streams „

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                                                              4
Temperature

There was a loss of fluorescence with increasing temperature
(approximately 2^ with each degree Centigrade increased).  With
tap or distilled water, recovery of emission after cooling is
essentially quantitative; however,, when stream water was used
as a substrate, emission recovery after a prior temperature rise
was variable„  This variability indicates a change in the dye
composition may occur, which is a function of stream conditions
and temperature„
Dye Loss at Power Stations

Dye passing through heat exchangers showed very high reductions
in quantity or- fluorescence upon return to the stream.  Probable
cause of the loss was dye decomposition at the high temperatures j;
however^ adsorption and metal inhibition probably contributed to
the problem.
Qye Adsorption in the Stream

Adsorption of dye in streams having significant amounts of sus-
pended solids and/or obstructive matter is visually evident,,
This adsorption greatly affects the concentration of the dye
front, as well as the time of resolution for the passage of the
peak concentration„  Also, the shape of the recovery curve is
considerably affected,, particularly as a result of the release
of adsorbed dye0
Metal Inhibition in. the Stream

Various metal ions, e0g^ copper, aluminum, arid zinc,, are known
to inhibit fluorescence emission„  The extent of fluorescence
inhibition from metal concentrations in the stream can be deter-
mined by comparing results with streams having low metal ion
concentrations and low inhibition,,
Limits of Dye Concentration

Fluorescence emissions of Rbodaudne B dye are characteristically
linear over a finite rar-ge of dye concentration,,  The lower limit
of concentration is set by natural background or interfering sub-
stances in the sample medium.  The upper limit of dye concentra-
tion is determined by the absorption o,t' incident ultraviolet

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light, with the consequent deviation from linear!ty.  Where work
is required at dye concentrations greater than the maximum range
selection of the instrument, a neutral density filter may be
used with the secondary filter to decrease sensitivity, i.e,,
extend the range of the fluorometer.
Estimation of amount of tracer required will be the function of
the physical and hydrologic characteristics of the stream, assum-
ing consideration has been given to the various inhibitory mech-
anisms which may be present„  Mr0 R. L0 O'Connell, Director,
Annapolis Field Station, Chesapeake Bay-Susquehanna River Basins
Project, has suggested a method for estimating dye requirements.
This information is contained in Appendix 11.  It should be noted
that where amounts of dye may be critical, e.g., dispersion and/or
comparison with previous studies^ consideration should be given to
the possible variation in dye content of the manufacturer's prep-
arations.  It is recommended that samples of the dye be compared
with each other, compensating for differences as required,,  On
this basis, the initial dye preparation used could be considered
to be the reference standard«,

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                          OBSERVATIONS
        I.  As stream flow decreases, time for peak concentra-
tion resolution increases„

        II.  Both leading and following edges of the dye front
become diffuse, causing an alteration in the shape of the con-
centration vs. time curve.  This alteration results in a positive
displacement in time of both the centroid of mass and the peak
concentration.

        III.  Using a single injection of tracer, greater dis-
placement and alteration of the shape of the curves are observed
at stations downstream,,  Peak concentrations are decreased at
downstream stations; and comparison of curves at various stations
will serve to indicate diffusion and/or inhibitory characteris-
tics of the reach of stream under consideration.,

        IV.  The time of passage curve for dye may be used to
estimate the time of arrival and probable concentration of waste
at a given point from a single waste injection, such as an ac-
cidental spill.  The leading and following edges of the curves
can be used to estimate duration of critical or emergency condi-
tions in the stream,,

        V.  At present, there appears to be little exploratory
work on other light fast tracers„  It is suggested that lignin
and/or lignin derivatives might be investigated„  These compounds
flucresce at the same wave length as the Rhodamines^ and,, based
on their method of preparation, these compounds might be applicable
for use in both acidic and normal stream environments.

        VI.  It is essential that a field reconnaissance be
made, sites selected, and the stream sampled for calibration and
water quality to determine the feasibility of use of a tracer,
Further determinations should be made at this time for auxiliary
equipment requirements 0

        VIIo  Estimated tune of travel should be established
for the reaches under consideration, in order to reduce excessive
time requirements in the field.

        VIII.  Injection of the dye into the environment should
be accomplished in such a manner to insure immediate maximum
dispersion.  Addition of concentrated dye preparation without
dilution may result in incomplete dispersion, particularly in
shallow streams, with cdnsequent undesirable effects on

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visualization of both the dye fiont and the shape of the time
of passage curves,,

        IX,,  An analysis of peak dye concentration should "be
made at the first and each succeeding station to determine if
enough dye exists to insure a measurable quantity at the next
station downstream,,  If dye additions are necessary, they should
be made at the time of peak concentration,,

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                          BlBLlOClRAHff
10  Carpenters J. H.s The Use of flhodamine  B  as  a Field Tracer.
    Chesapeake Bay Institute, The Johns Hopkins  University»

20  Feverstein, D0 L,, and Selleck, R.  '&,, Fluorescent, Tracers
    for Dispersion Measurements. Journal of the  Sanitary
    Engineering Division,, A.S.C.Ee>  August  1963.,

30  0'Connell? R0 L0 and Walter., Ct,  M0, A .Study  of Digpgrgion
    in Hilo Bay. Hawaii^ U. S, Public  Health  Service^  Robert A,
    Taft Sanitary Engineering Center,  Cincinnati,  Ohio, (1963).

4.  Buchanan^ T. J0|9 Tjjae M__Travel,_o_Ł.S_Qluble__CQntaminants  in
    Streams. Journal of the Sanitary Engineering Division,, AoSo
    June 19640

5<,  0'Cornell, R. !.„, et al», Report of Survey of the  Truckee
    River., U/S. Public Health Servicey Robert A.  Taft Sanitary
    Engineering Center, Cincinnati,  CMo,. (1962).

6Q  O'Connor^ Dc J^ Report __on. Arialysis oi"  the Qye Diffusion
    Data in the Delaware River jajtuarg;^ Delaware Estuary Compre
    hensive Study Technical Report Nou 1, U.  S,  Public Health
    Service^ August 1962,,

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                                         APPENDIX. I

                       INSTRUMENTS  AND BQMEvQiM HJUND MOST SUITABLE
                            FOR STREAMS IN THE SOSQUEHANNA BASIN
                      I.   Fluorometar - All measurements utilized the Turner
             Model  111 fluorometer equipped with"a 20 millimeter continuous
             flow curvette door ar»d recorder „

                      II.   Pump - in the field,  a 1/3 HP Lemming Model 2ALS4-
             115V submersible pump was utilized.,

                      Ill,  Power Supply - A Baker Heavy Duty generator was
             used to provide  11$ volt AC power  for instrument,  pump, and
             lighting requirements, plus 12 volt DC' power for vehicle opera-
             tion „

                      IV.   Laboratory - A modified Ford Econovan provides
             mobility and basic laboratory capability, including' cabinets,,
             sinlc^  and sufficient counter space for the fluorometer and its
             accessories.,

                      Vu   Irradiation Lamp - Maximum sensitivity was obtained
             using  a G. E.  G4T4/1 lamp as a light source^ plus  the proper
             excitation and fluorescence filters,,
1

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                                                             10
                          APPENDIX: n

    ESTIMATION OF DYE REQUIREMENTS FOR TIME OF TRAVEL STUDIES
An instantaneous release of dye to a river is planned to determine
travel between two points„  To find the amount of dye to be released,
                       M
                       M =
        M - Weight of dye in grams

Where:

        Cx = Pealc concentration desired at downstream point x
             parts per billion

        X  = Distance between release and monitoring points in
             feet

        A  = Cross sectional area of stream at release point in
             square feet

        R  = Mean depth of stream between release and monitoring
             points

        N  = Manning's coefficient n for stream roughness

For example, in a stream where:

        Width = 100 feet

        Depth = 4 feet

        Cx = 200 ppb (approximately 100 on 30 x scale for
             Rhodamine B)

        X  = 3 miles

        R  = 4 feet

        N  = 0.04

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                                                             11
                    APPENDIX II (Continued)
                             3
                       l.lxicr


        M = 32.6 grams required assuming 100$ dye content by weight



        Use M = 33 grams


Dye to be used:  Ktiodamine in Acetic Acid - 40$ (weight basis) -

                 sp0 gray, 1012
Volume of dye (V) = n   W /Q) = ?3 milliliters



Use 75 milliliters

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               ^~*
               B
Figure  1

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                        TABLE OF CONTENTS






                                                           Page




INTRODUCTION 	     1




RESPIROMETER DESIGN  	     2




METHOD OF OPERATION	     3




INTERPRETATION OF DATA	     U




PRELIMINARY RESULTS OBTAINED 	     6




CONCLUSION 	     8

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                 AN IN-SITU BENTHIC RESPIROMETER






INTRODUCTION




        In attempting to describe the oxygen balance of natural




waters, it is essential that all significant sources and sinks of




oxygen be considered.  Oxygen uptake by the bottom muds found in




rivers, lakes, and estuaries is such a sink and, in some situations,




a most significant one.  It's magnitude, however, is usually dif-




ficult to evaluate with the desired degree of confidence.  Most




methods of evaluation in current, use require removal of the muds




from their natural environment for oxygen uptake measurements in




the laboratory.  However, it is extremely difficult to reconstruct




the natural layering of solids in a laboratory flask, which would




appear to be a necessary condition for obtaining realistic results.




In addition, the interstitial water in bottom sludges is likely to




contain soluble constituents having a high oxygen demand, and these




materials may be lost or diluted in collecting the sludge sample.




The quality of water overlying the sludges may also influence oxygen




uptake rates in the natural environment.  For these reasons a benthic




respirometer capable of measuring the oxygen uptake rates of bottom




muds in-situ is highly desirable.   Such a device has been developed




and is described below.

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                                                              2




RESPIROMETER DESIGN




        The operating principle of the respirometer is to trap and




confine a volume of overlying water in contact with the bottom while




observing any reduction in dissolved oxygen content resulting from




uptake by the bottom muds.  The apparatus shown schematically in




Figure JL was designed to accomplish this purpose.  The respirometer




chamber was constructed from a 21-inch length of 19-inch diameter




metal pipe having a 1/16-inch wall thickness and a flange on both




ends.  The pipe was cut lengthwise along its centerline, creating




two sections—each of which could serve as a shell of a respirometer




chamber.  The semi-circular ends were closed with metal plates, and




a U-inch right angle metal section was attached around the periphery




of the 19-inch by 21-inch rectangular opening, providing a vertical




cutting edge and a horizontal supporting ledge.  A lifting ring and




a submersible 12-volt pump were attached to the exterior of the




curved top surface.  A hole was drilled through the top of the respi-




rometer to receive the pump intake line, while the pump discharge




was conducted by a length of plastic tubing to a flexible U-liter




rubber bag.  Another piece of plastic tubing connects this bag to



the respirometer chamber, entering through a port in the end wall.




The presence of the flexible bag permits the removal of samples from




the system without the necessity for replacement of an equivalent




volume of water.




        The respirometer chamber joints were sealed with sheet rubber




gasket material to prevent leakage, and all metal surfaces were coated

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                                                              3



with an epoxy paint before assembly to minimize the possibility of




corrosion accompanied by oxygen loss.  All elements of the system




were made impervious, to Light to eliminate possible photcsynthetic




effects.






METHOD OF OPERATION




        The respirometer is lowered through the water from a pier




or boat using the lifting ring.  The submersible pump, powered by a




battery at the water's surface, is operated while the chamber is




lowered,, so as to empty it of the surface water originally present.




