U.S. ENVIRONMENTAL PROTECTION AGENCY
LABORATORY EXPERIMENTS OF SUBMERGED
DISCHARGES WITH CURRENT
By
James P. Chasse
Lawrence Winiarski
PNERL WORKING PAPER #12
PACIFIC NORTHWEST ENVIRONMENTAL RESEARCH LABORATORY
An Associate Laboratory of
National Environmental Research Center—Corvallis
-------
LABORATORY EXPERIMENTS OF SUBMERGED
DISCHARGES WITH CURRENT
By
James P. Chasse
Lawrence Winiarski
PNERL WORKING PAPER #12
THERMAL POLLUTION BRANCH
Pacific Northwest Environmental Research Laboratory
National Environmental Research Center - Corvallis
Office of Research and Development
U.S. Environmental Protection Agency
June 1974
-------
ACKNOWLEDGMENT
The computer assistance of Judith Burton and Kenneth Byram of the
Laboratory Services Branch is gratefully acknowledged.
-------
Review Notice
This report has been reviewed by the Pacific Northwest Environmental
Research Laboratory, EPA. 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 recommendation for use.
-------
INTRODUCTION
The optimization of a submerged thermal diffuser design often implies
maximizing the effluent plume dilution by the receiving water body for
a given discharge flow rate and temperature. In some instances, it
may be more desirable to limit the plume spread and dilution rate, such
as. in a river where fish passage is required. Predesign analyses to
minimize the potentially harmful effects of a thermal effluent, thus
require an adequate estimate of the dilution, spread, and trajectory
of the discharge plume. These estimates are often obtained from
mathematical or laboratory models, which determine the physical charac-
teristics of the plume for a given set of source/ambient conditions.
The important parameters affecting dilution, spread, and trajectory include:
.1. the source strength as characterized by the ratio (K) of the
jet velocity (U.) to the ambient velocity (U );
J a
2. the angle of discharge (0) with respect to the horizontal
and the direction of ambient current; and
3. the ratio of the inertia forces, to the bouyancy forces in the
jet as described by the Froude number (F^).
The Froude number is defined as F = U.//p -p- " where D is the nozzle
r J 0 '3- qD
p
Mo
diameter, (p0"Pj)/p0 1s the normalized density excess at the source, .and
g is the gravitational constant. Other factors to be considered include:
-------
4. the proximity of the discharge port to any boundaries which
could limit the physical spread and dilution of the plume;
5. the turbulence level of the receiving water body; and
6. the existence of any temperature (density) gradients.
The relationships between certain of these parameters and plume behavior
have been studied directly or indirectly by various researchers. Most
applicable to the present study is the work of Fan^. Fan conducted a
series of experiments using a negatively buoyant salt water jet discharged
perpendicularly to an ambient current (cross flow). He reported vertical
trajectories, plume half widths, and concentrations as a function of the
distance downstream of the source. The experiments were conducted for
a Froude number range of 10 to 80 and velocity ratios (K) from 4 to 16.
Turbulence was present in the ambient stream although it was a constant
level throughout the experiments. Boundary effects and density gradients
were nonexistent.
Complementing the experiments of Fan are those of McQuivey, Keefer, and
2 3
Shirazi ' , who worked with a horizontal discharge in the direction
of the ambient current (coflow).. Measurements of temperature distribution
and trajectory were made using both warm water and salt water discharges.
Froude numbers varied from 4 to infinity and jet to current velocity
ratios ranged from 0.3 to 10. The surface of the laboratory flume
was altered to provide three different levels of turbulence in the
ambient stream. As with Fan's experiments, the receiving water body
was not density stratified.
Experimental data are sparse for the intermediate angles of discharge
4
from deeply submerged jets in ambient currents. Shirazi and Davis
have attempted to interpolate to intermediate angles using the previously
2
-------
reported data for angles of 0° and 90°.* To do this they employed the
5 6
analytical model of Hirst ' and forced it to agree qualitatively with
the data for References (1) and (2). Once this was accomplished, the
model was used to predict plume behavior for discharge angles of 30
and 60 degrees. The results of this interpolation as well as the
qualitative trend of data in References (1) and (2) are reported by Shirazi
and Davis in the form of nomograms. These nomograms provide estimates
of the temperature distribution and trajectory of the discharge plume
as it is influenced by the discharge angle (0), velocity ratio (K),
and Froude number (Fr).
The results of the interpolation scheme used in Reference (4) are untested
by experimental data. Indeed, the results. have raised unanswered questions
as to the relative effect of other parameters, especially turbulence. Shirazi,
Davis, and Byran/ have noted that the effects of ambient.turbulence are
greatly influenced by the angle of discharge and that more data are needed
to make quantitative predictions over a wide range of parameters.
8
Winiarski and Chasse attempted to include this effect but due to
limitations of the experimental apparatus the results are not conclusive.
More discussion of these experiments will follow.
It was the objective of this study to gain additional insight as to the
fundamental relationships between the physical characteristics of a
thermal plume and the initial source/ambient conditions. The principle
tool for this investigation was a laboratory model, which simulated a
submerged single port discharge to an ambient stream. So that the scope
might be limited,, the effects of ambient turbulence and density gradients
were not examined. The parameters which were varied are the velocity
ratio (K), the f-roude number (F^), and the discharqe angle (0). So that
*When using Reference 4 a multiplier factor of 1.4 for coflow width
data and 1.7 for.cross flow data must be applied. The data for these
conditions, were obtained from different sources with inadvertant
misinterpretation of the widths used.
3
-------
the relative effects of boundaries might also be examined, data pertaining
to shallow discharges (Ref. 8) is included for comparison with the more
recent data. Hopefully, the results of these experiments may be used
to test, at least qualitatively, the trends predicted by other data
or analytical models.
4
-------
EXPERIMENTAL METHODS
DEEPLY SUBMERGED DISCHARGES
Test Apparatus
Test equipment and instrumentation were nearly the same as those previously
8
reported by Winiarski and Chasse . These more recent experiments were
conducted in a towing channel, 40 feet (12 m) long and two (2)
feet (0.6 m) wide. The discharge nozzle was suspended from a carriage
mounted on rails along the top of the channel. Heated effluent was
discharged from a constant head tank, which was also mounted on a carriage
(see Figure 1). The reservoir was periodically refilled with hot water
from a constant temperature bath. Discharge velocities were fixed by
valves at the effluent reservoir.
A third carriage supported the temperature transducer and cable. Traversing
vertically through the discharge plume, the transducer monitored temperature
profiles at predetermined distances downstream from the nozzle exit. The
traversing mechanism was directly linked to the horizontal movement of
the carriage through a simple pulley arrangement. As with the experiments
of Reference (8), the transducer was a hot film anemometer with signals
processed through a Thermo-Systems Inc. Model 1050 anemometer and
recorded on an X-Y recorder.
A primary difference between these experiments and those of Ref. (8)
was the absence of the false bottom. These more recent data are
concerned with the behavior of deeply submerged jets uninfluenced by
boundary effects. As previously noted, the artificially generated
turbulence was also neglected. Unlike the experiments for shallow
discharges, three different nozzles were utilized to attain a wide range
-------
Constant Head
Cable Drum
Hot Water
Supply Tcnk
Tow Cable
Carriage Rail
Water Surface
Vertical Traversing Mechanism
Temperature Sensor
r^T^-Nozzle
Flume Bottom
Figure 1. Experimental Apparatus
-------
of Froude numbers and velocity ratios. These nozzles had diameters of
0.25 in (0.63 cm), 0.38 in (0.96 cm), and 0.55 in (1.40 cm). Jet
Reynolds numbers ranged between 2,000 and 15,000 although very few
experiments were conducted at Reynolds numbers less than 3,500:.
Test Procedure
The recorder was calibrated for temperature and position and the
discharge valves were adjusted to attain the desired discharge velocity.
With an attached chiller/boiler system, the water in the channel
was brought to approximately 20°C (68°F). The constant head reservoir
was then filled with heated water, such that the exit temperature
at the orifice would be approximately 38°C (100°F). Prior to each
series of test runs the actual exit temperature was monitored with
a Hewlett Packard Model 1801A quartz thermometer. The transducer
carriage was then located at a predetermined distance from the orifice
with the anemometer probe properly positioned. Next, the nozzle
was opened and the carriage assembly was towed through the channel
at a uniform velocity. The above procedure was repeated at various
stations downstream from the nozzle and for many combinations of
0, K, and F ;
Specifically, four angles (6) between the horizontal and the discharge
nozzle were studied: 0, 30, 60, and 90°.. Velocity ratios (K) ranged
from approximately 2 to 16. Froude numbers varied between 6 and 100.
These ranges provided a wide parameter space within which it is possible
to evaluate the effect of one parameter independently on one or more
plume characteristics.
Data Reduction and Analysis
Raw data, as plotted on the X-Y recorder, were in the form of a temperature
profile in the vertical direction through the axis of the plume. This
information was reduced to plume trajectory, width, and peak temperature
7
-------
at a given station. The trajectory was delineated by the vertical location
of the peak temperature and was made dimension!ess by dividing by the
discharge nozzle diameter. Vertical plume widths, taken from an X-Y
plot of temperature, were made dimensionless in a similar manner.
Temperatures along the trajectory were.expressed as the ratio of the
excess temperature at a point to the excess discharge temperature.
The temperature excess is with respect to that of the ambient water
body. Algebraically that is:
AT T -T
C = CO
AT T.-T
o jo
where T. is the discharge temperature; T is the ambient temperature; and
J *
Tc is the peak temperature in the plume at point C. A listing of the data is
in the Appendix A, Table A -1.
Data analysis was patterned after that, employed by Shirazi, Davis, and
Byran/. The plume characteristics of temperature (ATc/ATq), vertical
trajectory (Z/D), and width (W/D), were expressed as functions of the
dimensionless horizontal coordinate (X/D); the jet to ambient velocity
ratio (K); the jet Froude number (F^); and when appropriate, the
discharge angle (9). Multiple regression analysis was applied
to data sets separately (ie. 0 = constant), and to all the data
jointly (with 0 an independent variable). Simple exponential equations
were assumed to express the functional form of the plume relationships.
Thus:
AT
c Z W _ ^a _b „c rd
D
ATT > ~D ' n ~ e n K Fr
where n =X/D, the dimensionless horizontal distance, and a, b, c,
d, and f are the partial regression coefficients derived from the
exponential transformation. Although the correlations obtained in
this manner may hot adequately describe other situations which involve
additional parameters, they can be very useful in identifying the
relationships among those variables tested.
8
-------
SHALLOW SUBMERGED DISCHARGES
As noted previously, the information from Ref. (8) was examined for
comparison with the data for the condition of deep submergence. Details
as to equipment androperating procedure may be found in that reference.
Discharges were made from one nozzle diameter (1.40 cm) and jet Reynolds
numbers ranged from 4,000 to 12,000. Experiments were conducted both
with and without ambient turbulence. Because the data in Reference (8)
are nominal averages of several experimental runs, it was the raw data,
as listed in Appendix A (Tables A-2,and A-3), which were used in this
report. Numerical treatment is the same as that discussed on the
previous page.
