EPA-R2-72-005a
August 1972
Environmental Protection Technology Series
Workbook of Thermal Plume Prediction
Volume I
Submerged Discharge
National Environmental Research Center
Office of Research and Monitoring
U.S. Environmental Protection Agency
Corvallis, Oregon 97330
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and
Monitoring, Environmental Protection Agency, have
been grouped into five series. These five broad
categories were established to facilitate further
development and application of environmental
technology. Elimination of traditional grouping
was consciously planned to foster technology
transfer and a maximum interface in related
fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL
PROTECTION TECHNOLOGY series. This series
describes research performed to develop and
demonstrate instrumentation, equipment and
methodology to repair or prevent environmental
degradation from point and non-point sources of
pollution. This work provides the new or improved
technology required for the control and treatment
of pollution sources to meet environmental quality
standards.
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EPA-R2-72-005a
August 1972
WORKBOOK OF THERMAL PLUME PREDICTION
Volume 1
Submerged Discharge
By
Mostafa A. Shirazi
Lorin R. Davis
Pacific Northwest Water Laboratory
National Environmental Research Center
Corvallis, Oregon
Project 16130 FHH
Program Element 1B1032
NATIONAL ENVIRONMENTAL RESEARCH CENTER
OFFICE OF RESEARCH AND MONITORING
U.S. ENVIRONMENTAL PROTECTION AGENCY
CORVALLIS, OREGON 97330
I'orsalo by the Superintendent of Documents, <'.s.
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EPA Review Notice
This report has been reviewed by the Environmental
Protection Agency and approved for publication.
Approval does not signify that the contents necessarily
reflect the views and policies of the Environmental
Protection Agency, nor does mention of trade names or
commercial products constitute endorsement or recommenda-
tion for use.
11
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i i \L_ i r\
This workbook contains computational procedures in the form of
nomograms designed to satisfy several needs related to the discharge
of thermal waste into large bodies of water. They provide estimates
of physical spread and temperature distribution around the discharge
point for the assessment of biological and physical effects of heated
water. They can be used as guidelines for setting temperature standards
and for monitoring. Finally, they have utility in pre-design feasibility
analyses and outfall performance estimates.
Data and analyses from numerous sources constitute the back-up
material for this publication. An attempt has been made to unify and
present the material in a format that is sufficiently simple for a non-
specialist user. A number of illustrative examples are presented which
demonstrate the use of each set of nomograms in practical problems.
The status of analysis at this time is not sufficiently advanced
to encompass a wide range of experimentally verified predictive models.
For this reason, care must be exercised when applying the generalized
nomograms to specific situations. The major restrictions for each set
of nomograms are outlined in the text which the user is advised to review
carefully. In general, the nomograms provide meaningful qualitative
information for a wide range of problems of practical interest, but
their use is subject to scrutiny and proper interpretation when applied
to exacting design conditions.
This is a part of a continuing effort to present the current knowledge
on predictive models to the public. As more data are obtained in the future,
the nomograms will be refined and updated. This first volume is devoted to
submerged discharges. The analysis of surface discharge is the subject of
a separate volume to be prepared.
iii
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TABLE OF CONTENTS
Page
Preface in
List of Symbols, Dimensionless Numbers, and Notations vi
List of Figures viii
List of Tables ix
I. Introduction 1
II. Discharge into a Stagnant, Non-Stratified Water 11
A. Generalized Nomograms 11
B. Basic Assumptions 13
III. Discharge into a Stagnant, Stratified Water 17
A. Generalized Nomograms 17
B. Basic Assumptions 22
IV. Discharge into a Moving, Non-Stratified Water 23
A. Generalized Nomograms 23
B. Basic Assumptions 25
V. Discharge into a Moving, Stratified Water 31
A. Generalized Nomograms 31
B. Basic Assumptions 33
VI. Vertical Discharge into a Non-Stratified, Stagnant, Shallow Water 35
A. Generalized Nomograms 35
B. Basic Assumptions 35
VII. Example Problems 39
References 69
VIII. Appendices
A. Nomograms for Discharge into Stagnant,
Non-Stratified Water, (RNN, MNN) 71
B. Nomograms for Discharge into Stagnant,
Stratified Water, (RNS, MNS) 113
C. Nomograms for Discharge into Moving,
Non-Stratified Water, (RCN) 163
D. Nomograms for Discharge into Moving,
Stratified Water, (RCS) 197
E. Nomograms for Vertical Discharge into Shallow
Stagnant Water (RNN, Shallow Discharge) 217
F. Auxiliary Materials to Aid in Solving Problems 225
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LIST OF SYMBOLS, DIMENSIONLESS NUMBERS, AND NOTATIONS
A. STANDARD SYMBOLS AND DIMENSIONLESS NUMBERS
D Jet diameter
F Jet densimetric Froude number
U. GU,
F - ,.. J =
g Gravitational constant
Ap_ i/o
6 [ -^-g ] ' plotted on Fig. F-l
o
HC Waste heat load
k Velocity ratio j_
Uo
L Jet spacing on multiple jet diffuser
Q Volumetric flow rate
r Radial distance from plume center
S Distance along plume centerline
S. Stratification number
ApQ/D ATQ/D
St Apa/AZ ATa/AZ
T Temperature
U Velocity
W Plume width
X,Z Coordinates of plume centerline
-------
A()c
A( )(
A( ),
Subscripts
a
c
j
o
Linearized non-stratified depth
defined in Fig. 6
4r
W
Density
Discharge angle relative to horizontal
( )a at Z2 - ( )a at
Ambient
Centerline
Jet
Ambient at discharge depth
B. SHORTHAND NOTATIONS
A three-letter code is used for convenient reference. First
letter designates type of diffuser; second letter, the type of current;
third letter, the degree of stratification.
Diffuser
Configuration
Single
Round
Port
A Row of
Multiple
Round Ports
Condition of Ambient Water
Non-Stratified
No Current
RNN
MNN
Moving
RCN
MCN*
Stratified
No Current
RNS
MNS
Moving
RCS
MCS*
Nomograms not presented for these cases.
vii
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LIST OF FIGURES
No.
la A Single Round Port Diffuser at an Arbitrary Angle 6. 4
Ib The Trajectory and Width of a Single Port Plume for 9 = 4
0° and F = 10 in a Non-Stratified, Stagnant Large Body
of Water.
2a Multiple Round Port Diffuser with Equal Port Spacing. 6
2b A Multiple Port Plume with L/D = 1.5, F = 10 in a 6
Non-Stratified, Stagnant Large Body of Water.
3 Single Port Plume Trajectory and Width in a Stratified,
Stagnant Large Body of Water: e = 0°, F = 10, St = 500. 8
4 Single Plume Trajectory and Width in a Non-Stratified,
Moving Body of Water: 6 = 0°, F = 10, k = 1.0'. 8
5 Temperature Decay Curves for Various Diffuser Configura-
tions and Ambient Water Conditions. 9
6 Linearization of the Natural Density Stratification and
the Definition of Z . 20
7 The Range of Experimental Parameters and the Extent of
Extrapolation Reported in this Volume for Co-flow Data. 26
8 The Range of Experimental Parameters and the Extent of
Extrapolation Reported in this Volume for Cross-flow Data. 27
vm
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LIST OF TABLES
Np_. Page
I. Figure Numbers Corresponding to Plume Behavior From Submerged
Diffusers Discharging into Stagnant, Non-Stratified Water. 12
II. Figure Numbers Corresponding to Plume Behavior from Submerged
Diffusers Discharging into a Stagnant, Stratified Ambient Water 18
III. Figure Numbers Corresponding to Plume Behavior from Single Port
Submerged Diffusers Discharging into Moving, Non-Stratified
Water. 24
IV. Figure Numbers Corresponding to Plume Behavior for Diffuser
Discharging into Moving and Stratified Ambient Water. 32
V. Figure Numbers Corresponding to Plume Behavior for a Single
Port Diffuser Discharging Vertically Upward into Non-Stratified,
Stagnant, Shallow Body of Water. 36
VI. Variations on Problem 2 Showing Several Discharge Conditions. 44
VII. Variations on Problem 4 Showing Several Discharge Conditions
and Diffuser Jet Spacings (Plant Size 1000 MW). 49
VIII. Variations on Problem 6 Showing Several Diffuser Configurations
and Discharge Conditions. 56
IX. Variations on Problem 7 Showing Several Diffuser Configurations
and Discharge Conditions. 58
X. Variations on Problem 8 Showing Different Discharge Conditions 60
XI. Variations on Problem 10 Showing Several Discharge Configura-
tions and Ambient Conditions. 65
XII. Variations of Problem 11 Showing Surface Temperatures for
Several Discharge Conditions 67
IX
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I. INTRODUCTION
Warm water diffusers are commonly classified into two broad cate-
gories, namely, surface and submerged. A surface diffuser generally
produces a large zone of relatively high excess water temperature that
is spread in a thin layer above the cool unmixed ambient water. While
a surface diffuser can be designed to achieve a considerable degree of
mixing with the ambient water, rapid mixing of warm water effluent with
the ambient water is best obtained with a submerged diffuser.
A properly designed, deeply submerged diffuser can readily produce
adequate mixing and dilution before the plume reaches the water surface.
The factors affecting this design include (1) the diffuser configuration
such as single round port, multiple round ports, or slotted port, (2) the
discharge angle relative to the ambient current and gravity, (3) the dis-
charge excess temperature (or density) above the ambient, and (4) the dis-
charge velocity. Ambient temperature and density stratifications and the
presence of ambient current all significantly contribute to rapid mixing
and should be carefully considered in making plume analyses.
When analyzing plume behavior, one is usually interested in the
trajectory of the plume, its width and some information concerning the
local temperature within the plume along its trajectory. The plume tra-
jectories in this book are plotted with respect to vertical and horizontal
coordinates, both made dimensionless by dividing by the diffuser port
diameter. The width of the plume is conventionally taken equal to four
standard deviations of the local temperature distribution across the plume
trajectory where this distribution is assumed to be Gaussian. The informa-
tion on the plume temperature is best given for the center!ine of the plume
l
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and expressed in terms of the excess center!ine temperature difference
along the trajectory divided by the excess discharge temperature difference
AT
[TY=-]. In all cases, the temperature difference is calculated locally to
show the excess temperature above ambient.
The trajectory, the width, and the center!ine temperatures are expressed
in appropriate dimensionless numbers. Furthermore, the discharge character-
istics such as the velocity, excess temperature (or density), and diameter
are also collected in a dimensionless form called the Froude number. The
Froude number is the ratio of inertia! forces due to the jet discharge velo-
city to the buoyant forces due to the discharge density difference with respect
to the ambient. Formally, this is expressed as F = II./( p° gD) . This number
J Po
has been used extensively as a correlation parameter in plume analysis. Other
dimensionless numbers found useful in correlating plume data are the ratio of
the discharge velocity to the ambient velocity (k) when there is an ambient
current and the stratification number describing the vertical density (or
temperature) gradient within the ambient water when the ambient density is
not constant with depth. The reader is advised to familiarize himself with
the dimensionless parameters listed immediately behind the Table of Contents.
The reader should also review the shorthand notations (p.vii)since they
will be used extensively. The three letters of the the shorthand notation refer
to (1) the diffuser configuration, (2) the presence or absence of the ambient
current, and (3) the presence or absence of ambient stratification, respec-
tively. Single round port diffusers are designated by R and a diffuser con-
sisting of a row of multiple round ports is designated by the letter M. The
presence of current and stratification are designated by C and S, respectively,
-------
and their absence is designated by N. Thus, RNN refers to a single port
diffuser discharging into stagnant, non-stratified ambient water as listed
in the shorthand notation table. Other combinations readily follow.
The relative influence of such factors as ambient water conditions
and diffuser configuration on the plume trajectory, width, and centerline
excess temperature is best illustrated by the typical examples given below.
These examples are obtained from the nomograms of this volume with only a
slight modification in format. They are chosen only for the purpose of dis-
cussion at this point and in order to familiarize the reader with the scope
of this volume quickly and with a minimum of introductory work. The discharge
Froude number for all examples is taken equal to 10. The discharge angle with
respect to the horizontal is equal to zero. When the ambient water is moving,
the direction of the jet discharge is the same as the direction of the ambient
current and the discharge velocity is equal to the ambient velocity. The
stratification number when applicable is taken equal to 500. The plume
width and centerline trajectories are presented first on individual Figs. 1
through 4 and the centerline excess temperature decays are plotted jointly
on Fig. 5 for the purpose of comparison.
The centerline trajectory and plume width from a single port diffuser
discharging into a stagnant, non-stratified body of water (RNN) is plotted
in Fig. 1. The plume travels horizontally a short distance before the
buoyancy forces lift it upward as shown in the plot. The plume continues
to rise until it loses buoyancy or reaches the water surface. Meanwhile,
the plume centerline temperature continues to decay as shown in Fig. 5 by
the decay curve marked RNN.
-------
r
C3
M
0 L-.
0
20
X/D
Fig. Ib
40
Fig. 1 (a) A Single Round Port Diffuser at an
Arbitrary Angle 0, and (b) the Trajectory
and Width of a Single Port Plume for 0=0°
and F = 10 in a ilcn-Stratifiad, Stagnant
Large Body of Hater (RNN)
-------
The center!ine trajectory and plume width from a multiple port
diffuser is plotted in Fig. 2; the ambient water is at rest and is non-
stratified (MNN). Each port is equivalent to the single port discharge
shown in Fig. 1. Comparison with this figure shows that the plume from
a multiple port diffuser is wider and the trajectory less steep. The
reason for this difference in plume behavior is the interference between
the neighboring plumes in a multiple port discharge. For a short distance
from the discharge point, individual round plumes issue from each port
and maintain a trajectory identical to that in Fig. 1. The single round
plume entrains ambient water from all sides and grows radially as it moves
upward. After merging together with the neighboring plume to form a long
rectangular source, the ambient water is entrained only from the sides and
thus the plume is restricted to growth in only two directions. The multiple
port plume also fails to penetrate the ambient water as much as a single
round plume.
The consequence of plume interference on the centerline temperature
along a multiple port plume trajectory is a slower temperature decay as
seen from the comparisons of curves RNN with MNN in Fig. 5. It should be
noted that this example, while demonstrating the dynamics of plume behavior,
does not properly reflect the practical advantages of multiple port diffusers,
In a typical situation when multiple port diffusers are used, the discharge
from each port is only a small fraction of the total discharge from a single
round diffuser so that dilution with distance from a multiple port diffuser
can be substantially greater than at the same distance from an equivalent
single port diffuser.
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D
Fig. 2a
Fig. 2 (a) Multiple Round Port Diffuser with Equal
Port Spacing, and (b) a Multiple Port Plume with
L/D = 1.5, F = 10 in a Mor.-Stratified, Stagnant
Large Body of Water (MNN)
40 r
20
2b
20
X/D
40
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The plume trajectories for the two cases examined continue to rise
as discussed earlier because the environment is non-stratified. Within
a stratified environment, the plume trajectory may terminate as shown in
Fig. 3 and often descends slightly from that height due to entrainment of
cooler ambient water from lower depths. The plume trajectory and width
plotted in this figure are for a single round port diffuser (RNS). By
comparison with Fig. 1, the plume trajectory is less steep and the plume
growth is substantially greater. The center!ine plume temperature relative
to the ambient decays at a considerably greater rate. This is seen from
the comparison of curves marked RNN and RNS as well as MNN and MNS plotted
in Fig. 5.
The effects of ambient current on plume characteristics are demonstrated
by the plot of trajectory and width for a single port diffuser in moving,
non-stratified water (RCN) in Fig. 4 and by the temperature decay curve
RCN for the same diffuser as plotted in Fig. 5. The ambient current carries
the plume downstream before it has a chance to spread. In the same time
it exposes the plume to a greater ambient turbulence resulting in a substan-
tial dilution.
Recall that the foregoing examples were given for a Froude number equal
to 10 and for a fixed jet to ambient velocity ratio and stratification number.
