DOCUMENTATION FOR OUTFALL
A COMPUTER PROGRAM FOR THE
CALCULATION OF OUTFALL LENGTHS
BASED UPON DILUTION REQUIREMENTS
|W¥I*ONMENTAL PROTECTION AGENCY
REGION II
26 FEDERAL PLAZA
NEW YORK CITY, NEW YORK 10007
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OCEAN OUTFALL ANALYSIS
June, 1975
Prepared by:
David L. Guthrie
U.S. Environmental Protection Agency
San Juan Field Office
1225 Ponce de Leon Avenue
Santurce, Puerto Rico 00907
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PREFACE
This report has been prepared to illustrate the use of oceanographic
data and a digital computer program developed by the San Juan Field
Office of the U.S. Environmental Protection Agency to aid in the location
and analysis of ocean outfalls. The report has been reviewed by the
U.S. Environmental Protection Agency and approved for publication. This
approval does not signify concurrence or approval of any pfocedures or
results contained herein.
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ACKNOWLEDGEMENTS
The art work contained in this report was illustrated by Robert
Rauenbuhler of the Environmental Protection Agency in Edison, New Jersey.
The initial concept for the OUTFALL Program was advanced by Dr.
Donald R. Washington, former director of the Region II San Juan Field
Office. Much appreciation is extended to him for his cooperative work
and assistance with the theoretical aspects of the program. Thanks is
also given to Mr. Donald J. Baumgartner and Mr. Galloway, of the National
Environmental Research Center in Corvallis, Oregon.
Thanks must be extended to Ethan T. Smith, Chief, Data Systems Branch
for his encouragement and support of this effort and to Steve Chapra of
that same section for his many hours of assistance in debugging the
computer program.
Finally, I would like to thank Ms. Marie Smith and Mrs. Carmen
Lydia Martin for their typing of the report.
David L. Guthrie
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TABLE OF CONTENTS
Page
INTRODUCTION 1
THE SYSTEM: DEFINITION OF TERMS 2
THEORY 4
THE COMPUTER PROGRAM 9
Flow Chart 10
Restrictions 16
Input Requirements and Data Description 20
NOMENCLATURE 22
REFERENCES 24
APPENDIX A (listing of source deck)
APPENDIX B (example problem)
APPENDIX C (output)
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INTRODUCTION
After wastewater is treated, a method may be used to convey it
to offshore waters, where natural processes break it down further. A
common mechnanism is the ocean outfall.
Basically, the philosophy of the disposal of wastewater through a
submarine outfall is to maximize the initial dilution of discharged waste-
waters so to minimize any adverse impact(s) on the receiving waters.
Beneficial uses of receiving waters vary greatly from water supply to
aesthetic beauty, but usually the most important reference point is the
maintenance of the water quality standards which have been defined for
the applicable water usage.
The chemical biological and hydrodynamic characteristics of the
receiving waters are critical considerations in determining the actual
outfall routine and the ultimate disposal site.
OUTFALL is a computer program which can be used to evaluate a coastal
system under consideration as a disposal site. It is designed to evaluate
and/or predict the length of outfall needed to adequately dilute a proposed
discharge in order to provide compliance with coastal water quality stand-
ards.
Any coastal system is extremely complex, and as such requires many
considerations in its investigation. Some of the most important factors
which can be evaluated in OUTFALL include the effects of onshore currents,
tides, density and salinity gradients, ambient surface and hypolimnetic
velocities, the initial jet velocity, the quantity of discharge, the
slope of the ocean bottom, and coliform die-off rates in the vicinity
of outfall locations.
Analytical expressions are used to calculate the factors of dilution,
diffusion, and die-off in order to compute the total dilution, taking
into account the aforementioned variables. This value is then compared
to a dilution value needed to meet water quality standards and iterated
until an outfall length is reached where the calculated dilution value
meets that which is required to meet the applicable water quality stand-
ards both at the maximum point of plume rise above the diffuser and
the more stringent nearshore standards at a specified distance offshore.
This documentation consists of a description of the program as
well as its input. A listing of OUTFALL, which is compatible with
the IBM 370/155 system, a case study, and a sample output from the
program are included in the appendices.
-1-
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THE SYSTEM: DEFINITION OF TERMS
INITIAL DILUTION occurs when a wastewater is discharged through a
diffuser into a receiving water of greater density; it is diluted
by turbulent jet mixing. Due to its buoyancy, the plume rises to-
ward the surface, and a turbulence and mixing action is caused by
the velocity gradient between the edge of the plume and the sur-
rounding water.
DISPERSION takes place after initial dilution, when a rather homo-
genous mixture forms above the diffuser section, and the sewage
field begins to move according to prevailing ocean currents.
DECAY is the apparent die-off of bacteria in the sewage including
flocculation and sedimentation of the microorganisms as well as
mortality.
TOTAL DILUTION is the product of the initial dilution, the disper-
sion, and decay factors.
-2-
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Origin JL
u>
I
FIGURE 1. Definition Sketch for Input Specification and
Output Interpretation.
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THEORY
In the calculation of optimum outfall length, X, a development of
total dilution D^, which is composed of initial dilution, D-^, dispersion,
Do , and die-off or decay, Do, is necessary. These factors are multi-
plicative because as an initial concentration, Co» is multiplied by an
initial dilution, D^ , a secondary concentration, C-^, results which
is then multiplied by a secondary dilution factor, dispersion, D2, resulting
in a new concentration, C2, and so forth until the final concentration,
Co, is obtained. Mathematically, the expressions are: C^ = D^ C0, C2 = D2
and Co = Do C2, Substituting and rearranging by the associative law,
D3 (B2 (D-L C0)) or C3 = T>i D2 D3 CQ . Hence, it follows that
C3
DT = D! x D2 x D3 (1)
which has also been mentioned by Burchett, et . al.
When moderately strong currents are encountered, the initial dilution
may be estimated from a continuity relation between the sewage flowrate
and the flowrate of fresh seawater over the outfall diffuser as proposed
by Pearson and mentioned by Metcalf and Eddy:
D! =(VX bd) / Q (2)
It should be noted that the initial dilution value, D^, as presented in
equation (2) is subject to much controversy. As in most cases, density
gradients exist in the surrounding seawater, and the turbulence caused
by the velocity gradient between the edge of the plume and the surrounding
seawater must be incorporated. Also, the continuity equation requires
that the combining of the wastewater flow and the seawater flow is the
perfect mixing of the two flows at some distance above the diffuser section.
However, this approach is fairly simplified and neither takes density
stratification nor quiescent media into account. Therefore, a different
approach developed by Baumgartner, Trent, and Byram7 entitled "PLUME"
was used to find D]_ in the OUTFALL program. This method is based on
similarity prinicipals as presented by Baumgartner and Trent^. Solution
is carried out by a fourth-order Runga-Kutta technique, and calculation
of the potential core length is based on Abraham's method^ and is an
integral part of the results.
The effective diffuser system length is an important term in outfall
design. In this publication, it will be developed according to the design
value of 14 ft. diffuser/mgd wastewater^. The outfall is represented
diagramatically as having two legs as follows:
effective width
/XX" I
n
-4-
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Because it is an isoceles triangle, m=n and m+n=14 ft/mgd xQw, where
b is the effective width of the diffuser. Therefore, the effective width
can be determined by the following:
adj m
cos Q = hyp = b (3)
.5 (14 ft/mgd) Qw
cos Q = b (. 4 )
.5 (14 ft/mgd) Qw
b =
.707 (5)
Hence,
b = 9.9 ft/mgd , Qw = 6.4 ft/cfs , Qw (6)
D! = (.03281 ft/cm) V± bd/Q (7)
and substituting equation (6) for b, the following expression for D^
results in:
.03281 (6.4 Qw)
D-L = Qw = (.210) Vxd (8)
The theory of dispersion of the sewage field after it is initially
diluted has been developed by Brooks and has resulted in the following
equation, derived on the basis of the "4/3-law", in which the coefficient
of eddy diffusion, E, is a function of the diffuser length raised to the
four-thirds power. Thus, the following equations result; from Brooks •
D2 = l/erf(y 1.5 / ((1 + 2/3 B X /b)3 -1) ) (9)
and
E = 0.001 (b)4/3 (10)
o
It has also been determined by Brooks that:
B = 12E/V2b (11)
-5-
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This term was developed to take into account the horizontal diffusivify
of the spreading plume, as entrainment of the wastewater becomes important
in the dispersion mechanism.