9
-------
EXPERIMENTAL RESULTS
DEEPLY SUBMERGED DISCHARGES
Experimental data for the deep submergence configuration are listed in
Table A-l of Appendix A. These data were correlated according to- the
exponential form on Page 8 and the results of this analysis are tabulated
in Appendix B. The regression equations were then used to generate a
set of graphs which visually explain the quantitative and qualitative
experimental results. These nomograms are in Appendix C.
The most obvious result is that increasing the angle of discharge, (0),
promotes plume dilution and spreading. This is shown in Figure 2 for
Fp = 20 and K = 4. The velocity ratio, K, has the same relative effect
on the plume when all the data are considered in composite. For a
given 0 and X/D, as the velocity of the ambient stream is decreased
relative to the jet velocity (i.e. K increases), the plume becomes
wider and more diluted. Similarly, plume width decreases and temperature
increases as the jet Froude number increases although the relationship
is much less intense than with the other variables. These results
are illustrated in Figures C-l to C-8 for a wide range of parameters.
The results obtained when each angle is considered separately are shown
in Figures C-9 to C-24. The major difference between the plume behavior
for the different angles is the effect of the velocity ratio on plume
dilution. At a discharge angle of 0° plume temperatures increased as
K was increased while the reverse was true for angles of 60° and 90°.
At 30° there was no significant relationship between K and ATc/ATo.
10
-------
12
o
\
N
10
liJ
o
Q
8
<
o
f= -4
cr
LiJ
> .
90
30
W/D = 10
0.05
0.1
AT= 0.075
0.2 \
20 40 60 80
HORIZONTAL DISTANCE (X/D)
FIGURE 2. Temperature-Width-Trajectory
Chart, Deep Submergence, K=4, Fr=20
-------
SHALLOW SUBMERGED DISCHARGES
Qualitative results of the shallow discharge experiments, conducted with
and without ambient turbulence, were reported in Reference (8). Here
the data are treated in the same manner as the deep submergence data for
purposes of comparison. Because of boundary effects, plume widths
for the shallow configuration did not conform to the exponential function
and correlation of that parameter was not feasible. The data for these
experiments are also listed in Appendix A.
As with the deep submergence data, correlations were made of the combined
data (i.e. 0 included as a variable) and of the individual data sets
(with 0 not a. variable). These results, listed in Appendix B generally
substantiate the qualitative interpretations made in Ref. (8) and show
the trends of temperature and trajectory with respect to the independent
variables are the same as for the deep submergence condition.
The relative effect of boundaries on plume dilution may be seen in
Figure 3 which compares results for shallow discharges with those for
deeply submerged discharges. The bottom has a dominant influence as it
limits dilution of the coflow plume. The bottom effect is important
to the other plume characteristics, trajectory and width, as well. When
the coflow discharge was located on the bottom, the plume was attached
and spreading was limited.
An interesting feature of the bottom effect is revealed in the relationship
of temperature to relative jet velocity. For the deeply submerged coflow
discharges, increasing K was associated with higher relative plume
temperatures. When the discharge port was located on the bottom this
relationship of AT /AT to K was reversed. The difference may be
CO
even seen in comparing Figures C-ll and C-31.
12
-------
DEEP DISCHARGE
SHALLOW DISCHARGE
0.25
ui 0.20
LlI
0.15
90
0.10
LU
Q_
0.05
LU
20 40 60 80
HORIZONTAL DISTANCE (X/D)
FIGURE 3. Effect of Boundaries on Plume Dilution.
-------
Boundary effects due to the water surface are less evident. Because lateral
plume widths were not recorded and vertical plume widths for shallow
discharges were not correlated, direct comparison of these parameters
is difficult. Nevertheless, the gross effect of the surface boundary on
plume widths and trajectories may be anticipated; its influence on plume
temperatures is less apparent.
As noted in Reference 8, the.effect of ambient turbulence is not conclusively
revealed in the two shallow water data sets. The most significant effect
of turbulence is in the relationship of plume temperatures to the
relative velocity. Without ambient turbulence increased dilution
was associated with increased K-, with turbulence the opposite was
true. It is to be.remembered that conclusions drawn relative to
the effect of turbulence are concerned only with the presence or absence
of turbulence and not with its intensity or scale.
14
-------
CONCLUSIONS
At least two conclusions are apparent from an examination of the experimental
results:
1. For the cases of both deep and shallow submergence, the angle ,
of discharge was the most important variable affecting dilution
of the plume by the ambient stream. Plume widths were influenced
primarily by the relative jet strength, described by the ratio,
of the discharge velocity of the jet to the ambient stream velocity.
The Froude number of the issuing jet was a relatively minor variable
influencing plume behavior, although it did have an important effect
on trajectories of the coflow discharge.
2. The location of the discharge port relative to the bottom was an
important factor in determining the behavior of the horizontal
(coflow) discharge. The coflow discharges, which were located on
the bottom, had plumes which were warmer and narrower than those
for which the boundary was not a factor. The lower boundary
did not appear to have any influence on the plumes for the higher
angles of discharge. Proximity of the jet to the water surface did
not affect the relationship between temperatures and velocity ratio
or Froude nunber. There is insufficient data to make comparisons
on the basis of magnitude. The upper boundary had a more predictable
effect on the plume trajectory and width in that it limited plume
rise and vertical spread.
Additional data are required for the condition of a deeply submerged plume
discharging into a turbulent stream. Such information collected for a
15
-------
range of turbulence intensity and scale, may be compared with the data
reported herein to more adequately describe the effects of turbulence on
plume behavior. It is also suggested that, where possible, these laboratory
experiments be compared with other studies and field data.
16
-------
REFERENCES
1. Fan, Loh-Nien. Turbulent Buoyant Jets into Stratified or Flowing
Ambient Fluids. California Institute of Technology. Pasadena,
California. Rept. No. KH-R-15. June 1967. 196 p.
2. McQuivey, R. S., Keefer, T. N., and Shirazi, M. A. Basic Data Report
on the Turbulent Spread of Heat and Matter. U. S. Geological Survey
and U. S. Environmental Protection Agency. Fort Collins, Colorado.
August 1971. 166 p.
3. Shirazi, M. A. , McQuivey, R. S., and Keefer, T. N. Heated Water Jet
in a Coflowing Turbulent Stream. ASCE J. Hydraulics Div. Vol. 100,
HY 7. July 1974.
4. Shirazi, M. A. and Davis, L. R. Workbook of Thermal Plume Prediction,
Volume I. U. S. Environmental Protection Agency. Corvallis, Oregon.
Rept. No. EPA-R2-72-005a. August 1972. 228 p.
5. Hirst, E. A. Analysis of Round, Turbulent, Buoyant Jets Discharged
to Flowing Stratified Ambients. Oak Ridge National Laboratory.
Oak Ridge, Tennessee. Rept. No. ORNL-4685. June 1971. 36 p.
6. Hirst, E., A. Analysis of Buoyant Jets Within the Zone of Flow
Establishment. Oak Ridge National Laboratory. Oak Ridge, Tennessee.
Rept. No. 0RNL-TM-3470. August 1971.
7. Shirazi, M. A., Davis, L, R., and Byram, K. V. Effects of Ambient
Turbulence on Buoyant Jets Discharged into a Flowing Environment.
U. S. Environmental Protection Agency. PNERL Working Paper #2.
January 1973.
8. Winiarski, L., and Chasse, J. P. Plume Measurements of Shallow,
Submerged Model Discharges with Current. U. S. Environmental
Protection Agency. Rept. No. EPA-660/2-73-001. Corvallis, Oregon
54 p.
17
-------
APPENDIX A
Table A - 1 Deep Submergence Data
Table A - 2 Shallow Submergence Data,
No Ambient Turbulence
Table A - 3 Shallow Submergence Data,
With Ambient Turbulence
19
-------
Table A-l. Deep Submergence Data
o
= r ._ .
... . .W9'..
!© .~
1.7 .
..... 5, 3 -
... .... «¦> 06:
60
1.9
13.2
2.2
6.5
.357
60
3.4 ._
10.3
4.7 .
.7.5
...070
60
5.8
10.4
8.7
7.6
.070
90 .
. J. 4.
,10.5...
:.7.6...
8^9
.046 ...
90
2.0
10.6
4.4
• 6.5
.042
10 .....
2.1 —
...... . 12.3 _
..0 .
3.4
.380 . ^
10
2.1
12.3
.3
3.4
.370
10 . ..
. 4.3 . .
12.4
.... .3, .
.. 3.8
.413..... .
10
5.0
12.6
.3
4.0
.439
20;
6 . 2
12.7, ...
. ,1.4
. . . 6 . 0.
237.
20
6.0
12.8
1.0
6.0
.250
20
,2.0
.11.3
. ... .4 .
4.3
.190
30
2.0
11.4
.6
5.0
.140
30
2.0.
.. .11.4
.5 .
4.6
.122 . ..
30
5.9
11.5
2.4
7.0
.163
._4n
.. ..... 5.3. ..
11.6
. . ,3.6 . .
9.0
.. . .120 . ..
" * 40
2.0
. 11.7
1.2
4.7
.089
40
1.9 ..
1 1.8
1. 1
5.0
.116
60
1 .9
11.9
1.4
5.9
.07?
60
2.-0
: 11. ?.
. l.H...
6.0
.070
60
^.9
1 1.4
7.1
9.5
• 068
9.0.
2.0 _
1.1.2 .
. . .3, 1.
6.8
.•048..
90
2. 1
11.3
3.5
7.5
.044
90.'. ...
5.7 ..
. i i.e..
11.7
_ 12.5
.046 ...
10
1.9
20.2
.0
2.9
.477
JO
2
-------
Table
© = 0°
X/D
K
fr
Z/D
W/D
ATC/AT0
k 0
j
i
r-
P
•
1
30.4..
1.5
- -9.6
-.083
90
1.9
30.2
.4
6.6
.046
on
. 3.9-.
30.5
1
fl.4
... .065
90
10.1
30.9
4.2
1 1.2
.066
JO
-3.S-
—23.7-
...0
3.8
.430.
10
10.2
29.0
.0
3.8,
.435
. —20
3.9
-26.5
- — -.0 . - ....
._. 5.8
.210
20
3.8
26.4
.0
5.6
.209
?n
—LQ.JL-
26.6
.n
6.3-
.239-
20
10.?
27.0
.0
6.1
.233
30
...3..8
-- 27.3
.0 .
.... 6.6
.160 ..
30
9.1
27.5
.5
8.3
.161
30
.......... 9.4
27.7
.8 ...
8.6
.167 -
40
3.8
28.2
.0
8.1
.114
4Q_
3.9.
— 28.4_
.0
-1.9
.115
40
9.3
?8.5
.9
9.4
.120
40
9.4
-'-28.6-
: .8
.9.4
. . .126...
60
3.7
29.1
.3
8.8
.069
— 60.
3.6
29.2
.3
9.4
.07-4
60
9.3
29.3
1.6
12.5
.087
60
8^8
29. 6
bl.9
.
_~080.
60
2.1
28.9
.0
7.8
• 054
.90
2.0
_ 28. 1
. .9 . ...
. .9.6
.035
90
2.0
28.2
1.2
9.7
.040
90
3.7.
28.4
- . J.l_. ...
- 12.2
.035
90
3.8
28.5
1.4
1 1 .5
.040
95
*i. 3
-—28.6.
_A.A
16.6 .:
_ ... .-061 ..
1?0
3.8
28.8
2.8
10.2
.031
in
3.1 _ ...