The numerous nomograms presented in this volume bring out the interrelation-
ships between the discharge angle, discharge Froude number, ambient current,
and stratification for single and multiple port diffusers. It should be
pointed out that effects of such boundary conditions as ocean or river
floor, free surface or confining walls and structures are totally excluded
in all but Section VI. Sections II through VI are devoted to the discussion
-------
40
X/D
Fig. 3 Single Port Plume Trajectory and Width
in a Stratified, Stagnant Large Body
of Water: G = 0°, F - 10, $t = 500 (RNS)
20
20
X/D
40
ig. 4 Single P1ir.fi Trajectory and Hidth in a Non
Strati find, f.oving Body of Hater: 0 = 0°,
k == 1-0
= 10
-------
o
I<
DC
UJ
o;
UJ
C-
l/l
00
MNN - L/D = 1 .5 _
.01 -
40
60 30 100
DISTANCE ALONG PLUMf CENTERLINE S/D
120
140
150
Fig. 5 Temperature Decay Curves for Various Diffuser
Confiqurations and Antrient Water Conditions
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and presentation of the nomograms. Section VII is devoted exclusively
to illustrative examples for the use of the nomograms. The appendices
contain the nomograms themselves, as well as normal Gaussian curve and
temperature-density relations.
10
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II. DISCHARGE INTO STAGNANT, NON-STRATIFIED WATER
The monograms developed for this idealized situation are presented
in Appendix A. The 14 cases considered in examples 1 through 4 (Section
VII) illustrate the use of these nomograms. A description of the nomograms
and basic assumptions underlying their development are presented below.
A. GENERALIZED NOMOGRAMS
Figures A-l through A-35 of Appendix A are generalized nomograms
developed for a discharge from a single port or a multiple port diffuser
into a stagnant, non-stratified large body of water. The figure numbers
corresponding to four different discharge angles and four diffuser port
spacings are listed in Table I for easy reference.
The center!ine trajectories of the heated plume are plotted with
respect to the horizontal (X/D) and vertical (Z/D) space coordinates for
discharge Froude numbers (F) ranging from 1 to 600. For a 90-degree dis-
charge angle, the centerline trajectory is along the vertical space coordinate
only and thus the excess temperature decay lines are given with respect to
that coordinate alone. Superimposed on these curves are constant width lines
that vary with discharge Froude number and the vertical space coordinate.
For discharge angles other than 90 degrees, two identical centerline trajec-
tory nomograms are given. Superimposed on the first are the constant excess
centerline temperature lines and on the second the constant plume width lines.
All trajectory lines are dash-marked. The spacing between the asterisks
on the centerline trajectories is equal to 20 diameters.
11
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TABLE I
Figure Numbers Corresponding to Plume Behavior
From Submerged Diffusers Discharging into
Stagnant, Non-Stratified Water
Dif fuser
RNN
Single
Jet
CJ
CD S-
r GJ
CX (/>
r~ 13
J? '<-
"zr.
"-T"
LO
II
Q
_J
O
II
cn
_j
o
Csl
II
Q
_J
0
CO
1!
0
1
Discharge Angle
0°
A-1,2
A-8,9
A-15,16
A-22,23
A- 29, 30
30°
A-3,4
A-10,11
A-17,18
A-24,25
A-31S32
60°
A-5,6
A-12,13
A-19,20
A-26,27
A- 33, 34
90°
A-7
A-14
A-21
A- 28
A-35
12
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B. BASIC ASSUMPTIONS
The nomograms have been developed from the governing mass, momentum,
and energy equations as applied to a buoyant thermal plume. The solutions
have been obtained after applying the well known integral method to the
differential equations. Detailed derivations, assumptions, and computer
programs are given in Reference 1 and are not repeated here.
Briefly, the integral technique requires that the velocity, tempera-
ture, and density profiles within the heated plume be specified so that
these quantities can be integrated over the plume cross-section. It also
requires that after a short developing distance the profiles maintain
their form throughout the trajectory of the plume. Numerous laboratory
experiments have demonstrated that the velocity profile is normally dis-
tributed near the discharge point. Similarly, temperature distribution
measurements in the heated plume demonstrate that the temperature and
density profiles are also normally distributed.
The temperature profile within the plume of a round jet is locally
flatter than velocity profile. The degree of the relative spread of the
temperature and density profiles as compared with the velocity profile
is reflected in a constant turbulent Schmidt number taken equal to 1.16
in this study.
In the analysis, ambient turbulence is assumed not to contribute
directly to dilution. It is assumed further that the rate of entrainment
of the ambient fluid entering the plume radially is proportional to the
local center!ine velocity and hence the incremental rate of volume flow
through the plume cross-section. The proportionality constant commonly
known as the entrainment coefficient is assumed equal to 8.2 percent for
the entire plume trajectory for a round jet.
13
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The analysis of Reference 1 assumes that the initial development
region between the source and the point where Gaussian profiles may
be used is about 6.2 diameters downstream. It is further assumed
that buoyant forces in this region are negligible. These assumptions
are good for Froude numbers above about 10 but at lower Froude numbers
the development length becomes less and the initial deflection due to
buoyancy becomes apparent. The curves presented in this section include
modifications to the development length for Froude numbers less than 10
as determined from Reference 2. This modification was applied uniformly
to all discharge angles even though Reference 2 was developed specifically
for the horizontal angle of discharge. The initial deflection angles for
the stated Froude numbers were modified as suggested in the above reference
for the horizontal discharge and by interpolation between zero and the
vertical for 30 and 60 degree discharge angles.
Multiple diffusers are handled in the analysis of Reference 1 by
considering the jets as round up to some transition region and as a
slot after that. The transition point used in this work was where the
entrainment of the round and slot jets were equal. This sudden transition
from one solution to another results in a slight irregularity in tempera-
ture at the transition point.
The entrainment coefficient and turbulent Schmidt number used here
for slot jet were .16 and 1.00, respectively. The sensitivity of the
solution to the accuracy of turbulent Schmidt number and entrainment
coefficient was tested by varying them plus and minus 10 percent from
the values given above. It was found that varying the entrainment coeffi-
cient by 10 percent changed the position of the plume by about 2 percent;
14
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the width and center-line temperature of the plume by about 10 percent.
Varying the turbulent Schmidt number by 10 percent changed the location
of the plume by about 5 percent, jet center!ine excess temperature by
about 10 percent, and plume width by about 1 percent.
15
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III. DISCHARGE INTO STAGNANT, STRATIFIED WATER
The nomograms that were prepared for this situation are
presented in Appendix B. Example 5 and example 6, cases 1 through 6,
Section VII, illustrate the use of the nomograms. A description
of the nomograms and basic assumptions underlying their development
are presented below.
A. GENERALIZED NOMOGRAMS
Figures B-l through B-48 of Appendix B are generalized nomograms
developed for single port or multiple port diffusers discharging into
a stagnant, stratified large body of water. The figure and identifica-
tion numbers corresponding to four different discharge angles, three
discharge elevations, and four diffuser port spacings are listed in
Table II for easy reference.
When the ambient is stratified, several other variables come into
play making it difficult to express solutions in the general form used
for the non-stratified case. These variables are density and temperature
profiles within the ambient and depth of discharge relative to the strati-
fied region.
Most large bodies of water are stratified to some degree, and even
weak stratification can have a profound effect on the plume behavior.
As the plume rises in a stratified environment, it initially entrains
cool water and carries it into warmer layers of water. The plume
temperature continues to drop while the temperature of its surrounding
continues to increase with elevation. Meanwhile, the plume decelerates
due to the loss of buoyancy, but continues rising because of its excess
momentum even when its center!ine temperature at a point along its
trajectory equals the local ambient temperature. This excess momentum
17
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TABLE II
Figure Numbers Corresponding to Plume Behavior From Submerged
Diffusers Discharging into a Stagnant, Stratified Ambient Water
Diffuser
RNS
MNS
L/D=1.5
MNS
L/D=10
MNS
L/D=20
ZS/D = 0
0=0° 0=30° 0=60° 0=90°
B- 1 B- 2 B- 3 B- 4
B-13 B-14 B-15 B-16
B-25 B-26 B-27 B-28
B-37 B-38 B-39 B-40
ZS/D = 10
0=0° 0=30° 0=60° 0=90°
B- 5 B- 6 B- 7 B- 8
B-17 B-18 B-19 B-20
B-29 B-30 B-31 B-32
B-41 B-42 B-43 B-44
ZS/D = 30
0=0° 0=30° 0=60° 0=90°
B-9 B-10 B-ll B-12
B-21 B-22 B-23 B-24
B-33 B-34 B-35 B-36
B-45 B-46 B-47 B-48
-------
carries the plume from this point to its terminal height; i.e., the
maximum height of rise, while the centerline temperature continues to
drop below the local ambient temperature.
Ap /D
The parameter, S. = . z may be used as a correlation parameter
a
for stratification, where Ap /D is the difference in density between the
initial jet and the ambient divided by jet diameter and Ap /AZ is the
a
local ambient density gradient. If the coefficient of volumetric expan-
AT /D
si on is assumed constant, this parameter can be written as S. = T . -,.
a
Table F-l in Appendix F provides relationships between the ocean water
density and temperature for several salinity levels. This table may be
used for estimating St<
Although the computer program developed in Reference 1 can handle
any arbitrary stratification profile, it is not practical to consider all
possible cases here. Many profiles can be approximated, however, by the
combination of a non-stratified region and a linearly stratified region
as shown in Fig. 6.
For the sample case shown on Fig. 6, the natural water density strati-
fication is shown as a solid line. Water density is constant from the
bottom to a depth of Z = 20 ft. above the bottom. From this point all
the way to the water surface the ambient water density decreases non-
linearly as indicated. The discharge is assumed to take place at Z = 10
ft. from the bottom. In order to use the nomograms for the analysis of
plume characteristics we must: (1) linearize the natural density curve
by drawing a best straight line through it, (2) find the slope of this
line for the calculation of S., and (3) estimate Z which is the depth of
the non-stratified water above the discharge point that results in the
19
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STRATIFICATION
1st Approximation, Z ^
2nd Approximation, Z «
Water Surface
20 ft
10 ft
~T
M
CO
Discharge
Level
Bottom
0) C
r- O)
M- O
(O CD
S- »->
l-i rx3
CO 3
M- +J
O C
o> -r-
C JO
o g
fxl =2
O
O -r-
C -M
C -M
O 03
Jvl i-
Ambient Water Density
Fig. 6 Linearization of the Natural Density
Stratification and the Definition of Z
20
-------
process of linearization. It is best to try more than one way to linearize
the density curve so that a range of possible solutions is obtained. Two
such approximations are indicated in Fig. 6 leading to values of Z and Ic
Si S2
for the first and second approximations, respectively.
The nomograms are presented for several values of Z and several slopes.
Both parameters are expressed in dimension!ess numbers. They are Z /D and
the stratification number S. , respectively. In this report values of Z /D
= 0, 10 and 30 and St = 100, 500, 1000, and 2500 have been considered.
Since it is not possible to present complete temperature-trajectory
solutions for all combinations, the results for discharge angles of 0, 30,
and 60 degrees are presented as follows: For each Froude number and strati-
fication parameter a trajectory is given which is terminated at the point of
maximum rise. Since the plume centerline temperature varies with Froude number
as well as with stratification number, and since four values of each parameter
are presented in a single nomogram, constant temperature lines similar to
those for non-stratified case (Appendix A) cannot all be drawn without causing
the chart to become overly complex. Only the 5 percent temperature lines,
ATc
that is -rtp- = .05, are drawn and appropriately marked for the S, they represent.
Alo
Additional information on temperature is provided by plus (+) marks on each
trajectory to show the plume centerline coordinate where the excess temperature
ATc
above ambient becomes zero, that is where -TJ =0. In order to obtain an idea
o
of the temperature decay along the plume in a typical situation, the reader
should refer to Figure 5.
21
-------
For a 90-degree discharge angle where the trajectory is vertical,
curves are presented giving the terminal height and the 5 percent excess
temperature point as functions of Froude number with S. as a parameter.
B. BASIC ASSUMPTIONS
The nomograms for this case have been prepared from the solution
of the same set of equations discussed in Section III-B and Reference
1. All basic assumptions of that section apply here as well. The only
exception is that the ambient water is assumed stratified with respect to
density. This stratification is assumed to be linear and could be the
result of temperature or salinity variations with depth.
It should be repeated here that the restriction just discussed is
imposed to facilitate presentation of generalized nomograms. It is not
a basic limitation. The computer program of Reference 1 allows for arbitrary
density as well as temperature profiles in the ambient water.
22
-------
IV. DISCHARGE INTO MOVING, NON-STRATIFIED WATER
The nomograms for discharge into moving, non-stratified ambient
water are presented in Appendix C. The 11 cases considered in examples
7, 8, and 9 (Section VII) illustrate the use of the nomograms. A
description of the nomograms and the basic assumptions underlying their
development are presented below.
A. GENERALIZED NOMOGRAMS
Figures C-l through C-30 of Appendix C are generalized nomograms
developed for a single port diffuser discharging into moving, non-
stratified ambient water. The figure numbers corresponding to four
different discharge angles (9) and a wide range of velocity ratios
(k) are listed in Table III for easy reference.
The discharge angles are referenced with respect to the horizontal
space coordinate, thus at zero discharge angle, the jet discharge and
ambient current are in the same direction. At a 90-degree discharge
angle, the jet discharge is vertical and perpendicular to the direction
of the ambient current.
The center!ine trajectories of the heated plume are plotted with
respect to horizontal (X/D) and vertical (Z/D) space coordinates for
selected discharge Froude numbers. Superimposed on the center!ine tra-
jectories are the excess center!ine temperature lines and constant plume
width lines, each on a separate chart for a given velocity ratio.
The limited range of Froude numbers and velocity ratios presented
reflect the scarcity of data with ambient current. The absence of
generalized nomograms for multiple diffusers (MCN) is also evidence of
a lack of appropriate data.
23
-------
TABLE III
Figure Numbers Corresponding to Plume Behavior From Single Port
Submerged Diffusers Discharging into Moving, Non-Stratified Water
k
0.5
1
2
4
6
12
16
Discharge Angle
Co-flow
9=0°
C-1,2
C~3,4
C-5,6
C-7,8
C-9,10
Cross -flow
0=90°
C-19,20
C-21,22
C-23,24
C-25,26
C-27,28
C-29,30
9=30°
C-11,12
C-13,14
9=60°
C-15,16
C-17,18
24
-------
The reader is urged to carefully study the basic assumptions that
follow before attempting to use the nomograms.
B. BASIC ASSUMPTIONS
The nomograms in this set have been drawn from three different
sources and thus are subject to different limitations. However, they
are all limited to uniform velocities in the ambient current. The
three sources are: Reference 3 for co-flow (6 = 0°) data, Reference
4 for the cross-flow (9 = 90°) data, and References 5 and 6 for the
analysis of the remaining (i.e., 30 and 60 degree) nomograms.
The co-flow data obtained from Reference 3 are from a compre-
hensive set of experiments with heated and salt water jets performed
in a turbulent channel flow. The discharge Froude number and the jet
to ambient velocity ratio (k) were varied among a wide range of values
shown by the solid line in Fig. 7. Empirical equations developed by
correlating the experimental data were derived for plume width, center!ine
temperature and plume trajectory. The correlations were used in the
preparation of the nomograms for a range of parameter space both inside
and outside the experimental range. The dashed line in Fig. 7 show the
extent of extrapolation.
Reference 4 presents a comprehensive set of cross-flow (9 = 90°)
data obtained in laboratory experiments. A wide range of discharge
Froude numbers and jet to ambient velocity ratios (k) were tested. The
range of parameter space for k and Froude number are plotted in Fig. 8
as indicated by the solid line. The data from these experiments were
correlated to form expressions for the centerline temperature, the plume
width and the plume rise. The correlations were used in the preparation
25
-------
(X.
UJ
CO
UJ
o
:D
o
Cr~
U-
2 4 6 8 10
Discharge Velocity
Anibient Velocity
Fig. 7 The Range of Experimental Parameters and the Extent of
Extrapolation Reported in this Volume for Co-flow Data
-------
160
140
120
100
o;
LU
CO
^ 80
p
o
o;
60
40-
20 b
L.