The chamber is lowered to within a foot of the bottom and held there




for a few minutes while the pump draws bottom waters into the chamber




and tubing.  The pump discharge tubing is then connected to the




flexible bag from which the flow is returned to the respirometer„




The recirculating system may be purged of air through the sampling




port located in the tubing line at the surface.  The respirometer is




then lowered carefully to the bottom„  The weight of the chamber




(approximately 38 pounds) forces the cutting edge into the bottom,




while the supporting ledge prevents the chamber from sinking below




the sediment surface„




        The pump is run continuously throughout the test, providing




continuous mixing of the water in the chamber.  The pump discharge




rate may be varied to simulate the degree of turbulence believed to




exist at the water-bottom interface.  Since the water pumped from




the chamber is recirculated, no significant change in the volume of




pressure of the chamber contents will ocsur.

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                                                              u




        The test period begins when samples are initially taken from




the sampling port at the surface for dissolved oxygen analyses. Du-




plicate 300 ml, samples are collected for immediate analysis, while




another pair of samples are withdrawn into dark bottles which are




incubated in the water during the period of the test.  Another pair




of samples are withdrawn at the end of the test period.  Dissolved




oxygen is measured in this final pair and in the incubated dark bottles,




        As an alternate to this method of operation, a dissolved




oxygen probe may be inserted into the recirculation system.  The use




of a probe would permit continuous measurements to be taken without




the necessity for removing samples from the system.  The flexible bag




and sampling port shown in Figure JL could be eliminated.




        With either of these measurement systems, it is clear that




some dissolved oxygen must be initially present in the water overly-




ing the bottom in order to conduct a test.  Where anaerobic waters




are encountered, the approach described could be modified so as to




artificially introduce oxygenated waters into the respirometer.






INTERPRETATION OF DATA




        The difference between the initial and final dissolved oxygen



concentrations observed in the respirometer is directly related to




oxygen uptake by the bottom.  This change in concentration may be




expressed as an areal uptake rate (S) if the confined water volume (V)




and bottom area (A) are known.  In the expression;

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                                                              5




               ?        (Ci - Cf} V
        S (gm/rn /day) =   ^ A  	                              (l)




t is the test period in days; C. and C  are, respectively, the initial



and final observed dissolved oxygen concentrations (as milligrams per



liter or grams per cubic meter), and V and A are expressed in metric


                    3            2
units, being O.OU3 m  and 0.276 m , respectively, for the respirometer



previously described.  The oxygen concentrations of the incubated dark



bottles, as determined at the end of the test period, may be substituted



in equation (l) for C.  if a significant difference exists between these



values.  This difference represents oxygen uptake of the waters over-



lying the bottom and will usually be negligibly small for a short test



period.



        The length of test period required depends both on the size of



the respirometer and the uptake rate being measured.  A minimum oxygen



change of 1 mg/1 is considered desirable for reliable results, and this



also influences the test period length.  For the respirometer described



above, the length of test required to give a 1 mg/1 oxygen change is



given as a function of uptake in Figure 2_.



        In order to minimize the length of the test period, the ratio



of confined volume to bottom surface area or the effective depth



should be minimized.  This consideration influenced the respirometer



design adopted, in that the semi-circular cross-section of the chamber



has a relatively low volume:area ratio.  The effective depth of this



cross-section is y- or 0.78^ times the radius of the semi-circle.

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        The units used to express the areal uptake rate (grams/square




meter/day) can be readily converted to volumetric units "by dividing




S by the depth of the overlying water in meters.  This quotient has




the units gm/m /day, or mg/liter/day, and refers to the DO change




expected in the full depth of the vater due to the oxygen sink at




the bottom.




PRELIMINARY RESULTS OBTAINED




        The benthic respirometer shown in Figure !_was used to measure




bottom uptake rates in the Potomac estuary near Washington, D. C., dur-




ing August and September, 1965.  A total of 25 tests were carried out




in a twenty-mile length of the estuary.  Uptake rates from 0.15 to 8.5




gms/square meter/day were found at water temperatures in the range of




22.5 to 33 degrees centigrade.  To provide a basis for studying the




longitudinal variation in uptake rates along the estuary, the results




were converted to a common temperature of 25°•  The temperature correc-




tion factor of 6.5 per cent per degree centigrade, as determined by




Fair  for benthal decomposition, was used.  At this common temperature,




the adjusted uptake rates averaged 2.5 gms/square meter/day.  Slightly




higher values were usually found near the main waste source, and rates




below 1 gin/square meter/day were found at distances five miles above




and fifteen miles below this location.




        Since there is no known method for absolute measurement of




in-situ benthal oxygen demands, it is not possible to make any state-




ment regarding the accuracy of the measurements obtained using the

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                                                              7


benthic respirometer,   The magnitude of the rates observed, however,


generally fall within the range of those believed to exist in natural

                                             P
water subject to pollutional loads,  O'Connor , for example, states


that typical values range from 1 to 10 grams/square meter/day with


the majority of values lying between 3 "to 5 grams/square meter/day


for relatively polluted streams.  These conclusions were apparently


based both on laboratory studies and analyses of field stream survey


data.


        Certain operational difficulties were encountered in using the


benthic respirometer.   These were generally associated with disturbing


the surface sediment layer and led to anomalous test results.  It was


found that the respirometer must be brought into contact with the


bottom very carefully, to avoid putting any of the settled solids into


suspension.


        The water recirculation rate used in the Potomac tests was


estimated from measurements of the time required to fill a sample


bottle of known volume through the sampling port at the water surface.


The approximate horizontal velocity over the bottom muds confined by


the chamber was calculated from this flow rate to be less than 0.5


feet per minute.  Such a velocity is not believed to be sufficient to


unduly agitate the surface sediment layer,.  This conclusion was sup-


ported by the absence  of unusual amounts of suspended material in the


water samples removed  from the system for oxygen analyses during the


tests.

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                                                             8




        An initial concern in the operation of the respirometer was




whether an effective seal with the bottom could be obtained.  This is




essential to prevent the exchange of the oxygen-depressed chamber




contents with the surrounding waters.  To investigate this condition,




samples of unconfined water were routinely collected near the respi-




rometer at the beginning and end of a test.  Changes in dissolved




oxygen content occurring within the respirometer were not reflected




in the external samples, and differences greater than 1 mg/1 between




the two samples were frequently observed at the end of a test.  It




was concluded that for the particular respirometer and bottom mud




characteristics of these tests, an effective seal was obtained.  The




weight of the respirometer shown in Figure _!, being 38 pounds in air,




undoubtedly was an important factor in maintaining this condition




throughout a test.






CONCLUSION




        Preliminary field tests of an in-situ benthic respirometer



yielded reasonable results which are believed to be a satisfactory




measure of the benthal oxygen demands actually occurring in the waters




studied.  Further tests of this measurement technique under a variety




of conditions would be desirable to determine more precisely its reli-




ability and general applicability.

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                          BIBLIOGRAPHY
1.  Fair, G. M.;  Moore,  E.  W.;  and Thomas, H. A., Jr.,  "The Natural
    Purification  of River Muds  and Pollutional  Sediments," Sewage
    Works Journal,  13,  270  (l9^l).

2.  O'Connor, D.  J., "Stream and Estuarine Analysis," Mimeo notes,
    Summer Institute, Manhattan College, New York, N. Y. (June 196U)

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          LIFT RING
4 ANGLE
                         SAMPLE
                         PORTS
                            AT
                          SURFACE
                    4 ANGLE
     -*— 19'
                                            4 ANGLE
   BENTHAL  OXYGEN  DEMAND MEASUREMENT  SYSTEM
                                                   FIGURE I

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                               EFFECTIVE  DEPTH OF
                               RESPIROMETER * 0.156
                                    meters
   0         2        4        6        8        IO

      BOTTOM  UPTAKE  RATE,  S(gm/m2/doy)
TEST  PERIOD  REQUIRED  FOR  Ippm  D. 0.  DROP
                                                FIGURE 2

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                       TABLE OF CONTENTS
                                                           Page
INTRODUCTION ...........  	   1
THE SEGMENTED ESTUARY MODEL  	   3
TEST CONDITIONS	   6
    Dye Source ........... 	   6
    Observed Dye Concentrations   	 ......   8
    Segment Volumes  	  10
    Dye Loss Rate Constant		12
    Net Water Flow	ih
    Turbulent Exchange Factor  ...... 	  18
    Proportionality Factor ....  	  20
ANALOG SIMULATION  ......  	 ... 	  21
DISCUSSION .	2k
CONCLUSIONS	29
ACKNOWLEDGMENT 	  30
BIBLIOGRAPHY 	  31
APPENDIX ......... 	  32


                         LIST OF TABLES
Table 1  Segment Volumes	11
Table 2  Calculated Net Advective Flows	16
Table 3  Model Parameters—Final Analog Computation  ...  23

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                        LIST OF FIGURES

                    (Figures Follow Page 35)


 1      Potomac River Study Area

 2      Dye Discharge Rate

 3      Dye Loss Rate

 k      Observed and Calculated Dye Concentrations vs Time
          (Segments 1, 2, 3, and *0

 5      Observed and Calculated Dye Concentrations vs Time
          (Segment 5)

 6      Observed and Calculated Dye Concentrations vs Time
          (Segment 6)

 7      Observed and Calculated Dye Concentrations vs Time
          (Segments 7 and 8)

 8      Observed and Calculated Dye Concentrations vs Time
          (Segments 9 and 10)

 9      Observed and Calculated Dye Concentrations vs Time
          (Segments 11 and 12)

10      Observed and Calculated Dye Concentrations vs Time
          (Segments 13 and lh)

11      Observed and Calculated Dye Concentrations vs Time
          (Segments 15 and 16)

12      Daily Stream Flow—Potomac River at Washington, D. C.,
          June-July 1965

13      120 Amplifier PACE Model 231-R

lU      Chloride Concentration vs Distance from Chain Bridge

15      Dispersion Coefficient vs Distance from Chain Bridge

16      Effect of River Flow on Pollutant Distribution in
          Potomac estuary

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        A STUDY OF TIDAL DISPERSION IN THE POTOMAC RIVER




                               BY




               L. J. Hetling and R. L. O'Connell






                          INTRODUCTION






        The  Chesapeake Bay-Susquehanna River Basins Project of




 the Federal  Water Pollution Control Administration, U. S. Depart-




'ment  of the  Interior has as its primary objective the development




 of a  comprehensive program for water pollution control in the




 Chesapeake Bay drainage basin.  The lU,170-square mile Potomac




 River Basin, second in size only to that of the Susquehanna River




 (27,000 square miles) in this drainage area, possesses a variety




 of water  pollution problems which are most significant perhaps in




 that  portion of the tidal estuary near Washington, D. C. (Figure




 1).   To permit a better understanding of this complex body of




 water and to provide a satisfactory means for analysis of present




 and future pollution problems and selection of optimum control




 methods,  an  attempt has been made to model the system in mathe-




 matical terms.




        To mathematically describe the fate of pollutants enter-




 ing such  a tidal system, knowledge of its turbulent dispersion




 properties is required.  To gather this type of information for




 the upper Potomac estuary, a dye tracer study was carried out by




 the Project  during the 3^-day period from June 10 to July lU, 1965.

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        The purpose of this paper is to describe the procedure




used in this large scale tracer experiment, the results obtained,




the methods used in the analysis of these results,  and, finally,




to present the conclusions reached regarding turbulent dispersion




properties of this tidal system.