In order to find (2/3) BX/b in equation (9), equation (10) is substituted
in equation (11) to obtain B:
B = (12) (0.001) (b)4/3 = (1.2 x 10~2)b (12)
V2b V2
Therefore,
-21/3 -3 -2/3
(2/3) BX/b = (1.2 x 10 ) b (2X) = 8 x 10 b X (13)
V2 (3b) (.03281 ft/cm)V2
= (2.438 x 10~1)b"2/3 X (14)
V2
But equation ( 14) can be simplified even further, by substituting equation
(6):
-1 -2/3
(2/3) BX/b = (2.438 x 10 ) (6.4 QT.T) X (15)
V2
= (2.438 x 10~ ) (.290) QT.T ~2/3 X
V O
_9 _9/•}
= (7.071 x 10 ) Qw ' X (16)
V2
Hence, the final expression for dispersion is obtained:
D2 = l/erf| /1.5/ ((1 + (7.071 x 10~2)Qw~2/3X)3-1) ) (17)
2
Bacterial decay, the third significant factor in waste dilution, is
patterned after a first - order relationship as follows:
, X
D3 = e c = exp (K (V2)) (18)
This equation results from an expression defining reduction in bacterial
concentration from initial dilution to time t as follows:
-6-
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In the relationship in equation (18), K is actually a logarithmic
conversion to relate Tg0, the time required in hours for a 90 percent
reduction in bacterial concentration, to a time constant as follows:
-4
/T
90
(20)
K = 2.3/ (3600 sec/hr)T90 = 6.39 x 10
Therefore, expanding the decay term,
D3 = exp (K (X/V2)) = exp (KX/V2 (.03281 ft/cm)) (21)
and substituting equation (20) for K:
D3 - exp ((6.39 x 10 4) X/ (.03281) T9QV2)
= exp ((1.95 x 10~2) X/T90V2)
For convenience, constant values can be assigned as:
-1
(22)
e.
2.10 x 10
92 = 7.071 x 10
-2
93 - 1.95 x 10 2
Therefore, equations (8), (17), and (22) become:
V,
Dl -
1.5
('
-i
V,
D - exp (Q3X/T90V2)
(23)
(24)
(25)
Substituting (8), (17), and (22) into equation (1) yields the final
expression for total dilution, utilizing the continuity expression for
Dl:
e V de 3 X/T90 V2
- (26)
D =
T
V
)
In the model, the expression 9]_ V1 d, or DZ, is replaced by program
"PLTJME" as a subroutine. However, the expression given here can yield
a rapid estimation of T>i and thus DT, without conducting complex iterative
techniques. For a more concise discussion of these primary equations
and ocean outfall design criteria, see Beckman1, Brooks , Burchett3,
Frankel4, and Metcalf and EddyS.
-7-
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VARIABLE EXPLANATION
D Total dilution
D Initial dilution
D Dispersion
D» Decay
V Ocean current velocity
b Effective width of the dif-fuser system
d Average depth of the sewage field
0 Sewage flowrate
B Interim variable
X Distance along the plume centerline
E Coefficient of eddy diffusion
V- Ocean current velocity
K Bacterial decay constant
TCJQ Time required for a 90 percent
reduction in bacterial concentration.
-8-
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The Computer Program*
The program begins by reading the "city data", "physical data",
and the "plume data". Then the "density data" is read in and subroutine
SIGMAT is called to find the density. At this point, the number of
ports (FN) is found by the following formula:
FN = 14 ft., * .646 mgd * Qw(cfs)* 1 (27)
m§d cfs 10 ft diffuser spacing
where 14 ft/mgd and 10 ft diffuser spacing are design criteria. The
values of 14 ft/mgd and 10 ft. diffuser spacing were those chosen by the
author. If new values are desired, these must be changed in the pro-
gram itself. The "plume data" are then written. Having read the
initial values, a range of effluent coliform concentrations are assigned
by a test of NN, which is initially assigned to be equal to 0. The
class is then assigned by a test of NCLASS, and the "city data" is
written. The first Tgg value is assigned to be equal to 1 hour, and
JJ, the counter for the different respective treatment levels, is
initialized at 0. The first part of the program then ends with the
computation of the total dilution (E^) necessary to meet a given
water quality standard by the following formula:
*coliforms/100ml for a
corresponding treatment level (28)
DT (required)=
Water Quality Standard
In equation (28), the number of coliform organisms pertaining to
the corresponding treatment level must be known in order to calculate
the required dilution. Lower and upper coliform limits must be taken
into account when designing an outfall length, hence that outfall's
dilution ability. Table B-4 presents a summary of effluent coliform
data obtained from five different wastewater treatment plants in Ohio
and New Jersey. These data are presented herein because there are few
data indicating the range of effluent coliform values for different
wastewater treatment processes, although there are many data indicating
mean values. A final summary of the data presented in Table 1 is
shown as Table 2, these data are used in the example problem.
Having assigned the D^ values, the program now iterates the
outfall length (X) by 1000 feet from the shoreline. Subroutine EQN is
called, which calculates D^ by the PLUME subroutine. PLUME must, in
turn, call subroutine SDERIV to complete its calculations of D-. . It
is obvious in an ocean situation that the depth of the bottom is some
function of its distance from shore. Therefore, in subroutine EQN,
depth (DEPTH) is computed as shown diagramatically in Figure 2. For
more than three changes in bottom slope, the following equation can be
used:
*A listing of the program is in Appendix A and a flow chart is on
page 10.
-9-
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"FLOW CHART
START
READ "CITY DATA"
"PHYSICAL DATA"
"PLUME DATA"
CALL SIGMAT
(RETURN WITH SIGMAT=f (RHO, SAL) )_
/ WRITE "CITY DATA", "PHYSICAL DATA""/
ASSIGN COLI VALUES
FOR TREATMENT W/C12
ASSIGN COLI VALUES
FOR TREATMENT w/o C12
II = 0
YES
CLASS = SB
CLASS = SC
/ WRITE "CITY DATA""
ASSIGN T90 VALUES
JJ = 0
[_ ASSIGN DT VALUES"
x = o.
X X + 1000.
CALL EQN (IF SB AND X>1320., RETURN
WITH DTI = Dl (CALL PLUME (RETURN
WITH DTI Dl (CALL SDERIV (RETURN
WITH FK, FM))) * D2)) * D3. OTHERWISE
RETURN WITH DTI = Dl (CALL PLUME
(RETURN WITH DTI Dl (CALL SDERIV
(RETURN WITH FK, FM)))))
CALL EON (RETURN WITH DTI)
/ WRITE X,DTI,DT,TREATMENT/
-10-
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^ (29)
where m and n are integers. After Di is calculated by EQN and PLUME, the
generated X value is tested to see if it exceeds the total distance
from shore read into the program. If this occurs, a message indicating
this is the case is printed and the program goes to the next level of
treatment.
The dilution calculated is then compared to the dilution required.
If the dilution at the first depth (i.e. - 1000 feet) is greater than
that needed, the 1000 is subtracted and the same iteration proceeds
with'X=40 feet. This iteration is repeated in the same manner with
X=2 feet and X=0.25 feet, until the outfall length needed is within
0.25 feet of that required.
Now, the water quality classifications play an important role.
The program can evaluate two different situations: (1) where water
quality standards must be met directly over the end of the outfall,
and (2) where water quality standards must be met over the end of
the outfall but when part of the wastewater field is carried onshore
by the currents where a stricter water quality standard exists, that
stricter standards must be met at the boundary line between the two
standards. For example, if a standard of 70 coliforms/lOOml exists
from the shore to 0.1 mile in the ocean and after the 0.1 boundary
a standard of 10,000 coliforms exists, and the outfall is longer than
0.1, the number of coliforms in the wastewater must be reduced from
10,000 to at least 70 if the field drifts inside the 0.1 mile interface.
The model tests for this by the mechanism of SB, which can be any
coliform value (SB is the lower standard, SC is the higher standard).
If the class is SB (inside of the boundary because the higher standard
is assumed to be used outside the boundary). If X is greater than the
boundary limit, then the standard is changed to SC and XI is stored in
X2. DTI is again computed by EQN and PLUME and a second test is con-
ducted. However, this time EQN uses subroutine PLUME and ERF to compute
DT as presented in equation(l). If Dl is greater than DT, the values
are printed and the next higher level of treatment is investigated.
(JJ is increased by 1). If DTI is still less than DT, X is again in-
creased by 1000 feet, and the iteration begins again. For clarification,
the D~L value is calculated for the port closest shore. The program also
assumes that the plume from each individual port does not overlap with
any adjacent plume during its period of rise. Any overlap may tend to
reduce the dilution. Therefore, the required outfall length would have
to be longer than the program indicated in cases of significant plume
overlap.
-11-
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to
1
n
FIGURE 2 .
BOTTOM PROFILE: DISTANCE FROM SHORE VS. DEPTH
For a constant bottom slope or the first section:
v = x *
y A
n
For the second section or change in bottom slope:
yn = yl + (Xn - Xl> * VX2
For the third section or change in bottom slope:
X3^
Y
yn = yj_ + y2 + Otn -(XL + x2))
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TABLE 1
E. COH CONCENTRATIONS IN THE EFFLUENTS OF SEWAGE TREATMENT PLANTS
MEMBRANE FILTER
PLANT
Keasby
Keasby
Coleran
Hgts.
Coleran
Hgts.
Norbrook
Norbrook
i
£J Florence
i
Florence
Keyport
LOCATION
Raritan,
Raritan,
Cincin. ,
C inc in . ,
Cincin. ,
Cincinj,
C inc in . ,
Cincin. ,
Keyport,
N.J.
N.J.
Ohio
Ohio
Ohio
Ohio
Ohio
Ohio
N.J.
TREATMENT
Primary+Cl2
Primary+Cl?
Second. +C1
Secondary .