EXTRAPOLATION
EXPERIMENTAL RANGE
6
k =
8 10
Discharpe Velocity
Ambient Velocity
12
14
16
Fig. 8 The Range of Experimental Parameters and the Extent
of Extrapolation Reported in this Volume for
Cross-flow Data
27
-------
of nomograms for a range of parameter space both inside and outside
the experimental range. The limits of the extrapolation are plotted
in dashed lines in Fig. 8.
The use of nomograms for co-flow and cross-flow outside the
experimental range should be made with caution and the results should
be regarded as qualitative.
Experimental data are scarce for the intermediate discharge angles
of 30 and 60 degrees with respect to the direction of an ambient current.
However, an attempt has been made in this volume to gain a qualitative
understanding of the plume behavior from the interpolation between the
co-flow and cross-flow data. The interpolation scheme used for this
purpose was the analysis reported in References 5 and 6. It is outside
the scope of the present work to discuss at length the analytical methods
cited and the procedure followed to use such analysis for interpolation.
While a brief discussion is outlined below, the reader should keep in
mind the qualitative nature of all results obtained from interpolation.
The analysis of References 5 and 6 offers the most comprehensive
treatment to date of the submerged jet discharge. It handles generalized
space coordinates for a three dimensional plume and it includes generalized
entrapment functions that depend on the local Froude number, plume center-
line velocity, and the local plume orientation.
This analysis has been shown to have general agreement with a wide
range of experimental data. It agrees well with the experimental data
for cross-flow of Reference 4 but only at high values of k. The analysis,
however, does not agree with the co-flow data of Reference 3. In fact
28
-------
it even fails to predict the proper qualitative trend of the plume
behavior with respect to k and Froude number for co-flow discharge.
Consequently, the analysis of Reference 5 and 6 cannot be used directly
for predicting the plume behavior for the intermediate angles of 30
and 60 degrees.
The approach used herein was to force the analysis of References
5 and 6 to agree with data for co-flow discharge as closely as possible
without disrupting the acceptable qualitative agreement it is already
capable of with respect to cross-flow discharge. Once this was accomplished
satisfactorily, the analytical model was used to predict the plume behavior
between the co-flow and cross-flow discharge angles of 30 and 60 degrees.
In other words, the analytical model now was used as a powerful interpolat-
ing scheme between two sets of experimental data.
It should be of interest to some readers to know that the analysis
of References 5 and 6 was fitted to the experimental data of Reference
3 by manipulating the ambient turbulence terms that were originally
neglected in those calculations. This points to an intellectually curious
subject, namely; that the ambient turbulence terms while not affecting
the cross-flow prediction, does affect and indeed improve the co-flow
prediction in the analysis of References 5 and 6. This observation has
been verified experimentally in the cross-flow analysis of
Reference 4 and the recent co-flow data of Reference 3, respectively.
There is no published comprehensive analysis of the multiple jet
diffuser system with ambient current. The available data are scattered
and fragmentary. It is noted, however, that the behavior of a multiple
port diffuser up to the point of plume interaction can be obtained from
the analysis of a single port. This is demonstrated in examples 7 and 9
of Section VII.
29
-------
V. DISCHARGE INTO MOVING, STRATIFIED WATER
The nomograms for discharge into moving, stratified ambient
water is presented in Appendix D. Example 10, cases 1 through 6, of
Section VII, illustrate the use of the nomograms. A description of
the nomograms and the basic assumptions underlying their development are
presented below.
A. GENERALIZED NOMOGRAMS
Figures D-l through D-16 of Appendix D are generalized nomograms
developed for single port diffusers discharging at 0, 30, 60, and 90
degrees into moving and stratified ambient water. The figure numbers
corresponding to two different jet to ambient velocity ratios and two
ambient stratification numbers are listed in Table IV for easy reference.
The discharge angles are referenced with respect to the horizontal
space coordinate so that at zero degree discharge angle, the jet dis-
charge and the ambient current are in the same direction. At 90 degrees
discharge angle the jet is perpendicular to the direction of the ambient
current.
The nomograms are presented in pairs, giving the temperature chart
and the width chart on consecutive figures. For each discharge angle,
the center!ine trajectory of the plume is plotted with respect to the
horizontal and vertical space coordinates. If the maximum height of
rise occurs at less than 200 diameters downstream of the discharge, it
is marked by a cross in the nomogram, and the trajectory is terminated.
Superimposed over the center!ine trajectories are the constant
center!ine excess temperatures and constant width lines. If the plume
31
-------
TABLE IV
Figure Numbers Corresponding to Plume Behavior for Diffuser
Discharging into Moving and Stratified Ambient Water
st
100
500
k =
F = 10
D-1,2
D-9,10
-.
= 2
F = 30
D-3,4
D-11,12
k =
F = 30
D-5,6
D-13,14
= 4
F = 75
D-7,8
D-15,16
32
-------
has entrained enough cool waters from the lower elevations so that its
centerline temperature is less than the local ambient temperature, then
an appropriate negative excess temperature is designated.
The limited range of Froude numbers, stratification numbers, and
velocity ratios reflect the uncertainty in these data due to lack of
adequate experimental verification. The reader is urged to study the
basic assumptions that follow before attempting to use the data.
B. BASIC ASSUMPTIONS
All nomograms presented in this section were obtained analytically
from the modified programs of References 5 and 6 and thus are subject
to all limitations discussed in Section IV-B concerning the intermediate
injection angles of 30 and 60 degrees. Unlike the development of Section
IV where comprehensive experimental data for co-flow and cross-flow were
available and were used to interpolate for 30 and 60 degrees, such data
for stratified cases are scarce indeed and thus all nomograms of this
section should be used with caution.
33
-------
VI. VERTICAL DISCHARGE INTO NON-STRATIFIED STAGNANT SHALLOW WATER
(A SPECIAL CASE OF RNN)
The nomograms for the discharge into a non-stratified,
stagnant, shallow body of water is presented in Appendix E. The four
cases considered in example 11 of Section VII illustrate the use of
the nomograms.
A. GENERALIZED NOMOGRAMS
Figures E-l through E-6 of Appendix E are nomograms developed for
a single port diffuser discharging vertically upward into a shallow
body of water. Only a selected number of discharge conditions and Froude
numbers are presented. The corresponding figure numbers of these cases
are listed in Table V. Nomograms are given for the following types of
information: (1) the centerline excess temperature in relation to the
ambient from the discharge point to the water surface, (2) surface water
temperature directly above the diffuser at the center of the boil and
along concentric circles around this point, and (3) isotherms throughout
the plume.
The discharge depth enters these calculations as a new parameter
and it strongly affects the results. No attempt has been made at this
time to include this parameter in a unifying correlation function, nor
has an effort been made to cover a wide range of discharge conditions
and ambient stratification.
B. BASIC ASSUMPTIONS
A generalized submerged plume program that adequately analyzes the
combined subsurface transition and the surface spreading zones of the
plume is not yet available. The nomograms of this section are the results
35
-------
TABLE V
Figure Numbers Corresponding to Plume Behavior for a Single Port
Diffuser Discharging Vertically Upward into Non-Stratified,
Stagnant, Shallow Body of Water
Discharge
Depth
Z/D
5
8.4
10
40
F = 1, 5, 25, 100
Center! ine
Temperature
E-3
E-2
E-l
Surface
Temperature
E-4
Isotherms
F = 45
E-5
F = 51
E-6 \
36
-------
of an analysis of the transition zone of the submerged plume as it
reaches the water surface. The analysis is specifically suitable for
evaluating the plume behavior from a very large diffuser discharging
vertically in shallow water. This is a situation where effects of
water surface become important and analyses of previous sections become
invalid. This is particularly true when submergence is on the order of
10 diameters or less. Since numerous examples of this type of diffuser
are found among coastal power plant discharges, a special consideration
of the problem is in order.
The model for shallow discharge used here was developed for EPA
and is described in Reference 7. It consists of a finite difference
solution of a two-dimensional axisymmetric plume in ambient water that
is at rest. Like many mathematical models of fluid flow phenomena,
this model requires information on the turbulence characteristics of
the flow field and the results are altered for various assumptions made
on that input. It suffices to state, however, that as a consequence
of the input variables used in this model reasonable predictions are
obtained.
37
-------
VII. EXAMPLE PROBLEMS
Numerous examples are given in this section to familiarize the
reader with the use of the nomograms. Even though an attempt was made
to develop more or less realistic problem statements, the examples should
not be construed as representing a preferred design or recommended tempera-
ture zone. The numbers in these examples have been conveniently rounded off.
Example Problem 1
Given:
A 500 MW nuclear power plant is located on a open coastline. A
single port submerged diffuser is used to discharge the condenser cooling
water into the ocean. The following design data apply:
Q
a. Waste heat to cooling water = 3.2 x 10 Btu^hr
b. Condenser AT (AT ) = 20° F
c. Discharge angle 6 = 0.0°
d. Discharge velocity U. = 10 ft/sec
e. Ambient water is stagnant and non-stratified (RNN), T. = 50° F
a
and salinity = 25 ppt
f. Discharge depth IQ = 200 ft
Determine:
1. The location of the plume where the centerline temperature is
2° F above the ambient (i.e., 52°).
2. The centerline temperature and plume width when the plume
reaches the surface.
39
-------
Solution:
Part 1
The discharge Froude number is obtained first from the above infor-
mation as follows:
3.2 x 109 Btu/hr
C/(PCA Q) = (^ 1b/ft3)(1.0 Btu/lb-°F)(20°F)(3600 sec/hr)
Q - 700 ft3/sec
A - n/U - 70Q ft3/sec = 70 ft2
A 4/Uj 10 ft/sec /U Tt
D = (4A/u)1/2 = (4 x 70/3.14)172 = 9.5 ft
where Q is the volumetric flow rate of water and U. is the discharge
J
velocity in cfs and fps respectively, H is the waste heat load in
Btu/hr, p is the water density, c is the heat capacity of water usually
taken as unity and AT is the initial temperature difference, or the
condenser AT.
Ap -i/o Ap 1/2
The Froude number equals l)./(- gD) , where (- g) ' = G ~ 3.7
is obtained from Fig. F-l in Appendix F for S = 25 ppt, T = 50° F and
a
ATQ = 20° F.
Thus, F = GU. D"1/2 = 3.7 x 10 x (9.5)"1/2
J
F = 12
For a single port diffuser discharging into stagnant, non-stratified
water (RNN) with a discharge angle of zero with respect to the horizontal,
use nomogram A-l to find location of the plume where the centerline tempera-
ture is 2° F above ambient.
40
-------
The center!ine excess temperature ratio corresponding to 2° F is,
ATc
c- = 2/20 = 0.1
AT
ATc
Entering Fig. A-l at F = 12 and ~- = 0.1, the location of the
o
plume centerline is found to be
X/D = 29 and Z/D - 15
Therefore, since D = 9.5 ft,
X = 275 ft and Z = 142 ft (answer to Part 1)
Part 2
Since the discharge depth is 200 ft and D = 9.5 ft, water surface
is reached when Z /D = 200/9.5 = 21.
ATc
Fig. A-l at Z/D = 21 and F = 12 gives a value of ^p of about 0.08
o
at the surface. Therefore, the centerline excess temperature as it reaches
the surface is 50 + 1.6 - 51.6° F.
Entering Fig. A-2 at Z/D =21 and F - 12, the value of W/D is found
to be about 15. Thus, the plume width at the surface is 15 x 9.5 - 142 ft.
It should be noted the nomograms, except Appendix E, exclude the
effect of surface interference. Thus, surface temperatures calculated
from these nomograms in this and other examples are underestimated.
41
-------
Example Problem 2
Given:
A 1000 MW nuclear power plant is located on an open coastline. A
submerged single port diffuser is used to discharge the condenser cooling
water. The following design data apply:
g
a. Waste heat to cooling water = 6.4 x 10 Btu/hr
b. Condenser AT (AT0) = 20° F
c. Discharge angle 0 = 30°
d. Discharge velocity U. = 10 ft/sec
J
e. Ambient water is stagnant and non-stratified, Ta = 50° F and
salinity = 25 ppt
f. Discharge depth ZQ = 150 ft
Determine:
1. The location of the plume when the centerline temperature is
2° F above ambient.
2. The centerline temperature and plume width when the plume reaches
the surface.
Solution:
Part 1
The Froude number is calculated following the procedure of problem 1,
i-e., Q
6.4 x 10* Btu/hr
(64 Ib/ft3)(1.0 Btu/lb-°F)(20° F)(3600 sec/hr)
Q * 1400 ft3/sec
A = HOP ft3/sec _ . 2
A 10 ft/sec " 14° ft
D = (4 x 140/3.14)1/2 = 13.3 ft
42
-------
F = 3.7 x 10 x (13.3)"1/2 * 10
For a single port diffuser discharging into stagnant, non-stratified
water (RNN) with a discharge angle e = 30°, use nomogram A-3 to find loca-
tion of plume when centerline temperature is 2° F. Entering Fig. A-3 at
F = 10 and ^Jc = 2/20 = 0.1, it is found that
AT0
X/D * 20 and Z/D « 25
Since D = 13.3 ft, therefore
X * 270 ft and Z = 330 ft
Note that since the total depth (Z ) is only 150 ft, the plume cannot
extend to 330 ft above the discharge. Thus, the plume centerline tempera-
ture will exceed 2° F above the ambient at all points along its trajectory.
If the AT were restricted to 2° F before or at the surface, other discharge
configurations or discharge conditions than specified in this problem would
be required.
Part 2
The plume centerline temperature at the surface is found from Fig. A-3
for F = 10 and Z/D = 150/13.3 =11. The percent excess temperature at this
location is ATc = 0.25. Therefore, ATr = 0.25 x 20 = 5° F giving a plume
iTo
centerline temperature at the surface of 50 + 5 = 55° F.
The width of the plume is determined from Fig. A-4. Entering this
figure with Z/D = 11 and F = 10, it is found that
W/D * 6 or W = 6 x 13.3 * 80 ft
Variations of Problem 2 for different discharge angles and discharge
volume from a single diffuser have been solved to see if discharge condi-
tions other than the single port at 30 degrees could meet the 2° F surface
43
-------
temperature difference requirement. The results for the above example
and five additional cases examined are tabulated in Table VI. It is
seen that case number 4 satisfies the above requirement. This case is
for two ports each discharging 700 cfs horizontally. The ports are
located far enough apart so that their plumes do not interact. This
condition is satisfied if the spacing between ports is made greater
than the predicted plume width at the water surface.
TABLE VI
Variations on Problem 2 Showing Several Discharge Conditions
Case
No. of Ports
Port Diameter (ft)
Froude Number
Discharge Angle 6 (degree)
Plume Location for
ATc = 2° F
Tc at Surface (°F)
Width at Surface (ft)
Figures Used
Conditions Met?
:gree)
X(ft)
Z(ft)
1
1
13.3
10
30
270
330
5
80
A-3,4
No
2
1
13.3
10
0
320
230
2.4
134
A-1,2
No
3
1
13.3
10
90
0
430
8
67
A-7
No
4
2*
9.5
12
0
275
142
1.9
114
A-1,2
Yes
5
2*
9.5
12
30
200
230
3.2
76
A-3,4
No
6
2*
9.5
12
90
0
300
6
60
A-7
No
*The plumes from the two ports are assumed to be non-interacting.
44
-------
Example Problem 3
Given:
a. Discharge Froude No. F = 15
b. Discharge angle 6 = 60°
c. Initial temperature difference AT = 20° F
d. Single port diffuser
e. The receiving water is stagnant and non-stratified (RNN)
Determine:
1. The location and width of the plume where the centerline tem-
perature 1s 2° F above the ambient.
2. At this location, find the radial distance from the center of
the plume to the point where the plume has a temperature which is 1° F
warmer than the ambient.
Solutions
Part 1
For the dilution to a centerline excess temperature AT = 2° F, the
AT ?
dimensionless temperature ratio is <1 = ^= 0.1. Using Fig. A-5 for
RNN, a discharge angle (6) of 60 degrees, a Froude Number F = 15, and a
centerline excess temperature ratio c = o.l, one obtains X/D - 14 and
AT0
Z/D - 30. Using these trajectory values with Fig. A-6 gives W/D = 13.