- 30.0
.0
. 3.4
... .427
10
4.3
:n>. i
• 0
3.4
.431
10 _
8.0
30.7
: . .0
4.1
.44,4
?0
8.4
30.8
.0
6.5
.250
20
A..3__
. .3.0-..8.
... . 0
. .5.6
.234
20
?.9
31.2
.0
5.6
.198
30
,2. 7
. 31.4
.0
1 7.2.. -
.135
30
4.0
31 . 3
.0
7.0
.145
30
R.6_._.
- 31.6
. _. .0
__ 7.8
. .170
40
,8.9
3?. 0
.3
9.5
.118
40
..' &.l0
32 • 1.
.4
7.6
.104
40
2.ft
32.?
.0
7.6
.079
60 .
. , ?.a
_ 31.6
.... .0 .
.. . 8.8
... .058..
60
4.1
31.6
.1
8.3
.068
61
8.0
. 3?.0
. .1.1
,12.0
.073
90
7,5
32.5
1.9
11.9
.050
_ .. .90
.. . 4.1
32.9
1.4
.10.8
.041.
90
?. 7
33."
.4
8.9
.041
)?•> . . .
. .. 2.8
33.2
1.0 . ...
-.9.8- - .
. .. .026
120
4.1
33. 3
1.3
10.5
.028
10 _...
- ... 8.7
. 55.9.
. ... .0 . .
3.7
. .440
10
H.5
55.9
.0
3.8
.460
10
14. 2_.
56.5_
.0
.. -.4 . 0 ...
._. .^..'...446
10
l?.7
56.7
.0
3.9
.458
_ ... . _?3
12.7
.. 57. 1
.•o...
... 6.3.
. . .245
20
1 ?.5 '
57.4
.0
6.3
.218
¦>n
4.0
# ft
-_.0 . „
... 5.3__
. .223
Cont.
0 = 0°
X/D K Fr Z/D W/D ATC/AT(
20 3.9 _.54.7;_ .0 .5.0... .224 . .
20 5.4 54.9 .0 5.3 .255
_2Q J.-fl 55. 5 .0 5.5 .250 ....
30 3.9 55.9 .0 6.0 .153
..30 .3.9 55.6_ .. .0 6.3 -.152
30 4.0 56.? .3 7.2 .1'65
30 — I'.O 56.4 ._. . ... .A 7.5 .166...
30 15.0 56.6 .1 8.4 .177
AO 4^0 5k. 5 ..Q .6^3- J.17
40 3.9 54.7 .0 7.5 .11? •
_i_A0_ __ 5A.9 .2 9.4 : .123
40 8.1 55.4 .5 9.4 .120
AO Ji.7 55.5 5 1L.2 ^131_
60 14.R 56.? .6 15.7 .088
__60 Z_9 56 . 9 .8 L1-..9 .J) 8 1_
60 2-9 53.3 »2 9»1 *0 fiU
60 3 . 9 53.7. .0.. 9._7. ^063.
90 3.9 54.? .0 9.8 .056
90 54.5 .0 10.7 .051.—
90 8.1 54.9 1.1 12.2 .05?
SLO __li» . 6 —55,.5 2 .5 L9 .ft .J352_
1?0 3.9 56.0 1.1. 13.1 .0 35
1.0 „5.,.3. 78.6. ...0 3.5 : .497
10 7.3 78 . R .0 4.0 .484
_ tb 1.1.1 .79.6 .0 A..0 .523
20 ,11.9 60.1 .0 6.1 .256
..20 7..3_ 80.9 .0 5u. 9 _ ,248.....
20 5.3 81. i .0 5.8 .254
30 0.3 91.3 . . _ -0 7.0 .159 _
30 7.3 76.7 .0 7.2 .153
,30 1,1./-" 77.3 ' «.0_ 8.7 .164...
40 l?.l 7 R • 0 .3 10.9 .131
<.0 ; 7.,_3 '._.7rt,3 -O... 9.1 127. ._
40 5.3 78.6 .0 8.6 .114
60 5.3 . . 79.4__ .0 ... „_9.4._, .074 ..
60 7.5 7 7.7 .0 9.7 .077
SO 11.9 . 78.? . 3 . 12.5 . .077
90 11 .9 73. o .6 17.2 .041
9,0 7 ,.? 79 ..1 . 0. 12>_R .041....
90 5.1 79.6 " .1 11.9 .04?
10 I?-.'' 57. 8 _ .0. ._ 3.8 .433 .
?0 14.3 53.4 .0 7.1 .26?
?0 H.O 58.6 .0 6.0 .24.1 _
PO <».0 59.0 .0 4.9 .218
30 4.0 ^9.4 _ _ .0. 7,.5_ .... 1 18 ..
" ;»0 ' ' "..0 "59.6 " .0 8.0 .147
30_ 13.a . 60.0 .'4 R.P .17? .
40 13.6 60.4 .7 10.7 .135
40 7.5 . 60.9. .0 9.7 ..117
40 4.0 61.3 .0 8.0 .119
f>0 .-3.9 5;t.S_ • '. .0 ..8.3 ...061;..
"
-------
Table
A-
Cont.
e = o
© = 30
X/D
K
Fr
Z/D
W/D
90
3.9
60.3
.0
13.0
1?.*
5.0
f-O.f
• 5
12.3
IPO
j.9
61. n
2:0
16.0
10
6.4
«?.. 5
.0
2.5
10
. -16.0.. .
98.8- ..
¦ .0 - .
4. 1
20
15.9
99.5
.0
6.4
.20
9.7
100.1
.0
. 6.2
20
6.2
100.3
.0
5.3
. 30— .
— .6.2 ..
. - 101.4 .
.0
. 7.8
30
9.7
101.7
.0
8.0
30
16.4
102.1
.0
8.5
40
15.9
97.2
.0
10.3
40 . . .
9.S .
. .97.9
.0 .
10.1
40
6.3
98. 1
. 0
9.9
t.n
f.. ->
99.0 . -
_ .0
10.6-
60
10.0
99.3
.4
11.0
60 -
15.7
. 99.8 - - .
1.5 ..-
14.3
90
16.1
95.8
1.5
16.6
— .90
9.6
- 96.6 —
.8 :.
.13.0
90
6.2
97.1
.0
11.5
1
7.7
. 97.9
.(1
—12.3
120
13.3
98.8
• o
17.5
—:
.... - -
•
.
ATCMT0
.042
.027
.037
.520
. .534
.259
.246
.233
. . .151
.1*1
. 167
.127
.121
.103
—.068-
.073
.079
.051
.051
.040
.D29-
.034
X/D
. - 10 -
1 ?
10
2 J
20
21
- . 30
3n
33-..
40
40.
40 .
. . 60 .
60
90—
90
10 —
1 0
10-
10
2J—
20
— 20- -
30
...30.
30
_40
40
— 60 -
60
. 90
90
— 90 —
90
_.10_
10
..... 10 .. .
10
2CI-—
20
...20 ...
30
30
30
4Q_
40
_..40
40
_ -60— _
60
60 _
90
.. .90 ...
30
10
1.3
1 • 6
2.S
3.4
1 .*
1.2
1.?
1 .4
2.0-
3.4
2.1
1 .4
1.5
2.6
-3.0-
1.5
1 .9-
2. 1
3.2
5.7
3.0
1.9.-
2. 1
3.2
5.6
-4..1-
2.0
.2.1
3.5
3.6
3.0
. 2.1 .
1.9
2.0
2.0
-3.4..
7.4
-7.7
3.2
2.0.
2.0
-3.3
7.0
-2.0-
2.0
3.3-
6.6
5..7
3.4
—.4 . 4—
2.0
3.8
3. 3
3j;
6.?
6.4
- 6.5
6.5
- 6.6
6.5
- 6.6
6.1
6. 1
6.2
- 6.2
6.3
6 .
6.4
11.1-
I 1.4
— 1 1.4
11.s
1-1 .7-
II .8
-.11 .9 .„
10.5
10.6
10.7
io_a-
10.9
10.6
10.7
- io.a
10.9
1 l-.o.
11.1
17.2
17.3
... 17.5
17.6
17.7.
16.0
.. 16; 2 _
16.2
16.4,.
.16.5
_ 16.8-
16.9
— .17.1
17.2
. ... 17.5
16.5,
-^-16.7..
lb.9
17.0
17. 1
- 33.. 6 .
Z/D W/D ATC/AT0
1.3 3.5 .195
2.4 3.4 . 19 r>
2.9 4.2 .231
o.9 6 • ^ .138
- 3 • 5 - ¦ - • - - 4 .* 6 . 1 29.
i>.'1 3.6 .143
7.9 6<5 .094
2.8 ".7 .102
. <..7. . - 5.6 . .098
10.0 7.1 .070
6 » rt • 6 • ti .077
4 . 5.9 .043
5.1 7.1 .059
1J.3 7.3 .151
_1<..4 !l.0.0 .033-
7.6 7.9 .043
__2.5_ 3.5 .290
.3.0 3.5 .270
_ 3.a 4.4 .257
5.0 5.3 .314
_—7..9 a.-l -153-
5.4 6.2 .183
.. 3,3.....: 5.C .143
4.1 5.7 .120
6.2 7.1 .111
10.5 9.1 .108
.10.1 a.3— ; .084
4.4 6.4 -.099
. 5.7 . - ... 6.5 ' .069
10.1 7.7 .056'
11.2 .. 10.0 .035
11.3 9.2 .041
.. t. 8 _... 0.7 . . 050
/. 1 7.H .051
2.6 3.3 . . .281-
2.5 3.9 .267
. j.B . .. .4.3 . .278
5.3 5.3 .301
— y.2 7.9 1_ .178
4.9 5.2 .124
. 2.9 . . . 4.9 .150
3.1 5.0 .111
--5.7 6.B .._... .112.
10.8 9.0 .105
— 4.1— ^ 6.3 ...103
4.0 5.5 .112
6.6- ._7• 3 . ..OSfe
12.3 10.8 .075
:13.&_, . _. 10.0 —. - - .065
0.5 8.6 .055
... 4.4 7.1 .070-
6.0" 7.4 .055
_10.7 8.8 . .044
9.6 8.7 •045
3.3 _4.2 _ . .250
-------
e = 30°
X/D K _. Fr Z/D W/D
10 - - ' 5.4 7"}. 1 4.8 A.7
10 9.3 73.7 5.3 5.3
.10 .12.7. 74.4 • . . . 5.4 _ - 5.0
20 12.8 74.9 9.7 <5.0
-20 a.9-. • IS,2 ¦ 8.6 fl.l
29 5.2 75.4 6.6 7.0
30 • 5.0 74.2 7.6 8.5
30 8.5 74.9 10.7 10.4
— 30 12.4- 75.3 12.3 12.0
40 12.0 75.7 14.6 14.6
— 40 8.4 76.6 12.4 .12.8
40 5.2 77.1 9.6 9.4
,_60 - 5.1... ¦ 72.0 10.3... 11.7
60 9.9 74.5 16.0 15.7
-SO 5.3— 72.H 11.« 11.7
90 8.6 75.4 17.5 15.3
90 7.7 75.8 - 16.9 15.1
120 5.2 73.6 13.0 13.0
—20 2.6- 36.6-- 3.3 6.7
20 4.4 37.6 6.4 7.1
—ZO 6—3 3a»a 7-*6 7.5
30 6.3 38.2 rt.S 8.9
—30 , 4.4 38.4 7.3 8.0.