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                  THE SEGMENTED ESTUARY MODEL
        The mathematical model employed in this study was that


                    •7

developed by Thomann  .  This model consists of a system of "n"



equations, each describing a mass balance of the material being



studied for each of the "n" segments of an estuary.  For an



estuary where good vertical and lateral mixing may be assumed,



these segments are selected along the longitudinal axis of the



estuary.  The segmentation of the Potomac estuary, as used in



this tracer study, is shown in Figure 1.



        The mass balance over each of the 16 segments shown in



Figure 1 includes terms describing changes in dye concentration



caused by advection, dispersion, losses, and, in the case of the



segment to which the dye was added, a dye source.  A mass balance



constructed for the "i" th segment takes the form:



           dC.
                  - C.) + E.+1 (C.+1 - C.)
        -d V. C. + P.                                            (l)
            11    i                                            v  '


where



        V. = volume of "i" th_ segment, cubic feet (cf)



        C. = mean dye concentration in "i" th segment (ib/cf)
         1                                 ——



        Q. = net waterflow across the upstream boundary of the

         1   "i" th segment (cf/day)

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        Ł. = a dimensionless proportionality factor used to
             estimate concentration at upper boundary of the
             "i" th segment

        E. = turbulent exchange factor for upstream boundary
         1   of the "i" tb_ segment (cf/day)

        d  = dye loss rate constant (day  )

        P. = rate of dye addition from external source (ibs/day)

        t  = time (days)
        Since for this study sixteen estuary segments vere employed,

a like number of expressions similar to equation (l) were obtained.

This system of sixteen linear first order, non-homogeneous, ordinary

differential equations may be solved simultaneously by numerical

methods using a digital computer or by programing the equations on

a relatively large analog computer.  In either case, all terms of

the equations must be known in order to solve for the dye concen-

tration of each segment as a function of time.  In this dispersion

experiment, however, the segment concentrations were known from the

results of sampling the estuary, while the turbulent exchange factor,

"E," for each segment was unknown.   It was necessary, therefore, to

solve for the "E.'s" by trial and error methods.  By this procedure,

initial values for "E." were chosen and a solution for "C." obtained.

The calculated concentrations were then compared with observed

values, suitable adjustments made to the "E." values, and a new

solution for "C." found.   This process was repeated until a satis-

factory agreement between observed and calculated concentrations was

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found.  Because of the repetitive calculation-comparison process




required, analysis by analog computer was considered to be the




most efficacious method for obtaining a solution in this case.




        In the following sections, each of the terms of equation




(l) is discussed in terms of the dye tracer experiment.

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                        TEST CONDITIONS



Dye Source (P.)


        A dye was released into estuary segment 5 via the outfall


sever of the District of Columbia Water Pollution Control Plant


(Blue Plains).  This outfall consists of two parallel 90-inch


diameter lines and extends 900 feet into the estuary from the


eastern shore, terminating at the eastern edge of the shipping


channel in about 17 feet of water at mean tide level (MTL).  The

                         *
dye used was Rhodamine WT , selected for its fluorescent proper-


ties and relatively low affinity for adsorption on particulate


matter.  The dye was added as a 20 per cent solution in methanol


to the elutriation wash water discharge sump which rapidly drained


to the outfall sewer line.  Travel time in this sewer was esti-


mated to be less than five minutes.  Chlorine was not applied to


the waste during the period of these tests.


        The dye solution was pumped to the sewer initially at a


rate of 19 milliliters per minute (ml/min.), or approximately 12


pounds of dye/day.  It was intended that a constant dye addition


rate be maintained throughout the 13-day dye release period.   How-


ever, on two occasions sudden large fluctuations in pressure  of


the flushing water line connected to the discharge side of the dye


feed pumps caused the pump ports to jam, and large amounts of dye
   See disclaimer at end of paper.

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were released to the estuary in a short period of time.   The




actual rate of dye addition is shown in Figure 2.  During the




test period, a total of 3^1 pounds of dye was used.




        Since dye was added to only one segment of the estuary,




the "P." term in each of the model equations was zero except in




segment 5.  In this segment the actual dye addition  rate, which




varied with time, as shown in Figure 2, was used as  input to the




model.

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Observed Dye Concentrations (C.)


        During the 13-day period of the dye release, and for 21


days thereafter, dye concentrations vere measured in the estuary.


Measurements were made using a fluorometer (G. K. Turner & Assoc.)


which was equipped with exitation and emission light filters


designed to selectively measure the fluorescence of the dye being


used.  With this tracer measurement system, a sensitivity of 0.01


parts per billion (ppb) may be attained.


        Samples were pumped continuously from the estuary to a


moving boat which carried the fluorometer.  The estuary waters


were pumped directly to the fluorometer which was equipped with


a recorder so that a continuous record of dye concentrations was


obtained for the waters through which the boat moved.  The sample


was withdrawn from 18 inches below the water's surface into a


hollow streamlined metal strut suspended from the side of the


moving boat.


        Measurements were made along the complete 25-mile length


of the upper segmented estuary at time of slack water.  Two suc-


cessive slack waters were normally measured, so that by averaging


the measurements obtained at a given location, a mean value for


the tidal cycle could be obtained.


        In addition to this longitudinal surface sampling, dye


distribution in the vertical and lateral directions was determined
*
   See disclaimer at end of paper.

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periodically at each of 32 cross-sections.  These cross-sections




were located at varying intervals along the length of the estuary,




being more closely spaced near the dye release point.  By means




of this sampling network, an adequate knowledge of the temporal




and spatial distribution of dye in the estuary was obtained.




        The dye concentrations found in each segment through  the




period of the test are shown in Figures k - 11.

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                                                                  10






Segment Volumes (V.)




        The segment volumes were determined from the latest (1965)




USCGS navigation charts for the Potomac estuary which give sound-




ings at mean low water.  The water volumes determined by planimeter-




ing these charts were increased by an appropriate amount to give




estimates of mean tide level volumes.  The product of these mean




tide level segment volumes and the mean of the high and low water




dye concentrations shown in Figures h - 11 give the total mass of




dye in each segment during each day of the test.  No corrections




were made for the small deviations of the mean tidal elevations




occurring during the period of the test from the long term mean




values upon which the volume calculations were based.  The segment




volumes used are given in Table 1.

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                                                 11
          TABLE 1


      SEGMENT VOLUMES
 Distance from  Chain Bridge

to Upper Boundary of Segment     Volume at MTL
          /_-T	\                 /_.Ł>„ TI-I~I\
Segment
1
2
3
It
5
6
7
8
9
10
11
12
13
Ik
15
16
Lower Limit
(miles )
3.3
k.Q
5.8
6.7
7.7
11.8
12.8
13.6
Ik. 6
15.9
17.1
18.3
19.3
20. k
21.9
23-5
25.8
(cf x 10" ' )
25.3
30.6
35. k
HO. 7
62.3
67.6
71.8
77.1
8H.O
90.3
96.6
101.9
107.7
115.6
124.1
136.2


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                                                                  12





Dye Loss Rate Constant (d.)



        It was expected that some loss of dye vould occur, pri-



marily due to adsorption on bottom sediments and silt suspended



in the waters of the estuary.  This loss was estimated by observ-



ing the change in total dye mass in the estuary over a 20-day



period immediately following the dye release period.  Since dye



was observed below the downstream boundary of the most seaward



segment on the 15th day of the test, the sampling network was



extended downstream, as necessary to assure that all of the dye



in the system was being measured.  The observed change in dye



mass, as shown in Figure 3, appears to follow first order reac-



tion kinetics.  Determination of the slope of the line in Figure



3 yielded a reaction rate constant "d" of 0.03^ per day (base e).



This means that 3.U per cent of the dye present in the estuary



is lost from solution each day, equivalent to a half-life of


                                                                 2 1
20.k days.  These loss rate kinetics have been observed by others '



for similar dyes, although most of the reported values for "d"



exceed that found in the Potomac for Rhodamine WT.



        It may be noted from Figure 3 that the total dye mass



found in the estuary on the day following cessation of the dye



release (lUth day of test)  was 270 pounds, while the total



amount of dye released was  3^1 pounds.  Using a dye loss rate



constant of 0.03^, the dye  mass remaining on the lUth day may



be calculated and compared to the observed value to provide an

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                                                                  13
additional check on the accuracy of the rate constant.  The mass



of dye present in the estuary at any time, M , may be calculated
                                            t


from the expression
                                                                 (2)
vhere t  and tp are times since instantaneous dye releases M  and



Mp, respectively,- and the other terms as previously defined.



        Results of performing this calculation for the l^th day



of the test indicated that 267 pounds of dye should be remaining



in the estuary.  Since essentially the same amount of dye (270



pounds ) was actually found to be present at that time , it vould



appear that the value used for "d" is a satisfactory estimate



for the dye loss rate constant.



        It should be noted, however, that any dye present in the



estuary at concentrations below the lower limit of the detection



instrument would also appear to have been "lost."  The rate con-



stant value found thus reflects this apparent loss as well as



actual losses by adsorption or other mechanisms.  Although it is



believed to be small, the significance of this apparent loss has



not been evaluated, and thus, the value determined for "d" must



be considered as an upper limit.

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Met Water Flow  (Q.)
'"""	~"~•.._._.,-—   ]_


        The term "Q." refers to the net flow into the "i" th
                   i                                      ~~~


segment from the adjacent upstream segment, i.e., the net flow



across the i-l,i or upstream boundary of the "i" th segment.



Net flow in the seaward or positive direction across a boundary



occurs as the net  result of river inflows, waste discharges,



water withdrawals, and evaporation.



        For this study, the inflow to the first segment was taken



as the Potomac River flow reported for the U. S. Geological Survey



gaging station  iLeiter Gage) at Washington, D. C. , adjusted for



inflows and evaporation occurring in the 5-8-mile stretch of the



river between the gage and the upper boundary of the first seg-



ment.  The daily flow rates reported for this gage during the



study period are shown in Figure 12.  These flows, adjusted as



described above, were assumed to occur through all segments of



the upper estuary on the same day they were measured at the gage.



        Losses by evaporation from the segmented portion of the



estuary were subtracted from the adjusted river inflow.  The



daily evaporat;on loss was calculated for the upper estuary us-



ing Meyer's formula and data from the Washington National Airport



weather station and the District of Columbia Water Quality Monitor-



ing Station at t.'-e Woodrow Wilson Bridge.  The calculated net



evaporative loss -eached a maximum of ^00 cfs on one day of the



test, but averagec: 135 cfs for the 25-mile length of the upper



estuary during the ibudy period.

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                                                                  15




        There are no significant withdrawals of water from the




upper estuary.  Daily inflows of natural drainage to each segment




were calculated based on its tributary area and the average daily




flow per unit area obtained from U. S. Geological Survey records




for the gaging stations shown in Figure 1.  A major inflow was




the waste effluent from the District of Columbia Water Pollution




Control Plant which discharged an average flow of 339 cfs to seg-




ment 5 during the study period.  Significant waste flows from the




five additional waste treatment plants shown in Figure 1 were also




included.  The few remaining waste flows discharged to the estuary




are relatively small in volume and were disregarded.




        Summing up these flows gave a net flow rate across each




boundary for each day of the tracer test.  Upon examination of




these net flows, it was found that the inflows to the estuary




(excluding the Potomac River flow and the District of Columbia




waste discharge) were approximately balanced by losses due to




evaporation.  Therefore, in order to reduce the number of flow




input functions, Q  through Q  were taken as being equal to Q ,




the adjusted Potomac River flow, and Q,- through Q s were set




equal to Q^, essentially the adjusted river flow plus the District




of Columbia Water Pollution Control Plant discharge.  These net




advective flows are given in Table 2.