Part 2
In order to solve for the radial distance at this point in the tra-
jectory to the 1° F excess temperature line, the Gaussian distribution
curve given on Fig. F-2 is used. This figure presents the approximate
radial temperature distribution within the plume as a fraction of the
maximum excess temperature at the center. The radial parameter n = 4r/W,
45
-------
where r is the radial distance from the center of the plume and W is the
local plume width (or diameter). T -T is the excess temperature within
r 3
the plume which depends on the radius and T -T is the center!ine excess
C cl
temperature at this point in the trajectory. For this problem, r a _
V^T
1/2 = 0.5. At this value on Fig. F-2, the value of n is found to be 1.2.
Using n = 4r/W and W/D = 13 from Part 1 one finds the desired value of the
radial distance from the center of the plume to be r/D - 1.2 x 13/4 = 4.5.
The procedure in this example can be used to generalize all tempera-
ture and width nomograms presented in this volume. Namely, based on the
center!ine temperature data of nomograms and the Gaussion distribution
curves of Fig. F-2, the temperature at an arbitrary radial distance in a
plume cross-section can be found.
46
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Example Problem 4
Given:
The problem statement is the same as given in Problem 2 except
a multiple port cliff user is used that consists of a single row of 10
equal jets spaced 10 diameters apart, i.e., MNN with L/D = 10.
Solution:
Part 1
From Problem 2, the total volumetric flow rate and the total dis-
o p
charge area are Q = 1400 ft /sec and A. . ^ = 140 ft , respectively.
For ten equal ports, the discharge area per port and the single port
diameter are:
A' = No. ofports = 140/1° = 14 ft2 Per port
D = (4 x 14/3.14)1/2 = 4.2 ft
With this information and for the values of G and U. of Problem 2,
J
the discharge Froude number becomes:
F = 3.7 x 10 x (4.2)"1/2 = 18
The plume location when the centerline excess temperature is 2° F
above ambient is obtained from Fig. A-17 for a multiple port diffuser
with L/D = 10 and e = 30° discharging into a stagnant, non-stratified
ambient (MNN L/D =10). Entering this figure with F * 18 and £ =
ATO
0.1, the location of the plume is found to be at
X/D * 25 and Z/D = 20
47
-------
For a port diameter of 4.2 ft, the absolute center! ine location is
at X = 105 ft and Z - 85 ft measured from the discharge point.
Part 2
With a total depth of 150 ft and a port diameter of 4.2 ft, the
dimensionless depth is ZQ/D - 150/4.2 = 36. Entering Fig. A-17 with
Z/D = 36 and F * 18, one finds the center! ine excess temperature ratio
AT
Therefore, the excess temperaure in the center of the plume as it
reaches the surface is 0.06 x 20 = 1.2° F.
Entering Fig. A-18 with Z/D * 36 and F * 18, it is found that
W/D = 25
Therefore, the width of the plume as it reaches the surface is
25 x 4.2 = 105 ft
The approximte length of the plume can be found from the total
diffuser length plus the growth of the plume on the ends as follows:
Length - (N - 1) (L/D) (D) + W
- (9) (10) (4.2) + 105 = 480 ft
Variatons of Problem 4 have been solved and results listed in
Table VII, where Case 1 is the problem just discussed. Similar procedure
to the latter has been used throughout. As a point of interest when
comparing the results of this problem with Problem 2, the 2° F temperature
difference at the surface required in that problem is satisfied in all
cases here by using a multiple port diffuser.
48
-------
TABLE VII
Variations on Problem 4 Showing Several Discharge Conditions
and Diffuser Jet Spacings
(Plant Size 1000 MW)
Case
No. of Ports
Port Dia. D (ft)
Port Spacing L/D
Froude Number
Discharge Angle e (degree)
Diffuser Length (ft)
Plume Location at X(ft)
ATc = 2° F Z(ft)
AT at Surface °F
c
Plume Width at Surface W(ft)
Plume Length at Surface (ft)
Figure Used
1
10
4.2
10
18
30
378
105
85
1.2
105
. 483
A-17
A-18
2
10
4.2
10
18
0
378
127
30
1.0
140
518
A-15
A-16
3
10
4.2
10
18
90
378
0
135
1.8
64
442
A-21
4
100
1.34
1.5
30
30
200
96
88
1.4
140
340
A-10
A-ll
5
100
1.34
1.5
30
0
200
134
47
1.3
174
374
A-8
A-9
6
100
1.34
1.5
30
90
200
0
134
1.6
100
300
A-14
49
-------
Example Problem 5
Given:
Warm water at 75° F is to be discharged from a multiple port
diffuser from the bottom of a stratified lake. The following design
conditions apply:
a. The diffuser consists of a single row of nozzles, 1.0 ft in
diameter, spaced 1.5 feet apart.
b. Discharge angle 6 = 0.0°
c. Discharge Froude number is calculated to be 25
d. The temperature variation within the lake is represented by the
curve shown below
O
c;
t- OJ
>
> O
-Q
I Water Surface
GO
40
20 »
Q ,
50 51 52 53 54
Ambient Temperature °F
Determine:
1. The maximum height of rise of the plume.
2. The location of the plume when the difference between the plume
centerline and local ambient temperatures is 5 percent of the initial
temperature differences, i.e., ^Il = 0.0,5.
o
50
-------
Solution:
Part 1
The stratification number S, and the dimensionless distance from
discharge to the start of stratification Z /D are two parameters in
this problem that must be calculated following the procedure outlined
in Section III and Fig. 6 in the text. Accordingly, two possible approxi-
mations to the given stratification for this problem are shown in the
sketch below.
80 r
OJ
o
.a
O
c cu
to 01
O
(SI
o
O)
o
60
40
20
R'ater Surface
0 I-
50 51 52 53 54
Ambient Temperature °F
For approximation I, stratification is assumed linear from discharge
to the surface, and the above mentioned parameters are:
% - *»
ATa/AZ
and
ZS/D = 0
51
-------
For approximation II, stratification is assumed to be linear after
an initial 10 ft. region that is non-stratified and the alternate parameters
of the problem are:
AT /D
c
S
t " AT7AZ ~ O5770 ~
a
and ZS/D = 10
Using Fig. B-13 for stratification I, MNS L/D =1.5, ZS/D = 0, Q = 0, and
F = 25, the terminal height is found to be at Z/D ~ 75.
Using Fig. B-17 for stratification II MNS L/D =1.5,ZS/D = 10 9 = 0,
and F = 25, the terminal height is found at about Z/D -- 70. Note that
in this case curves fora stratification number of 410 are not given and
thus interpolation was necessary.
Part 2
ATr
To determine the location where ^-j- =?.0b, enter the fiaures with
° ATc
F = 25 and locate where the dashed line representing -y- =0.05 crosses
the trajectory line for a given stratification.
ATr
For approximation I with S. = 500, the location of -~ =0.05 is
AiQ
found from Fig. B-13 to be at X/D - 8?. and Z/D 26 The location where
the plume center! ine temperature reaches the local ambient temperature
is found from the (-*) mark on the trajectory curve for F -- 25, S, = 500.
This is at X/D * 100 and Z/D =M3.
For approximation II using Fig. B-i7 with F = 25, St = 410 the loca-
tion of flic uC<05 1s found to ),,, ^prrcixirnateiv X/D -- 82 and Z/D ^ 2o.
-------
Example Problem 6
Given:
The condenser cooling water from a 500 MW fossil-fueled power plant
is to be discharged horizontally from a single port diffuser into coastal
ocean water at a depth of 100 ft. The following design data apply:
Q
a. Waste heat to cooling water = 1.9 x 10 Btu/hr
b. Condenser AT (ATQ) = 25° F
c. Discharge angle 9 = 0.0°
d. Discharge velocity U. = 10 ft/sec
-J
e. Salinity = 40 ppt
f. The ambient water is stagnant and is stratified. The stratifi-
cation is approximated by the graph given below.
Determine:
1. The maximum height of the plume rise.
2. The location of the plume when its center!ine temperature is
1.25° F above the local ambient temperature.
\7
01
CO CO
r- S-
Q ro
f O
-------
Solution:
Parts 1 and 2
The diffuser port diameter (D) and the discharge Froude number
are calculated following the procedure outlined in Problem 1, i.e.,
Q = 1.9 x ID9 Btu/hr . 330 ft3/sec
(64 Ib/ft3)(1.0 Btu/lb-°F)(25°F)(3600 sec/hr)
. _ 330 ft3/sec _ -3 ft2
A ~ 10 ft/sec" JJ Tt
D =
(4 x 33/3.14)1/2 = 6.5 ft
F = GU.(D)"1/2 « 3.0 x 10 x (6.5)"1/2 * 11.7
J
Following the procedure of Section III, the stratification number
$t and dimensionless distance from discharge to the start of stratifica
tion number Z /D are obtained from the information given on the graph
for approximating the ambient stratification. Thus,
and ZS/D = 25/6.5 = 3.8
. _
AT/AZ " (55-50)7(100-25)
Since ZS/D is 3.8, interpolation is required between the nomograms
for ZS/D = 0.0 and ZS/D =10. As a first approximation, however, it is
assumed that Z$/D = 0.0.
For ^Jc. = 1.25/25 = 0.05, F = 10, and extrapolating to S. = 58,
ATo
Fig. B-l gives a Z/D of about 5, and X/D of about 18, and a maximum height of
rise Zmax/D of about 10. Therefore, the desired 1.25° F excess tempera-
ture is located about 33 ft above and 120 ft horizontally away from the
54
-------
point of discharge. The maximum height of rise is about 65 ft above
discharge.
Variations of Problem 6 have been solved using the nomograms in
Appendix B. The results are tabulated in Table VIII where Case 1 was
just discussed. Note that multiple as well as single port diffuser
problems are treated in Table VIII.
If the reader finds his problem outside the range of parameters
covered in nomograms as in the above, he may either choose the next
closest parameter or come nearer to the answer by extrapolation. The
extrapolation procedure is arbitrary. In the above example Z /D,
* if id X
for instance, was found by plotting the terminal heights against $t
for St = 2500, 1000, 500 and 100 all for F = 10 as obtained from B-l.
The extrapolation to S. = 58 led to the result given for Zrnax/D.
55
-------
TABLE VIII
Variations on Problem 6 Showing Several Diffuser Configurations
and Discharge Conditions
Case
No. of Ports
Port Dia. D (ft)
Port Spacing L/D
Froude Number F
Stratification
Number S.
ZS/D
Discharge Angle 9 (degree)
Plume Location at
ATr M Z(ft)
AT; =0-05 x(ft)
Terminal Height (ft)
Figures Used
1
1
6.5
12
58
0
0
33
120
72
B-l
1
1
6.5
12
58
2
10
2
10
21
188
3
100
.64
10
38
580
4
100
.64
1.5
38
580
5
1
6.5
12
58
6
10
2
10
21
188
10
38
38
30
26
90
14
45
90
**
10
90
43 98 50
35
**
60 45 77
B-29 B-33* B-22 B-4a&b B-32a&b
*Fig. A-15 could be used to give more details for Z/D < 38 since for
Case 3 the fluid is assumed to be non-stratified below Z/D of 38
and the desired dilution to 1.25° F occurs at a Z/D of about 30-
**Plume reaches the water surface
56
-------
Example Problem 7
450 cfs of warm water is discharged into a river in the general
direction of flow at an angle of 30 degrees from the horizontal through
12 equally spaced nozzles. The following conditions apply:
a. The initial temperature difference AT = 30° F
b. Discharge velocity U. = 10 ft/sec
J
c. Average velocity of the ambient water U =2.5 ft/sec
d. The river is 40 ft deep and has a uniform temperature of 50° F
Determine:
1. The nozzle spacing so the jet plumes will not merge by the time
they reach the river surface.
2. The center!ine temperature at the surface.
Solution:
Parts 1 and 2
The port area (A1) and diameter (D) of each jet are calculated from
the data given as follows:
Q = 450 ft3/sec A1 = 45/12 = 3.75 ft2/port
2
A = 4^Q ft/secC = 45 ft2 D = (4 x 3.75/3.14)1/2 = 2.2 ft
From Fig. F-l with T = 50° F, ATrt = 30° F and fresh water, the
3 U
G factor is found to be about 3.2. Therefore, the Froude number is
F = 3.2 x 10 x (2.2)"1/2 = 21.5 or F ^ 20
The jet-to-ambient velocity ratio (k) is:
k = U./U = 10/2.5 = 4.0
J o
57
-------
The nomograms for discharge into non-stratified water with a current
are found in Appendix C. For k = 4 and 6 = 30°, Figures C-13 and C-14
should be used. If the river is 40 ft deep, Z/D = 40/2.2 - 18 at the
surface. Entering Figures C-13 and C-14 at Z/D - 18 and F - 20, the values
of W/D and ^£ at the surface are found to be 11 and 0.02, respectively.
*To
If the plumes are not to merge, then the jet spacing (L) should
exceed the plume width at the surface. Thus, L should exceed 2.2 x 11 -
24 ft. Since the initial temperature difference was 30° F, the center!ine
excess temperature of the plumes will be 0.02 x 30 = .6° F when they reach
the surface. The location of the plumes when they reach the river surface
is found from either Fig. C-13 (or C-14) to be at X/D - 115 which is about
250 ft downstream from the discharge point.
Variations of Problem 7 have been solved using the same procedure
outlined above. The results are tabulated in Table IX.
TABLE IX
Variations on Problem 7 Showing Several Diffuser Configurations
and Discharge Conditions
456
5 5 12
3.4 3.4 2.2
40 40 40
0 90 90
17.3 17.3 21.5
448
95 22 18
0.3 1.5 1.5
665 150 49
C-7 C-21 C-25
C-8 C-22 C-26
58
Case
No. of Ports
Port Diameter D (ft)
River Depth (ft)
Discharge Angle 6 (degree)
Froude Number F
k
Port Spacing L (ft)
ATc at Surface (°F)
Plume Location at
Water Surface (ft)
Figures Used
1
12
2.2
40
30
21.5
4
24
0.57
250
C-13
C-14
2
12
2.2
40
0
21.5
4
Off chart
<0.3
>440
C-7
C-8
3
12
2.2
40
90
21.5
4
23
0.6
308
C-21
C-22
-------
Example Problem 8
Warm water is discharged vertically from the bottom of a river at
a velocity of 10 ft/sec through a 5.0 ft diameter pipe. The discharge
Froude number is 20. The river at this location is deep, non-stratified
and has an average velocity of 1.0 ft/sec.
Determine:
1. The river depth required so that the center!ine excess tempera-
ture of the plume will not exceed 2.0 percent of the initial temperature
difference.
2. The plume width at this point.
Solution:
Parts 1 and 2
Discharge diameter and Froude number are given:
D = 5.0 ft
F = 20
The jet-to-ambient velocity ratio is
k = U./U = 10/1 = 10
J ^*
The nomograms for discharge into a moving, non-stratified ambient
(RCN) are found in Appendix C. Since RCN plots for 6 = 90° are given for
k = 8 and 12 but not for k = 10, interpolation between the two values of
k is required. Entering Figs. C-25 and C-27 with ^I
-------
The results of variations to this problem with different values of
F, k, and e are presented in Table X. Note that D is held constant and
thus variations in F reflect the effects of different ambient as well as
discharge conditions.
TABLE X
Variations on Problem 8 Showing Several Discharge Conditions
Case
Froude Number F
Port Diameter D (ft)
Velocity Ratio k
Discharge Angle f
Plume Location
at AT^
" AT =°'°2
0
Width at
ATr
~ = 0.02 W(ft) 65 " 80 113
o
Figures Used
(ft)
6 (degree)
X[ft)
z(ft)
1
20
5
10
90
185
155
2
20
5
4
0
650
38
3
50
5
8
90
540
150
4
50
5
4
0
500
15
C-25
C-26
C-27
C-28
C-7
C-8
C-25
C-26
C-7
C-8
60
-------
Example Problem 9
Given:
A 1000 MW nuclear power plant discharges its cooling water at 20° F
above ambient at a velocity of 10 ft/sec through three ports spaced 40 ft
apart. River conditions are as follows:
a. Depth = 40 ft
b. Temperature = 50° F
c. Velocity UQ = 2.5 ft/sec
d. The discharge is horizontal in the direction of the current
(co-flow).