Second. +C12
Secondary
Second. +C12
Secondary
Primary+Cl^
NO. SAMPLING DAYS LOW
39
5
11
11
10
10
9
9
106
10
20
1
8700
1
17,600
2
36,180
10
MEDIAN
7,224
4,042
21
217,391
12,759
162,830
445
251,620
18,545
RESULTS
HIGH
10,000
10,000
99
677,000
113,000
546,000
1888
587,000
1,000,000
Sources of Information: Mr. Edwin Geldrich, National Environmental Research Center, Cincinnati, Ohio.
U.S. Environmental Protection Agency
Mr. Francis Brezenski, National Environmental Research Center, Edison, N.J.
U.S. Environmental Protection Agency
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TABLE 2
TREATMENT LEVEL
Raw: upper
Raw: lower
Primary: upper
Primary: lower
Secondary: upper
Secondary: lower
Tertiary: upper
Tertiary: lower
EFFLUENT COLIFORM DATA
E. COLI CONG. WITH CHLORINATION REFERENCE
1.0 x 107 (1)
5.0 x 105 (2)
1.0 x 106 (3)
10.0 (4)
1.13 x 105 (5)
2.0 (5)
1.0 x 103 (7)
2.0 (7)
E. COLI CONG. WITHOUT CHLORINATION
upper
lower
Raw:
Raw:
Primary: upper
Primary: lower
Secondary: upper
Secondary: lower
Tertiary: upper
Tertiary: lower
2.2 x 10?
1.2 x 105
1.65 x 108
9.0 x 104
6.77 x 105
,7 x 103
.0 x 105
8.
1.
1.0 x 103
(1)
(2)
(8)
(8)
(6)
(6)
(7)
(7)
References:
(1) Keyport, N.J. Plant Sampling Days = 4
(2) Keyport, N.J. Plant Sampling Days = 30
(3) Keyport, N.J. Plant Sampling Days = 106
(4) Keasby Plant, Raritan, N.J. Sampling Days = 39
(5) Norbrook Plant, Cincinnati, Ohio Sampling Days = 10
(6) Coleran Hgts Plant, Cincinnati, Ohio Sampling Days = 11
(7) Personal Communication with Dr. Don Reasoner, EPA-NERC, Cincinnati, Ohio
(8) Calculated using 25 percent as reduction in coliform concentration re-
sulting from primary treatment without chlorination.
-14-
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In the event, JJ is increased by 1 and DT2 is tested for being
greater than 0. If it is, the CLASS is reassigned as SB and DT2 is set
equal to 0. The next higher level of treatment then is investigated.
II is increased by 1 and the class is again tested. If the water has
the higher standard, CLASS=SC, then NN is increased by one, the pro-
gram continues once more and stops. If CLASS=SC, II is then used to
increase the TQQ value, and the program starts over.
Any TgQ values can be used. If only one TgQ value is desired,
statements OUTFL062-OUTFL069 and OUTFL169-OUTFL171 can be eliminated
from the program. Only the maximum coliform values were used (MAX)
because they generated longer outfall lengths, based on public health
constraints.
-15-
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SUBROUTINE EQN
The CALL and SUBROUTINE statements for EQN are:
CALL EQN(X,V1,V2,V1,X1,Y2,X2,Y3,X3,
QW,T90,DT,CLASS, DTI,
XSTOR1,SC,SB,DT2)
SUBROUTINE EQN (X,VI,V2,Y1,X1,Y2,X2,
Y3,X3,QW,T90,DT,CLASS,DTI,
XSTOR1,SC,SB,DT2)
Equations for DEPTH are computed using those given in Figure 2, and D^
is computed by subroutine PLUME. D£ is computed using the distance,
X-1320 feet to equal the distance from the end of the outfall to the
boundary demarkation. D£ * D-j is computed by multiplying equations
(17) and (20) and D^ is found by using equation (1). The erf (as shown
in equation (17) is calculated by subroutine ERF.
RESTRICTIONS
If the £x is less than the iterative value of X, a termination of that
step in the program will result. If this happens, X has been extrapolated
in the following manner :
IF(X.GT. (X1+X2)) DEPTH = Y1+Y2+(X-(X1+X2) )*Y3/X3
-16-
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SUBROUTINE PLUME
The CALL and SUBROUTINE statements for PLUME are:
CALL PLUME (DEPTH, DTI)
SUBROUTINE PLUME (DEPTH, DTI)
This subroutine has been described in the Theory section, and more
information can be gleamed in detail from reference (7). Basically,
it calculates D^ based on the behavior of a plume in density stratified
surroundings. These type of conditions are very common in most aquatic
environments. Hence, PLUME gives more reliability to D^_ than does
equation (2). If desired, the program can be easily modified to convert
to the Pearson formula as follows:
IF(CLASS.EQ.SC) DT1=THETA1*V1*DEPTH (30)
and so forth.
-17-
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SUBROUTINE SDERIV
The CALL and SUBROUTINE statements for SDERIV are:
CALL SDERIV (SPDS2,E+.5*FK,R+.5*FM)
CALL SDERIV (S+DS,E+FK,R+FM)
CALL SDERIV (S,E,R)
SUBROUTINE SDERIV (S,E,R)
Subroutine SDERIV calculates the derivatives de/ds and dr/ds which are
the incremental changes of bouyancy and monentum as the plume develops.
Incremental angle changes of the centerline are also a by-product of this
subroutine.
FUNCTION ERF
The FUNCTION and call statements for FUNCTION are:
ERF (ARC)
FUNCTION ERF (ARC)
This program calculates the error function, which is a mathematical
series expansion based on the following formulas :^3
Case I, 0 ^ X = 3:
erf x = 1 - erfc x
erfc x =
where a^O. 14112821
a=0. 08864027
a =0.02743349
and Case II,
X
)
(31)
(32)
a4=0. 00039446
a=0. 00328975
-18-
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-x2
erfc x = e * (1 - 1 + 3 - 15 + 105 - 945 + 10365 ) (33)
2x3 22X5 23X7 24X9 25X11 26X13
This function subroutine was developed for the use in several
oceanographic computer programs by EPA.
-19-
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INPUT REQUIREMENTS AND DATA DESCRIPTION
Column
Variable
Description
Format
Card One; "City Data"
1-64 A
65-67 NCIT
Degree of treatment
Number of Cities
Card Two; "City Data"
1-12 CIK1-3)
13-14 NCLASS
Card Three: "Physical Data"
City Names 1-3
Water Quality
CLASS: SB=1;
1-4
6-9
11-20
22-26
28-33
35-39
40-49
51-56
58-67
Card Four:
1
2
3-5
VI
V2
XI
Yl
QW
Y2
X2
Y3
X3
"Plume Data"
NDC
METERS
NPTS
Avg. velocity of ocean water in
effective mixing region
Ocean current velocity
Distance from shore to first
slope change
Depth at first slope change
Design Discharge
Depth at second slope change
Distance from shore to second
slope change
Depth at third slope change
Distance from shore to third slope
change
(Blank)
Logical: T=MKS Units; tf-FPS Units
Number of ambient density points
16A4
13
3A4
12
F4.1
F4.1
E9.3
F4.0
F5.1
F4.0
E9.3
F5.0
E9.3
LI
LI
13
-20-
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Column Variable Description Format
6-10 ANGLE Port Angle from horizontal F5.0
21-30 DIA Port Diameter F10.0
31-40 RHOJ Density of Effluent F10.0
41-50 KFD (BLANK) F10.0
51-60 Q Design Discharge F10.0
61-70 FN Number of Ports (BLANK) F10.0
71-80 PS Desired data Printout along
Centerline F10.0
Card Five through Card NDP; "Density Data"
Cards are read until the number of density points is reached. Example card:
1-10 DP Depth corresponding to its respective
density point F10.0
11-20 RHO Ambient density of seawater F10.0
-21-
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NOMENCLATURE
Variable Name
Program
A
ANGLE
ARC
CIT
CLASS
COL
DEPTH
DIA
DP
DT
DTI
DT2
METERS
NCIT
NCLASS
NPTS
PS
Q, QW
Other
E Coli/100 ML
Description Units
Degree of treatment
Angle of port orientation from Degrees
horizontal
Equation(24) Error Function Argument
City Name
Water Quality Classification
Coliform Number Corresponding to
various degrees of treatment
d Depth of water over the diffuser ft
Port Diameter ft
Depth corresponding to its
respective density point ft
D>P Total dilution required to meet
water quality standard
DT Total dilution calculated in
subroutine EQN with varying X values
DT Total dilution calculated if
different water quality standard
exists past a given distance from shore
If "T", MKS units used
If "V", FTS units used
Number of cities included in model
Number designating water quality
classification
Number of density profile points
Printout interval ft
Qw Design Discharge ft3/sec
-22-
-------
NOMENCLATURE -cont.-
Variable
Program
RHO
RHOJ
T90
VI
V2
X
XI
X2
X3
Name
Other
P
Pj
T
i90
1
V2
X
Xl
x2
X3
Description
Ambient Density of water
Density of wastewater plume
Time required for a 90 percent
reduction in bacterial concen
tration
Average velocity of ocean water
in effective mixing region
Ocean current velocity
Distance from shore to end of
outfall along water surface
Distance from shore to first sl<
change
Distance from shore to second s
change
Distance from shore to third sl<
XXX
Yl
Y2
Y3
X - 1320 ft (1/4 mile)
Depth at first slope change
Depth at second slope change
Depth at third slope change
Units
3
gm/cm
gm/cm
hrs.
cm/sec
cm/ sec
ft
ft
ft
ft
ft
ft
ft
ft
-23-
-------
REFERENCES
1. Beckman, W.J. "Engineering Considerations in the Design of an
Ocean Outfall". JWPCF. 42,10, 1805 (1970).