30 2.6 38.5 4.5 7.0
—•40 2.6 38.6- 4.9.. £.2
40 4.4 38.9 8.0 8.6
_40- A.4. 39.0. 10.B 10..8
60 5.9 39.3 11.8 11.3
6Q 4.3 .39.6 9.4 . 9.7
60 2.8 39.7 5.6 9.0
90 2.7 ._ 40.0 ._ . .. 6.6 12.3
90 4.6 . 40.1 13.0 11.4
-120 S-0 ¦— 40.4 -13.-5 12.6.
1?0 2.6 40.8 6.3 12.5
' -20 4.1 . ... 64.8. -- —6.0 7.7
20 6.9 65.0 7.8 8.3
-20 10.3—.: .65.5 9.7 ... 9.5
30 9.9 66.2 11.4 13.2
30. 6^5: 66.5 9.9. t 9.9,
30 4.0 ' 67.1 6.6 8.1
—40 4..0 67.6 7.1 9.5
40 6.5 67.B 10.8 12.1
— 4.0 9.3 68.4 14.5. 15.0
60 9.9 68.6 17.0 16.4
—61) 7...0 69.4 13.4 ..13. 7.
60 4.0 70.2 9.0 10.6
4.0_ . ._ _.70.5 9.5 . .12.8
<50 8.2 71.3 18.1 16.6
20 6.4 . 92.6 7.2. ... 7.5
20 10.8 93.4 8.7 10.0
—20 14.6 93 . B 1 0 . 0. 1.0 ,.7..
30 14.6 95.0 13.5 13.7
-.30 10.6 95-5... 11.3 11.7.
30 6.4 96.1 8.8 10.3
. _4fl. ! 6.3 96.8 9.6 .11.5-
Table A-l. Cont.
0 = 30°
ATC /AT0 X/D K . Fr Z/D W/D ATC/ATQ
.299 ... . 10 6.1 33.9 4.7 5.5 .352
.387 10 10.1 3^.2 5.5 5.3 .340
.»29 - - - .- 20 . _.9.-9 32.6 9.4 9.0 .ISO
.193 20 6.8 32.8 B.l ~'.Z .136
.171 -20 3.1- . 33.0 4.6. _ 6.0 ... .170
.163 30 3.1 33.2 5.2 6.2 .127
.114 .30— 4.3- - . 33.5 6.5 ....... . 7.6 .HO
.112 30 6.8 33.6 9.7 9.4 .118
..122 40- 5.6- ... .34.5 V.P .-10.2 .094
.089 40 3.1 34.7 5.8 6.4 .097
.0 86 . : 60 -3.1. - 34.4 _ 6.6.. 7.3 .058
.087 60 5.3 35.0 11.3 10.5 .064
.061 90 3..L 34.7 .7.5 ....10.4 ... . .. .046
.051 90 5.2 35.5 12.3 11.0 .050
. .043 10 2.3 23.3 2.1 3^9.. .201
.033 10 2.3 23.5 3.1 4.1 .220
.035 10 4.1 23.7 _4.4 4.7 .262
.032 10 9.2 23.9 5.4 5.6 .315
.110 : 20 7.«.9 - 24.0 8.3. 9.6 .160
.126 20 4.1 24.2 6.0 6.8 .142
.152 ?o 2.4 24.4 :US 5.3 .13 L.
.088 30 2.4 . 24.6 4.4 6.3 .111
.081. 10 3^.9 24.. 7 6.6 8 • B .099;
.097 30 3.9 24.8 7.2 7.0 .099
.032 ; 30 . . 7. ! 24,o a.a 9.*»„ .ICS
.078 40 7.4 25.1 12.1 11.0 .080
_ .076 - 40 3.8 25*3 &..1 10.2 .081
.050 40 2.3 25.4 5.2 7.0 .082
.. .059 .40 2.4 _.22.4 4.5 ..7.6 .083
.062* 60 2.4 22.4 ¦ 4.7 9.1 .06^
.049 60 .... 3.9. 22.5 8.7 10.4 . .061
.041 60 6.2 .22.6 14.0 11.8 .064
. .033 9.0 ; 6.2 22.8 __.lc..0 13..%.. - ... __.0 37
.039 90 3.8 22.9 11.0 12.0 .047
.147 90 2.4 23.0 6.7 10.4. . .049
.138 120 2.3 23.1 7.2 10.3 .040
.155 10 3.4 46.8 3.8. • . . ..4,2 .275
.115 10 5.8 47.1 4.4 5.4 .319
.098 1.0 1.0*6 4.7 ..3 5,8 ...5.. 4. .42 7.
^091 20 ' 10.9 47.6 9.4 9.0 .184
.076 .20 6,;0._ _ .43.1 7.3. 7.9._ . ...... .160
.076 20 3.4 48.5 5.2 6.6 .145
.. .083- 13.0 3.3 49.0 5.3 7.2__ .121
.053 30 5.7 49.3 H.3 a.. 5 .104
.054 30 1JL..2 49..5 1.1-..S 1 1 ,5__: :..12Q
.057 40 9.6 49.8 .12.5 12.5 .082
.049 : 49..1 9.4 10.6.. _.. .087
.038 .40 3.4 49.4 6.7 8.3 .104
.134 65 3.4 49.7 7.5 _ _ _8.6 . _. .069
.1^5 60 5.8 50.0 9.7 11.5 .060
^167_- - 60 9.5 50.2 ; 16..° 13.8 .054
.111 90 7.7 50.9 ' 16.5 l4.r~ .038
.102 90 3.7 51.-3 „8.6 10.7 _ .051
.095 1?0 3.6 51.7 . 10.1 12. r .037
.077 : JO : .5. 2 _;72.8 4.9_ .4.7 .308
-------
0 = 30
X/D.
..K,
Z/D
W/D
— 4 0'.-
40
. 60 .
60 .
—60—
90
,90
-10.1-
1-.3
19.3 -
10.7
— 6.5.;
b . 5
10.9-
97.5
94.3
53.2
Si. 1
at. 7.^
95.2
9ft. 4
ia.9
15.->
19.5
16.9
12.0.-
13.2
19.1 .
13.0
16.0
18.A
17.0
-13.0 .
16.5
16;2
ro
Table A-l. Cont.
0 = 60°
ATC/AT0 X/D. - K , Fr Z/D W/D ATC/AT0
. .076 10 . 1.9 5.3 3.3 -.5 .203
.-.092 " , . lr' 2.4 i.3 4,£ r • r .172
. 045 . 1 0 . ... „ 4 • 1. . .. .vf . 5 • 4 .7.6 ~ t .170
.051 20 1.6 3. 4 5. 6 *137
.057 . _ J 20 1 . 9 5.4 i.9 . 5 . ¦? .117
.042 23 2-3 5.5 5.7 5.? .114
¦ .035- . ?0 : 3.3.. 5^5. , 7.5 6.5 ,.094
31 2.7 5.6 7.6 6".0 .077
.30 1,7 5.6 . 4.6, 6.6 .035
4i> . ..1.9 . 5.3 7.4 -6.3 .065
4 0 2.8 5.3 10.6 .-.1 .045
60 2. 1 5.4 9.8 .r.3 .041
_ _90; 2.0 5.5 . . . 11.0 - .4 .031 .
' 10 1.9 . 9.4 3.1 3.7 .245
__ ; 1.0 1.9 9, 5 2.. P. 3 . 7 20 5... .
. 10 4.1 9.5 6.4 6.2 .186
20 U8 9.* ; 3-2 _ 5.6 ...129.
20 "" 1.9 9.7 3.2 5.7 .126
20 3.7 9. 7_ 8.1 ,. 7.3 ,098. _
¦30 1.8 9.7 3.4 6.-t .088
^ . 30_ U9 9_. 8 3j.i 5. .T .097
30 3.6 9.8 9.2 8.4 .078
__ -«0 3.7 ; 9 ,_1 : 11.3 r..J)_ ; . 062_.
40 1.8 9.2 3.7 6.5 .074
40 _J . 9 L 9. ? _ 4,1 k,7 ,.-.077
60 2.0" 9.3 " " 5.4" " 7.4 .057" .'
_ _J ^ __60 3. 9_ 9.4 J 3 .9 9 . 2 _,.J . 045
90 1.9 9.5 6.3 8.1 .040
10 2.3 14.7 3.6, 4.8 .235
• 10 3.6 14.8 4.9 5.2 . 183*
. ¦ 1_0 6.1 14.9 7 . 0_J 6._? 169 _
20 6.1 15.2 11.I 9.6 .093
L _20 3.8 14 »_9 6.0 _7.1 ...114
20 2.2 "15.0 3.5 5.? .124
30_ 2^2 J.5.1 4.1 *.0 . .093
30 " 4.4 " 15.2 <•.* . .0/4
40 4.1 j 15.4 _ 10 . 3 ' 9.4 . 0 62_.
40 2.1 15.6 3.7 , 5.4. .068'
.- ._ 61 _ 2.2 14.7 ' •. 5.H • 7.3 .. . .065
." " (iO " 4.2 " . " 14. H ." 9.2 10.0 .041'
_ .' €0 4.i _^'_14.9.. ^ 12-.8 9.": . .041 '.
' " "• '"'90 ' 2.2 15.1 ' 6.'6 ?.:¦> .037
_¦ 10 2_.0___ ¦ 4.0 _ .252
" ¦ 1C! 3.' 21.0" -5.8 5. > .155
._. 10 1 6._0 21.? h.7 7.0 .167
: ' . .~0- •• - ?'.o' ¦ * 21.3 2.9 5.0 .140
_ _ . 20 3.7 21.5 __7.6_ 7.9 .... .109
"""" •" " ' 20 ' . h.n 22.0 10.9 8.5 .104
-30 _ _ 2.0 ''2.3 3.5 ....... 6.."' .105
" " .10 2-0 22.8 3.4 5.7 .100
:_30 4.0 23.1 *.5 8.1 .079
: " 40* 2.0 23.4 3.9 7.1 .069
_• _J\_ 4«> . 3.J?_- . _??. 6... -9.3 7. 7 ... .059-
"4'J 6.1 22.4 " 13.7" 9.9 .040
_ _ 60 __ 2._0_ 22.7 4.? 7.4 .056
-------
Table A-t. Cont.
0= 60° 0 = 60°
X/D K Fr Z/D . W/D ATC/AT0 X/D K Fr Z/D W/D ATC/AT0
'SO.. 3.8 „23.? 9.5 9.4. _ .047 . 20 4.4 53.0 £.5 «.3 .103
90 ?.0 22. 'i v.3 H • 1 .036 ?0 7.4 58.3 13.0 10.5 .09?