Determine:
1. If the plumes merge before they reach the surface.
2. The downstream plume location where the centerline temperature
is, at most, 1° F above the ambient.
Solution:
Part 1
The port diameter (D) is calculated following the procedure outlined
for Problem 2 for a 1000 MW power plant with ATQ = 20° F.
Q = 1430 ft3/sec
A = 143 ft
For three equal ports, the area per port is
A' = 143/3 - 47 ft2
D = (4 x 47/3.14)1/2 - 7.7 ft
For fresh water with AT = 20° F and Ta = 50° F, the G factor is
o a
found from Fig. F-l to be about 4.5. Therefore, the discharge Froude
number is F = 4.5 x 10 x (7.7)"1/2 = 16.
61
-------
The jet-to-ambient velocity ratio is
k = U./U = 10/2.5 = 4
J V
For a river depth of 40 ft and a jet diameter of 7.7 ft, the surface
is at Z/D = 5.2, For discharge into a moving, non-stratified ambient,
use the nomograms in Appendix C (RCN). Entering Fig. C-8 at Z/D * 5 and
F * 16 gives a value of W/D a 10. This gives a plume width VI * 10 x 7.7
- 77 ft which is greater than the 40 ft jet spacing, indicating that the
plumes have already merged at the water surface.
A plume width of W/D = 40/7.7 = 5.2 (i.e., where the plume width
equals the port spacing) is obtained at Z/D =< 2-0- This is where the plumes
start to merge.
Part 2
ATc
Entering Fig. C-7 with Z/D = 2.0 and F = 16 gives a value of ^p =
o
0.15 or ^TC = 3° F. This indicates that the centerline excess temperature
of 1.0° F occurs after the plumes have started to merge. Since information
on merging jets in a current are not presently available, only an approxi-
mation can be made as to where the lower temperature will be reached.
The exit ports would have to be 77 ft apart to prevent the plumes
from merging by the time they reached the surface. If this were the case,
AT
a 1° F excess temperature where -^ = 0.05 is found from Fig. C-7 to
o
occur just as the plumes reach the surface at Z/D - 5 and X/D = 75.
62
-------
Example Problem 10
Given:
Warm water is discharged vertically upward into a deep layer of a
large body of moving water. The following conditions are given:
a. Discharge Froude number = 20
b. Discharge port diameter D = 5 ft
c. Discharge velocity = 5 ft/sec
d. Ambient velocity UQ = 1.0 ft/sec
e. Receiving water is linearly stratified with a temperature
gradient ATa/AZ = 0.07° F/ft
Q
f. The initial temperature difference AT = 20° F
Determine:
1. The location of the plume when the centerline excess temperature
is 2° F.
2. If the total depth is 150 ft, does the plume reach the surface?
Solution:
Part 1
The jet-to-ambient velocity ratio is
k = uyuo =5/1=5
The stratification number S. is
St - AVD . 20/5 .
1 AT_/AZ 5757 "'
Q.
Since the ambient water temperature is linearly stratified through-
out,the dimensionless discharge depth Z$/D is zero.
63
-------
This problem is for a single jet discharging into a moving, stratified
ambient water (RCS). The corresponding nomograms are found in Appendix D.
The closest values plotted are for k = 4, St = TOO, and F = 30, which are
found on Figs. D-5 and D-6.
Entering Fig. D-5 with flic. = 2/20 = 0.1 and 6 = 90°, the location
AT0
of the plume is found to be at Z/D - 7 and X/D - 5. This is 35 ft above
and 25 ft downstream of the discharge point.
Part 2
It is seen from Fig. D-5 that the maximum height of rise for vertical
discharge with the given ambient conditions is approximately at Z/D = 19
or Z - 95 ft. Since the total depth is 150 ft, the plume will not reach
the surface. This is particularly true since the stratification number
is 60 rather than 100 as used in the calculations.
Variations of this problem with different discharge and ambient con-
ditions have been solved and the results are listed in Table XI.
64
-------
TABLE XI
Variations on Problem 10 Showing Several Discharge
Configurations and Ambient Conditions
Case
Froude Number F
Port Dia. D (ft)
Temperature
Gradient (°F/ft)
St
Discharge Angle 6 (degree)
k
Plume Location X (ft)
at ATc = 2° F Z (ft)
Terminal Height (ft)
Figures Used
1
20
5
.07
60
90
4
25
35
95
D-5
2
20
5
.07
60
0
4
200
5
*
D-5
3
20
5
.07
60
90
2
33
25
*
D-3
4
10
10
.025
80
90
2
80
50
125
D-l
5
75
2
.025
400
90
4
16
16
*
D-15
6
75
2
.025
400
0
4
76
0
*
D-
* Off Chart
65
-------
Example Problem 11
Given:
Condenser cooling water is discharged vertically upward into shallow
sea water. The following conditions apply:
a. Discharge velocity IL = 15 ft/sec
J
b. Discharge diameter D = 5 ft
c. Ambient is stagnant and non-stratified with a salinity of
40 ppt and a temperature of 60° F
d. The discharge depth is 50 ft
e. The initial temperature difference ATQ = 30° F
Determine:
The temperature at the center of the plume when it reaches the surface.
Solution:
From Fig. F-l with T = 60° F, AT = 30° F and salinity of 40 ppt,
a o
the value of G is found to be about 2.5. Therefore, the Froude number is
F - GU.(D)"1/2 = 2.5 x 15 x (5)"1/2 = 16.7
J
The shallow water nomograms of Appendix E are used for this problem.
The appropriate figure to enter is E-2 for Z/D = 50/5 =10. From this
AT
figure and for a Froude number of 17, it is found that -r=£- = 0.4 at the
o
surface. Therefore, the temperature at the center of the plume as it
reaches the surface is 60 + 0.4 x 30 - 72° F.
Variations of this problem with different discharge conditions and
depths have been solved and the results are listed in Table XII.
66
-------
TABLE XII
Variations of Problem 11 Showing Surface Temperatures for
Several Discharge Conditions
Case 1234
Port Dia. D (ft) 5 5 2 10
Discharge Velocity 15 15 10 10
U. (ft/sec) 15 15 IU 1U
v
Froude Number F 16.7 16.7 17.8 7.9
Depth (ft) 50 200 10 100
Surface Temperature -,/, -, r ?/l in
ATC (°F) 12 Kb ^
Figures Used E-2 E-l E-3 E-2
67
-------
REFERENCES
1. Koh, Robert C.Y., and Fan, Loh-Nien, "Mathematical Models for the
Prediction of Temperature Distributions Resulting from the Discharge of
Heated Water into Large Bodies of Water," Environmental Protection Agency,
Water Quality Office, Water Pollution Control Research Series Report
16130 DWO 10/70, October 1970.
2. Abraham, G., "Horizontal Jets in Stagnant Fluid of Other Density,"
Journal of Hydraulics Dry.. ASCE, July 1965, pp 139-154.
3. McQuivey, R.S., T.N. Keefer, and M.A. Shirazi. "Basic Data Report
on the Turbulent Spread of Heat and Matter," U.S. Department of Interior
Geological Survey and the U.S. Environmental Protection Agency, Open-file
Report, Fort Collins, Colorado, August 1971.
4. Fan, L. N., "Turbulent Buoyant Jets into Stratified or Flowing Ambient
Fluids," Report No. KH-R-15, W. M. Keck Lab of Hydr. and Water Resources,
California Institute of Technology, Pasadena, California, 1967.
5. Hirst, E. A., "Analysis of Buoyant Jets Within the Zone of Flow Estab-
lishment," Oak Ridge National Laboratory, ORNL-TM-3470, August 1971.
6. Hirst, E. A., "Analysis of Round, Turbulent, Buoyant Jets Discharged
to Flowing Stratified Ambients," Oak Ridge National Laboratory, ORNL-4685,
June 1971.
7. Trent, D. S., "A Numerical Model for Predicting Heat Dispersion in
Thermal Plumes Issuing from Large, Vertical Outfalls in Shallow Coastal
Waters." Doctoral Dissertation, Oregon State University, Corvallis, Oregon,
to be published, 1972.
69
-------
APPENDIX A
Nomograms for Discharge into Stagnant,
Non-Stratified Water, (RNN, MNN)
71
-------
TABLE I
Figure Numbers Corresponding to Plume Behavior
From Submerged Diffusers Discharging into
Stagnant, Non-stratified Water
Diffuser
RNN
Single
Jet
o>
-3
O) $-
i O)
Q- l/>
r- 23
iE 0
s:
LT5
1!
_J
O
II
Q
O
CM
II
Q
_J
O
oo
II
O
_J
Discharge Angle
0°
A-1,2
A-8,9
A-15,16
A-22,23
A-29,30
30°
A-3,4
A-10,11
A-17,18
A-24S25
A-31,32
60°
A-5,6
A-12,13
A-19,20
A-26,27
A-33,34
90°
A-7
A-14
i
A-21
A-28
A-35
73
-------
LU
O
2 S
IX
140"r
120
1 .. _ J.__,
-t
/
/ RNN
1 TEMPERATURE CHART
- (-0 /
V /
80 TOO
HORIZONTAL DISTANCE X/D
n\JI\l<.UINIML UiOIMII^C. «/U
Fig. A-l Temperature-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Stagnant Large Body of Water: RNN, 9-0°
-------
140
UJ
<_3
I
>4
o
<
<_>
" RNN
/ WIDTH CHART
0 = 0.0°
60
80 "TOO 120
HORIZONTAL DISTANCE X/D
K^OU I
* 200"t
F_= 60p_J-_
140 160
180
200
Fig. A-2 Width-Trajectory Chart for a Singl'e Jet Discharging into a
Non-Stratified, Stagnant Large Body of Water: RNN, 9 = 0°
-------
UJ
O
I/O
RNN
TEMPERATURE CHART
0 = 30°
-t
40
60
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
Fie. A-3 Ternperature-Trajec:ory Ch?.rt for a Sing's Jet D^ischarqirq into a
Non-Strdtified, Stdgr,ant Large Body of Water: RNN, 9~= 30°
200
-------
140
to
«
o
a:
' /.av
20
/ y
/ -'"<* &
/\^>*2°
^
W/D = 10
RNN
WIDTH CHART
0 = 30°
^
20
40
60
80 100 120 HO
HORIZONTAL DISTANCE X/D
Fig. A-4 Width-Trajectory Chart "or a Single Oet Discharging into a
160
180
200
:XO"-o^ra"i r
-------
00 5
CtL
140
120
TOO
80
60
40
20
W^\^r-
///> T/W
I / »- ST "^
{-/,yi M'~+r
VsT ^7
'/ l^y
tf$
20
40 60
HORIZONTAL DISTANCE X/D
RtNN
TEMPERATURE CHART
0 = 60°
80
100
Fig. A-5 Temperature-Trajectory Chart for a 3ir,ole Jet Discharging -into a
Non-Stratified, Stsgna.iL Large Body of Water: RNN, 9 = 50°
-------
o
10
140
^ ^V*
' s,
y-
20
40 60
HORIZONTAL DISTANCE X/D
Fig. A-6 Width-Trajectory Chart ^or a Single Jet Discharging into a
80
, . x f/y
11 1 / >
i ( /" K ^" W/D = 10
" / //
i//^-
. 1 .
1
i
!
RNN
WIDTH CHART
9 = 60°
100
ton-Stratified, Stagnarc Large Body of Water:
RNN, 9 = 60°
-------
UJ
a.
oo
1.0
0.1
o.o
W/D « 10
RNN
TEMPERATURE/WIDTH CHART
0 = 90°
20
40
60
80
100
120
140
160
180
200
VERTICAL DISTANCE Z/D
Fig. A-7 Temperature-Width Chart for Single Jets Discharging into a
Non-Stratified, Stagnant Large Body of Water: RNN, 0 = 90°
-------
UJ
a
" MNN L/D = 1."
TEMPERATURE CHAi
0 = 0.0°
30 100 120
HORIZONTAL DISTANCE X/D
160
180
200
Fig. A-8 Temperature-Trajectory Chart for Multiple Jets Discharging into a
Non-Stratified, Stagnant Large Body of Water: MNN L/D = 1.5, u = 0.0°
-------
03
c/o
S
o:
MNN L/D = 1.5
WIDTH CHART
0 = 0.0°
/ -/-
^J- ~zl I I - -,
^±?.._--.i=f _. y - - i_=±^ * i^n_^^
80 TOO 120
HORIZONTAL DISTANCE X/D
iiuixii-uiiinL. ixj.vPinJtUL. '*/ v
Fig. A-9 Width-Trajectory Chart for Multiple Jets Discharging into a
Non-Stratified, Stagnant Large Body of Water: MNN L/D =1.5, 9 = Oc
-------
140;
o
M
00
a:
UJ
//'/<>
MNN L/D = 1.5
TEMPERATURE CHART
0 = 30°
20 40 60 80 100 120 140 160 180
HORIZONTAL DISTANCE X/D
Fig. A-10 Temperature-Trajectory Chart for Multiple Jets Discharging into
temperature-irajectory unart Tor Multiple oets Discharging into
a Non-Stratified. Stagnairc Large Body of Water: MNN L/D = 1.5, 0 =30C
1
200
-------
c»
en
UJ
140
120
100
MNN L/D = 1.5
WIDTH CHART
G = 30°
60
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
Fig. A-11 Width-TroJecto^y Cha^t 'or f'u'i tip^e Oets Discharging into a
Non-Stratified, Stacrid;; Large Body of Water: :-'NN L/0 = 1.5, G = 30'
200
-------
oo
LU
O
140
'/
//
-W
P'
<&
X/>^
20
40 60
HORIZONTAL DISTANCE
MNN L/D = 1.5
TEMPERATURE CHART
0 = 60°
80
Fig. A-12 Temperature-Trajectory Chart for ''.ulfipls Jets !>;scharcir,g into a
Nor.-Straflfisd, Staonar.t. Large Bcc'y of l-.'a'cer: f-'N'M L/C - 1.5, 0 = 50'
1
i
TOO
-------
140
CO
UJ
o
z:
-------
UJ
cc
3
QJ
O.
CO
to "1
UJ
1.0
0.1
- W/D - 10
0.0
20
40
Fig. A-14
MNN L/D - 1.5
TEMPERATURE/WIDTH CHART
6 « 90°
30
40
50
60
60
80
100
120
140
160
180
200
VERTICAL DISTANCE Z/D
Temperature-Width Cha^t for Multiple Jets Dischargino into a
Non-Stratified, Stagnant Large Body of Water: MNN L/D = 1.5, 0 = 90°
-------
IO
o
i/o
»t
O
MNN L/D = 10
/ TEMPERATURE CHART
.. _ . , _F = 600
80 100 120
HORIZONTAL DISTANCE X/D
F1g. A-15 Tenperature-Trajectory Chort for Multiple Jets Discharging into
a Non-Stratified, Stagnant Large Body of Water: MNN L/D ="10, 0=0°
-------
140
a:
UJ
KNN L/D = 10
WIDTH CHART
0 = 0.0°
»/ /
1 .-' / /
H/1V//
'
zoo
F - 600 .. '_
20
80 TOO 120
HORIZONTAL DISTANCE X/D
F1g. A-16 Width Trajectory Chart for Multiple Jets Discharoing into a
Non-Stratified, Stagnant Urcs Body of Water: MN'N i, 0 = 10,
e =
-------
o
t/1
II
o
I
IS §
/ / X, "V*
MNN L/D = 10
TEMPERATURE CHART
9 = 30°
80 100
HORIZONTAL DISTANCE
Fig. A-17 Temperature-Trajectory Chart 'or Vulfirle Oe-cs Discharging into
a Men-Stratifi:d, Steor^-.t La; ge Body or Water: ;-'NM L/D = 10, 0
= 30C
-------
140
UJ
CO
f <
o
o
i
c;
MNN L/D - 10
WIDTH CHART
9 = 30°
80 100 120
HORIZONTAL DISTANCE X/D
Fig. A-18 Width-Trajectory Chart for reticle .]-:.t:. LMscherrnro Into e
N-r'-Strotified. S':?^"cr.i; Lcrr^ Eody of V'alc--: ;':;!' L/D = '0, 0 - 30°
-------
o
tvl
UJ
«_>
"3Z
-------
140
VD
O
LO
> «
O
KNN L/D = 10
WIDTH CHART
0 = 60°
HORIZONTAL DISTANCE X/D
Fig. A-20 Width-Trajectory Chart for Multiple Jets Discharging into
a Non-Stratified, Stagnant Large Body of Water: MNN L/D - 10, 0 = 60e
-------
i.or
UJ
C£.