2. Brooks, N.H. "Diffusion of Sewage Effluent in an Ocean Current".
Proceedings First International Conference on Waste Disposal in
The Marine Environment. University of California. Berkeley,
Pergamon, New York, 1960. pg. 246
3. Burchett, M.E. Tchobanaglous, G. and Burdoin, A.J. "A Practical
Approach to Submarine Outfall Calculations". Public Works. _5,
95 (1967).
4. Frankel, R.J. and Gumming, J.D. "Turbulent Mixing Phenomena of
Ocean Outfalls", JASCE, Sanitary Engineering Division. SA2,
4., 33 (1965).
5. Metcalf and Eddy Engineers, eds. Wastewater Engineering: Collection,
Treatment, Disposal. McGraw-Hill, Inc. New York. pp. 691-705.
6. Pearson, E.A. "Marine Waste Disposal". The Engineering Journal.
Engineering Institute of Canada. November, 1961.
7. Baumgartner, D.J., Trent, D.S., and Byram, K.V. "User's Guide
and Documentation for Outfall Plume Model". Working Paper #80:
EPA Pacific Northwest Water Laboratory. May, 1971.
8. Baumgartner, D.J. and Trent, D.S. "Ocean Outfall Design: Part I,
Literature Review and Theoretical Development". FWPCA, April, 1970.
9. Abraham, G. "Jet Diffusion in Stagnant Ambient Fluid". Delft Hydrau-
lics Laboratory Publication Number 29, Delft, Holland, 1963.
10. Lin, Shundar. "Evaluation of Coliform Tests for Chlorinated
Secondary Effluent". JWPCF. 45, _3, 498 (1973).
11. Kaye, C.A. "Shoreline Features and Quaternary Shoreline Changes,
Puerto Rico". U.S.G.S. Professional Paper 317-B. 1959.
12. Puerto Rico Department of Natural Resources and Engineering Science,
Inc. Puerto Rico Oceanographic Study: Data. 1972.
13. Puerto Rico Aqueduct and Sewer Authority. Ten-Year Construction
Grant Program for Wastewater Treatment Facilities. EQB, EPA,
PRASA. April 30, 1971.
14. Weston, R.F. and Sarriera, R.E. Wastewater System and Ocean Out-
fall, Aguada-Aguadilla. PRASA. 1970. p. 20.
-24-
-------
REFERENCES (CONTINUED)
15. Bogert-Spectrum Associates, Engineers. Arecibo Oceanographic
Study. PRASA. October, 1972. P. 21.
16. Black and Veach, Engineers. Report on OCean Outfall and Wastewater
Treatment Plant Location at Barceloneta. PRASA. 1971. p. 37.
17. 0'Kelly, Mendez, and Brunner. Wastewater Treatment and Ocean Dis-
posal for the Humacao Area. Camp, Dresser, and McKee, Engineers.
Boston, Mass. PRASA. 1971. pp. 3-17.
18. Bogert-Spectrum Associates, Engineers. Isabela Oceanographic Study.
PRASA. 1970. p. 14.
19. Ramon M. Guzman and Associates, Sanitary Survey and Oceanographic
Study for Proposed ET Main Wastewater Treatment Plant at Mayaguez,
Puerto Rico. PRASA. 1970. p. 47.
20. Black and Veatch, Engineers. Report on Ocean Outfall and Wastewater
Treatment Plant Location at Barceloneta, Puerto Rico. Prepared for
PRASA. February, 1971. p. 27.
21. Hazen and Sawyer, et. al. Engineering Investigation of a Sewage
Outfall for the City of Ponce. PRASA. 1970. p. 19.
22. Herez, Alfredo. Preliminary Wastewater Report. PRASA. March, 1971.
p. V-6.
23. Lerman, Abraham. "Time to Chemical Steady-States in Lakes and Oceans'
Adv. in Chem. Series Reprint No. 106 "Non-Equilibrium Systems in
Natural Water Chemistry'". A.C.S. 1971. pp. 30-76.
24. Callaway, R.J. "Computer Program to Calculate ERF". EPA Pacific
Northwest Environmental Research Laboratory, Cowallis, Oregon.
July 17, 1973.
-25-
-------
APPENDIX A
(Listing of Source Deck)
-------
APPENDIX 1 - LISTING
COMMON/CRITCH/NPTS,ANGLE,DIA,RFD,Q,FN,PS,RHCJ
CONNON/WOOD/ZD(5C),DG(50) ,RHO(50),DP{50)
DIMENSION A( 16)
LCGICAL NDC,METERS
NOCASE=0
READ(5,103)(A(I),I=1,16),NCIT
103 FORMAT(16A4, 13)
DO 9COO KK=1,NCIT
DT2=0.
C ASSIGNING T9C CONSTANT VALUES
C MECHANICAL LOOP
7 READ(5,1111)CIT1,CIT2,CIT3,NCLASS
REAC(5,5COO) V1,V2,X1,YL,QV,,Y2,X2,Y3,X3
20 READ(5,73,END=74)NCC,METERS,NPTS,ANGLE,DIA,
73 FORMAT(2L 1 ,13, F5.0,lOX,6F10.0)
DO 102 I=1,NPTS
READ(5,75)DP(I),RHC(I),SAL
IF(SAL.EQ.O.)GO TO 102
RHO(I) = 1. + .001*SIGI"AT(SAL,RHO(I))
102 CONTINUE
75 FCRMAT(8F10.0)
WRITE(6,888)CIT1,CIT2,CIT3,V1,V2,X1,Y1,UW,Y2,X2,Y3,X3
888 FORMATf ' I1,4CX, ' INPUT DATA FOR THE CITY OF ',3A4,/// ,25X,
1V.1 V2 XI Yl QW
1 Y3 X31 ,//,20X,9(E9.4,lX) )
1111 FORMATf3A4, 12)
RHCJ,RFD,Q,FN,PS
Y2
X2
FN=14.*.646*G/10.
IFIN DC) WRITE (6f 104)
104 FORMAT('0 UNITS NON D I MENS I CNAL ' )
IF( . NOT. NDC. AND. METERS) WRITE! 6,105)
105 FORMATt'O UNITS MKS1)
IF(. NOT. NDC. AND. .NOT. METERS) V,RITE(6, 106)
106 FCRMAT( '0 UNITS FPS1 )
WRITE(6, 108 )ANGLF, PS, RHOJ
108 FORNATf
*40H- PORT ANGLE ............. ,F7.1/
*AOH PRINTOUT INTERVAL ........ .,F8.2/
*40H DISCHARGE DENSITY ......... ,F11.5)
IF( .NOT.NDC)VvRITE(6,62)G,FN, DIA
62 FORMATC
*4CH FLOWRATE .............. ,E15.5/
*40H NUMBER OF PORTS .......... ,F5.0/
*4CH PORT DIAMETER ............ ,E15.5)
WRITE (6, 24) ( (DP( I ) ,RHO( I)),I=1,NPTS)
24 FORMAT( '-DENSITY STRATIFICATION DEPTH RHC ' // 10 ( 23X , F7 .2 , Fll . 5/ )
1038 FCRNAT( '!' )
WRITE(6, 1038 )
NN = C
DO 9COO N=l,2
IF(NN.NE.O) GC TC 8590
C ESTABLISHING A LOOP TO CALCULATE TOTAL DILUTION FACTORS FOR
C DIFFERENT LEVELS OF SEViAGE TREATMENT , WITH A CORRESPONDING
C EFFLUENT COLIFORM CONCENTRATION. NOW, E. COLI VALUES WILL BE
OUTFLCOO
OUTFL001
OUTFLC02
OUTFL003
OUTFLC04
OUTFL005
OUTFL006
OUTFL007
OUTFL008
OUTFLC09
CUTFL010
OUTFL011
OUTFL012
OUTFL013
OUTFL014
OUTFL015
OUTFL016
OUTFL017
OUTFL018
OUTFLC19
OUTFL020
OUTFL021
•OUTFL022
OUTFL023
OUTFLC24
OUTFL025
OUTFL026
OUTFL027
OUTFL028
OUTFL029
OUTFL030
OUTFL031
OUTFL032
OUTFL033
OUTFL034
OUTFL035
OUTFL036
OUTFL037
OUTFL038
OUTFLC39
OUTFL040
OUTFL041
OUTFL042
OUTFL043
OUTFL044
JOUTFL045
OUTFL046
OUTFL047
OUTFL048
OUTFL049
OUTFL050
OUTFL051
OUTFL052
OUTFL053
A- 1
-------
APPENDIX 1 - LISTING
DEFINED
SCO
510
520
530
540
550
560
570
8990
COL1 =
COL2 =
COL3=
CCL4=
COL5 =
2.