....10..:. J. I ?f.4_ 4.1 4.t» .164 . ?0 . . 12.4 SS.6. . 1?.7 14.3 .103
10 5.7 34.6 h.L 7.2 .156 30 11.7 59.0 ?3.0 17.2 .073
Lft 8._5 ; 3,4.9 1,0.0 ...9.1 .179 _ 30 6.8 59.6 ... 14.4 12.2 .063
20 8.8 32.5 14.2 10.0 .105 30 4.4 60.0 8.9. 10.3 .071
— 2.0 5..J7 33.0 11.0 J 9.2: . .094 40. 6.9 56.8. .. . 16.4 12.0 .054
20 3.0 33.3 5.1 6.0 .112, 40 10.3 57.3 21.3 16.0 .052
..JO 3..1 32.0 ... 5.4 6.0, _ .090' _40 4.4 56.3 - . . 10.3. 10.9 .067
30 S.6 32.fl 11.9 9.2 .05R 60 8.4 57.5 21.1 15.0 .036
,_4Q • 3.1 32.? . .. . ... 5.9. 6.9 . . .077. 60 . 4.5. . .. 5fl.2 11.4 12.2 .044
40 5.7 13.2 13.1 9.6 .04*3 90 4.5 56.6 13.0 14.1 .035
&Q 3. ..ft : .'32 ..1 7.6. .9.0. .059.. 90 ti.S : 5b.9 25.2 ....... . 16.0 .030
60 4.6 32.6 10.9 9.4 .047 20 4.9 73.1 10.1 7.9 .099
__9JJ itQ 32.9 9.3 9.-4: ..036 20 6-9 ZA.2_: 12^4 10.3. !.... . . .099 ..
20 2. 1 21.7 ¦ - ¦ 3.6 7.5 .122 20 9.3 75.4 15.6 12.0 .109
20 2.1' 21.8 3j»X 6.6 . 102_ 3J3 JOjJ 1 7.5.8 20.9 13.7 .074
20 3. 1 21. R 6.2 6.9 .107 JO 7.0 73.1 15.2 11.7 .067
20 3.6 21..9 7_. 6 .093 10 .4^9 73.5 10.0. 9.4 .070
20 10.0 22.0 19.5 13.0 .098 40 4.8 74.1 10.9 10.0 .064
30 3^6 22.3 7.8 7.8 . .0 72 40 £l.S 74^ L5^3 Ll—6 ! ^OSJ
.... 30 3.7 22.4 7.8 7.5 .073 40 10.6 74.7 22.3 14.2 .057
30 6j4 22.5J 14.4 10.9 .059_ 6X1 Id. 4 75.5— 26.7 15.7 .047...
^ 30 2. 1 22.8 3.6 ,7.8 .0&7- 60 6.7 72.3 16.3 13.6 .037
30 2.1 22.9 3.5 7.2 - .076 _ ; 4...Z 72.? .11.? 11.3 .045..
40 2.1 23.2 3.8 8.0 .066 90 4.8 73.3 12.9 l'l.O .040
40 2.1- 23.4 3.8 7.8 _ .066 9Q iiS 73.8 24.7_ 15.8 .025. ..
40 3.5 23.5 7.3 8.7 .067 20 4.5 57.2 7.0 7.7 .104
__40 3.5 23j6 8.7 9.7 .067 _20 4^ 57.5 6.9 7.5.. .108. .
40 5.6 23.7 12.9 . 11.3 ".049 20 7.6 57.7 13.2 9.8 .08$
60 5.6 23.8 12.4 11.9 _ _ .037 j?0 1,£ 5.«..1.J. 12.7... 9.8. .: .095 .
ISO 3.5 . 24.1 ¦ 9.3 9.5.. .051 ~ ~ 20 11.5 . 58.3 16.7 14.3 .106
60 _ £.,0 24y_R • _ 9.4 . .. .053 3.0. 4,2 5A.5 8.5 7.5 ... .075. _
90 3.5 24.3 7.2 11.7 " .039 30 4.3 59.3 9.6 9.3 .U31
90 2.0 ?4.7 4...1 10.2. .039 30. £.Q "551.5 14.5 1.0.9 ... .066 .
20 2.9 40.0 7.4 7.7 .111 30 10.9 59.9 18.0 15.) .072
_ 20 5.3 ...40,7. 10.0 . .7.7, . . .087 _ 4.0 10.JZ 60..3 22.8 .15.2 .053 ...
20 2.9 40.3 5.6 7.6 .102 40 h.7 61.1 15.0 11.1 ,05)
._2* 5.1 ,40 .£ V. _V.4 1 .09? _ ,_4iJ 4.J 55. m 6.5 _ ...9.3.. .064. .
20 7.7 4i.0'~" "" ' 13.5 9.8 ".094 . " 40 4.2 56.1 8.9 8.9 .067
30 8.2 ^ M.3_ _ 16.6 12.3 .064 4.2 56.5___ ..11,2 11.0 .053,
30 5.0 41.7 10.6 9.2 .071 60 4.1 56.7 10.8 10.4 .053
30 5.3 4i.fi . 10.- 9.8 .063 _ 6P 7.0 57.J 16.8 !. 12.8 . ,036...
3° 2.9 41.9. 6.0 7.7 .075 ~60 10.9 57.9 24.0 16.6 ..03*
,.J0 2„._9 „.._4?...l 6«-2... ~ ..7.5 _ _ . .081 _ 9 0 _ \0..6 5,7.9 26.6 17.8 _ .026
40. 2.9 39.2 6.4 8.6 .06? QO' 6.7 58.5 16.2 15.2 .029
-*<> 2-9._ 3=>.'3_ ,_. :_-f>.4 , 8.6 . .062 _ 90_ 4,.2_^ 53.. 7_ 11.1 11.7._ .. .043
40 6.? 39..P 15.2 11.0 .056 20 6.6 80.1 ' 11.8 10.3 .102
. .40 ; _.7;9 _ 39.o. _ _ 1«.5 " 13.2 _ .050 _ ?0 6.2 30.7 1.1.4' _ 9.4 .094
60 6.5' 40.1 13.6 13.0-/ .037 ¦ 20 11.1 81.6 16.9 . 14.3 .111
..60 _-_4.9 ,40.6..:__; 11.7-. . _ .038 ._?/L: IJjJB. .82..0^_ 16._7..._ 1 3.. ?_.. ..108.
60 3.0 '*40,8 .. 6.7 • 9.ft .055 - 20 - 18.4 . .62.fl 22.6 20.0 _ .106 .
. :?_Q 3...0 ; 41.2 .8.6 10.4 .039 30 17^6 ,"3.4 ...27.4 21.* _ .074
90 5.5. 41.5 ' 17.0 12.0 .028 30 11.0 84.1 21.0 14.5 .073
_2Q 4.4 57.6 ; 7.6 _ 8.7 ^.105 30 ,6.4 67.3 1 3.5 . 10.1. . .069
-------
Table A-1. Cont.
0 = 60° 0 = 90°
_X/D.
. —K. _ Er ... .Z/D W/D .
ATC/AT0
X/D
_-.__K.__
Fr Z/D
W/D
ATC/AT0
.. _3 o :
6.5,_.. 88.7. 13.6 . . _ - 10.9 ..
. .073
l" .
1 .
_ 5.4.- 4.3
4.8
.146
4G
6. 3 1^.? 11.7.
.053
10
.1.9
.-5.5 3.9
<• . 4
.131.
_.6.3 . _ ,._£?• 5 . , _• " 1^.2 . .. . 11.1 '. ,
.051
... l"
. .2.0.
. ... 5.4. 3.0
3.7
.163
4 0 •
11.2-' *0.9 23.0 1^.8
.052
20
1.8
5.4 4.7
5.1
.095
' "4Q
17.5 91.5 33.S 18.8
. 067_
20
1.9 .
. 5.4 ... 5.2
T>. 2
.088
60
11.8 «9.^ 29.2 16.0
. .041
?0
2.0
5.4 5.5
5.=
.03?
.... 60
3 90,1.. , , 1^.2 .. 13.6 . ... .
.047
30
... .1.8
5.5 6.1
7.0
.062
90
• 6.2 90.8 17.7 14.2
.033
30
2.0
5.5 7.4
6.4
.074
90
11.4 91.5 30.9 17.8
_.. .024 -.
.__.__4 0.,.___
..... . l.e ..
-.5.6 I.'. 7.6 . ..
.6.6
.047
40
1.9
. 5.6 7.1
6.5
.046
. . . .
•_ . ..... . • ."
60. .
.. 1..9.
_ 5.4 . .. .. 9.5
6.4
.044
60
1.9
5.4 9.6
5.9
.039
90
?.o
5..A ,12.4
. . 8.7
.022
90
2.1
5.5 13.0
7.6
.028'
10
4.7
6.9 8.3
7.1
.116
10
5.7
7.1 11.2
9.0
.107
10
5.8
7.0 12.4
_ 1 1 .0
. 1 10
10
6.5
7.0 13.4
9.7
.103
?0
4.3
6.7 11.P
8.5
_ -..067.
20
4.8
6.8 14.9
8.5
.063
20
6.1
6.8 14.8
7.5
.060
30
3.6
6.7. 11.0
7.0
.054
-•
1(1
4.8
6.9 14.8
8.3
.056
30
6.4
6.6 18.5
9.9
.053
/. n '
i p'
6. H ! 1 . C
. . _..7.fc, ...
. P"
40
3.3
6.8 -¦ 11.8
7.3
.046'
40
3.6
7.7 12.7
8.7
.057
40
4.1
6.9. 13.1
8.2
.047
60
3.9
7.7 16.1
8,2....
.038
60
4.6
7.6 18.6
- 8.4
.032'
60
5.1
7.6 21.3
8.3
.032
90
3.4
7.6 18.4
9.3
.0 32
Qi)
3.6
7.5 18.8
10.2
..032
.90
4.0
7.5 19.6
1 1 .5
. .021
i
TO
2.0
14.4 3.1
4.2
. 158
10
2. 1
14.5 3.3
4.3
. 141
10
2.4
14.5 4.3
... -4.4 .
_ ..126;
- ;<¦
20
2.0
14.9 i..O
4.7
.089
20
2.1
14.6 3.5
5.5 _
.. _.. .096
20
2.1
14.7 3.7
4.6
.102
-
30
2.0
14.9 *..6
5.1
.0 74
30
2.0.
15.1 4.2
5.0
. .074
30
2.0
!5.3 4.3
4.1
.074
40
2.1
14.1 <,.7
4.9
.062
40
2. 1
14.2 5.4
5.3
• 056
40
2.2
14.1 5.6
5."
.053
60
2.0
;14.5 _ _5.8 ... .
6.1
. i 045
60
2.1
14.3 6.1
7.0
.044
V
60
2.1 .
14.4 f,.l
6.8
.045
90
2.0
14.6 7.4
7.2
.030
po-
2.0.
14.7 6.3
6.7
. 031 -
lo
3.9
!3.9 6.7
5.0
.122
10
4.1
13.7 7.0
6. 1
._ . 124
10
4. 1
13.8 7.2
5.7
.112
-------
e = 90°
X/D
_ K.
... Fr
Z/D
W/D
?f> .
-. j
1 4. i)
«. i
5.8
20
-. C:
l->. 1
8. a
6.2
-.30
3.7
. . 14.3
9.2
7.'-
30
3.8
1 4
9.4
7.9
30
3.a
13.4
. 9.8
8.5
40
3.H
1 3.6
10.5
9.2
40
3.9
13.5
11.0
8.5
40
3.9
13.7
11.3
9. 7
_JJ0
3.8.
13.R
. 13.5 .
9.9
60
1.9
14.0
13.7
9.8
,b0
.. 3 .9.
13.3
. .13.?