0.1 -
X
UJ
UJ
0.01
MNN L/D = 10
TEMPERATURE-WIDTH CHART
0 = 90°
W/D = 10
e.s
20
40
60
80
TOO
120
140
160
180
200
VERTICAL DISTANCE Z/D
Mg. A-21 Temperature-Width Chart for Multiple Jets discharging into
a Non-Stratified, Stagnant Large Body of Water: MNN L/D = 10, 0 = 90C
-------
Ct
M
UJ
/
X MNN L/D = 20
TEMPERATURE CHART
G = 0.0°
/
/
/
80 100 120
HORIZONTAL DISTANCE X/D
Fin. A-22 Tenperature-Trajecto^;/ Chavt for Multiple Oets Discharcirc into
a Non-Stratified, St-sgnent Body of Water: i»'NN L/D = 20, 0 = 0°
-------
140
vO
oc
MNN L/D = 20
WIDTH CHART
e = 0.0°
W/D = ,
70 / /
80 TOO 120
HORIZONTAL DISTANCE X/D
Fig. A-23 Width-Trajectcry Cha-': for Krltiple Jets Discharging into
a Non-Stratified, Sc.i'jn^.t L-: rge Bc/'y of '\'dter: M'XN L/D = 20, 0 = 0°
-------
UJ
8 §
Cf.
140
120
100
80
60
40
20
-C^'-;
/--
-------
140
UJ
Q
MNN L/D = 20
WIDTH CHART
0 = 30°
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
Fig. A-25 Width-Trajectory Char; for N:i1tip!e -."sts Discharging into
a ilon-Stratified, Sl^rant La~?e Body of Water: \>!NN L/D = 20, 0
200
= 30C
-------
O
-------
140
UJ
o
3
CO
o «*
CO O
20
40 60
HORIZONTAL DISTANCE X/D
MNN L/D = 20
WIDTH CHART
0 = 60°
80
100
Fig. A-27 Width-Trajectory Chart for liultiple Jets Discharging Into a
Non-Stratified, Stagnant Large Body of Water: MNN L/D = 20, 0 - 60C
-------
1.0
Ol Q
2 0.1
tu ,
0.
o i-
w
o:
Lu)
0.0
W/D - 10
20
40
MNN L/D » 20
TEMPERATURE/WIDTH CHART
6 « 90°
5 .-
60
SO
100
120
140
160
180
200
VERTICAL DISTANCE Z/D
F1g. A-28 Temperature^Width Chart for Multiple Oets Discharging Into
a Non-Stratified, Stagnant, Large Body of Water: MNN L/D = 20, 8 * 90°
-------
s
CT»
MNN L/D = 30
TEMPERATURE CHART
0 = 0.0°
80 'TOO 120
HORIZONTAL DISTANCE X/D
Fig. A-29 Temperature-Trajectory Chart for Multiple Jets Discharging into
a Non-Stratified, Staunar.t, Lar~c Bcdy of Water: f.'NM L/D = 30, 9 = oe
-------
o
-4
oe.
ui
MNN L/D " 30
WIDTH CHART
0 « 0.0°
50 X 100 110 120.130 140
X / / / "I
80 TOO 120
HORIZONTAL DISTANCE X/D
Fig. A-30 Width-Trajectory Chart for Multiple Jets Discharging into a
Non-Stratified, Stagnant Large Body of Water: MNN L/D = 30, 6
-------
O
«C
o
MNN L/D - 30
TEMPERATURE CHART
0 « 30°
80 100 120
HORIZONTAL DISTANCE X/D
F1g. A-31 Temperature-Trajectory Chart for Multiple Jets Discharging into
a Non-Stratified, Stagnant Large Body of Water: MNN L/D = 30, 0 = 30°
-------
140
Q
M
LU
C_>
{$£'180
MNN L/D 30
WIDTH CHART
0 - 30°
160
20 40 60 80 TOO 120 140
HORIZONTAL DISTANCE X/D
F1g. A-32 Width-Trajectory Chart for iailtiple Jets Discharging into
a Non-Stratified, Stagnant Large Body of Water: "MNN L/D = 30, 6= 30
180
200
-------
o
t/o
K- <
o
O
60
HORIZONTAL DISTANCE X/D
MNN L/D = 30
TEMPERATURE CHART
0 = 50°
80
100
Fig. A-33 Temperature-Trajectory Chert for i-'ultiple Jets Discharging into
a Non-Stratified, Stagnant Large Bcdy of Water: KNN L/D = 3Q, 0 = 60°
-------
140
£
C/1
»4
Q
_l
O
L/O = 30
WIDTH CHART
0 = 60°
40 60
HORIZONTAL DISTANCE X/D
Fig. A-34 V.'idth-Trajectory Chert for r*'j!tiplc -Jets Discharqirg irto a
100
Ncn-Stratif'ied, St-irrarc LergG. Body of Water:
L/D = 30, 0 =
-------
r\>
o
x
L/D = .30
TEMPERATURE/WIDTH CHART
0 = 90°
120
140
160
180
200
VERTICAL DISTANCE Z/D
Fig. A-35 Temperature-Width Chart for Multiple Gets Discharging into a
Non-Stratified, Stagnant Large Body of Water: MNN L/D = 30, 0 = 90°
-------
APPENDIX B
Nomograms for Discharge into Stagnant,
Stratified Water, (RNS, MNS)
113
-------
TABLE II
Figure Numbers Corresponding to Plume Behavior From Submerged
Diffusers Discharging into a Stagnant, Stratified Ambient Water
Diffuser
RNS
M.NS
L/D=1.5 '
MNS
L/0=10
L/D=20
ZS/D = o.
0=0° 0=30° 0=60° 0=90°
B- 1 B- 2 B- 3 B- 4
B-13 B-14 B-15 B-16
B-25 B-26 B-27 B-28
B-37 B-38 B-39 B-40
ZS/D = 10
0=0° ©=30° 0=50° 0=90°
B- 5 B- 6 B- 7 B- 8
B-17 B-18 B-19 B-20
B-29 B-30 B-31 B-32
B-41 8-42 B-43 B-44
ZS/D = 30
0=0° 0=30° 0-60° 0=90°
B-9 B-10 B-ll B-12
3-21 8-22 B-23 B-24
B-33 B-34 B-35 B-36
B-45 B-46 3-47 B-48
-------
740
120
AT
.05
RNS
ZS/D = 0
e = o°
1
100
UJ
o
o
80
60
40
20
20
40
60
160
80 100 120
HORIZONTAL DISTANCE X/D
Fig. B-l Temperature-Trajectory Chart for Single Jet Discharging into a
Stratified, Stagnant Large Body of Water: RNS, Z$ /D = 0, 0 = Oc
180
200
-------
140
<£.
to
><
Q
O
120
100
80
60
40
20
RNS
ZS/D = 0
0 = 30°
20
40
60
140
160
80 100 120
HORIZONTAL DISTANCE X/D
Fig. B-2 Temperature-Trajectory Chart for Sing!a Jet Discharging into a
Stratified, Stagnant Large' Body of Water: RNS, Z /D = 0, 0 = 30°
180
200
-------
140
o
-------
200
e = 90°
TERMINAL HEIGHT
10
Fig. B-4a Terminal Height of Rise for Single Jet Discharging Vertically
into a Stratified Large Body of Water: RNS, Z /D = 0, 0 = 90°
140
120-.
100 |
Q
M
LU 80
O
I
2 60
-------
140
CO
*^
o
20
20
40
60
80 100 120
HORIZONTAL DISTANCE X/D
Fig. B-5 Temperature-Trajectory Chr.rt for Sir cue Jet Discharging ir:to a
Stratified, Stagnant Large Body of Water: RNS, Z /D =~1Q, G = 0°
-------
140
120
100
UJ
fl 80
10
O
t\3 <->
o *-
60
40
20
, c » .05
AT
AT
zr
= 0
* 100
RNS
Z./D = 10
6S= 30°
20
40
60
140
80 100 120
HORIZONTAL DISTANCE X/D
Fig. B-5 Temperature-Trajectory Chart for Single Jet Discharging into
160
180
200
Stratified, Stagnant l.eroe Body of Water:
RNS, ZS/D = 10, 0 =
-------
UJ
o
in
o
_j
«£
>
o:
40
20
O1
0
20 40 60 80
HORIZONTAL DISTANCE X/D
Fig. B-7 Temperature-Trajectory Cha^t for Singie Jet Discharging into a
Stratified, Staar.*nt i.«rge Body of Water: RNS, Z./D ="lO, 9 = 60°
TOO
-------
200
e= 90°
TERMINAL HEIGHT
10 20 40 60 80 100
Fig. B-8a Terminal Height of Rise for Single Jet Discharging Vertically
into a Stratified Large Body of Water: RNS, Z$/D = 10, 9 = 90°
140
120..
100
U4 80
O
i
S 60
o
40
20.
10
100
20
RNS
ZS/D - 10
6 = 90°
40
60
100
FROUDE NUMBER
Fig.B-8b Height Where Plume Centerline Temperature Difference is 5% of Initial
for Single Jet Discharging Vertically into a Stratified Large Body of
Water: RNS, ZS/D = 10, 0 " 90° a *
122
-------
740
PO
00
RNS
ZS/D = so
9=0°
20
40
60
80 TOO 120
HORIZONTAL DISTANCE X/D
Flo. B-9 Temperature-Trajectory Chart for Sir.gle Jet Discharging into a
Stratified, Stagnant Large Bcc'y of V.'ater: RNS, IJD ="30, 9 = 0°
-------
140
o
^^
M
UJ
120
100
80
60
20'
= .100
» L = .05
= 0
' AT.
RNS
l/D = 30
6S= 30°
20
40
60 80 100 120
HORIZONTAL DISTANCE X/D
160
180
Fig. B-10 Temperature-Trajectory Chart for Single Jet Discharging in
Stratified, Stagnant L?.rge Body of Water: RNS, Z /D = 30,
into a
e = 30C
200
-------
140
NJ
UJ
z
£
to
Q
I
o
tn
' T^ « .05
ZS/D = so
e = 60°
40 60
HORIZONTAL DISTANCE X/D
Fig. B-11 Temperature-Trajectory Chart for a Single Jet Discharging into a
Stratified, Stagnant Large Body of Water: RNS, Z /D = 30, 0 = 60'
-------
200-
' 30
e = 90°
TERMINAL HEIGHT
40
60
80
100
Fig. B-12a Terminal Height of Rise for Single Jet Discharging Vertically
into a Stratified Large Body of Water: RNS, Zg/D = 30, 0 = 90°
FROUOE NUMBER
Fig. B-12b Height Where Plume Centerline Temperature Difference is 5% of Initial
for Single Jet Discharging Vertically into Stratified Large Body of
Water: RNS, Z$/D = 30, 0 = 90°
126
-------
140
20
40
60
140
160
80 100 120
HORIZONTAL DISTANCE X/D
Fig.B-13 Temperature-Trajectory Chart for Multiple Jets Discharging into a Stratified
Stagnant Large Body of Water: MNS L/C = 1.5, Z /D = 0, 0"= 0°
180
200
-------
r>o
oo
UJ
o
a:
UJ
20
40
60
140
160
Fig. B-14
80 100 120
HORIZONTAL DISTANCE X/D
Temperature-Trajectory Chart for .'-Vitiple Jets Discharging ir.to
a Stratified, Stagnant Large Body of Water: MNS L/D = 1.5, Z /D
180
0, 0 = 30°
200
-------
140
MNS L/D = 1.5
= 60°
20
40 60
HORIZONTAL DISTANCE X/D
80
Fig. B-15 Temperature-Trajectory Chart fcr Multiple Jets Discharging into a
Stratified, Stagnant Large Body of Water: hNS L/D = 1^5, I /D = 0, 0
= 50C
-------
200
Fig. I6a Terminal Height of Rise for Multiple Jets Discharging Vertically
into a Stratified Large Body of Water: MNS L/D = 1.5, Z$/D = 0, 0=90C
FROUDE NUMBER
Fig. 165 Height Where Plume Centerline Temperature Difference is 5% of Initial
for Multiple Jets Discharging Vertically into a Stratified Large Body
' of Water: MNS L/D = 1.5, Z /D = 0, 0 = 90°
130
-------
o
M
Ul
CXL
UJ
140
120
2 80
20
40
60
140
160
80 TOO 120
HORIZONTAL DISTANCE X/D
Fig. B-17 Temperature-Trajectory Chart for Multiple Jets Discharging into a
180
Stratified, Stagnant Large Body of Water: MMS L/D = 1.5,"Z /D = 10, G = 0°
200
-------
00
o
M
UJ
<_>
z.
-------
CO
00
20 40 60
HORIZONTAL DISTANCE X/D
Fig. B-19 Temperature-Trajectory Ci^rt for Multip'c Jets Discharging into a
Stratified, Stagnant Larqe Body of Water: KMS L/D = ]".5/Z /D = 10,
100
= 50C
-------
e= 90°
TERMINAL HEIGHT
Fig. B-20a Terminal Height of Rise for Multiple Jets Discharging Vertically
into a Stratified Large Body of Water: MNS L/D = 1.5, Z /D = 10
0 = 90° s
140
FROUDE NUMBER
Fig. B-205 Height Where Plume Center!ine Temperature Difference is 5% of Initial
for Multiple Jets Discharging Vertically into a Stratified Large
Body of Water: MNS L/D = 1.5, Z./O = 10, 0 = 90°
134 S
-------
140
00
tn
o
I
o
I
<<
a:
LU
MNS L/D =1.5 |
ZS/D = 30
Fig. B-21
80 100 120
HORIZONTAL DISTANCE X/D
Temperature-Trajectory Chart for Multiple
-------
Q
M
UJ
o
10
i «
Q
^ ~
o
II
DC
ZS/D - so
e = 30°
140
160
180
80 100 120
HORIZONTAL DISTANCE X/D
Fig. B-22 Temperature-Trajectory Chart for '-'ultiple Cets Discharging into a
Stratified, Stagnant Large Body of Water: MNS L/D = I'.'B, Z /D = 30, 0 = 30
200
-------
140
oo
OJ M
o:
' «£« .05
ZS/D = 30
6 = 60°
20
40 60
HORIZONTAL DISTANCE X/D
Fig. B-23 Temperature-Trajectory Chart for Multiple Jets Discharging into a
Stratified, Stagnant Larce Body of Water: MNS L/D = 1.5, ZS/D = 30, 0
100
= 60C
-------
MNS L/D = 1.5
= 30
SAL HEIGHT
10 20 40 60 80 100
Fig. B-24a Terminal Height of Rise for Multiple Jets Discharging Vertically
into a Stratified Large Body of Water: MNS L/D = 1.5, Z /D = 30,
0 = SO0 s
140
8U 100
FROUDE NUMBER
Fig. B-24b Height Where Plume Center!ine Temperature Difference is 5% of Initial
for Multiple Jets Discharging Vertically into a Stratified Large Body
of Water: "" ' '" ----- -- -
MNS L/D = 1.5, Z /D = 30, 0 = 90°
138
-------
140
20
40
60
140
160
80 100 120
HORIZONTAL DISTANCE X/D
Fig. B-25 Temperature-Trajectory Chart for Multiple Oets Discharging into a
180
Stratified, Stagnant Largs Body of Water: MNS L/D = 10, Z /D = 0, 0 = Oc
200
-------
HORIZONTAL DISTANCE X/D
Fin. B-25 T-:rr.re;-at'jrc-Trajectory C lart fcr y.Mtip'Ie Oets Discharging into a
Lif v-rf. Strnt-^rt ;..;'.. Eo'ry of Iv
i / ri
»-/ L.