        The net tidal flow into and out of each segment was as-




sumed to be zero over a complete tidal cycle.   No consideration

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                                                               16
 Date

June 10
     11
     12
     13
     11+
     15

     16
     17
     18
     19
     20

     21
     22
     23
     21+
     25

     26
     27
     28
     29
     30
July
 1
 2
 3
 6
 7
 8
 9
10

11
12
13
11+
                        TABLE 2
          CALCULATED NET ADVECTIVE FLOWS  (Q.)
                                (cfs)
 1
 2
 3
 1+
 5

 6
 7
 8
 9
10

11
12
13
Ik
15

16
17
18
19
20

21
22
23
2k
25

26
27
28
29
30

31
32
33
3k
                                                        T.6
                                 k390
                                 3881+
                                 3081*
                                 2761
                                 2562
                                 238)4

                                 2367
                                 2377
                                 221+6
                                 2235
                                 2181+

                                 2173
                                 2121+
                                 1883
                                 1962
                                 1932
1790
1661
11+31
1201

1199
1109
1339
1371+
1261+

1397
1301+
1168
1132
1150

1622
291+6
2691
2096
(cfs)

 1+831+
 1+115
 31+88
 3106
 2937
 2778

 269!+
 2803
 2653
 2619
 2553

 2578
 2538
 2293
 21+32
 2311+

 21+07
 2116
 201+2
 1839
 1596

 1560
 11+70
 1760
 1727
 1733

 1826
 1693
 1597
 1535
 1611+

 3000
 3566
 3196
 2570

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                                                                  IT
was given to the small changes in tidal elevation and, therefore,




tidal flow which occur on succeeding days during a lunar tidal




cycle.

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                                                                  18
Turbulent Exchange Factor (E. )

        The turbulent exchange factor "E" is calculated for each

segment boundary from the expression:

                         K  A
        Ei
                       .          ^

where the "i" subscript refers to the boundary between segments

i-1 and i, "K" is the longitudinal dispersion coefficient (analo-

gous to the classical Fickian diffusion coefficient, expressed in

areal units per day), "A" is the cross-sectional area of the

boundary plane, and "L" is the segment length.

        The above expression is based on Fick's first law of

diffusion, i.e. ,

        Ni (Ib/sf/day) = K ~                                    (k)

where "N" is the rate of mass transfer of substance per unit area

across a boundary where the spatial gradient of the substance is

"dC/dx" ("C" is in Ibs/cf) and "K" is defined as above.

        If the mean concentration in two adjacent segments is

assumed to occur at their midpoints, and the gradient between

these midpoints is linear, it can be shown by geometry that:

        ac _    ci-i " ci
        dx   0.5 (L^ + L.)
        Substituting (5) into equation (k) gives:
                          K (C.    - C.)
        N.  (Ibs/sf/day) = 0.5 fc^ A.)                         (6)

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                                                                    19
Multiplying equation (6) by the cross-sectional area across which


the turbulent exchange takes place, yields the mass flow rate "D. :"


                       A. K. (C.   - C. )

        D. (Ibs/day) =  ^(^T.t-                         (7)


        Substituting equation (3) into (7) yields:
which is the expression used in equation (l) to describe the mass


flow of substance across a boundary due to turbulent exchange.


        The "E" term, or more specifically "K," was the unknown


parameter which the study was designed to evaluate.  The "K" term


as used herein is defined as the coefficient of longitudinal dis-


persion.  This term applies to net longitudinal mass transport


resulting not only from turbulent diffusion but also from velocity


and concentration variations in a cross-section.  The latter effect


has been shown  to be of greater significance in estuary type flows.


It has been assumed that dispersion is analogous to Fickian diffu-


sion with the diffusion coefficient replaced by a dispersion


coefficient.


        As mentioned previously, initial values of "K" were assumed


for each boundary.  These values were then adjusted to obtain good


agreement of the model output with the dye concentrations observed


in the estuary.  The initial values were chosen on an empirical

     ^
basis  and ranged from 1.5 sq mi/day for the boundaries at the


upper end of the estuary to 5.9 sq mi/day at the lowest boundary.

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                                                                  20
Propprtionality Factor  (Ł. )
        The proportionality factor "Ł." is used in the first two
terms of equation (l) that describe the advective movement of dye
into and out of a segment.  This mass movement across the i-l,i
boundary due to advection may be expressed simply as the product
of the net advective flow "Q." and the concentration at the
boundary.  However, since only the average concentration of the
adjacent segments is considered in the model, the concentration
at the boundary must be calculated.  It can be shown by geometry
that for the case of a linear gradient between the midpoints of
two adjacent segments, the concentration at the boundary is given
by the first two terms in brackets in equation (l) where:
               i-l    i
Equation (9) gives a satisfactory first approximation for the
proportioning factor applicable to the i-l,i boundary.  To assure
a realistic solution, however, the following relationship must
be observed:
                                                                (10)
To simplify computations where "E" was changed frequently, the
inequality given by (10) was treated as an equality.  So long as
the proportionality factor "Ł" remains within the lower limit
defined by equation (10) and an upper limit of unity, the solu-
tions obtained by the model are relatively insensitive to the
value chosen for "Ł."

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                                                                  21
                       ANALOG SIMULATION



        The set of sixteen differential equations similar to

                                     *
equation (l) were programed on an EAI  231-R analog computer,


pictured in Figure 13.  The output selected from the computer


was a record of concentration versus time for each of the six-


teen segments of the estuary.  These calculated concentration-


time histories were automatically plotted as a continuous ink


trace on graph paper, as shown in Figures h - 11.  The other two


lines on these plots describe dye concentrations observed in each


segment at high and low slack water.  Repeated solutions were


obtained by the computer for each different set of "K" values


supplied as input.  The objective of each succeeding run was to


bring the ink trace output of the computer closer to a point


midway between the observed high and low slack water values.


The set of "K" (and associated "Ł") values which gave the best


fit are shown in Table 3.


        In carrying out such computations, it is necessary to


specify the proper initial and boundary conditions for the test.


Prior to the start of the  dye release there is, of course, no dye


present in the estuary and the "C.'s" are all initially set to


zero.  For the upper and lower boundaries of the system, the


concentration-time histories actually observed were used as the


boundary condition input function.  Since no dye was ever found
*
   See disclaimer at end of paper.

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                                                                  22




at the upper boundary of segment 1, the upper boundary condition




vas zero throughout the test.  The lower boundary condition vas




likewise zero until the 15th day of the test when dye was found




there.  The dye concentration at the lower boundary then gradually




increased over the succeeding twelve days when a relatively steady




level was maintained for the remainder of the test period.

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                                              23
        TABLE 3
    MODEL PARAMETERS
FINAL ANALOG COMPUTATION
i
1
2
3
U
5
6
7
8
9
10
11
12
13
lU
15
16
17
K.
i
(sq mi/day)
0
0.2
0.2
0.2
0.25
0.3
0.3
o.i*
Q.k
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
fi.
1.0
0.95
0.94
0.92
0.93
0.5
0.88
0.70
0.91*
0.88
0.77
0.88
0.84
0.85
0.87
0.89
0.89

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                           DISCUSSION






        In general, the final curves obtained as output from the




analog computer correspond satisfactorily with the observed data.




Good agreement was obtained for the segments at and near the dis-




charge point during the dye release period when changes in dye




concentration took place most rapidly.  In the six segments just




below the discharge point, there was an obvious tendency for the




computed concentrations to drop off faster toward the end of the




test than was actually observed.  No reasonable manipulation of




the dispersion coefficients was capable of eliminating this anomaly.




It was concluded that this effect was produced by the two large




instantaneous dye releases which occurred midway through the dye




discharge period, as shown in Figure 2.  Quite possibly, some




significant portion of this large amount of dye was trapped in




the coves and inlets along the shoreline near the release point.




This entrapped dye could then have fed slowly back into the main




channel of the estuary and thereby maintained higher dye concen-




trations for a longer period of time than otherwise would have




occurred.  This effect has also been observed in hydraulic model




studies when instantaneous dye releases were carried out .  It is




also possible that the upper limit value used for the dye loss rate




constant was too large.  This would tend to cause the concentra-




tions calculated for the later stages of the test period to be




smaller than those observed.

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                                                                  25
        The variations in river flow during the study period and




the superposition of the two instantaneous releases upon a con-




tinuous release provided a rather severe simulation test for the




mathematical model.  In addition, the simplifying assumptions




required for use of the one-dimensional model were obviously not




met in certain respects.  In spite of these factors, the degree




of agreement between calculated and observed dye concentrations




leads to the conclusion that the model with the estuarial disper-




sion properties as finally established can be expected to describe




the distribution of soluble pollutants in the Potomac estuary with




a reasonable degree of accuracy.




        During the initial simulations on the analog computer, it




was apparent that good agreement would not be possible near the




discharge point with the segment sizes originally employed.  It




was necessary to enlarge segment 5, which received the dye dis-




charge, to approximately three times its original size to achieve




meaningful results.  The reason for this is related to the water




movement occurring during a tidal cycle.  Dye added as a continu-




ous discharge to oscillating tidal waters will be rapidly distrib-




uted above and below the release point during a single tidal cycle




over a distance equivalent to a tidal excursion, or about four




miles in this case.  This distribution, of course, is not related




to net advective movement or dispersion, but simply to the physical




movement of the receiving waters themselves.  A similar effect

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                                                                  26
could be achieved by visualizing the receiving water as being




stationary while the discharge pipe moved upstream and downstream




a total distance equivalent to a tidal excursion.  It would be




possible to account for this effect in the model in a similar




manner by distributing the tracer inflow to adjacent segments




above and below the outfall.  However, this procedure was not




used, and instead, the segment to which the tracer was discharged




was enlarged to half the tidal excursion distance in both the up-




stream and downstream directions.




        The range of dispersion coefficients finally determined,




0.2 to 0.6 square miles/day, were significantly lower than those




commonly calculated from observed chloride distributions in more




brackish waters.   This is in agreement with the findings of Harle-




man  and others that the dispersion coefficients found in saline




waters are strongly influenced by longitudinal density currents.




This circulatory movement which occurs where vertical salinity




gradients exist is the result of upstream movement of the denser




bottom waters and downstream flow of the less saline surface waters.




This type of gravitational circulation would tend to be reflected




in higher dispersion coefficients in the classical advection-




diffusion model such as employed in this study.




        Estuary chloride concentrations measured during the tracer




test are shown in Figure lU.  The low concentrations of chlorides




measured in the study area indicate that the density current effects

-------

-------
                                                                  27
mentioned above would not be expected in the upper Potomac estu-




ary during the test period.  Since salinity steadily increases




downstream toward the Bay, a downstream rise in the dispersion




coefficient might also be expected.  This was the case, as shown




in Figure 15.  The higher values shown for the estuary below the




point where the tracer study terminated were obtained from anal-




ysis of historical chloride records using a digital computer




solution of the model.  The solid line in Figure 15 represents




a visual approximation of a. line of best fit to both sets of data




and will be used in future calculations requiring solution of the




model.  The dramatic change in the value of the dispersion coef-




ficient over the upper ^0 miles of the Potomac estuary illustrates




the hazards involved in extrapolating brackish water dispersion




phenomena to tidal fresh waters.