. 8.2
90
3.7
13.6
15.0
11.4
90
3.a
13.5
15.2
1 1.0
90
3.8
13.4
14.8
10.8
10
5.3
18.7
8.6
5.6
10
7.2
18.8
12.4
7.1
10
9.a
18.4
17.3
12.8
20
5.8
19.4
13.0
9.0
20
7.4
19.2
15.9
11.1
20
10.9
18.9
20.6
14.3
30
5.5
19.0
9.6
10.3
30
7.2
19. 1
17.0
10.2
30
7.4
18.7
18.4
11.9
30
5.2
19.2
9.9
9.9
40
5.5
1 8.5
13.8
8.6
40
5.6
18.7
14.5
9.6
40
7.2
18.9
18.8
12.0
40
7.4
18.3
18.0
12.9
63
5.5
18.4
15.8
9. 1
60
5.6
17.7
17.9
10.8
60
7. 1
18.?
20.0
12.5
60
7. 3
18.0
21 .0
14. 1
9(1
5.*
1*.?:
20.0
12.0
90
6.7
18.4
23.6
15.4
10
2.0
29.5
4.1
5.8
10
2.0
29.8
4.2
5.9
10
4. 1
30.0
7.5
5.9
10
4. 1
30.3
7.5
6.0
20
2.0
30.5
4.7
6.4
20
2.7
29.4
4.3
6.3
20
4.0
30.4
8.4
6.5
20
4.2
29.5
8.6
6. <~
30
2.0
30. 1
4.9
6.0
30
?. 1
30.2
5.0
6.3
30
4.2
29.7
9.7
8.8
30
4.2
30.0
9.4
8.5
40
?. 1
23.5
5.2
6.6
40
2.1
28.7
5.2
6.6
-40
4.1
?8. 7
10.3
8.2
40
4.2
29.0
10.2
8.1
60
2.0
29.4
7.0
8.2
60
2.0
28.7
6. 1
7.5
60
_ 1
29.2
12.0
9. 1
60
4.1
28.4
11.8
9.5
90
2.1
28.9
7.7
7.8
Table
A-l. Cont.
0 = 90°
.086
.0??
.054
.070
.067
.060
.059
.056
.033
.031"
.035
.032
_• 0 3?
.027
... 123
.101
.099
.075
.055
.067
.063
.046
_.053„
.060
.053
.049
.041
.043
.035
.037*
.034
.034
.03 0
~ 028
_• 125
. 1 36
.147
.139
.093
.0 93
.097
.10?"
.087
.077
.070
. 086
.079
.071
.062
.059
.04 7
• 054
.046
.057
.0 36
T0 XZD
.K
Fr._ Z/D
W/D
ATc/AT(
.90
2.1
29.1 ?.3
7.8
.041
90
4.2
29.2 14.3
9.8
.04 1
.90
. .4.1
2*.4 lJ.fr
.*•9
.04?
1 20
2.1
29.5 7.6
7.7
.02?
10
8.6
28.8 14.4
9.6
.102
10
9.4
?9.1 15.Q
9.8
.104
. 10
10.3
2^.4 16.8
9.7
.095
20
8.3
26.3 15.6
11.3
.071
.. ..20
9.4
.26.6 . 18.0.
11.5
'.055
20
6.9
26.9 13.3
9.3
.0 65
30
9.5
?7.1 19.0
12.2
.047
30
8.0
27.2 17.2
11.2
.043
. . . ... JO...
7..?
27.5 16.3
9.6
.043
40
10.0
28.4 22.2
14.1
.040
40
8.1
PS.8 18.8
1X..7
.047
40
6.7
29.2. 15.9
10.5
.042
60
8.4
30.3 22.0
.. .14.6
... .039
60
7.3
30.7 20.0
11.1
.040
90
7 ._1__
..2,9.2 23.5 ...
-.15.6.
_ - .032
90
7.0
29.7 23.5
13.8
.033
90
8.0
29.R 24.6
15.1
.033
10
4.7
25.3 8.1
7.4
.132
10
4.2
?5.4 6.7
7.4
.122
10
2.3
25.5 4.8
5.7
.111
10
2.3
?5.6 4.8
5.8
.107
iO
7.4
25.8 12.4
9.b
• 0 86
10
7.5
25.9 13.1
9.5
.086
20
4.5
25.3 10.6
8.2
.078
. 20
4.6
25.4 9.8
7.7
.0 78
20
2.2
25.6 5.8
6. 1
.068
20
2.2
25.7 4.9
6.7
.068
30
4.6
25.8 10.8
9. 1
.063
30
4.5
25.9 11.9
10.4
.058
30
2.2
26.0 5.5
7.6
.058
30
2.2
26.1 5.2
7.3
.058
40
2.3
23.8 5.8
7.4
.046
40
2.3
23.9 6.3
7.9
.046
40
4.7
24.0 12.6
10.2
.043
40
4.5
24.] 12.2
• u ** **
60
4.6
24.3 12.8
12. 4
.037
60
4.6
24.4 13.6
11.3
.037
60
2.2
24.7 7.0
8.3
.0 32
60
2.3
.6 7*0
7.9
.032
90
4.3
24 . H 1 4 . *5
11.3
.0 32
90
4.4
24.9 14.5
12.5
.033
90
2.2
25.0 7.3
10.4
.030
90
2.2
_?S.? 8.2
8.9
.029
120
2.2
25.2 9.8
7.9
.022
10
8.6
30.0 14.2
11.3
.086
10
9.0 •
30.3 . . 14.6
11.0
.075
20
8.7
30.6 16.?
11.2
.053
20
9.7
30.8 19.2
12.4
.053
30
9.2
31.0 21.1
13.7
.045
30
10.3
31.4 22.0
15.0
.048
40
1 1.0
29.1 25.8
15.4
.033
-------
Table
0 =
0
O
0>
X/D
. _ K
..... Fr
Z/D
W/D
ATC/AT0
40
10.6
29.4
25.9
14.3
-0.33
60 '
9.9
29.6
27.6
16.2
.0 34
" 60
° . 9
29.9
26.3
15.6
.029
90
8.8
30.2
28.3
16. 1
.026
90
8.5
30.3
27.7
14.0
.026
10
2.6
57.4
4.7
. 6.3
.138
10
2.9
56.8
5.1
6.4 ,
.131
10" '
4.1
58.0"
6.7
7.0
.130
10
4.3
58. 2
7.2
7.3
.131
10"
9.4
58.4
16.3
12.9
.109
10
10.7
59.1
19.1
12.8
.111
20
2.6
55.0
5.5 .
6.5
.100 1
20
4.3
54.0
8.8
8.5
. .082
20
4.3
54.5
9.3
8.4
.089
20
9.6
59.8
19.?
11.3
.052
20
10.5
60.7
21.6
12.2
.053
30
2.6
55.5
b. /
7. 1
.078
30
2.6
55.7
6.2
7.8
.074
30. .
4.3
56.0
10.0
9. 1
.066
30
4.3
56.5
10.4
8.6
.059
30
10.3
57.0
22.4
... ; 15.6
.0 39
30
10.5
56.4
23.6
14.8
.038
40 '
2.7
58.5
7.0
7.6
.060
40
2.7
59.0
6.7
'7.6
.066
<*0
4.3
57.6
1 1 .8
9.3
.054
40
4.3"
58.0
10.8
9.5
.060
40
10.4
..60.0
24.3
14.4
.039
4 0 ~~
10 ;"6
59.5
25.0
14.8
.041
60
2.6
56.5
7.1
8.9
• 055
60"
2-6
56.8
7.7
8. 3
.048
60
4.3
56.3
12.2
10.6
.049
60
-4.'3'
56.5
12.4
9. 7
.040 + "
60
10.3
59.6
27.8
17.3
.028
"90
2.6
57.11
8.8
"" 8.81
.0321"
90
2.6
57.4(
8.3
a. 21
.0 39 I
90 " "
4.3
57.7 >
13.9
12. i y
.034 (
90
4.3
58.0 (
14.4
i i.p
.0351
90
"TO .5 "
5B.2J
27.8"
16. 7 j
• 025J
1 0
8.5
. 74.7*'
14.3
,10.0
. 104
10
a.5
75.0
14.0
10.4 "
.097
10
3.2
75.7
6.1
6.0
.143
10
3.2"
76.2 *
5.5
6.0
. 155
20 .
3.2
76.5
6.6
7.2
.113
20
3.2
76.9
6.7
7.2
.111
20
8.7
74.3 -
18.3
11.6
.057
20
8.6
74.5
18.3
11.6
.052
1.0
8.2
75.0
18.7
12.4
.047
30
8.2
75.5
18.9
12.7
. .04?
30
3.2
76.4
6.5
7. 1
.086
40
3.2
72.7"
9.0
8. 1
.075
40
3.2
73.0
8. 7
6.2
.070
40
8.4
73. 1
20. 3
13.8
.040-r
40
8.2
73.3
20. 7
13.5
.035
60
8.8
73.8
"23.6 .
15. h
.028
60
8.4
74. 1
23.6
15.B
.031
A-l. Cont.
0= 90°
X/Q K Fr . JZ/D. W/D__. . . ._ATC/AT0
60. .3.2^ 72.6. 9.0 ... . .9.9.- .050'
60 3.2 72. o -J. 3 9.6 .050
9.0 _3. 2_ 7 3. 3: ___10.S: __ 9.. 6 .OA 1 _fc_
90 3.2 73. P 10.is 10.2 .038
90. ...3.2 ¦ 74.4 . 26.5 It.5 .021 =
90 ^.1 75.1 ?7.6 13.6 .026.
120 .3.2. . .74.1 11.A . 9.1 .034 ,-
10 4.0 69.3 7.0 6.0 .150
10 _ 10.4 __.69.6_. 17.0. 11.8 .. . .086 ...
10 10.9 70. 1 17.3 15.5 .087.
20 11.1. . 70.8 _ 23.0 12.7 ..047 . _
20 11.n 71 . 1 23.3 1 1.0 .062
20 4.0 71.* 6.9 8.2 ...0 84
20 4.0 72.2 8.7 7.7 .090
30 4.0 _Z2_.J3 10... 4. 8.5 __ ,.0 73
30 4.0 73.1 10.4 9.0 .065
30 10.3 73.4 24.0 13.a ...044
30 10.0 74.0 24.8 13.4 .044
40 __1Q_._1 63.7 25,0 15.3 ,040+1
40 10.4 69.3 25.3 15.8 .030
40 _ 4 .J .69.6 1 0.J5 8.9 .058
40 4.1 ,70.0 10.5 8.7 .059
60 3.9 _ 70.4 11.8 9.3 »041___
60 3.9 70.7 11.7 10.0 .047
60 9.8 71. 3 27. 1 16.8 .031' ,
60 9.8 71.7 27.6 17.0 .029
OO _10.0.. 72.0 '31.5 __1 7. 3 *0.21?
90 10.1 72.5 31.5 18.4 .021^
90 3.9 _ 73.1 13.1 .11.7 .0 38
90 3.9 73.3 U.S 13.? .033-
120 4.0 7.1.6 15.3 _ 12.5 .028
10 '..0 85.9 7.3 7.5 .145
10 3.? *6.4 6.9 7.1 .135 _
10 " 10.8 86.9" ~ 17.6 12.? .098
10' 10.8 3 7.9 17.7 13-5__. ; .096
20 10.4 R*.? 21.8 13.5 " .055
20 10.6 _ 88.3 _ 21.1 14.1 .046
20 ' 4.0 ,0S.9 8.0 8.<» .088
20 3._9 , «9. 1 7.P _ ,8.9 _._093.