1.
5.
3.
6.
CCL6=8.
COL7 =
COL8=
GO TO
COL1 =
COL2 =
COL3=
CCL4 =
COL5 =
COL6 =
COL7=
COL8=
1.
1.
2E + 8
2E + 5
5E + 7
OE + 4
77E+5
7E + 3
CE + 5
OE + 5
8580
1.
5.
1.
10
1.
1.
1.
1.
OE + 7
OE + 5
OE + 6
.0
13E+5
0
OE + 3
0
8980
OUTFL054
OUTFL055
OUTFL056
OUTFLC57
OUTFL058
OUTFLC59
OUTFL060
OUTFL061
OUTFL062
OUTFL063
OUTFL064
OUTFL065
OUTFL066
OUTFLC67
OUTFL068
OUTFL069
OUTFL070
OUTFL071
OUTFL072
OUTFL073
OUTFL074
OUTFL075
OUTFL076
OUTFL077
11 FORMAT!•!','THIS PROGRAM CALCULATES THE CORRECT OUTFALL LENGTH COROUTFL078
1RESPONDING TO DIFFERENT DEGREES OF TREATMENT FOR THE CITY OF «,3A40UTFL079
I,/' CLASS=SC') OUTFL080
GO TO 23 OUTFL081
33 CLASS=SB OUTFL082
WRITE(6,12) CIT1,CIT2,CIT3 OUTFL083
12 FORMAT! 'I1 , 'THIS PROGRAM CALCULATES THE CORRECT OUTFALL LENGTH
1RESPONDING TO DIFFERENT DEGREES OF TREATMENT FOR THE CITY OF '
It/' CLASS=SB') OUTFL086
PRINT 95GC OUTFL087
OUTFL088
ARE FOR EFFLUENTS RECEIVING NO CHLORINAOUTFL089
OUTFL090
ARE FOR EFFLUENTS RECEIVING CHLORINATICOUTFL091
OUTFLC92
I 1 = 0
SC=1CCOC.
SB=70.
IF(NCLASS.EC
33
1)GO TC
IF(NCLASS.EQ.O)CLASS=SC
WRITE(6,11) CIT1,CIT2,CIT3
1
COROUTFL08A
,3AAOUTFL085
23
PRINT 96CC
•E.COLI. VALUES
•E.COLI. VALUES
I F ( N N . E C . C )
IF(KN.GT.O)
9500 FORMATl'0',
IT ION' )
9600 FORMAT!'0'
IN')
IF(CLASS.EQ.SC)GO TO 7CG1
PRINT 7C02
GO TO 886
7C01 PRINT 7COO
7C02 FORMAT! '-','DISTANCE(S6 )
DILUTION
DISTANCE(SC)
DILUTION
2 T90*,31X,'LEVEL OF TREATMENT1)
7000 FORMAT!•-«,'DISTANCE',5X,'DILUTION CALCULATED',5X,'DILUTION KNOWN
',3CX,'LEVEL OF TREATMENT')
886
T90=2.
JJ = C
GO TO
2 T90=4.
JJ = 0
GO TO
3 T90=5.
1
OUTFL093
OUTFL094
OUTFL095
OUTFL096
OUTFL097
OUTFL098
OUTFL099
OUTFL100
OUTFL101
OUTFL102
OUTFL103
OUTFL10A
OUTFL105
OUTFL106
OUTFL107
A- 2
-------
APPENDIX 1 - LISTING
GO TO 1
4 T90=10.
JJ = C
1 CONTINUE
FINDING TOTAL DILUTION FACTORS
200 DT=COL1/CLASS
IF(DT.LT.l.O) GO TO 9CC
GO TO 201
202 DT=COL2/CLASS
IF(CT.LT.1.0) GO TO 9CC
GO TO 201
203 DT=COL3/CLASS
IFtCT.LT.1.0 ) GO TO 9CO
GO TO 201
204 DT=COL4/CLASS
IFtCT.LT.1.0) GO TO 9CC
GO TO 201
2C5 DT=COL5/CLASS
IFtCT.LT. 1.0) GO TO 9CC
GO TO 201
206 DT=COL6/CLASS
IFtCT.LT. 1.0) GO TO 9CC
GO TO 201
207 DT=COL7/CLASS
IF(DT.LT.l.C) GO TO 9CG
GO TO 201
208 DT=COL8/CLASS
IFtCT.LT. 1.0) GO TO 9CC
201 CONTINUE
ESTABLISHING THE ITERATION SERIES TO CALCULATE DT EQUAL
KNOWN CT, WHICH WAS CALCULATED ABOVE.
X = 0.
28 DO 25 1=1,50
X = X-HCOG.
CALL EQN(X,V1,V2,Y1,X1,Y2,X2,Y3,X3,QW,T90,DT,CLASS,DT1,
1B,DT2)
IFtX.GT.(X1+X2+X3)) GO TO 304
IFtCT1.GT.CT) GO TO 30
IF(DTl.EQ.DT) GO TO 905
D = CT1
CONTINUE
LM=2*JJ+1
25
WRITE(6,4COO) X , A(LM),A(LL)
4000 FORMTt'O OUTFALL LOCATION EXCEEDS',F7.0,' FEET WHICH
1ENT LIMIT OF THIS INVESTIGATION't9X,2A4)
GO TO 210
3C4 LN=2*JJ-H
LL=LM+1
WRITE(6,6000) X,A(LM),A(LL)
6000 FORMATt'O OUTFALL IS LOCATED AT',F7.0,« FEET , WHICH IS
1 POINT AT WHICH DEPTHS HAVE BEEN INPUT',2X,2A4)
GO TO 210
OUTFL108
OUTFL1C9
OUTFL110
OUTFL111
OUTFL112
OUTFL113
OUTFL114
OUTFL115
OUTFL116
OUTFL117
OUTFL118
OUTFL119
OUTFL120
OUTFL121
OUTFL122
OUTFL123
OUTFL124
OUTFL125
OUTFL126
OUTFL127
OUTFL128
OUTFL129
OUTFL130
OUTFL131
OUTFL132
OUTFL133
OUTFL134
OUTFL135
OUTFL136
OUTFL137
TO THE OUTFL138
OUTFL139
OUTFL14C
OUTFL141
OUTFL142
XSTOR1,SC,SOUTFL143
OUTFL144
OUTFL145
OUTFL146
OUTFL147
OUTFL148
OUTFL149
OUTFL150
OUTFL151
OUTFL152
IS THE PRESOUTFL153
OUTFL154
OUTFL155
OUTFL156
OUTFL157
OUTFL158
BEYOND THEOUTFL159
OUTFL160
OUTFL161
A- 3
-------
APPENDIX 1 - LISTING
30 X=X-1CCO. OUTFL162
DO 50 J=l,25 OUTFL163
X=X+40. OUTFL164
CALL EQN(X,V1,V2,Y1,X1,Y2,X2,Y3,X3,QW,T90,DT,CLASS,DTI,XSTOR1,SC,SOUTFL165
1E.DT2) QUTFL166
IF(CTl.GT.DT) GC TC 60 OUTFL167
IF(CT1.EG.DT ) GO TO 9C5 OUTFL168
50 CONTINUE OUTFL169
60 X=X-40. OUTFL170
CO 80 K=l,20 OUTFL171
X=X+2. OUTFL172
CALL £QN
-------
APPENDIX 1 - LISTING
MECHANICAL CC-LCOP.
1CCC 11=11+1
IF(CLASS.EG.SC) GG TO 89
IFUI.EG.l) GO TC 2
IF(II.EG.2) GO TO 3
5 COO FORI"AT(F4.1TlXtF4.1, IX , E9 . 3 , IX , F4 . 0, IX, F5. 1 , IX, F4.0 , IX, E9 .3, IX, F5
$0,1X,E9.3)
89 CONTINUE
9COO CONTINUE
74 STOP
END
SUBROUTINE EQN(X,V1,V2,Y1,X1,Y2,X2,Y3,X3,QW,T90,DT,CLASS,DT
$1,SC,SBTDT2)
COfNCN/CRITCH/NPTS, ANGLE, DIA, RFC, 0,FN, PS, RHOJ
THETA1=.21C
THETA2= .07071
THETA3=.0195
KK=0
LL=C
Xl) DEPTh=X*Yl/Xl
(X1 + X2) .AND.X,GT.X1 ) DEP TH = Y 1+ ( X-X 1 ) * Y2 /X2
X.GT. (X1+X2) ) DEPTH = Y1+Y2-KX-(X1+X2)
cQ. SO CALL PLUME ( DEPTH , DT 1 )
EG.SB.ANO.X.LE.1320. ) CALL PLUME ( C EPTH , DT 1 )
EQ.SB.AND.X.GT.1320. ) GO TO 35
LE
LE
IF(X
IF(X
IF(
IF( CLASS
IF(CLASS
IF(CLASS
GO TO 39
35 XXX=X-1320.
ARG=l.+THETA2*CH**(-2
ARG=ARG**3
ARG=ARG-1.