        The knowledge of dispersion characteristics of the upper




Potomac estuary which was gained in this study will permit the




mathematical model described previously to be used with a reason-




able degree of confidence in analysis of the water pollution




control problems of this area.   One such use, for example, would




be an examination of the influence of river inflow upon the dis-




tribution of pollutants in the  estuary.  Using the dispersion




coefficients described by the smooth curve in Figure 15, a digital




solution of the model for various rates of fresh water inflow




produced the family of curves shown in Figure l6.   The same set

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                                                                  28
of dispersion coefficients was used for each river inflow investi-




gated, since it is not known to what extent the magnitude of net




advective flow may affect the value of the dispersion coefficient.




These effects, however, are not believed to be significant over




the range of flows shown in Figure 15, based on their relatively




small contribution to the total tidal flow which is experienced




in the estuary.




        In these calculations, the pollutant was assumed to enter




the estuary ten miles below Chain Bridge, which is the location of




the District of Columbia Water Pollution Control Plant effluent




discharge.  The pollutant is non-conservative with a first-order




decay rate constant of 0.23 per day (base e) comparable to the




rate of exertion of the biochemical oxygen demand of organic




materials in waste effluents.  A waste flow of 350 cfs also




enters the estuary at the pollutant discharge point.  The condi-




tions depicted are those which would exist at steady state.




        Figure 16 shows that the magnitude of pollutant concentra-




tions in the estuary is influenced by the amount of flow entering




from the Potomac River, and that this influence varies depending




upon the distance below the head of the estuary.  This type of in-




formation, of course, is extremely useful in conducting a rational




examination of the benefits of flow regulation as well as various




other pollution control measures which must be considered before




the optimum program can be selected.

-------

-------
                                                                  29
                          CONCLUSIONS


        1.  The segmented estuary model satisfactorily describes

the distribution of an artificially introduced tracer in the up-

per 25 miles of the Potomac estuary and, similarly, can be used

to predict the distribution of soluble pollutants which may be

introduced in this area.

        2.  The turbulent dispersion characteristics found dur-

ing the period of this study are best described by coefficients

which increase from 0.2 sq mi/day near the head of tide to about

1.0 sq mi/day at a distance of 25 miles downstream.

        3.  The loss of Rhodamine WT dye found in the relatively

fresh waters of the upper Potomac estuary can be described by a

first order reaction rate constant which has an upper limit of

O.Q3h day"1.
   Mention of products and manufacturers is for identification
   only and does not imply endorsement by the Federal Water
   Pollution Control Administration and the U. S.  Department
   of the Interior.

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                                                                  30
                         ACKNOWLEDGMENT






        The cooperation and assistance rendered "by Messrs. A.




Fay and H. Schreiber of the District of Columbia Department of




Sanitary Engineering were invaluable to the conduct of this study




and are gratefully acknowledged.

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                                                                  31
                          BIBLIOGRAPHY
1.  Feuerstein, D. L. and Selleck, R.  E. ,  "Fluorescent Tracers  for
    Dispersion Measurements," Journal  of the Sanitary Engineering
    Division, American Society of Civil Engineers,  Vol.  89,  No.  SAh,
    pp. 1-22, August 1963.

2.  Gunnerson, Charles G. and McCullough,  Charles A., "Limitations
    of Rhodamine B and Pontacyl Brilliant  Pink B as Tracers  in
    Estuarine Water," presented at Symposium on Diffusion in Oceans
    and Fresh Waters, Lamont Geological Observatory, Palisades,  New
    York, August 31 - September 2, 196k.

3.  Harleman, D. R. F., "The Significance  of Longitudinal Dispersion
    in the Analysis of Pollution in Estuaries," presented at the
    Second International Conference on Water Pollution Research,
    Tokyo, Japan, August 1963.

k.  Hetling, Leo J. and O'Connell, Richard L., "Estimating Diffusion
    Characteristics in Tidal Waters,"  Water and Sewage Works, Vol.
    112, No. 10, pp. 378-380, October  1965.

5.  Holley, E. R. , Jr. and Harleman, D. F.,  "Dispersion of Estuary
    Type Flows," MIT Hydrodynamics Laboratory Report No.  jk,
    Cambridge, Massachusetts, January  1965°

6.  Pritchard, D. W., "The  Movement and Mixing of Contaminants  in
    Tidal Estuaries," Proceedings, First International Conference
    on Waste Disposal in the Marine Environment, p. 512,  Pergamon
    Press, Inc., New York,  July 1959.

7.  Thomann, Robert V., "Mathematical  Model for Dissolved Oxygen,"
    Journal of the Sanitary Engineering Division, American Society
    of Civil Engineers, Vol. 89, No. SA5,  Proc.  Paper 3680,  pp.
    1-30, October 1963.

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-------
                                                                  32
                           APPENDIX A

                  Procedure Used to Reduce and
               Validate Observed Dye Measurements

SLACK RUN MEASUREMENTS

        1.  Slack water run fluorometer recorder tapes were

            digitized at lA-inch intervals.   With a tape speed

            of 30 inches/hour and a boat speed of approximately

            25 miles/hour, readings were obtained at approximately

            1000-foot intervals along the length of the estuary

            at low and high slack water for almost every day of

            the test.

        2.  These digitized fluorometer readings were converted

            to dye concentrations by using appropriate calibra-

            tion curves and correcting for water temperature.

        3.  Slack water dye concentrations were plotted against

            distance along the estuary.  This type of plot is

            referred to as Figure A in the succeeding discussion.

        h.  From the Figure A plots , two plots of dye concentra-

            tion versus time (days) were constructed for each  of

            32 points along the estuary, one  for low water slacks

            (Figure B) and one for high water slacks (Figure C).

        5.  Background (apparent) dye concentrations were then

            subtracted from the Figure B and  C plots.

-------

-------
                                                                  33






CROSS-SECTION MEASUREMENTS




        6.  The fluorometer readings obtained at each of 32 cross-




            sections were converted to dye concentrations as in




            step 2 above.  These dye measurements obtained laterally




            across the estuary and vertically through the water




            column were contoured at each cross-section.




        T.  The average concentration in each cross-section was




            determined by planimetering the contour plot and




            calculating a weighted average of the planimetered




            areas.






ADJUSTMENT OF SLACK WATER CONCENTRATIONS




        8.  For each day of the test period, a mean concentration




            was available at each of 32 cross-sections during




            either low or high water slack (step 7).  The ratio,




            R, of each mean cross-section concentration to the




            appropriate slack run concentration found at that




            cross-section and slack water (from Figure B or C)




            was determined.




        9.  For each cross-section the ratio R (step 8) was




            plotted against time (date) as Figure D and a smooth




            curve was drawn through these points.




       10.  Taking values from Figure D, the ratio R was plotted




            against distance along the estuary, and a smooth




            curve drawn through these points (Figure E).

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-------
                                                           31*
11.  Step 9 was repeated using data from Figure E.   Steps




     9, 10, and 11 were carried out to average R over both




     space and time.




12.  The R values obtained in Step 11 were used to convert




     all slack run concentrations in Figures B and C to




     mean concentrations applicable to the complete cross-




     section.




13-  The mean concentrations obtained in step 12 were




     plotted against distance along the estuary.  Two




     plots were developed for each day of the test period;




     one each for low (Figure F) and high (Figure G) slack




     water.




lU.  The dye concentrations given in Figures F and G were




     used to determine the mass of dye in each of 16 pre-




     viously selected longitudinal volume segments.  The




     total mass of dye in the estuary at a given time was




     found by adding the calculated mass in each segment.




15-  For the period following the end of the dye release




     when the total amount of dye in the estuary should no




     longer be changing, the logarithm of the calculated




     total mass was plotted against time.  The downward




     slope of this line is a measure of the rate (K) of




     dye loss in the estuary due to adsorption on silt,




     photochemical decay, and possibly other mechanisms.

-------

-------
                                                            35


l6.  The mass of dye, ŁM, which should have been present


     in the estuary each day of the test was calculated


     as follows:
          _..    lr / .     ~K."C \   _.  •""iC'G
          ZM.  = — (i - e   )+M.e
            0   IV               1
     where P    = constant dye discharge rate


           M.   = instantaneous dye releases


           k    = dye decay rate

              i
           t ,t  = elapsed time


IT-  The mean segment dye concentrations (Figures F and G)


     were adjusted by multiplying them by the ratio of the


     calculated dye mass (EM ) to the observed dye mass
                            "C

     (step Ik) for each segment and each slack water.  This


     correction resulted in 32 plots of final validated


     mean segment concentrations against time; a high and


     low water slack plot for each of l6 volume segments.

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                                         \  LEGEND
                                                    PENNSYLVANIA
                                                 LOCATION  MAP
                                                    = MAJOR  WASTE
                                                      TREATMENT  PLANT


                                                    = ESTUARY  SEGMENTS
                                                    = GAGING  STATIONS
                                                   LITTLE  FALLS  BRANCH-
                                                     BETHE5DA, MD

                                                   POTOMAC  RIVER-
                                                     WASHINGTON, D C
                                                   ROCK CR -SHERRILL DRIVE-
                                                     WASHINGTON, D C

                                                   N E BR  ANACOSTIA  RIVER-
                                                     RIVERDALE,  MD

                                                   N W BR  ANACOSTIA  RIVER-
                                                     HVATESVILLE , MD

                                                   FOURMILE RUN-
                                                     ALEXANDRIA, VA
                                                   LITTLE  PIMMIT  RUN -
                                                     ALEXANDRIA, VA

                                                   CAMERON RUN-
                                                     ALEXANDRIA, VA,

                                                   HENSON  CREEK -
                                                     OXEN HILL ,  MD

                                                   POHICK  CREEK-
                                                     LORTON, VA

                                                   MATTAWOMAN CREEK-
                                                     PO MON KEY,  MD
                                                  DISTRICT  OF  COLUMBIA


                                                  ARLINGTON  COUNTY

                                                  ALEXANDRIA  SANITATION

                                                      AUTHORITY

                                                  FAIRFAX COUNTY - WESTGATE

                                                      PLANT

                                                  FAIRFAX  COUNTY - LITTLE

                                                      HUNTING CREEK PLANT

                                                  FAIRFAX COUNTY - DOGUE

                                                      CREEK PL ANT
POTOMAC   RIVER   STUDY   AREA
                                                                FIGURE  1

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1 1 1 1 1 1 1 1 1 1

UJ.
h-
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FIGURE 2

-------

-------
                     DYE  LOSS  RATE
   SLOPE (d)  =  0.034
                               33
DAY    OF   TEST
                                       FIGURE 3

-------

-------
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«*-
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                                   DAILY   STREAM    FLOW
                              POTOMAC   RIVER   AT  WASH., D.C.
                                     JUNE  - JULY   1965
                            STUDY      PERIOD
          10     15
             JUNE
                               20    25   301
 10     15
- JULY
                                                        20    25    3O
                                         DATE
                                                                                FIGURE \2

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-------
120 Amplifier PACE Model  231-R
        Analog Computer
                                           FIGURE  13

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-------
NV31/M
               FIGURE  14

-------

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                                          FIGURE

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          A MATHEMATICAL MODEL FOR THE POTOMAC RIVER--

               WHAT IT HAS DONE AND WHAT IT CAN DO


        "In a comprehensive water pollution program it is not suf-

ficient to know what the existing situation is.  To operate ration-

ally and efficiently the program must be able to forecast water

quality and predict what will happen if waste loads are changed or

other control measures are taken."-1-  The most significant area with-

in the Chesapeake Bay-Susquehanna River Basins Project study area

is probably the Potomac estuary in the Washington Metropolitan Area.

        To satisfy this need for prediction capability, it was

necessary to develop a mathematical model capable of simulating

water quality in the Potomac River estuary.