30 " 4.0 09^ 9 * "" ' 9.5 9.5 .066
30 4.0 „ 69.9 9.2 9.1 .. ,.07l' __
" 30 10.8 90.4 2A.0 15.0 .045
3.0_ !_')_• 3 5.U) 23.6 14. 2 ; . _,041
40 4.0 88.0 8.7 9.3 .064
40 4.1 88.3 8.0 9.7 _.064 .
40 10.9 88.5 25.3 18.0 .035
40 11. n 89.1 ..... .. 25.0 ' 16. r. ...... ...035 ._
60 11.2 89.5 29.6 17.4 .031
60 _ 10.9 89.8 28.5 _ _17.9 . ,031...
60 4.0 90.7 10 i 3 ' 9.2 .048
60 3.8 91.1 10.0 10.2 ... . 053
90 3.9 91.4 9.7 11.7 .039 X
00 3-S 91.6 _ 10.2 . 11 . = .039 + ,
90 10.9 92.5 29.3 18.1 .025
... ?0 1.0_.jL: 1 9_2. 8_ ...29.4 18.9 .027
-------
Table A-2. Shallow Submergence Data, No Turbulence
0 = 0° 0 = 15°
X/D K ^ Z/D WD ATC/AT0 X/D K Fr ZZD W/D ATC/AT0
9.1
2.0
12.3
0
1.9
.475
9. 1-
2. 1
11.3
1.60
2.9
.356
9.1
?.o
12.3
0
2.0
.469
9. 1
2.1
11.4
1.70
2.8
.328.
9.1
6.2
12.3
0
2.8
.491
9. 1
5.3
12.2
2.60
3.6
.425,
<>.1
5*8
12.4
0
3.0
.510
9.1
6.0
12.3
2.50
3.7
.424
cl'8.2
2.0
12.3
0
2.9
.314
) 8.2
2.0
11.5
2.30
3.7
• 191.
18i2
2;3
12^4
0
2.9
.310
18. 2
2.0
11.6
2.30
3.7
.188
18.2
6.6
12.5
0
3.8
.295
18.2
6. 1
12.0
4.50
5.5
.200
IB. 2
6.0
12i6
.10
4.0
.299
18.2
6.0
12.2
4.70
5.6
.223
27.3
2.0
12.4
.03
3.S
.223
27.3
2. 1
11.4
2.90
3.8
• 1A0
27.3
2.0
12.5
.20
3.5
.244
27. 3
2.0
11.9
2.60
3.9
.139
27.3
2.0
12.5
.20
3.3
.219
27.3
2.0
12.6
2.60
4.0
. 146
27.3
¦5.9
12.7
.40
4.9
.204
27.3
6.2
12.4
5.90
7.0
.156
27.3
5i3
12.8
.40
4.9
.207
21. 3
5.7
12.5
5.90
6.0
.143
2.0
12.6
.50
4.5
.175
27.3
5.4
Id.6
b.80
6.5
.162
36. A
2.0
12.6
.50
3.7
. 188
36.4.
2.0
12. 1
2.70
4. 1
.113
36. A
5.7
12.9
.50
6.0
. 169
36.4
2.0
12. 1
2.80
4.2
. 108
36. A
6.6
12.5
.50
6.0
.172
36.4
2.0
12.2
3. 10
4.2
.120
54.5.
-,2.0
12.7
.90
4.9
.138
36.4
6.0
11.4
8.00
6.2
• 108.
S4i5
2.0
12.7
1.10
5.2
.126
36.4
5.9
11.5
8.50
6.5
.115
54i5
6.3
12.6
2.00
7.9
.104
36.4
5.7
11.6
8.40
6.4
.100
54.5
6.2
.12.7
2.40
7.6
. 105
54.5
2.0
11.9
3.SO
4.6
.076
81.9
2.0
12.8
2.80
5.3
.087
54.5
2.0
12.0
. 3.60
5.0
.082
81.8
2.0
12.8
2.40
4.7
.074
54.5
5.8
11.1
d.50
A.4
.081
ei.0
5.1
12.8
4.00
8.6
.074
54.5
5.7
11.3
8.50
4.9
.075
81.8
5.8
12.9
4.20
8.7
.069
81 .8
2.0
12.2
4.90
$.2
.061
9.1
1.8
33.4
0
1.8
.532
81.8
2.0
12.4
4.70
5.5
.067
. I
1 c
33.4
V
l.v
.550
81.8
6.5
J 1 A
* A •
£.50
3.5
* -
9. 1
1.8
33.0
0
1.9
.544
81.8
6.3
11 . 1
8.50
3.5
.068
9.1
5.5
32.6
0
2.3
.521
».l
2.0
33.8
1 .60
Hit
.361
,9.1
5.5
32.9
0
2.3
.557
9. 1
2.0
34. 1
1.60
2.6
.370
19.2
1.8
34.0
0
2.2
.382
9. 1
2.0
34.4
1.60
2.6
.362
18 .2
1.8
34.2
0
2.3
.353
9. 1
6.5
32.7
2.40
3.6
.470
13.2
1.8
34.2
0
2.2
* 396'
9.1
5.7
32.9
1.80
3.6
.482
IB.2
5.6
33.1
0
3.0
.331
18.2
1.9
.. 34.4
2. 10
3.5
.193.
13.2
¦ 5.6
33.1
0
3. 1
• 364
18.2
1.9
34. 6
2.10
3.5
.200
18.2
5.6
33.4
0
3.1
.363
18.?
1.9
35.0
2.20
3.4
.190
27.3
1.8
34.5
0
2.5
.281
18.2
5; 7
32.2
3.50
5.5
. .252
27.3
1.9
- 34.5
0
2.6
".298
IB.2
5;8
32.4
3.70
5.3
.253
2?.3
1.9
34. A
0
2.7
.300
18.2
5.6
32.7
3.50
b. 3
.256
27.3
5.6
33. 1
0
3.6
.235
27.3
1.9
34. 1
2.50
4.3
. 144
27.3
5.5
33.4
0
3.2
.231
27.3
1.9
34.3
2.50
4.2
. 152
'27-. 3
5.4
33.7
0
3.6
.251
27.3
1.8
34.4
2:40
4.0
.165
36. A
1.8
33. 1
0
2.5
.220
27.3
5.8
33. 1
5. 10
6.0
.165
36. A
1.8
33.4
.10 .
2.9
.234
27.3
5.8
33.2
5.30
5.6
.167
36.A
5.5
34.0
.30
4.1
..167
..27.3
5.5
33.5
4.80
5.6
.156
36. A
5.5
32. 1
. 10
4.2
.182
36.4
1.8
33. 7
2.80
3.8
. 123
36.4
5.5
32.4
.20
4.2
.185
36.4
1.4
34.0
. 2.60
4.0
.131
36.4
5.5.
34.2
0
4.2
.174
36.4
1.8
34.2
2.90
4. 1
.131
¦ 36i'4
5.5
34.4
.20
4.1
.163
36.4
5.4
32.3
S.60
7.8
.121
54.5
1.8
33.4
.30
3.4
.. 143
3S.4
5.5
32.5
5.70
7.5
.120
54.5
1.8
33.7
.40.
3.4
.144
36. 4
S.5
32.7
6.00
7.7
.121
54.5
1.8
34.0
.30
3.6
.146
54.5
1 .<*
32.3
2.90
3.9
.103
*4.5
5.5
32.8'
.30
4.3
.127
54.5
1.9
32.7
3.10
3. 7
.099
54.5
5.5
33.0
.50
4.7
.145
54.5
1.9
32.9.
2.90
4. 1
.094,
81.8
1.8
34.0
.10
3.6
.122
54.5
H>.4
31 .7
8.20
8.2
.0 86
. 81.8
1.8
34.3
.10
3.8
. 104
5^.5
5.4
31.8
3.20
8.2
.073
81.8
S.S
33. 3
.90
5.8
.085
'¦ -il .3
1.9
32.7
3.70
4. 1
.081
- 81 .a
1.9
33.0
3.60
4.0
.082
81.8
1.9
33.3
3.50
4.1
.077
81.8
5.6
31 .8
8.50
7.5
.064
81.8
5.4
32.0
8.50
7.3
.076
81 .8
5.3
32.2
8.50
7. 3
.060
-------
Table A-2. Cont.
© = 45° 0 = 90°
X/D K ^ im W/D ATC /AT0 XZD Z/D WZD. AI^AI^
•5. 1
?. 1
11.8
2.30
3.5
.1
9.1
2.0
12. 1
3.20
*..0
. 1 37
. 9. 0
12.?
3.40
3.9
.136
9. 1
6.2
12.4
8.70
3.8
.135
l - .?
2. 1
12.3
3.50.
4.1
. 1 37
I * • 2
2.0
12.2
3.70
4.2
. .0 99
18.2'.
7,0
12.3
- 8.70
5.2
.169
18.2
2.0
12.3
4.10
4.8
.08 1
- 1"J . 2
6.3-
12 .4
8. 70
5.S_
.147
1».2
2.0
12.3
3.80
4.8
. 0-75
i.e. 2
. . 5.4
12.5
8.60.
5.0
.124
18.2
6.4
12.3
8.'70
3.3
.057
1 v. 2
2.0
12.2
3.20
4.2
.124
18.2
5.7
12.3
>1.70
3.3
.051
.. .. Z'/ .i
2. 1
12. 1
3.90
4.8
.105
?7.3
2.0
12.3
4.70
5.1
.'0 70
?T.3
2. 1
12. 1
4.00
4.4
106
27. 3
2.0
12.3
4.50
5.0
.0/0
27 . 3
... .2.1
12.2
A.20
4.5
.100
27.3
6.5
12.3
8.70
3.2
.038
2 7.3 -
b-6
12.1
8.50
4.5
.093
36.4
2. 1
12.4
5.40
5.4
.057
27.3
. . 6.6
12.2.
8. 50
4.5
.080
36.4
2. 1
12.4
5.40
5.5
.058
36.4
2. 1
12.3
4.7U
5.7
.077
36.4
5.9
12.6
6.70
3.4
.026
36.A
2.0
12.5
A.00 -
5.1
.089
36.4
5.7
12.7
8.70
3.4
.026
¦36.4
6.3
12.0
8.50
3.2
.073
54.5
2.1
12.5
¦ 5.7.0
5.3
.055
.36.4
5.8
12. 1
d.50
3.5
,06ft
54.5
2. 1
12.5
5.60
5.2
.052
5A. V
2.0
1 1 .9.
4.90
5.8
.068
54 . 3
5.5
12.3
8.70
2.7
.019
. 54.5
2.0
12.0
4.80
5.4
.063
81.8
2.0.
12.6
6,40
5.5
.039
54. 5
?.o
12. 1
4.80
5.5
.058
81.8
6.0
12.5
8. 70
2.7
.014
. . .54.5
5.8
12.0
8.50
2.6
.061
9.1
1.7
32.2
2,90
3.9
. 160
Hi . H ¦
2'. 0
12.3
5.60
5.6
.053
9. 1
¦ 1.8
32.3
3.00
3.5
.161
« 1 .3
2.0
12.5
5.40
5.3
.049-
9. 1
1.8
32.3
2.90
4.0
.162
« 1 . *5
5.9
12. 1
8.50
2.6
.037
^ . 1 '
5.5
32.3
8.70
4.9
»'i 3 C
8 1.8
5.8
12. 1
8.50
2.6
.031
9.1
5.5
32.3
8.70
4.9
.130
9. L
i;9
34.9
2.30
2.9
.204
18.2
1 . 8
32.6
3.20
4.4
.103
9.1
1 .9
35. 1
2.40
2.6
,199
18.2.