=. r\
-
-------
a
r-4
UJ
in
ti
a
_j
CJ
140
120
100
HORIZONTAL DISTANCE X/D
Fig. B-27 Temperature-Trajectory Chart for f'ultiple Jets Discharging into a
Stratified, Stagnant La-oe Body of Water: MNS L/D =10, Z /D = 0, 0 = 60C
-------
ZS/D = o
e = 90°
TERMINAL HEIGHT
Fig. B-28a Terminal Height of Rise for Multiple Jets Discharging Vertically
into a Stratified Large Body of Water: MNS L/D = 10, Z /D = 0
9 = 90°
140
120
100-
80-
CJ
3 60
_i
£ 40
C£
UJ
>
20
MNS L/D = 10
Z$/D - 0
e = 90°
ATc = .05
St = 2500
100
10
20
40
60
80 100
FROUDE NUMBER
Fig. B-28b Height Where Plume Centerline Temperature Difference is 5% of Initial
ofrWatlr-PleMNSetL/DD=Sfoa,li58 V=eroVCea1=^Oint0 a Strat^^d Large Body
142 S
-------
00
140
120
100
2 80
60
40
20
4 ms L/D = 10
ZS/D = 10
6 = 0°
20
40
60
140
160
180
80 100 120
HORIZONTAL DISTANCE X/D
Fig. B-29 Temperature-Trajectory Chart for .'-'ultiple Jets Discharging into a
Stratified, Stagnant Large Body of Water: MNS L/D = 10, ZC/D = 10, 0 = 0
200
-------
UJ
O
.
O
140
120
100
80
60
40
20
MNS L/D = 10
ZS/D = 10
9 = 30°
20
40
60
140
160
80 100 120
HORIZONTAL DISTANCE X/D
Fig. B-30 Temperature-Trajectory Chart for r'ultiple Jets Discharging into a
180
Stratified, Stagnant Lerge Body of Water: MNS L/D = 1C, Z /D = 10, 0 = 30°
200
-------
140
O
t-4
LU
o
<
to
tI
o
20
Fig. 8-31
40 60 80
HORIZONTAL DISTANCE X/D
Temperature-Trajectory Chart for Multiple Jets Discharging into a
Stratified, Stagnant Large Body of Viater:
KNS L/D = 10,
ZS/D = 10, G
= 60C
-------
200,
Fig. B-32a Terminal Height of Rise for Multiple Jets Discharging into a
Stratified, Stagnant Large Body of Water: MNS L/D - 10, Z /D = 10,
8 - 90° s
140
120 .
100 -
ui 80
I
S 60
40
20 .
H h
MNS L/D = 10
ZS/D = 10
e = 90°
100
10
20
40
60
-t 1-
80
100
FROUDE NUMBER
F1g. B-32b Height Where Plume Centerline Temperature Difference is 5% of Initia1
for Multiple Jets Discharging into a'stratitied, Stagnant
Body of Water: MNS L/D = 10, Z /D = 10, G = 90°
146 s
-------
140
o
MNS L/D = 10
Z$/D = 30
6 = 0°
80 100 120
HORIZONTAL DISTANCE X/D
Fig. B-33 Temperature-Trajectory Chart for Multiple Jets Discharging into a
Stratified. Stagnant Larae Bodv of Water: M,NS L/D = 10, Z_/'D = 3
30, 6 = 0'
-------
to
O
t_>
H-«
fe
80 TOO 120
HORIZONTAL DISTANCE X/D
Fig. B-34 Temperature-Trajectory Chart for Multiple Jots Discharging into a
Stratified, Stagnant Urge Body of Water: .YNS L/D = 10, Z /D = 30, 0 = 30°
-------
140
20
Fig. B-35
40 60
HORIZONTAL DISTANCE X/D
Temperature-Trajectory Chart for f'ultiple Jets Discharging into a
Stratified, Stagnant Large Body of Water: MNS L/D = 10, Z$D = 30, 0 = 60C
100
-------
200
6 * 90°
TERMINAL HEIGHT
10 20 40 60 80 100
F1g. B-36a Terminal Height of Rise for Multiple Jets Discharging Vertically
into a Stratified, Large Body of Water: MNS L/D = 10, Z /D = 30,
0 = 90° s
140
120
100
uj 80
o
I
S 60
40.
20-
MNS L/D = 10
ZSD = 30
e = go0
ATc = .05
o
10
20
40
60
100
FROUOE NUMBER
Fig. B-36b Height Where Plume Center!ine Temperature Difference is 5% of Initial
for Multiple Jets Discharging Vertically into a Stratified Large
. Body of Water: MNS L/D = 10, ZSD = 30,0= 90°
150
-------
740
20
40
60
140
160
180
80 100 120
HORIZONTAL DISTANCE X/D
Fig. B-37 Temperature-Trajectory Chart for MuHif.le Jets Discharging into a
Stratified, Stagnant Large Body of Water: f-'NS L/D = 20, ZS/D = 0,0 = 0
200
-------
Q
M
UJ
<_>
z.
-------
140
tn
to
o
20
80
40 60
HORIZONTAL DISTANCE X/D
Fig.B-39 Temperature-Trajectory Cr-art for Multiple -Jets Discharging into a
Stratified, Stagnant Laroe Body of Water: i'NS L/D = 20, Z./D =0,0
= SOC
-------
e = 90°
TERMINAL HEIGHT
Fig.B-40a Terminal Height of Rise for Multiple Jets Discharging Vertically
into a Stratified Large Body of Water: MNS L/D = 20, Zg/d = 0, 0=
140
120
100
80 -
O
g
S 60
o
Of
UJ
40
20
^ h-
MNS L/D = 20
ZS/D = o
e= 90°
^=.05
St = J500_
1000
500
JOO.
10
20
40
60
80 100
FROUDE NUMBER
Fig. B-40b Height Where Plume Center!ine Temperature Difference is 5% of Initial
for Multiple Oets Discharging Vertically into a Stratified Large Body
of Water: MNS L/D = 20, Z_/D = 0, e = 90°
154 s
-------
140
en
LU
Q
I
ATc
* v« _
AT. ~
1
.05
H . 1 1 1 1 I 1
20
40
60
140
160
80 100 120
HORIZONTAL DISTANCE X/D
Fig. B-41 Temperature-Trajectory Chart for .""'M Hi pie Jets Discharging irto a
180
Stratified, Stagnant Large Body of Water : KMS L/D = 20,z /D = 10, 0 = Oc
-------
o
1
<:
a:
UJ
20
40
Fig. B-42 Temperature-Irejecto
60 80 100 120
HORIZONTAL DISTANCE X/D
140
160
I IWI \dk A. VI 1 I nil. W A */ I * M IV L. * / \J
'emperature-Trejectory Chart for ''ultiple Jets Discharcir.g irto a
Itratified, Stagnart Lerge Body of Water: MNS L/D = 20, ZS/D = 10,
180
G = 30°
200
-------
ts>
»»
Q
140
120
100
80
60
40
20
MNS L/D = 20
ZS/D = 10
e = 60°
20
40 60
HORIZONTAL DISTANCE X/D
80
Fig. B-43 Temperature-Trajectory Chart for Multiple Jets Discharging into a
<\tr;»-M'fipH. ^tnnnant iarnp RnHv nf Uatpv. f'.N.S 1 /n = ?f). 7 /D = 1
Stratified, Stagnant Large Body of
ZS/D
10, 0 = 60(
L
100
-------
o
Kl
LU
O
<
e = 90°
TERMINAL HEIGHT
10 20 40 60 80 100
Fig. B-44a Terminal Height of Rise for Multiple Jets Discharging Vertically
into a Stratified Large Body of Water:. MNS L/D = 20', Z /D = 10,
Q = 90°
140
120
TOO-
Q
M
U4 80
O
I
S 60
40.
20-
MNS L/0 = 20
ZS/D = 10
e = 90°
100
10
20
40
60
80
100
FROUDE NUMBER
Fig. B-44b Height Where Plume Centerline Temperature Difference is 5% of Initial
for Multiple Jets Discharping Vertically into a Stratified Larae
Body of Water: MNS L/D ="20, Z$/D « 10, 0 = 90°
158
-------
140
Ixl
en
-------
CO
>«
Q
ZS/D = 30
6 = 30°
160
80 100 120 140
HORIZONTAL DISTANCE X/D
Fig. B-46 Temperature-Trajectory Chart for rultiple Jets Discharging into a
Stratified, Stagnant Lerce Body of Water: K"~ ' " " ~ '
180
200
L/D = -20,- Zs/D = 30, G = 30°
-------
140
120
100
80
2 I 60
40
20
St = 2500
S. = 1000
' 2
100
20
* -T^= .05
» o
, -=
MNS L/D = 20
ZS/D = 30
e= 60°
80
40 60
HORIZONTAL DISTANCE X/D
Fia. B-47 Temperature-Trajectory Chart for f^ultiple Jets Discharging into a
Stratified, Stagnant La-ge Body of water: KNS L/D = 20, Z$/D = 30, 0 = 60C
100
-------
200
Q
10 20 40 60 80 100
Fig. B-48a Terminal Height of Rise for Multiple Jets Discharaing Vertically
into a Stratified Large Body of Water: MNS L/D ="20, Z D = 30,
a = 90° s
120-
100
80-
20.
MNS L/D = 20
Z$D = 30
=-90
05
St = 2500
10
20
40
60
80
100
FROUDE NUMBER
Fig. B-48b Height Where Plume Centerline Temperature Difference is 5% of Initial
for Multiple Jets Discharging Vertically into a Stratified Laroe Body
of Water: MNS L/D = 20, Z.D = 30, 0 = 90° e° Ldrye D *
162
-------
APPENDIX C
Nomograms for Discharge into Moving,
Non-Stratified Water, (RCN)
163
-------
TABLE III
Figure Numbers Corresponding to Plume Behavior From Single Port
Submerged Diffusers Discharging into Moving, Non-stratified Water
k
0.5
1
2
4
6
8
12
16
Discharge Angle
Co-flow
0-0°
C-1,2
C-3,4
C-5,6
C-7,8
C-9,10
Cross -flow
9=90°
C-19,20
C-21,22
C-23,24
C-25,26
C-27,28
C-29,30
0=30°
C-11,12
C-13,14
0=60°
C-15,16
C-17,18
165
-------
14
12
RCN k - 0.5
TEMPERATURE CHART
0 = o;o°
10
S 8
o
(ft
CTl
20
40 ' 60
HORIZONTAL DISTANCE X/D
80
100
120
Fig. C-l Temperature-Trajectory Chart for a Single Oet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 0.5, 9 = 0.0°
-------
14
12-
10
00 c.
6
RCN k = 0.5
WIDTH CHART
0 = 0.0°
F =
40 60
HORIZONTAL DISTANCE
80
100
120
X/D
Fig. C-2 Width-Trajectory Chart for a Single Jet Discharging into a Non-
Stratified, Moving Large Body of Water: RCN k = 0.5, G = 0.0°
-------
14
12
RCN k = 1.0
TEMPERATURE CHART
0 = 0.0°
10
cr>
Co
o
«».
rvi
UJ
o
<
00
t1
Q
ex:
UJ
20
Fig. C-3
40 60
HORIZONTAL DISTANCE X/D
80
100
120
Temperature-Trajectory Chp.rt for a Single Jet Dische^ing int
Non-Stratified, Moving Large Body cf Water: RCN1 k = 1, G =
into a
-------
<£>
o
12 -
10
8 -
=c
5 6
Q
uj 4
RCN k = 1.0
WIDTH CHART
0 = 0.0°
F =
40 60
HORIZONTAL DISTANCE
80
100
120
X/D
Fig. C-4 Width-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 1.0, 0 = 0.0°
-------
Ul
o
t/1
» I
a
o
RCN k = 2.0
TEMPERATURE CHART
© = 0.0°
80 100 '120
HORIZONTAL DISTANCE X/D
Fig. C-5 Temperature-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Moving l.args Body of Water: RCN k = 2.0", 0 = 0°
-------
35
1 1 1 1
1 1 1 1 1
X
30-1
25+
20r
RCN k = 2.0
WIDTH CHART
0 = 0.0°
20
40
60
80 100
HORIZONTAL DISTANCE
120
140
160
180
200
Fig. C-6 Width-Trajectory Chart for a Single Jet Discharging into a Non-
Stratified, Moving Large Body of Water: RCN k = 2.0, 0 = 0.0°
-------
35
a
ivl
30
25
20
RCN k = 4.0
TEMPERATURE CHART
0 = 0.0°
O
O
15
10
5.
20
HORIZONTAL DISTANCE X/D
Fig. C-7 Temperature-Trajectory Chart for a Sir.gls Jst Discharging into a
Non-Stratified, Mcvirg La.-go Body cf V!-ter: RCN < = *.0, r-: = 0°
-------
35
LU
o
30
25 -.
20
a
s 15
»I
I
Qi
10
RCN k = 4.0
WIDTH CHART
0 = 0.0°
HORIZONTAL DISTANCE X/D
Fig. C-8 Width-Trajectory Chart for a Single Jet Discharging into a Non-
Stratified, Moving Large Body of Water: RCN k = 4.0, 0 = 0.0°
-------
UJ
o
l/l
"
O
a:
6.
.3,
RCN k = 6.0
TEMPERATURE CHART
0 = 0.0°
20
40
60 80 100 120
. HORIZONTAL DISTANCE X/D
140
160
180
-oO
Fig. C-9 Temperature-Trajectory Chart for a Single Jet Discharging irto a
Non-Stratified, Moving Lerge Body of Water: RCN k = 5.0, 6=0°
-------
F = 50
6 -.
5
00
»I
Q
00 O
ii O
=- 2 -
1 ..
X
30
RCN k = 6.0
WIDTH CHART
0 = 0.0°
75
100
20
40
60 80 100
HORIZONTAL DISTANCE
120
140
160
180
200
Fig. C-10 Width-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 6.0, 0 = 0.0°
-------
35
en
UJ
oo
I «
o
o
I(
1
o;
30 ..
25
20
15 ..
10
5 ..
AT
RCN k = 2
TEMPERATURE CHART
0 = 30°
-f-
F = 5
20
40
Fig. C-ll
60 80 TOO
HORIZONTAL DISTANCE X/D
120
140
160
180
Temperature-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Keying Large Body of Hater: RCN k = 2, 9 = 30°
200
-------
35
LU
O
30
25
20
15
10
.. 5
RCN k « 2
WIDTH CHART
0 = 30°
W
20
40
60
80
TOO
/120
140
160
180 - 200
HORIZONTAL DISTANCE X/D
Fig. C-12 Width-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 2, 0 = 30°
-------
oo
35
30 --
25 --
20 --
10
5 "
AT,
F = 15
RCN k = 4
TEMPERATURE CHART
0 = 30°
20
40
60
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
Fig. C-13 Temperature-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 4, 0 = 30°
4-
i
200
-------
35
CO
><
Q
o
30
25
20
15
10
. 5
RCN k = 4
WIDTH CHART
0 = 30°
20
40
60
80
100
'120
HORIZONTAL DISTANCE X/D
140
160
180 200
Fig. C-14 Width-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 4, Q = 30°
-------
00
o
oo
o
o;
UJ
RCN k = 2
TEMPERATURE CHART
0 = 60°
20
40
60 80 100 120
HORIZONTAL DISTANCE X/D
Fig. C-15 Temperature-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 2, 0 = 60°
-------
35,
Ul
O
2 o
30
25
20
10
5.
RCN k - 2
WIDTH CHART
0 = 60°
200
HORIZONTAL DISTANCE X/D
Fig. C-16 Width-Trajectory Chart 1'or 'a Single ost Discharging into a_
Non-Stratified, Moving Large Body of Water: RCN k = 2, G = 60°
-------
35
F = 15
CD
r\>
LU
o
o:
UJ
30--
25--
20 --
15 --
.06
.08
AT
.04
RCN k = 4
TEMPERATURE CHART
0 = 60°
20
40
80
100
120
140
160
180
HORIZONTAL DISTANCE X/D
Fig. C-17 Temperature-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 4, 0 = 60°
200
-------
35
oo
Ul
o
o
t«
C£.