ARG=1.5/ARG
ARG = ARG**( 1./2. )
CALL PLUME(DEPTH.DTl)
DT1=(DT1 ^
39 RETLRN
END
FLNCTIGN ERF(ARG)
C THE ERROR FUNCTION
c ***# THIS IS A FUNCTION
XX=ARG
NEG=0
IF(XX.LT.C.C) NEG=1
IF(XX.GE.3.0.0R.XX.LE.
SUM=XX
Y=XX
FMULT=1.0
DC 5 N=l,50
/3. )*XXX/V2
THETA3*XXX/(T90*V2) ) )/ERF( ARC)
SUBPROGRAM ****
(-3.C) ) GO TO 10
FN=N
Y=-Y*XX*XX/FN
TER^=Y/FMULT
SUM=SUK+TERM
IF( ABS( TERM/SUM
.LT. l.E-7) GO TO 6
1,XSTOREQN
EGN
EGN
EQN
EGN
EQN
ECN
EQN
EGN
EQN
)*Y3/X3EON
EGN
EQN
EQN
EQN
EQN
EGN
EQN
EGN
EQN
EGN
EQN
EGN
EQN
EQN
ERF
ERF
ERF
ERF
ERF
ERF
ERF
ERF
ERF
ERF
ERF
ERF
ERF
ERF
ERF
ERF
ERF
OUTFL216
OUTFL217
OUTFL218
DUTFL219
OUTFL220
0UTFL221
OUTFL222
OUTFL223
OUTFL224
OUTFL225
OUTFL226
OUTFL227
000
001
002
CC3
004
CCS
006
C07
008
C09
010
Oil
012
013
014
015
016
017
018
019
020
021
022
C23
024
COO
001
002
C03
004
CC5
006
CC7
008
009
010
Oil
012
013
014
015
016
A- 5
-------
APPENDIX 1 - LISTING
5 CONTINUE
STOP 5
6 ERF=1,1283792*SUK
GC TO 20
10 SUM=1./XX
Y=1./XX
YLAST=1./XX
CC 15 N=l,50
Y=-Y*FNUM/2./XX/XX
IF( ABSfY/YLAST) .GT.l. .OR. ABS ( Y / SUK ) . GT . 1 . E-7 ) GC TO 16
YLAST=Y
SUM=Y+SUM
15
16
17
18
19
20
CONTINUE
STOP 15
IF( XX.GT.3C. ) GO TU 18
ERFC=(.5641896*EXP(-(XX*XX)))*SUM
GC TO 19
ERFC=0.
ERF=1.-ERFC
IF(NEG.EO.l) ERF=-ERF
RETURN
END
SUBROUTINE P LUM E ( C E PTH , Cl)
COM MON/CRITCH/NPTS, ANGLE, OIA,RFD,Q,FN, PS, RHCJ
CCI^QN/WOOC/ZC(5C),DG(5G),RHO(5C),DP(50)
COKPCN/BLECH/G,FK,FM,COSTH,SINTH,COSTHE,DS,C1,C2,E13,FLAG,GRAV
LCGICAU NDC,TRAPPC, FLAG, CHG DEN, PETERS
PROGRAM PLUME, VERSION OF A/6/72
FD=ABS(RFD)
METERS=. FALSE.
NDC=. FALSE.
IF(,NPTS.NE.1)GO TC 76
NPTS=2
CP( 2)=DEPTH
RHCI 2)=RHO( 1 )
NOCASE=NOCASE+1
FORPAT(BFIO.O)
GRAV=32.172
IF(PETERS)CRAV=9.8C665
DC 55 I=1,NPTS
IF( CP( I ) .GE.CEPTF1GO TO
CONTINUE
HRITE(6,59)NCCASE
FORPAT('-NO DENSITY INFORMATION FOR JET LEVEL. EXECUTION FOR',
* ' CASE NC.',I2,« DELETED.')
GO TO 20
NP=I
NM= 1-1
RHOB=(CEPTH-DP(NM))*(KHO(NP)-RHO(NM))/(DP(NP)-DP(NNI))+RHO(NM)
DISP=RHOJ-RHCB
76
75
55
59
56
56
ERF 017
ERF 018
ERF 019
ERF 020
ERF 021
ERF 022
ERF 023
ERF C24
ERF 025
ERF 0?6
ERF C27
ERF 0?8
ERF 029
ERF 030
ERF C31
ERF 032
ERF 033
ERF 034
ERF 035
ERF 036
ERF 037
ERF 038
ERF 039
ERF 040
PLUMECOO
PLUMEC01
PLUME002
PLUME003
PLUMECC4
PLUME005
PLUME006
PLUMEC07
PLUME008
PLUME009
PLUME010
PLUME011
PLUME012
PLUME013
PLUME014
PLUME015
PLUME016
PLUMEC17
PLUME018
PLUME019
PLUME020
PLUME021
PLUME022
PLUME023
PLUME024
PLUME025
PLUME026
PLUME027
PLUME028
PLUME029
A- 6
-------
APPENDIX 1 - LISTING
DO 54 1=1, NM
J=NP-I
ZD( I )=(DEPTH-DP( J) )/DIA
54 DG(I)=(RHU(J+l)-RhC(J))*DIA/(DISP*(DP(J-H)-DP(J)))
IF(NDC)GC TG 58
UC=G/(FN*.7853982#DIA*DIA)
RFC=UfmjO*RHCJ/(-CISP*CIA*GRAV)
FC=ABS(RFD)
58 IF( FC.LE.4.01.0R.FC.Ge.9.99)GO TO 61
S=. 113*FD+4.
GO TC 62
61 IF(FC.LL.4.C1)S=2.8*FC**.333333
IF(FD.GT.LC.)S=5.6*Fn/SQRT(FC*FD+18.)
62 TEKP=ATAN( 1 . 4 166 6 7* S / FC )
THETAO=. Oil L*ANGLE* ( 1.570 8- TEMP )+TEMP
CCSTHE=CQS(TI-ETAO)
SIIMTHE = SIN(THETAC)
DS I=DEPTH/( 177. *CI A )
IF(CG( 1 ) .EQ.C. )GC TC 77
CGTEMP=.01/DG( 1)
IF(CGTEfP.LE.O.)CGTGMP=-DGTEMP
DSI = .12*1.6**(ALCG10(FD/10.))'!:2.**(ALCG10(CGTEN'P))
77 NPO=IFIX(PS/(CSI*CIA)+.5)
N = 0
Z = S*S INTHE
X=S*COSTHE
E=(4./S )**3
R = .25
C1=E**. 6666667
C2=.75/RFG
IPTS=1
G=DG( IPTS)
ZLIM=ZD( IPTS )
CHGCEN=. FALSE-
FLAG=. FALSE.
TRAFPC=. FALSE.
XP=X*CIA
ZP=CEPTh-Z*DIA
DSIP=DSI*DIA
SP=S*CIA
C SET INITIAL CONCITICNS
CS=CSI
GC TC 16
11 DS=CSI
45 DELX=CCSTH*CS
CELZ=SINTH*DS
CELE=FK
DELT=FM
SPDS2=S+DS/2.
DO 10 1=1,2
CALL SDERIV(SPCS2,E+.5*FK,R+.5*FM
DELX=DELX+2.*CCSTH*DS
PLUMEC3C
PLUME031
PLUME032
PLUME033
PLUMEC34
PLUFE035
PLUME036
PLUMEC37
PLU^EOBB
PLUMEC39
PLUME040
PLUN'EC41
PLUME042
PLUME043
PLUMEC44
PLUNE045
PLUMEC46
PLUME047
PLUME048
PLUME049
PLUME050
PLUMEC51
PLUME052
PLUME053
PLUME054
PLUMEC55
PLUME056
PLLJMEC57
PLUME058
PLUME059
PLUME06C
PLUN'EG61
PLUME062
PLUME063
PLUMEC64
PLUKE065
PLUMEC66
PLUME067
PLUMEC68
PLUME069
PLUME070
PLUME071
PLUME072
PLUME073
PLUME074
PLUME075
PLUME076
PLUMEC77
PLUME078
PLUMEG79
PLUME080
PLUME081
PLUME082
PLUME083
A- 7
-------
APPENDIX 1 - LISTING
DELZ=DELZ+2.*SINTh*DS
CELE=DELE+2.*FK
10 CONTINUE
CALL SDERIV(S+CS,E+FK,R+FM)
ZLAST=Z
ZINCR=(CELZ+SINTh*CS)/6.
Z=Z+ZINCR
TC 41
)GO TC 40
IF(ChGCEN)GC
IF( Z.GT.ZLIH
43 X=X-
E=E+(DELE+FK )/6.
R=R+( CELT+FM )/6.
S-S+DS
IF( E.LE.O. )FLAG=.TRUE.
THIS STOPPING CRITERIA IS BASED CN VELOCITY GCING TO ZERO
IF(FLAG)GO TO 13
16 CALL SCERIVI S,E,R )
IF(TRAPPD)GC TC 14
IF(R.GT.O. )GO TO 16
RAT=R/(RO-R)
E13TRP=E13+( E13-E130)
ZTRAP=DEPTH-(Z+ZINCR*RAT)*DIA
SMTRAP=.245*(S+DS*RAT)*E13TRP
TRAPPD=.TRUE.