        Several models capable of simulating water quality in an

estuary have been developed.  After detailed investigation of the

models available, the segmented estuary model developed by Dr. Robert

Thomann while he was employed by the Federal Wnter Pollution Control

Administration at the Delaware Estuary Comprehensive Project was

selected as the one which most nearly conformed to the requirements

of the Project.  The model is highly flexible, capable of being

utilized to describe any conservative or nonconservative substance.

Solutions are available for both transient and steady state condi-

tions.  Its accuracy is sufficient for engineering design purposes.
   Coulter, James B.  "What Is A Comprehensive Water Pollution Control
   Program?"  Journal Water Pollution Control Federation,  Vol. 38,
   No. 6, pp. 1011-1022, June 1966.

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                                                              2




        Wait a minute.  What am I talking about—mathematical models,




simulation, conservative, nonconservative, steady state, transient,




engineering design „  „




        This technical jargon of a new breed of engineers now stands




in the way of the use of many new techniques which make us capable of




better design and operation of the huge public facilities now con-




sidered as necessary to control water quality.




        What I would like to do here is to describe in simple, under-




standable terms what a mathematical model for prediction of water




quality in the Potomac estuary means, the progress made in its develop.




ment to date, and its possible future uses.




        A scientific model is a representation of some subject of




inquiry.  In our case, it is the quality of water in the estuary.




Perhaps the most vivid examples of scientific models are the physical




models of river systems and estuaries constru :ted and operated by the




U. S, Corps of Engineers at Vicksburg, Mississippi,  These are actual




scale models of the estuary with every significant detail built in.




With a machine capable of simulating tides and pumps discharging water




into the estuary to simulate river inflow, all of the major physi 'al




properties of the actual estuary are represented.  These include such




things as salinity distribution, tidal heights, and currents.  With




this model operating, it is possible to evaluate the effects of  such




physical structures as jetties and piers on currents, sediment dis-




tribution, dredging needs, etc.  Since the time scale is approximately

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                                                              3




1 to 100, it is possible to evaluate effects which would take years




to occur in the estuary by operating the model for a few days.




        A mathematical model is similar to the physical model in




concept.  But, in a mathematical model, instead of using concrete,




the physical system is represented by equations which describe all




of its significant details.




        Anyone who has a checking account works with a mathematical




model.  All deposits are positives, and all withdrawals are negatives.




Monthly service charges and a charge per check further completes the




model.  Using technical jargon we can say that the model has a lower




limit (or bound—using the correct mathematical term) in that a




negative balance cannot in theory exist.  Knowledge of all the inputs




(deposits and withdrawals), the initial conditions (original balance)




and other sources and sinks (service charges), it is possible to com-




pute the balance at any time (a transient model).




        In the same way, by proper bookkeeping and a knowledge of




bounds or limits, inputs, initial condition, sources and sinks, it




is possible to develop a set of equations which describe water quality




in the estuary.  The number of computations, of course, in this




system when compared with a checking account is enormous.   To solve




such a system would require many man-years.  But, luckily, most of




the computations are routine addition,  subtraction, and multiplica-




tion.  Within recent years digital computers have been developed




which can do such routine computations  in a fraction of a  second.

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                                                              u




Properly instructed (programed),, the digital computer makes possible




solutions of the system available in minutes.




        A key step in the development of any model is its verifica-




tion, i.e., to check and see if the model truly simulates water




quality.  This involves a comparison of measured or observed values




with compared values„




        A checking account is verified every so often when a state-




ment is received from the bank.  When we compare the balance in our




checkbook with the balance in the bank statement, we find time after




time that we made a mistake.  More often than not, it is a blunder;




an input (deposit or withdrawal) was forgotten, the bank service




charge was changed, or perhaps even the "bank made a mistake„




        This is what we have been doing with the Potomac Estuary




Model for the past few years.  For each water quality parameter we




started by writing the equations utilizing all the inputs which we




felt would affect the given water quality parameter,   Then, the model




(equations) would be solved and compared with what is actually




measured.  We would find at first that the calculated values did not




match the measured values„   We would then search for our mistake and




find that we missed an important input or that a biochemical reaction




which was assumed to occur did not occur.  By this process of trial




and error, we have finally arrived at what we have now--a verified




model.




        I would like to describe a large-scale experiment which was




carried out to verify the model and discuss some other verification




results in order to give you a better feel for its capabilities,

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                                                              5



        Because most natural water quality parameters are involved




in so many complex chemical, biochemical, and physical reactions,




they do not lend themselves to a good simple test of the model.




Our first serious attempt at verification was a dye diffusion study.




We injected a lipstick dye (Rhodamine WT) into the river at a con-




stant rate and measured the resultant concentrations of dye in the




river.  In this case, the only significant input was the dye which




we pumped into the river, and we knew the rate of pumping exactly.




        The dye was pumped into the river through the effluent pipes




of the District of Columbia water pollution control plant just above




Marbury Point (Figure l).  Figure 2 shows the resulting average dye




concentration measured opposite the plant outfall.  The solid center




line shows the concentration of dye predicted by the model, while




the other two lines represent the actual measured concentrations at




high and low water.  This nice matching of the observed data and




calculated data did not, of course, occur on our first try with the




model.  Many repetitive runs of the model were required to get the




match you see here.  Each run required a correction of some error




or a change in a coefficient in order to get closer to the measured




values.




        The close agreement between the measured and calculated dye




concentrations found in the above experiment shows that the segmented




estuary model can satisfactorily describe water quality which will




result from the introduction of a simple soluble pollutant into the




estuary if the correct coefficients are known.

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                                                              6

        Getting to some more complicated parameters, I would like

to show our results in modeling chlorides, dissolved oxygen, and

phosphorus„

        Figure 3 shows the observed and calculated variation in

chlorides  in the estuary at Possum Point near Quantico.  Chlorides

enter the  estuary by diffusion upstream from the bay.  The rate of

diffusion  depends on the tidal currents and river flow.  Here you

can see that, during the spring months when the river flow is high

and chloride concentration is low and in the late fall when the

river flow is low, the concentration of chlorides rose dramatically.

Figure 3 shows a good match between predicted and observed chloride

values.

        Dissolved oxygen (DO) is probably one of the most important

parameters to know when talking about the quality of the estuary.

It is also the most difficult to model, since it can enter or leave

the estuary in so many different ways.  Figure k* will give you an

idea of the system which involves DO concentration in an estuary.

        Our results in modeling DO, however, have been very encourag-

ing.  Figure 5 shows measured and computed values of DO at Woodrow

Wilson Bridge in 1965.
* Thaddeus A0 Wastler, III, Physical Science Coordinator, Chesapeake
  Field Station, Chesapeake Bay-Susquehanna River Basins Project,
  Federal Water Pollution Control Administration, U. S,  Department
  of the Interior, Annapolis, Maryland.

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                                                              7



        One of the problems which has recently become more prominent




in water quality control is algal blooms.  The system which controls




algal blooms in estuaries is so complex that no one has even dared to




suggest that a mathematical model of it is possible.  I do not think




that such a model is now technologically possible; however, models of




the sub-systems which affect algal blooms are possible.  One of our




own efforts in this direction can be seen in Figure 6.  A significant




factor in prediction of algal blooms is the concentration of phosphorus,




This preliminary attempt to model phosphorus (as shown in Figure 6)--




while not as good a match as that for DO and chlorides—shows promise.




Experiments are now being carried out to refine this model.




        This is where we are now.  The only question that remains is—




what do we use the model for?  This is where you come in.




        You are the people who will decide the fate of tidewater




Potomac.  You represent the engineers, the biologists, the planners,




the heads of the leading citizens' groups who collectively influence




the actions of government.  What the model offers you is a method of




trying ideas and learning the consequences without great economic




loss.




        Let us look at some examples.  A frequently heard proposal




is that the Washington Metropolitan Area use the estuary as a source




of water supply.  Another proposal is to clean up the present pollu-




tion in the upper Potomac estuary by pumping all of the waste-water




from the Metropolitan Area to the Chesapeake Bay or the Atlantic




Ocean.  Such action would certainly drastically change the biological

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                                                              8




and chemical state of the estuary.  One of the most significant




changes would be in the concentration of chlorides (sea salts) in




the estuary.  The concentration of chlorides which diffuse upstream




from the Chesapeake Bay is affected by the net downstream river flow.




The proposed pumping of waste-waters to the Bay or the ocean would




reverse the direction of flow and, in this way, significantly change




the chloride concentrations.  The proposal raises the following




questions!  Would the chloride concentrations at the head of the




estuary- be so high as to interfere with the use of the estusry as a




water supply?  What would the change in chloride concentrations do




to the ecology of this portion of the estuary?  Certainly the type




and quantity of fish would be affected.  Would there be crabs and




oysters at Indian Head?  Would boat owners be plagued with barnacles




attaching to their craft?  What would happen to the oyster industry




now prospering in the lower reaches of the estuary?  Certainly any




dramatic changes in chlorides will affect it.  These questions can




be answered only if the quality of the water can be known.  The




mathematical model gives us a method of obtaining this knowledge.




        In answer to the first question, a simulation run using  the




chloride model gave the results shown in Figure 7.  As you can see




with this figure, such a proposal would cause the chloride levels




in the upper estuary to rise so high that desalinization of the upper




estuary would be necessary to make it fit for drinking water.  In




a similar manner, the model can be used to determine the day-to-day




variations in chloride concentration at any point in the estuary and,

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                                                              9



in this way, give the engineers and scientists the necessary data




to answer the above questions.




        Let us look at another example.  Figure 8 shows the varia-




tions in DO that can be expected at the Woodrow Wilson Bridge in




1985 under several different levels of waste-water treatment and




flow.  Here it is immediately evident that in 1985, if the river




flow is kept at a minimum of 1,500 cfs, only 92% removal of BOD




will be required at the treatment plants to maintain a minimum DO




of k mg/1; while, if the river flow drops to 500 cfs, 95fo removal




of BOD will be required.




        These are examples of the basic uses of the model.  There




are others.  One of the most promising is its use in conjunction




with economic techniques such as linear or dynamic programs, but




that is a different story as long as the one I have just related,




and I am sure that I have given you enough to absorb in one afternoon,

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                                                      PENNSYLVANIA
                                              J       TM n   ^	
                                                    LOCATION  MAP
                                                         MAJOR WASTE
                                                         TREATMENT  PLANT
                                                      =  ESTUARY  SEGMENTS
                                                         GA6ING  STATIONS
                                                     LITTLE  FALLS BRANCH-
                                                        BETHESDA, MO

                                                     POTOMAC RIVER-
                                                        WASHINGTON, D C

                                                     ROCK CR -SHERRILL DRIVE-
                                                        WASHINGTON, D C
                                                     N E BR ANACOSTIA RIVER-
                                                        RIVERDALE, MD

                                                     N W BR ANACOSTIA RIVER-
                                                        HYATE SVILLE , MD

                                                     FOURMILE  RUN-
                                                        ALEXANDRIA,  VA

                                                     LITTLE PIMMIT RUN
                                                        ALEXANDRIA,  VA

                                                     CAMERON RUN-
                                                        ALEXANDRIA, VA,

                                                     HENSON CREEK -
                                                        OXEN  HILL, MD

                                                     POHICK CREEK-
                                                        L 0 R T 0 N ,  VA

                                                     MATTAWOMAN CREEK-
                                                        PO MON KEY, MD
                                                     DISTRICT OF COLUMBIA

                                                     ARLINGTON  COUNTY

                                                     ALEXANDRIA  SANITATION

                                                         AUTHORITY

                                                     FAIRFAX  COUNTY - WESTGATE

                                                         PLANT

                                                     FAIRFAX COUNTY- LITTLE

                                                         HUNTING CREEK PLANT

                                                     FAIRFAX  COUNTY- DOGUE

                                                         CREE K  PLANT
POTOMAC   RIVER  STUDY   AREA
                                                                  FIGURE  1

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                        ABSTRACT




The diffusion coefficients presented in this tabulation


hare been computed for a velocity range from 0.01 knots
                                           t-

to 5.00 knots at an interval of 0.01 knot.  The equations


employed for the computation vere derived  from the FOUR-


THIRDS law and the RASDOM PROCESS analogy  equations.  A


difference function and mean value function are also


tabulated.