30"
25
20
15
10
RCN k = 4
WIDTH CHART
0 = 60°
1
20
40
60 80 100 '120
HORIZONTAL DISTANCE X/D
140
160
Fig. C-18 Width-Trajectory Chart 'ror a Single Jet Discharging into a
Non-Stratified, Moving Large Body .of Water: RCN k"= 4, 0 = 60°
180
200
-------
CO
UJ
o
-------
35
30"
RCN k = 2.0
WIDTH CHART
0 = 90°
25
CO
in
UJ
<_>
2=
«=:
o
cc
UJ
20
15
10
2.5
_ 30
'Z- "75
-150
- 1
20
40
60 80 100 '120
HORIZONTAL DISTANCE X/D
140
160
180
200
Fig. C-20 Width-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 2.0, 0 = 90e
-------
oo
cr>
ce.
UJ
RON k = 4.0
TEMPERATURE CHART
9 = 90°
HORIZONTAL DISTANCE X/D
Fig. C-21 Temperature-Trajectory Chart for a Single Oet Discharging into a
Non-Stratified, Moving Urge Body of Water: RCN k = 4.0, 0 = 90s
-------
03
LU
CO
Cl
o
RCN k = 4.0
WIDTH CHART
0 = 90°
HORIZONTAL DISTANCE X/D
Fig. C-22 Width-Trajectory Chart for a Single Oet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 4.0, G = 90'
-------
00
oo
UJ
1/1
I I
a
RCN k = 6.0
TEMPERATURE CHART
0 = 90°
80 100 '120
HORIZONTAL DISTANCE X/D
Fig. C-23 Temperature-Trajectory Chart for a Single Oet Discharging into
a Non-Stratified, Moving Large Body of Water: RCN k = 6.0, 9 = 90°
-------
35
00
Kl
l/l
tt
o
-------
70
UJ
o
oo
60.
50
40
30
20
10
F = 2.5
RCN k = 8.0
TEMPERATURE CHART
0 = 90°
20
40
60 80 ' 100 120
HORIZONTAL DISTANCE X/0
140
160
Fig. C-25 Temperature-Trajectory Chart for a Single Jet Discharging into
a Non-Stratified, Fovi-.-j Large Body of Water: RCN k -- 8.0, ? = 90'
180
200
-------
70
a
KI
Ul
O
z
«C
CO
»I
a
a:
60
50
40
30
20
10
12
RCN k = 8.0
WIDTH CHART
0 = 90°
20
40
60 80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
200
Fig. C-26 Width-Trajectory Chart for a Single Get Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 8.0, 0 = 90C
-------
70
r\j
IM
Lul
oo
l-«4
a
o
»«
fe
60
50
40
30
20
10
RCN k = 12.0
TEMPERATURE CHART
0 = 90°
20
60 80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
200
Fig. C-27 Temperature-Trajectory Chart for a Single Jet Discharging into
a Non-Stratified, Moving Large Body of Water: RCN k = 12.0, G =90°
-------
Co
O
to
» <
O
RCN k = 12.0
WIDTH CHART
0 = 90°
80 100
HORIZONTAL DISTANCE
F1g. C-28 Width-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 12.0, 0 = 90°
-------
<£>
INI
RCN k = 16.0
TEMPERATURE CHART
0 = 90°
80 ' TOO 120
HORIZONTAL DISTANCE X/D
Fig. C-29 Temperature-Trajectory Chart for a Single Jet Discharging into
a Non-Stratified, Moving Large Body of Water: RCN k = 15.0, G = 90'
-------
O
1
CO
UJ
RCN k = 16.0
WIDTH CHART
6 = 90°
20
40
60
80 TOO
HORIZONTAL DISTANCE
120
X/D
140
160
180
Fig. C-30 Width-Trajectory Chart for a Single Jet Discharging into a
Non-Stratified, Moving Large Body of Water: RCN k = 16.0, 6 = 90°
200
-------
APPENDIX D
Nomograms for Discharge into Moving,
Stratified Water (RCS)
197
-------
TABLE IV
Figure Numbers Corresponding to Plume Behavior for Diffuser
Discharging into Moving and Stratified Ambient Water
st
100
500
k = 2
F = 10
D-1,2
D-9,10
F = 30
D-3,4
D-11,12
k = 4
F = 30
D-5,6
D-13,14
F = 75
D-7,8
D-15,16
199
-------
24
22
20
id
16
RCS k » 2
F = 10, St - 100
TEMPERATURE CHART
no
o
o
o
14
12
10
8
6
4
20
40
60
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
Fig. D-l Temperature-Trajectory for^a Single Jet Discharging into a
Stratified, Moving Large Body of Water: RCS_ k = 2, S,. * 100, F = 10
200
-------
ro
o
RCS k - 2
F = 10. St
WIDTH CHART
20
40
60
80 100 120
HORIZONTAL DISTANCE X/D
F1g. D-2 Width-Trajectory Chart for a Single Oet Discharging into a
Stratified, Moving Large Body of Water: RCS k = 2, St = TOO, F = 10
-------
ro
o
24
22
20
id
16
14
o-
£ 12
UJ
10
4
2
0
AT
RCS k - 2
F = 30, St - 100
TEMPERATURE CHART
20
60
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
F1g. D-3 Temperature-Trajectory Chart for a Single Oet Discharging Into
a Stratified, Moving Large Body of Water: RCS k = 2, S. = 100, F «= 30
200
-------
o
CO
20
40
60
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
F1g. D-4 Width-Trajectory Chart for a Single Jet Discharging into a
Stratified, Moving Large Body of Water: RCS k = 2, St = TOO, F = 30
200
-------
ro
o
TEMPERATURE CHART
20
40
60
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
200
F1g. D-5 Temperature-Trajectory Chart for a Single Jet Discharging Into
a Stratified, Moving Large Body of Water: RCS k = 4, St = TOO, F = 30
-------
INS
O
20
40
60
80 TOO 120
HORIZONTAL DISTANCE X/D
140
160
180
200
fig. D-6 Width-Trajectory Chart for a Single Oet Discharging into a
Stratified, Moving Large Body of Water: RCS k = 4, St = 100, F = 30
-------
ro
o
TEMPERATURE CHART
40
60
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
200
F1g. D-7 Temperature-Trajectory Chart for a Single Oet Discharging into
a Stratified, Moving Large Body of Water: RCS k = 4, St = 100, F 75
-------
IV)
o
vl
RCS k - 4
F = 75. St
WIDTH CHART
80 100 120
HORIZONTAL DISTANCE X/D
Fig. D-8 Width-Trajectory Chart for a Single Jet Discharging Into a
Stratified, Moving Large Body of Water:
RCS k = 4, St = 100, F = 75
-------
o
00
F - 10, St - 500
TEMPERATURE CHART
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
Fig. D-9 Temperature-Trajectory Chart for a Single Oet Discharging into
a Stratified, Moving Large Body of Water: RCS k = 2, S. = 500, F
200
= 10
-------
F - 10, St - 500
20
40
60
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
200
Fig. D-10 Width-Trajectory Chart for a Single Jet Discharging into a
Stratified, Moving Large Body of Water: RCS k = 2, S = 500, F = 10
-------
TEMPERATURE CHART
40
60
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
200
F1g. D-11 Temperature-Trajectory Chart for a Single Jet Discharging into
a Stratified, Moving Large Body of Water: RCS k = 2, S = 500, F «= 30
-------
ro
20
40
60
80 100 120
HORIZONTAL DISTANCE X/D
F1g. D-12 Width-Trajectory Chart for a Single Jet Discharging into a
Stratified, Moving Large Body of Water: RCS k = 2, St = 500, F = 30
-------
r\>
ro
RCS k - 4
F = 30, St «
TEMPERATURE CHART
80 100 120
HORIZONTAL DISTANCE X/D
Fig. D-13 Temperature-Trajectory Chart for a Single Oet Discharging Into
a Stratified, Moving Large Body of Water: RCS k = 4, S. = 500, F = 30
-------
ro
F - 30, S 500
80 100 120
HORIZONTAL DISTANCE X/D
140
160
180
Fig. D-14 Width-Trajectory Chart for a Single Oet Discharging into a
Stratified, Moving Large Body of-Water: RCS k = 4, S. = 500, F = 30
200
-------
TEMPERATURE CHART
20
40
60
80 100 120
HORIZONTAL DISTANCE X/D
Fig. D-15 Temperature-Trajectory Chart for a Single Oet Discharing Into
a Stratified, Moving Large Body of Water: RCS k = 4, St = 500, F = 75
-------
ro
20
40
60
80 100 120
HORIZONTAL DISTANCE X/D
F1g. D-16 Width-Trajectory Chart for a Single Oet Discharging into a
Stratified, Moving Large Body of Water: RCS k = 4, S. = 500, F = 75
-------
APPENDIX E
Nomograms for Vertical Discharge into Shallow,
Stagnant Water (RNN, shallow discharge)
217
-------
TABLE V
Figure Numbers Corresponding to Plume Behavior for a Single Port
Diffuser Discharging Vertically Upward into Kon-Slratified,
Stagnant, Shallow Body of Water
Discharge
Depth
77 D
5
8.4
10
40
F = 1, 5, 25, 100
Centerl ine
Temperature
E-3
E-2
E-l
Surface
Temperature
E-4
Isotherms
F = 4r-
E-5
F = 51
E-6
218
-------
no
vo
UJ
O-
oo
o
RNN (Shallow Discharge)
Depth = 40 Diameters
0 = 90° '
Fig. E-l
10 20 30 40
VERTICAL DISTANCE Z/D
Temperature Chart for vertical Discharge into a Shallow, Non-
Stratified, Stagnant Body of Water: RNN, 0 = 90°, Depth = 40 Diameters
-------
1.0..
Qi
ID
ro
ro
o
0.5--
OO
OO
LU
O
X
LU
RNN (Shallow Discharge)
Depth = 10 Diameters
0 = 90°
i
1 1 1
1 1 1
3123
1 1 1 1
4567
i i
i i
8 9
10
VERTICAL DISTANCE Z/D
Fig. E-2 Temperature Chart for Vertical Discharge into a Shallow, Non-Stratified
Stagnant Body of Hater: RNN, 0 = 90°, Depth = 10 Diameters
-------
RNN (Shallow Discharge)
Depth = 5 Diameters
G = 90°
I\J
oo
en
UJ
o
X
UJ
1.0
100
0.5--
i-'J
o
0
VERTICAL DISTANCE Z/D
Fig. E-3 Temperature Chart for Vertical Discharge into a Shallow, Non-Stratified,
Stagnant Body of Water: RNN, 0 = 90°, Depth = 5 Diameters
-------
O
fo
ro
oo
00
X
LU
UJ
o;
0.5 *
0.4 --
0.3 --
0.2 --
0.1 .-
RNN (Shallow Discharge)
SURFACE TEMPERATURES
RADIAL DISTANCE r/D
Fig. E-4 Temperature Distribution at Surface for Shallow Discharge of a
Vertical Jet into a Non-Stratified, Stagnant Body of Water:
RNN, 9 = 90°, Depth = 10 Diameters
-------
10-
PO
ro
UJ
4 5
RADIAL DISTANCE FRCM CENTERLINE
R/D
Fig. E-5 Isotherms for a Single Get Discharging Vertically into a
Non-Stratified, Stagnant Shallow Body of Water: RNN 0
-------
5 -
4 -
3 -
o
r>o z;
ro <:
* fe
2 -
1 -
= .025
Discharge Level
RNN (Shallow Discharge)
G = 90°
F = 51
Depth of Discharge = 5 Diameters
i
12
468
RADIAL DISTANCE FROM CENTERLINE
10
R/D
Fig. E-6
Isotherms for a Single Oet Discharging Vertically into a
Non-Stratified, Stagnant Shallow Body of Water: RNN e = 90°
-------
APPENDIX F
Auxiliary Materials to Aid in Solving Problems
225
-------
I
J 1 _
0
QJ
I/)
CD
en a.
11
CD
10 +
5 J-
G Values for Froude
Number Calculations
C
/U
To = 50° F
To = 70° F
-+
10 20
INITIAL TEMPERATURE DIFFERENCE ATQ °F
Fig. F-l Temperature-Density Relations for Froude Number Calculations
30
-------
T T
u
ro
ro
a:
UJ
a:
UJ
Q-
oo
t/1
CJ
X
UJ
o
o
o
o
1.0
0.8 -
0.6 _
0.4 _
0.2 .
iiiiir
GAUSSIAN DISTRIBUTION CURVE
1.0 2.0
RADIAL DISTANCE PARAMETER, n « 4r/W
3.0
i i i
4.0
Fig. F-2 Gaussian Distribution Curve used to find Off-Centerline Temperatures
-------
ro
00
H
Z
o
o
TABLE F-l
DENSITY OF WATER AS A FUNCTION OF
SALINITY AND TEMPERATURE*
Temperature
°C/°F
Salinity ppt
0
5
10
15
20
25
30
35
40
0/32
.999,868
1.003,970
1.008,014
1.012,840
1.016,065
1.020,083
1.024,101
1.028,126
1.032,163
5/41
.999,992
1.004,006
1.007,967
1.011,915
1.015,858
1.019,799
1.023,743
1.027,697
1 ,031 ,663
10/50
.999,728
1.003,670
1.007,562
1.011,444
1.015,321
1.019,198
1.023,080
1.026,971
1.030,878
15/59
.999,127
1.003,012
1.006,847
1.010,674
1 .014,496
1.018,320
1.022,150
1.025,990
1.029,846
20/68
.998,234
1.002,068
1.005,857
1 ,009,638
1.013,416
1.017,196
1.020,983
1.024,781
1.028,595
25/77
.997,077
1.000,867
1.004,617
1.008,360
1.012,102
1.015,846
1.019,598
1.023,362
1.027,144
30/86
.995,678
.999,567
1.003,147
1.006,858
1.010,568
1.014,283
1.018,008
1.021,747
1.025,504
*From U.S. Naval Hydraulic Office W.D., 1952, Pub. #615
-------
Accession Number
w
Subject Field & Group
17B
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization
Environmental Protection Agency, National Environmental Research Center, Pacific
Northwest ^ater Laboratory '» National Thermal Pollution Research Program,
.. Con/all is
Title
Workbook of Thermal Plume Prediction: Volume 1, Submerged Discharge
10
Authors)
' ornrcui, must a id H.
Davis, Lorin R.
16
21
Project Designation
16130 FHH
Note
Heated Plume Behavior
22
Citation
Environmental Protection Agency report
number EPA-R2-T2-005a, August 1972.
22 I Descriptors (Starred First)
Jet flow, Thermal pollution*
25
Identifiers (Starred First)
Submerged Oet
271 this workbook contains computational procedures in the form of nomograms designed to
satisfy several needs related to the discharge of thermal waste into large bodies of water.
They provide estimates of physical spread and temperature distribution around the discharge
point for the assessment of biological and physical effects of heated water. They can be
used as guidelines for setting temperature standards and for monitoring. Finally, they have
utility in pre-design feasibility analyses and outfall performance estimates.
Data and analyses from numerous sources constitute the backup material for this publica-
tion. An attempt has been made to unify and present the material in a format that is suffi-
ciently simple for a non-specialist user. A number of illustrative examples are presented
which demonstrate the use of each set of nomograms in practical problems.
The status of analysis at this time is not sufficiently advanced to encompass a wide
range of experimentally verified predictive models. For this reason, care must be exercised
when applying the generalized nomograms to specific situations. The major restrictions for
each set of nomograms are outlined in the text which the user is advised to review carefully.
In general, the nomograms provide meaningful qualitative information for a wide range of
problems of practical interest, but their use is subject to scrutiny and proper interpreta-
tion when applied to exacting design conditions.
A
Hoi
ct
;t<
WR:I02
WRSI C
if a A
(REV
. Shirazi
Institution
National
Envirnnmpntal
JULY I969J SEND, WITH COPY OF DOCUMENT. TO
Research Center
. Con/a 11 ic
: WATER RE"SOUR"C^S"5ctENT IFIC INFORM*
VJ.S. DEPARTMENT OF THE INTERIOR
WASHINGTON, D. C. 20240
Oreaon^
AT ION SEW^r
ER
* GPO: 1970-369-930
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