GC TC 14
15 RO=R
E13C=E13
14 N=N+1
IF(N-(N/NPO)*NPC.NE.O)GC TC 11
13 XP=X*DIA
ELEV=Z*DIA
ZP = CEPTf--ELEV
SP=S*DI A
DILN=.245*S*E13
THETA=ARCCS(COSTh)*57.2958
IF( .NOT.TRAPPOGC TO 72
Cl= SN'TRAP
71 IF( .NOT. FLAG) GC TC 11
GC TC 20
72 D1=CILN
GO TO 71
C FIND NEXT STRATIFICATION AND RECOMPUTE LAST STEP IF NECESS)
C
4C DS=DS*(ZLIM-ZLAST)/(Z-ZLAST)
CALL SDERIVIS,E,R)
CHGCEN=.TRL'E.
Z=ZLAST
GC TO 45
41 ChGCEN=.FALSE.
IPTS=IPTS+1
PLUME084
PLUME085
PLUME086
PLUME087
PLUME088
PLUME089
PLUME090
PLUMEC91
PLUME092
PLUMEC93
PLUME094
PLUME095
PLUME096
PLUMEC97
PLUME098
PLUVE099
PLUME1CO
PLUI^ElOl
PLUME102
PLUME1C4
PLUME105
PLUME106
PLUME107
PLUME108
PLUME109
PLUME110
PLUME111
PLUME113
PLUME114
PLUME115
PLUME116
PLUME117
PLUME118
PLUME119
PLUME120
PLUME121
PLUME122
PLUME123
PLUME124
PLUME125
PLUME126
PLUME127
PLUME128
PLUME129
PLUME130
PLUME131
PLUME132
PLUME133
PLUME134
PLUNE135
PLUME136
PLUME137
A-
-------
APPENDIX 1 - LISTING
IF( IPTS.GT.NVIGC TC 42
G = CC-( IPTS )
ZLIP=ZD
-------
APPENDIX B
(Example Problem)
-------
The design of outfalls for ten different coastal cities on the
Island of Puerto Rico can be modelled using OUTFALL. The cities chosen
are listed as follows: Aguadilla, Arecibo, Barceloneta, Carolina, Guayanilla,
Humacao, Mayaguez, Ponce, San Juan, and Yabucoa. As shown in Figure
B-l, the current patterns for Puerto Rico flow basically from east to west
except for a recirculation current which appears during the summer near
the northern coast. During the summer, the southeast winds cause the current
to run northward through Vieques Passage, but in the winter, the northeast
wind produces a southern current through the Passage. Table B-l indicates
the location of the proposed outfalls and their true azimuth in degrees
perpendicular from their respective location on shore. Basic outfall
sites, also shown in Figure B-l, are located in areas of widely differing
environmental conditions. Water quality standards, promulgated by the Puerto
Rico Environmental Quality Board, change the amount of the dilution of the
wastewater needed to meet those standards in each area. This factor is
incorporated within OUTFALL as the variable CLASS, as indicated in the
section concerning the computer program. SB class waters are defined as
those waters having less than 70 coliform organisms per 100 milliliters
of seawater, and SC class waters are defined as those waters having less
than 10,000 coliform organisms per 100 milliliters of seawater.
In equation (26), the final expression for total dilution involving
the Pearson, Brooks and first order decay equations, D^ is a function of
six variables: the average velocity of ocean water in the effective mixing
region (V-^), the ocean current velocity (V2), the distance from the shore
to the end of the outfall along the water surface (X), the design discharge
of the treatment plant (Qy), the depth of water over the diffuser (d), and
the TgQ decay value. These variables are presented in Table B-2, along
with the water quality classification for each outfall location.
As sources for the data given in Table B-2, V^ and V2 were taken from
a recent study conducted by the Puerto Rico Department of Natural Resources
and Engineering Science, Incorporated1 , and Qy values were obtained from
the Puerto Rico Aqueduct and Sewer Authority.13 The Tgg values presented
a special problem, as several conflicting studies have been conducted. A
summary of the results of ten different studies encompassing seven geographical
locations is presented as Table B-3. In the Puerto Rico situation, standards
must be met at the maximum point of rise over the end of the outfall in
the areas, regardless of the type of water quality standard. Therefore,
only initial dilution (Dj) needs to be calculated in these cases. A
boundary of one-quarter mile (1320 feet) was assumed for the Puerto Rico
water quality standards (in other words, the standard would extend from
the shoreline out to a distance of one-quarter mile). After that distance
is reached, it is assumed that all waters outside of one-quarter mile
limit would be SC class waters, i.e., discharges must comply with the
lowest water quality standards (Class SC). If the outfall extends
greater than this boundary, D2 and D3 must be also calculated. Thus,
TQn values must be assumed for SB class waters. The outfall locations
at Barceloneta, Carolina, and Humacao have SB class standards. Data were
extrapolated from Table B-3 and are presented in Table B-2.
B-l
-------
Density data and water depth used in the PLUMP subroutine are presented
in Table B-4 for each city. RHO is inputed as gm/cnr', and the depth is
in feet.-'--'- Other data used in the PLUME subroutine were assumed as
indicated in Table B-5.
Finally, the data are punched onto computer cards as described on page
and as shown in Table B-6, and OUTFALL is run. The resulting output is
attached.
The necessary outfall length needed to meet the water quality
standard and corresponding to a certain level of treatment is listed in
the "DISTANCE" column. The dilution calculated (essentially a modification
of equation 26) and the known dilution (equation 28 appear in their
respective columns. Three other messages may appear in the output. If
either "OUTFALL IS LOCATED AT X FEET, WHICH IS BEYOND THE POINT AT WHICH
DEPTHS HAVE BEEN INPUT" or "OUTFALL LOCATION EXCEEDS X FEET, WHICH IS
THE PRESENT LIMIT OF THIS INVESTIGATION" appears, it means that either
in-plant chlorination must be added or a higher degree of treatment must
be attained in order to meet water quality standards within the limit
of 3t. If the following message appears in the output, it indicates that
more bottom slope (depth/distance) data is needed to be inputed: "NO
DENSITY INFORMATION FOR JET LEVEL EXECUTION FOR CASE NO. **DELETED".
B-2
-------
ARECIBO
BARCELONETA
.MAYAGUEZ PUERTO RICO
HUMACAO
YABUCOA •
FUENTE DE INFOftMACION:
0 10 20 MILLAS
( KAYE . 1939). USGS PROFESSIONAL PAPER, 317-B
City
Aguadilla
Arecibo
Barceloneta
Carolina
Guayanilla
Humacao
Mayaguez
Ponce
San Juan
Yabucoa
FIGURE B-l
TABLE B-l
OCEAN OUTFALL LOCATIONS
Outfall Location
0.22 mi. NE of Rio Culebrinas
3.78 mi. SW of Pta. Caracoles
3.78 mi. E of Pta. Palmas Altas
0.018 mi. W of Rio Grande de Loiza
8.2 mi. NE of Pta. Ventana
7.58 mi. NE of Rio Humacao
0.01 mi. N of Quebrada del Oro
0.125 mi. W of Rio Matilde
From Puerto Nuevo Plant
3.79 mi. SW of Cano Santiago
True Azimuth from
Point on Shore
331°
335°
357°
9.5°
177°
137°
279°
178°
st
Sect. - 312C
2nd Sect. - 331°
135'
B-3
-------
TABLE B-2
PHYSICAL AND BIOLOGICAL PARAMETERS
CITY
Aguadilla
Arecibo
Barceloneta
Carolina
Guayanilla
Humacao
Mayaguez
Ponce
San Juan
Yabucoa
V
1 cm/ sec
"10.0
8.5
8.5
22.0
9.5
11.0
12.0
21.5
10.0
11.0
V
2 cm/sec
19.0
17.5
17.5
33.0
15.5
14.0
16.0
27.5
15.5
14.0
Q T
w f 90 ,
cfs hrs
27.8
46.4
46.4 5
92.8 2,4
92.8
18.6 2,4
46.4
46.4
290.8
18.6
X /y
1 1 feet
3160/60
4390/120
1770/60
6350/18
3530/108
24700/60
14700/120
10800/60
20300/30
30800/30
X /y
2 2 feet
1425/60
2630/180
1770/60
1600/42
48400/12
3490/60
2800/78
7610/1
5600/60
4840/12
X /y
3 3 feet
4250/480
1760/300
6130/480
13400/540
4860/1200
2690/1255
6500/402
1900/540
5020/480
1795/558
C1ASS
(Water Quality)
SC
SC
SB
SB
SC
SB
SC
SC
SC
SC
w
I
-------
TABLE B-3
ESTIMATES OF COLIFORM
DIE-OFF (Tg0) BY LABORATORY
AND FIELD STUDIES IN PUERTO RICO
CITY
AGUADILLA
ARECIBO
BARCELONETA
HUMACAO
ISABELA
MAYAGUEZ
MAYAGUEZ
MAYAGUEZ
MAYAGUEZ
PONCE
GUAYAMA
GUAYAMA
T (hrs) STUDY
90
2.1 - 4.9 Western (1970)14
18 Bogert (1972)15
16
5 Black & Veatch (1971)
17
0.95 - 4.0 0' Kelly (1971)
18
18 Bogert (1970)
0.9 - 1.3 Engineering Science (1972)
12
2.9 Engineering Science (1972)
1.5 Guzman (1970) 19
90
1.3 - 3.1 Black & Veatch (1971)
21
1.45 - 1.55 Hazen & Sawyer (1970)
(Apparent Regrowth) Engineering Science (1972)
11 Heres (1971)22
B-5
-------
TABLE B - 4
DENSITY STRATIFICATION DATA FOR
VARIOUS COASTAL CITIES IN PUERTO RICO
DEPTH (feet)
RHO (gm/cm3)
AGUADILLA:
ARECIBO:
BARCELONETA:
0
2.00
8.00
20.00
44.00
54.00
62.00
96.00
120.00
137.00
149.00
158.00
200.00
0
00
00
6
17
26.00
54.00
72.00
92.00
119.00
200.00
0
6.00
13.00
26.00
38.00
76.00
98.00
118.00
200.00
02267
02300
1.02310
1.02320
1.02330
1.02340
1.02350
1.02400
1.02450
1.02500
1.02550
1.02600
1.02600
1.02310
1.02330
1.02340
1.02350
1.02400
1.02450
1.02500
1.02550
1.02550
1.02300
1.02310
1.02320
1.02340
1.02350
1.02400
1.02450
1.02500
1.02500
B-6
-------
CAROLINA:
TABLE B
DEPTH (feet)
0
2.00
10.00
37.00
56.00
70.00
84.00
92.00
102.00
112.00
119.00
123.00
130.00
134.00
138.00
142.00
144.00
148.00
152.00
154.00
158.00
160.00
200.00
- 4 (CONT.)