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BIBLIOGRAPHY
                       TABLE OF CONTENTS
                                                           i'a,
                           SECTION I
INTRODUCTION 	
GENERAL DISCUSSION OF THE DIFFUSION
  COEFFICIENT EQUATIONS  	
                           SECTION II
Tabulation of the Diffusion Coefficients
  as a Function of Velocity.  Values are
  given in units of centimeters squared/
  second; miles squared/day; and feet
  squared/second.  (For each tabulation) 	  1-13

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                           SECTION  I






                          INTRO r^'TICN






        Down through the apes ra^n have been fascinated ty math-




ematical  formulation and. the solving of complex problems, but




usually nave been bored witn the drudgery c f computation.  In




utilizing mathematical models fcr pollution snaiynis  in estuarine




systems, theoretical estimates of the diffusion coefficients are




usually required.  The strong point in favor of obtaining these




coefficients from theoretical equations rests on the  fact that




information utilized in the equations is readily available in




tidal current tables published by the United States Coast and




Geodetic Survey.




        The estimated values of the diffusion coefficients may




hav« to suffice until auch time as empirical data is obtained




either from dye tracer studies or a knowledge of the longitudinal




salinity distributions of estuaries.  When empirical information




is obtained, it would be preferred over the equation, since




characteristics pertaining to a particular system would be repre-




sented by the observed data that may not be expressed in the




equations.




        It is hoped tnat this tabulation of diffusion coefficients




will help to relieve the investigator from a certain amount of

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computational drudgery.   For thus reason, trie units >.'




ficients are expressed  in centir- ev-r s aquared/secorja,




squared/day, and  feet squarei/se .ona.

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      GENERAL DISCUSSION OF, DIFFUSION COEFFICIENT KCWri
                                is the maximum
max                         max
         The  basic  equation state,- by Bowcien as:



 (l)  K(cm /sec)  *  0.02U6I        where L is Jn cent^ireters an-



                                 may be cons -ae red as trie length



                                 of « tiaa'j excursion,



 was  reformulated by  Hetling and C'Connell—  in a form more suit-



 able for calculation of the diffusion coefficient in te;rn:: of



 readily  available  hydrographic  data to be:



 (2)  K = CV  /3                   vhere V
                                        n


                                 velocity  in knots and may t>e



                                 obtained  for most estuaries



                                 from tidal current tables.



         The  value  of the constant "C" in  the FOUR-THIRDS equa-



 tion was  varied  in the  computation of the diffusion coefficients



 in this  tabulation to yield diffusion coefficients in  centimeters



 squared/second;  miles squared/day;  and feet squared/second.



 These values for "C"  are given  be.ow as:

                      /-~

         C =  1.56 x 10            for K in  centimeters'Ysecond.
        r
          - 5.;
        C = 1.66 x 10            for K jn  feet'/seccn-?



and were derived by Hetling and  O'Connell,



        Tne second equation employed in computing  coefficients



tabulated nerein was originally  proposed  by Diachishin and



described as:

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            2
 (3)  K  « nL /2                  where  L  is  the  length  of  each



                                ranaom step,  and  n  is  the fre-



                                quency of steps.  For  the tidal



                                system,  n = 1/12.U  per hour.



        The above equation vac developed, using  probability theory



 and has as  its origin a random walk type of process.   The equa-



 tion is often referred to as the RANDOM  PROCESS analogy equation.



        In  terns of the BAXLBUB velocity V    ,  equation (3) may



 toe written  as:



 (k)  K  » Dv                    where  V     is defined  the same
            max                         max


                                as it  is in (2) above.



        For calculating "K" in the same  units as  equation (2),



 the constant employed is given as:


                     6                              ?
        D = 6.2 x 10           for K  in centimeters /second



        D « 20.7                for K  in miles  /day



        D - 6.68 x 103         for K  in feet2/second



        The tabulation of the coefficients has been arranged



 s« that the FOUR-THIRDS and RANDOM PROCESS analogy equations,



 reformulated in terms of the maximum velocity in knots, are



 grouped according to the units of "K" desired, i.e., centimeters



 squared/second is the first tabulation; miles squared/day is the



second; and feet squared/second is the last.  Section II of this



Paper contains these tabulated coefficients.

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        Each tabulation  is  arranged  by  first  shoving  the  line




number.  The velocity  in knots  is the next  column,  and  on each




nev line the velocity  is incremented by 0.01  knot.  The third




column represents the  value of  the diffusion  coefficient  corres-




ponding to that velocity computed for the FOUB-THIRDS equation.




The fourth column gives  the diffusion coefficient value computed




for the RANDOM PROCESS analogy  equation.  The fifth column gives




a mean value function  for both  equations (2)  and (M  and  was




coaputed as:





(5)  FT- [CV^3 + DV2  ]/2  for  V     from 0.01 to 5-00 knots
            max     BMX         max




        It has been generally found that in the brackish portions




of estuaries, both equations (2) and  (k) yield coefficients in




an order of magnitude that makes both acceptable for reasonable




estimates .




        Column six of the tabulation shows the computations for



the difference function.  This was computed as:
        When JK_[ is small, the investigator nay find either the




values for equations (2) or (k) may be employed for an estimate.




When JKpl is large, it may be desirable to use the value computed




for equation (.5) •

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                          BIBLIOGRAPHY






1.  HetJing and O'Connell, "Estimating Diffusion Characteristics




    of Tidal Waters," CB-SRBP Technical Paper No. 4, Department




    of the Interior, FWPCA, Middle Atlantic Region.




2.  IBM 7090/709^ IBSYS Operating System, Version 13, IBJOB




    Processor, File So. 7090-27, FORM C28-6389-1.

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 I.   INTRODUCTION




         Much concern is voiced over the pollution potential of




 boating activity, but little definitive data exists concerning




 the extent of human fecal pollution contributed from pleasure




 boats.




         A scheduled rendezvous of the Annapolis Yacht Club on




 July 22-26, 1966, at the Miles River Yacht Club located on Long-




 haul Creek, adjacent to the Town of St. Michaels, Talbot County,




 Maryland, afforded the Chesapeake Field Station an opportunity




 to conduct a study under field conditions to determine the rela-




 tionship of coliform densities to pleasure boat count in the




 Area.  Temporary bacteriological laboratory facilities were set




 up in a nearby motel to determine coliform and fecal streptococci




 population densities, and sampling stations in the vicinity of




 the Yacht Club were established (Figure l).  The sampling program




 began at 12:00 Friday, July 22, 1966.






II.   MATERIAL AND METHODS




         Coliform confirmed population estimates were made by




 the 5-tube, 3-dilution MPN method.   Difco lauryl tryptose broth




 was used for presumptive media, and Difco Brilliant Green lactose




 bile broth, two per cent, was used for confirmation of coliforms.




         Fecal streptococci were estimated with the same MPN




 technique, with presumptive Difco azide broth and confirmed in




 BBL ethyl violet azide broth.

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          Samples were gathered from a lU-foot aluminum jon boat




  by hand dipping into sterile 6-ounce prescription bottles.   Im-




  mediately after collection,  samples were returned to shore and




  inoculated into the media,  using the,back end of a station wagon




  for working area.   Consequently, samples were inoculated approxi-




  mately 15 minutes  after collection.




          Incubation of tubes  was at 35° C. in bacteriological




  incubators established in the nearby motel,  and transfers from




  positive tubes were accomplished in the makeshift laboratory




  using a portable propane torch to flame the  bacteriological loops.







III.  THE INVESTIGATION




          Preliminary to sampling, a reconnaissance was made of




  Longhaul Creek (Figure l).   In addition to the Miles River Yacht




  Club facility, four homes were located along the creek,  and the




  adjacent land was  cultivated farmland.  One  home, approximately




  150 yards upstream from Station D, had two dozen or so domestic




  ducks penned on the bank of the creek.  An occupied house trailer




  was noted on the west shore  of the creek.




          A count of the number of boats in the Area was made during




  the study.  All boats were  counted during the reconnaissance, but




  during the study only occupied boats with toilet facilities were




  counted.  The initial count  made at 11:30 Friday, July 22, showed




  IT small boats with no toilets and 32 unoccupied boats with




  toilets.  The number of small boats without  toilets remained

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essentially the same throughout the study, except for a few




satellite dinghies with the transient craft.




        Observation of activities at the Miles River Yacht Club




indicated that, although it is in rural surroundings, the Club




is contantly a focal point for various activities.   The Club has




a swimming pool and, apparently, a swimming team.  During the




study, two separate crab feasts were catered on the veranda of




the Club House.  One of these was rather small, restricted to




the Annapolis rendezvous group only.  The other was sponsored




by a local organization for the general public and was well




attended.  At the outset of the study, several boats with New




Jersey registration were noted, apparently the departing vestiges




of a smaller rendezvous or cruise of a New Jersey club activity.




The rendezvous during the study period, however, far exceeded the




normal weekday routine activity.




        No precipitation occurred during the study, and weather




conditions could best be described as a portion of a drought cycle,




        Samples were collected from four stations (see Figure l)




three times daily, at approximately 0800, lUOO, and 2000 hours.




Station A was located by the red nun buoy No.  12 in the Miles




River, approximately 500 yards from the mouth of the Creek.




This control station was presumed to indicate the quality of




water inflow into the Creek on flooding tide.

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         Station B was located at the mouth of Longhaul Creek,




 approximately 30 yards off the offshore end of the docking area,




 and approximately in mid-stream.  All boats were docked or moored




 inside the Creek with respect to this station.




         Station C was located in mid-stream at the opposite end




 of the dock facilities, at approximately the point where the




 Creek "bifurcates.  This station was often in the area of anchored
                                                    *



 boats.




         Station D was made at the entrance of the southwest branch




 of Longhaul Creek,  This was upstream from all yacht club boating




 activities, yet downstream from three homes, including the one




 with ducks penned on the Creek bank.







IV.  RESULTS




         Data resulting from this study are shown in Table 1.




 Tides were estimated from the U. S. Coast and Geodetic Survey




 Tide Tables, 1966, corrected for St. Michaels, Miles River.




         Two things should be noted from the tabular presentation:




 (l) fecal streptococci were nearly always so low in density as




 to be immeasurable during the study, at all stations; (2) no




 apparent relationship seems to exist between tidal stage and




 bacterial population density.




         Coliform bacteria and number of boats are shown graphi-




 cally in Figures 2 through 5.  Station A, Figure 2, in the Miles




 River, showed a low incidence of coliforms throughout the study.

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         Station B, Figure 3, at the mouth of the Creek, showed




 a low incidence of coliforms before the boats arrived, then a




 general increase to 200-500 coliforms/100 ml.  Persistence of




 these counts after the departure of the boats is evident,,




         Figure h shows Station C, off the marina in the Creek.