RHO (am/cm )
1.02370
1.02380
1.02390
1.02410
1.02420
1.02430
1.02440
1.02450
1.02460
1.02470
1.02480
1.02490
1.02500
1.02510
1.02520
1.02530
1.02540
1.02550
1.02560
1.02570
1.02580
1.02590
1.02600
GUAYANILLA:
MAYAGUEZ:
0
6.00
18.00
24.00
31.00
40.00
90.00
122.00
144.00
200.00
0
6.00
20.00
40.00
58.00
66.00
74.00
100.00
120.00
136.00
156.00
200.00
.02307
.02310
.02320
.02330
1.02340
1.02350
1.02400
1.02450
1.02500
1.02500
1.02299
1.02300
1.02310
1.02320
1.02330
1.02340
02350
02400
02450
02500
02550
1.02550
B-7
-------
PONCE:
SAN JUAN:
YAEUCOA/HUMACAO:
TABLE B - 4 (CONT.)
DEPTH (feet)
0
10.00
24.00
59.00
76.00
84.00
88.00
90.00
108.00
124.00
200.00
0
4.00
6.00
8.00
10.00
12.00
23.00
32.00
38.00
49.00
58.00
67.00
76.00
84.00
91.00
98.00
104.00
110.00
116.00
121.00
126.00
131.00
136.00
140.00
145.00
149.00
200.00
0
2.00
10.00
42.00
70.00
92.00
115.00
153.00
200.00
RHO (gm/cnr)
1.02169
1.02186
1.02200
1.02250
1.02300
1.02350
1.02400
1.02450
1.02500
1.02550
1.02550
1.02208
1.02300
1.02320
1.02340
1.02360
1.02380
1.02400
1.02410
1.02420
1.02430
1.02440
1.02450
1.02460
1.02470
1.02480
1.02490
1.02500
1.02510
1.02520
1.02530
1.02540
1.02550
1.02560
1.02570
1.02580
1.02590
1.02590
1.02267
1.02300
1.02350
1.02400
1.02450
1.02500
1.02550
1.02600
1.02600
B--8
-------
TABLE B-5
SUBROUTINE PLUME
ASSUMPTIONS OF INITIAL CONDITIONS
VARIABLE
METERS
ANGLE
DIA
RHOJ
PS
VALUE
4=FPS units used.
0 degrees
1.0 ft.
0.999 gm/cm
2.0 ft.
B-9
-------
Appendix C
-------
INPUT DATA FOR THE CITY OF BARCELONETA
VI V2 XI Yl QW Y2 X2 Y3 X3
.8500E+01 .1750E+02 .1770E+04 .6000E+02 .4640E+02 .6000E+02 .1770E+04 .A800E+03 .6130E+04
UNITS FPS
PORT ANGLE . 0.0
PRINTOUT INTERVAL 2.00
DISCHARGE DENSITY 0.99900
FLOWRATE 0.46400E+02
NUMBER OF PORTS . 42.
PORT DIAMETER ". " . ... . 0.10900E + 01
DENSITY STRATIFICATION DEPTH RHO
-0.-_9. - J,«
19.68 1.02310
42.65 1.02320
85.30 1.02340
124.67 1.02350
249.35 1.02400
_3J1..53 l.Q2_45Q
387.15 1.02500
656.19 1.02500
-------
THIS PROGRAM CALCULATES THE CORRECT OUTFALL LENGTH CORRESPONDING TO DIFFERENT DEGREES OF TREATMENT FOR THE CITY OF BARCELONETA
CLASS=SB
E.COLI. VALUES ARE FOR EFFLUENTS RECEIVING NO CHLORINATION
DISTANCE(SB) DILUTION DISTANCEISC) DILUTION T90 LEVEL OF TREATMENT
.Og.TFAU._.LS_.LOC_ATE_p_.AT..10.0p.Q.. FEET _i ...WHJC.H .Li B£YJ3N.O...THE-..PQ1NJ._ AT ..WHICH. QEP.THS.HAVE BEEN INPUT RAW MAX
OUTFALL IS LOCATED AT 10000. FEET , WHICH IS BEYOND THE POINT AT WHICH DEPTHS HAVE BEEN INPUT PRI MAX
0.7459.5E+P4 Q.96746E+04 0.74595E+04 0.87529E+02 2. SEC MAX
^r468_4J^tD4_.0. 14.28 7EtP_4 _0. 46845Et_04 0 ._! 0 27 6E+ 0 3 __2_. TER_ MAX
OUTFALL IS LOCATED AT 10000. FEET , WHICH IS BEYOND THE POINT AT WHICH DEPTHS HAVE BEEN INPUT RAW MAX
OUTFALL IS LOCATED AT 10000. FEET , WHICH IS BEYOND THE POINT AT WHICH DEPTHS HAVE BEEN INPUT PRI MAX
_0-.85997J±Pj4___Oi9574._2Et.04 _.P._859_9_7E.+g4..__QjL29644.E+Q3.. 4_._ SEC MAX
0.72895E+04 0.14286E+P4 0.72895E+04 0.77042E+02 4. TER MAX
PUTFALL IS LOCATED AT 10000. FEET , WHICH IS BEYOND THE POINT AT WHICH DEPTHS HAVE BEEN INPUT RAW MAX
OUTFALL IS LOCATED AT 10000. _FEET j_. WH.ICH. J S_.BEY_QND.jrHE__POIN_I..AT. WHICHL.DEPT_HS_ HAVE BEEN. INPUT PRI MAX
_P_i8935_2_E_t_p_4__ 0.96728E + 04 0.89352E>04 0.39357E+03 5. SEC MAX
0.75620E+Q4 0.14289E+04 0.75620E+04 0.96787E+02 5. TER MAX
~~~ """ -------
-------
THIS PROGRAM CALCULATES THE CORRECT OUTFALL LENGTH CORRESPONDING TO DIFFERENT DEGREES OF TREATMENT FOR THE CITY OF BARCELONETA
CLASS=SB
E.COLI. VALUES ARE FOR EFFLUENTS RECEIVING CHLORINATIDN
DISTANCE(SB) DILUTION DISTANCE(SC) DILUTION T90 LEVEL OF TREATMENT
OUTFALL IS LOCATED AT 10000. FEET., WHICH IS BEYOND THE .POINT. AT .WHICH DEPTHS HAVE .BEEN .INPUT RAH MAX
0.76815E+04 0.14286E+05 0.76815E+04 0.11026E+03 2. PRI MAX
0.48392E+04 0.16146E+04 0.48392E+04 0.10291E+03 2. SEC MAX
0.63950E+03 0.14294E+02 2. TER MAX
OUTFALL IS LOCATED AT 10000. FEET , WHICH IS BEYOND THE POINT AT WHICH DEPTHS HAVE BEEN INPUT RAW MAX
0.89042E+04 0.14289E+05 0.89042E+04 0.38532E+03 4. PRI HAX
0.73960E+04 0-16146E+04 0.73960E+0^ 0.83079E+02 4. SEC MAX
0.63950E-I-03 0.14294E + 02 4. TER MAX
OUTFALL IS LOCATED AT 10000. FEET , WHICH IS BEYOND THE POINT AT WHICH DEPTHS HAVE BEEN INPUT RAiL MAX
OUTFALL IS LOCAT£JD__AI..1DOO.Q._.FE.E.T. ,- WWICH IS BEYOND. THE POINT AT WHICH DEPTHS HAVE BEEN INPUT PRI MAX.-
0.76437E+04 0.16144E+04 0.76437E+04 0.10600E+03 5. SEC MAX
0.63950E+03 0.1A29AE+02 5. TEJUMAX
------- |