 An anomalous figure of 2,^00 coliforms/100 ml is shown, before




 the boats arrived.  This study assumes the integrity of the




 shore facilities, and a "rested" condition from previous boats,




 which may riot be entirely sound.  However, two of the initial




 bacterial determinations showed counts less than 20, and the




 same general increase with the arrival of the boats as found at




 the other two stations in the Creek.




         The station farthest upstream, Station D, is shown in




 Figure 55 and again the same trend of a coliform increase with




 the arrival of the boats and persistence after the departure is




 apparent„






V.   DISCUSSION




         These data collectively indicate a slight increase and




 persistence of coliforms with the congregation of pleasure yachts,




 An estimation of the degree of significance of yacht contribution




 was attempted by analyzing the coliform counts with respect to




 increased number of boats.  The data from the initiation of the




 study to the point where the maximum number of boats with toilets




 (85) occurred, were analyzed with simple regression.  This does

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not take into account any persistence of bacteria after the




departures, and assumes also that only boats contributed coliforms,




        Logarithms of the number of coliforms, rather than




arithmetic figures, were used because the logarithms of coliform




MPW's have been shown to be normally distributed, while the raw




data are generally skewed.  For these analyses, a zero count of




boats was assumed to be one, and coliform densities less than 20,




the lower limit of determination with the procedure used, assumed




to be 2 coliforms/100 ml.  These assumptions tend to make errors




on the conservative side.




        Station A, Figure 6, shows no relationship between number




of boats and coliforms, as should be expected from the control




station.




        Station B, Figure 7, shows the regression between the




increase of boats and the logarithm of coliform MPN.  The slope




of this line showed a significant fit at the five per cent level




with the "t" test-  This slope, b = 0.0225, indicated an incre-




ment of approximately 1 coliform per 100 ml water for each boat




(antilog 0,0225 = 1.053).




        Station C, Figure 8, showed no significant regression




when all data were considered.   If the 2,^00 coliform MPN,




anomalously found before the boats arrived, were disregarded, a




good regression was found, b = 0.01316, t = 3.26,  d.f. = U.




This slope, shown as the dotted line on Figure 8, agrees fairly




close with Stations B and D.

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                                                              7






        Station D, Figure 9, indicates an increase similar to




that at the other Creek stations, b = 0.0097, but the "t" test




for goodness of fit fell just short of significance at the five




per cent level.




        These data collectively indicate the order of magnitude




of the increase of pollution by boats, under the conditions of




this study.  The persistence of bacterial counts is not con-




sidered, nor is the duration of stay of boats, in this case a




little over 2k hours, and these factors should be considered




in future study designs.




        Boundary conditions undoubtedly affect values, due to




mixing and dilution.  The estimated size of Longhaul Creek,




taken from a U. S. Geological Survey topographic map, was




1,800,000 square feet or kl.3 acres.  With depths from the




appropriate U. S. Coast and Geodetic Survey chart, an approxi-




mate volume of 18,266,000 cubic feet or 136.6 million gallons




was calculated.  With a tidal range of 1.2 feet, or 2,l60,000




cubic feet, or l6.1 million gallons, this would indicate a 12




per cent augmentation on the average flood tide.  No stratifi-




cation of termperature with depth was found at any station during




this study, as measured with an electronic thermometer.  Exchange




or excursion values were not obtained from these data, but this




Creek would seem to be relatively homogeneous, with respect to




the sampling program undertaken.

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                                                              8






        Another factor to "be considered is marina habits; i.e.,




the degree to which on-board facilities are used with respect




to the facilities available on shoreside.  This factor would




probably vary with each study situation.




        A second study was contemplated by the Chesapeake Field




Station staff in 1966 at the Rose Haven Marina, Herring Bay,




Anne Arundel County, Maryland.  Preliminary to an extensive study,




the waters were sampled to establish background bacteriological




levels under conditions of minimum boat occupation.  These results




are shown in Table 2.




        As can be noted from Table 2, the degree of change in




bacterial level anticipated from approximately UOO boats, an




estimated increase of UOO coliforms/100 ml/boat/day,  could probably




not have been detected because of the pollution contribution




from one shore-based septic tank system.




        These observations indicate that the relative significance




of pleasure boats contaminating the waters is much less than




contributions from nearby domiciles, served with individual septic




tank systems, and under conditions of these studies.




        The results of this study are illuminating, but not




definitive.




        Further elucidation of the magnitude of bacterial con-




tribution from pleasure boats can be accomplished in field designs




which incorporate:

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        1.  More extended observations of the background bacterial




densities in "rested" water prior to occupation by boats.




        2.  Determination of coliform, fecal coliform,  and fecal




streptococci, for possible interpretation of human and  animal




contribution, and as an indicator of recent, as opposed to remote,




pollution.




        3.  Observations extending to include the subsequent




decline of bacterial densities, which would depend on local




boundary conditions, duration of boat stay, etc.




        i+.  If possible, detailed studies of the hydrology that




would further quantitate the effects of small boats per unit




volume of water should be concurrently executed.




        5»  Studies conducted in different aquatic environments,




to minimize local effects, are necessary to quantitate  the cause




and effect relationships.

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                                                             10




                          BIBLIOGRAPHY







I,  Sanderson, A, E. , and Hopkins, T. C., Coliform and E_. coli




    bacteria counts at a major Chesapeake Bay boating-bathing




    site during the Independence Day holiday period 196^.




    Mimeographed report.  Maryland Department of Water Resources,




    Water Quality Division.




2.  Hopkins, T. C., and Sanderson, A. E., Report Number Two on




    coliform and E_. coli bacteria counts at a major Chesapeake




    Bay boating-bathing site during the Independence Day holiday




    period 1965.  Mimeographed report.  Maryland Department of




    Water Resources, Water Quality Division.

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                  Table 1

Bacterial Counts in Longhaul Creek, Maryland
          During a Yacht Rendezvous
                                                   11
Station Date /Time
A. Red nun "12" 22
in Miles River
off Longhaul
Creek.
(Control 23
Station)

2k


25


26


Be Longhaul Creek 22
mouth. Sea-
ward of
moorings. 23


2k


25


26


C. Longhaul Creek. 22
Directly off
docks and
among moored 23
boats „

- 111*5
1335
1650
1958
- 0755
131*5
1952
- 0802
131*5
191*8
- 0813
1320
1957
- 0807
131A
161*8
- 13UO
1702
2005
- 0801
1353
1956
- 0805
131*9
1955
- 0818
132'4
2003
- 0812
131*8
1653
- 131*3
1701*
2008
- 0803
1356
1959
Coliform
<20
20
<20
1*5
<20
<20
<20
18
<20
<20
<20
<20
20
1*5
<20
1*5
<20
<20
20
220
78
330
170
1*90
170
1*90
20
220
110
1*90
110
2,1*00
20
170
1*5
230
330
Fecal
Streptococci
20
<20
18
<20
<20
<20
<20
<20
20
20
<20
<20
<20
<20
<20
20
<20
<20
<20
<20
<20
20
20
<20
<20
<20
<20
<20
<20
20
<20
<20
18
<20
<20
<20
<20
Occupied
Boats With
Toilets Tide
0
0
10
23
29
6k
81*
85
10
0
0
0
2
2
0
0
0
10
23
29
6k
81*
85
10
0
0
0
2
2
0
0
0
10
23
29
61*
81*
Ebbing
Ebbing
Flooding
Flooding
Slack Flood
Ebbing
Flooding
Flooding
Ebbing
Flooding
Flooding
Ebbing
Flooding
Slack Ebb
Ebbing
Ebbing
Ebbing
Flooding
Flooding
Slack Flood
Ebbing
Flooding
Flooding
Ebbing
Flooding
Flooding
Ebbing
Flooding
Slack Ebb
Ebbing
Ebbing
Ebbing
Flooding
Flooding
Slack Flood
Ebbing
Flooding

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Table 1 (Continued)
                                       12
Station Date /Time
C. (Continued) 2 it - 0808
1351
1958
25 - 0820
1326
2005
26 - 0815
1352
1656
D. Longhaul Creek .22 - 1135
Upstream from 13UU
all boats. In 1707
mouth of south 2008
branch, 23 - 0805
1358
2001
2k - 0811
11*00
2001
25 - 0822
1329
2007
26 - 0817
1351*
1659
Coliform
330
1*90
1*90
170
330
790
110
1+90
790
20
20
330
ll*0
1*5
1*90
130
330
110
5,1*00
790
330
700
68
790
790
Fecal
Streptococci
<20
<20
1*5
20
<20
<20
52
<20
20
<20
<20
<20
<20
<20
<20
<20
20
<20
1*5
20
<20
20
<20
<20
<20
Occupied
Boats with
Toilets Tide
85
10
0
0
0
2
2
0
0
0
0
10
23
29
6k
81*
85
10
0
0
0
2
2
0
0
Flooding
Ebbing
Flooding
Flooding
Ebbing
Flooding
Slack Ebb
Ebbing
Ebbing
Ebbing
Ebbing
Flooding
Flooding
Slack Flood
Ebbing
Flooding
Flooding
Ebbing
Flooding
Flooding
Ebbing
Flooding
Slack Ebb
Ebbing
Ebbing

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                                                                   13
                             Table 2

             Bacterial Population Density Estimations
Rose Haven Yacht Club, Herring Bay, Anne Arundel County,  Maryland

                    10U Boats, 150 Empty Slips
                         August 29, 1966

1.
2.
3 =
h.
5.
Location
Pier, farthest upstream
J-Dock, upstream from
clubhouse
Apparent septic discharge
behind clubhouse
Main dock behind clubhouse
Channel into harbor
Coliform
MPN/100 ml
170
2,UOO
>l60,900
5,^20
TOO
Pecal Coliform
MPN/100 ml
50
50
27,800
50
100

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LOCATION  MAP  OF STUDY  AREA
                                                   FIGURE

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CD
  90-


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u. 60-
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         COLIFORM  POPULATIONS AND NUMBER OF

                         STATION  A
                                                   BOATS
                                                         FIGURE 2

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  600	




  500 -j	





  400	

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          COLiFORM  POPULATIONS  AND  NUMBER  OF  BOATS

                             STATION  B
                                                                         FIGURE  3

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 I.OOO

  900-

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  500-



  400
  300-r-
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          COLIFORM  POPULATIONS AND  NUMBER  OF  BOATS
                            STATION  C
                                                                        FIGURE  4

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                        5400'
COLIFORM POPULATIONS AND  NUMBER OF  BOATS
               STATION  D
                                                    FIGURE 5

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5
o:
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90'
80
70
60
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•— • * •
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1 1." II 1
10 20 30 40 50 60
1
7O
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80
I
90
                   NUMBER  OF  BOATS
 REGRESSION OF
             INCREMENTS OF  BOATS AND COLIFORMS
                STATION   A
                                                  FIGURE  6

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 1,00 O —<-
 900 —«•
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 5 OC

 40O


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 200 •
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 IOO
  9O
  80
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r
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                                     -i—s—f-
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         NUMBER OF  BOATS
                                     70
                                          80
                                           90
 REGRESSION  OF INCREMENTS OF BOATS AND COLIFORMS
                   STATION  B
                                                FIGURE

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                  NUMBER OF  BOATS
70
     8O
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                 STATION  C
                                BO.TS  ANO  COL1FORMS
                                                 FIGURE  8

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9OO
8OO
fOO

t>oo

;. oo •
 4OO
                        4-
     -\	1-
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                  NUMBER OF  BOATS
7O
80
90
REGRESSION  OF INCREMENTS OF BOATS AND COLIFORMS

                  STATION  D
                                                   FIGURE 9

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