1 .8
32.9
3.30
4.4
.110
•?. 1
5.0.
33.2
5.10
5.4
.194
M.2
1.9
33. 1
3.50
4.5
.099
9. 1
5.0.
33.3
5.30
5.6
.190
18.2
5.5
32.«
8.70
<..5
.084
lb.2
1.8
33.7
3.00
3.5
. 150
18.2
5.5
33. 1
8.70
4.5
.086
18.2
1.8
34.0
2.90
3.6
.140
2 7.3
1.8
33. 1
3.70
5.1
.077
18.2
1.9
33.0
2.90
3.5
.152
27.3
1.8
33.3
3.80
5. 1
.0 74
18.2
1.9
33.4
3.20
3.6
.155
?7. 3
5.5
31.0
8.70
4.6
.068
18.?
1.9
33.6
3.30
3.6
'. 148
27.3
5.5
31.2
8.70
4.4
.050
18.?
5.6
32.3
8.50
5.5
.123
27.3
1.8
32.8
4.10
5. 1
.073
18.2
5.6
32.6
H.50
5.5
.125
.36.4
1.8
33.6
4.30
5.4
• 05 7
27.3
1.9
32.1
3.30
3.6
.123
36.4
! . 9
33.8
4,10
S.4
.051
27.3-
1.9
32.3
3.50
3.5
.129
36.4
1 .9
33.8
4.10
5.5
.064
27.3
1.8 ,
32.4
3.00
3.9
.107,
36.4
5.4
32.5
8.70
4.4
.047
27.3
S.6
32. 1
8.50
S.5
.092
36.4
5.4
¦ 32.2
0.70
4.5
.04 S
27.3
5.7
32.2
8.50
5.5
.099
54.5
1.9
33.0
5.10
5.4
.056
27.3
fv.7
-32.3
8.50
5.5
.082
54.5
1.9
33. 1
5.00
5.3
.044
36. 4
1.9
'32.5
3.60
4. 1
.107.
- 54.5
5V6
32.3
8.70
4.5
.030
36.4
1 .9
32.7
3.30
3.9
.102
54.5
b.5
32.6
8..70
4.2
• 0 2 7
36.4
1.9
32.9
3.60
3.9
.114
81 .H
1.9
33.2
5.40
5.4
.041
36.A
5.9
iZ.l
6.56
5.5
.076
.81.8
1.9
33.4
5.10
5.5
.038
36.<4
5.8
32.5
8.50
5.5
.083
81.8
6.0
32.8
8.70
5. 1
.021
54.5
1.9
32.0
4.50
4.6
-.081
Si. 5
1.9
32.2
4.20
4.5 .
.070
5'-*. 5
1.8
32.3
4.70
4.7
.071
5^.5
5.6
32.7
8.50
5.0
.060
81.8
1 .«
32.5
S.O
.065
81.8
1.9
32.7
A.80
4.6
.060
31 .b
1.9
32. 8
4.90
5.1
.060
s i. e
5.6
31 .5
8.50
4.4
. 0S9
81.8
" "5.6--'-
"31.7 —
8.50
4.7
.0 29
-------
Table A-3. Shallow Submergence Data, With Turbulence
0=0° 0 = 15°
X/D K Fr 2/D W/D AT,. /ATQ XZD K_ E, Z/.D W12 ATC/AT0
¦qTI T7i I2.n 5 2.5 . 375 .256 18.2 2.7 izTS : 3.50 ?75 .144
IB.2: 2.7 12.? .20 3.3 .279 18.> 2.7 12.4 3.50 _ 'j^I . 1 54-
18.2. 8.0 12^"S " .20" 4"."2"" 7Tf4 ' 18.2 7.4 11.8 5.60' 7.0 .214
18.2 7^S 12. d .J?0 4^0 .311 27.3. 2^9 12.4. 4.50 5.4 , 1 24 .
18.2 7.8 13.0 .20 4.2 .301 27.3 2.8 12.2 4.60 5.1 .116
27. 3 2^7. 12.3 .40 3iH .201 27. 3 9^5 1Z.l _H.5_n_ 5^8 j_l/> 1
27.3 2.7 12.4 ,h>J 4.2 .196 27.3 u.3 12.2 8.60 6.3 .170
27:3 7^6 13.2 .50 5.7 .200 16.4 2.9 12.2 5.60 7.2 .096
27.3 7.7 13.2 .50 5.5 .198 36.4 2.9 12.3 b.50 6.8 .097
36. 4 2.6 12.6 ^50 4^5 .175 36.4 8.0 11.9 h.70 6.1 .138
36.4 2.7 12.7 .50 4.5 .157 36.4 8.0 12.0 c).70 6.5 .129
36.4 8^3 12.1 1 .BO 6.4 .153 54.5 2^7 11.8 6.50 ]V3 .068
36.4 8.0 12.3 1.60 7.6 .138 54.5 2.9 11.8 6.BO 7.3 .058
36. 4 2.7 12.5 .80 4^5 . 148 54.S 8^0 12.2 8.70 5^ .095
54.5 ?.7 12.7 1.90 5.9 .086 54.5 7.2 12.2 8.70 5.5 .066
54.5 ?. 7 12jJ 1.90 5_._9 . 100 81.8 2.8 12.0 8.70 6^9 .053
54.5 6.0 12.4 2.70 8.7 .102 HI.8 8.3 12.2 8.70 4.0 .054
54.5 7.2 12.6 2.40 8.7 .111 81.8 8.3 12.3 8.70 4.0 .055
81.8 2.7 12.9 3.50~"~ 677 7®6"l 9.1 3.0 35.2 2.40 3.0 .375
fj. 81.3 2^7 13.0 4.30 6i7 .062 9;J 3^0 35.0 2.50 _ 2.9 .385
— 81.8 7.5 12.7 5.00 8.7 .073 9.1 H.V 35.3 "~3.10 3.'8 .506
9. 1 3^0 34'. 8 0 2. 1 .532 Q^J 35.5 . 2. BO 3;H .509
971 ~~37S 35. 1 0 271 : 971 S75 3571 TTOO 371 : 7521
9.1 3.0 35.7 0 2.1 .518 18.2 3.0 34.7 3i50 4.9 .181
971 STeT 3^72 0" ?75~ ."53? T«75 5715 34.5 j7fT<5 570 7T83
o - 9.1 876 35. 3 ._10 2^6 .521 18. ? H_;5 35.6 5.20 6;2 .256
£ 9 'j, fTl 876 3576 TTO 275 7S5l : 1 1875 : 872 35.7 : 4.90 : 674 : .251
< z, r 18.2 3.0 36.0 .20 2.5 .293 1«.2 8.1 35.9 5.00 6.0 _ .255
?. ¦ 18.2 3.0 36.3 0 2.6 .333 2773 37o 337B 3.70" 5.4 .130
-i 18.2 3;0 36.5 .10 2.7 .337 27. 3 3^0 33.9 4.00 5.1 L126
~ . I • . M.? ~ 876 357* : : 5 ! 373 733T" ; 27.3 371 347] 3.90 479 7139
V % :¦ S' 18.2 a;6 36.0 0 3^4 .305' 27.3 8^6 35.9 6.80 7.6 . 174
g f J' Ta72 876 3fT71 0" 373 .343 27.3 8.2 36.1 6.80 7.6 .169
rj~, 9, :• 27.3 3.0 ' 36.7 . 10 2.8 . .227 27.3 6.2 36.3 o.aO 7.0 iAU
_ ~ 3 ¦ 27.3 3.0 : 3o.9 u J. o .ccv 36.4 3.1 34.9 4.10 6.0 .109
SO® S 27^3 3.0 37.1 0 3.3 .243 36.4 3.1 35. 1 4.00 6.0 .094
^ ~ 2 Z773 ' T75 3-T75 720 ' 378 7226 3b74 876": 3671 7.5(3 775 7T26
S - 27.3 8.4 35.7 -^20 3^6 ^17 36.4 Cu6 36.2 7.30 7^5 .120
3 27.3 8.« 36.0 .10 4.1 .207 36.4 ^.3 36.3 7.80 7.4 .1 lH
2 '36.4 3.0 34.6 .10 3.6 .183 54.5 3.2 34.1 4.00 6.8 .079
£ 36.4 375 34.8 .10 3.6 .235 rTT£ 357? 4.20 <^78 .07?
S 36.4 3.0 35.0 .10 3.6 .192 54.5 8.3 35.2 8.70 8.5 .103 _
tr 3674 573 36.2 .i'o 475 . f?4 54.S- ST3 35.6 '8.70 7.7 .092
Ci 36.4 8.3 36. 1 ^20 4^4 .149 54.5 35. P fa. 70 7;3 '093
S475 ITT 357? 72^ 475 .124- 5T7S J7o 34.4 ; 5Tso 677 .058
£¦ 54.5 2.7 35.7 .20 4.6 .127 81.» 3.0 34.6 5.10 6.7 .063
^ 5171 §74 3?7T 7S5 : 479 : : .117 8T78 57T! :3"57b a.tO T73 .06'h
54.5 8.3 35.3 .40 4.5 .113 81.8 *.2 35.7 8.73 6.5 .063
T775 873 r353 75^3 - 4.8 .114
81 .8 2V9 35. 9 iflO 5^1 .061 ; ¦
5T71 r—1 275 357? : 74® ~477 7074 1 ' :
81.6 8.4 35.8 .50 6.4 .079. .
-------
Table A-3. Cont.
© = 45° 0 = 90°
£/Q K Fr_ ZZO WZD ATc/ATe X/P JS E,. ZZD_ W/Q_ atc /at^
9.1
3.0
12.ft
«.30
4.5
. 161
1
2.7
12.3
4.80
5.5
.125
V.J
2.9
12.7
4.40
4.8
. 163
9. 1
2.7
12.4
4. 81
5.7
. 144
9.1
2.8
12.8
3.°0
4.7
.160
T. 1
2.7
12.4
4.60
5.4
.139
9.1
8.0
li. a
8.20
5.7
.211
9. 1
7.4
11.9
8.50
4.2
.131
•*. 1
7. 1
12.0
/ • :>0
5.3
.215
9. 1
7.4
12.0
8. 70
3.9
.138
13..2
3.0
12.4
5.20
6.1
. 109
9. 1
*.0
12.0
8.70
3.3
. 146
1?.?
?. 9
12.5
5.40.
3.5
.103
1*.2
2.7
12.5
4.80
6.2
.121
1 8". 2
7. 1
1 l.S
8.70
4.e
. 1 7ft
18.2
2.7
12.6
4.10
5.8
.091
1".?
7.9
11.ft
8.70
5.3
.164
1 8.2
2.7
12.7
4.60
5.7
.091
27.3
•2.P
12.8
5.00
6.3
.083
1 «.2
8.0
12.2
8.70
2.7
.105
27.3
2.0
12.9
5.00
6.3
.088
18.2
8.7
1?.4
8.70
. 2.9
.108
27.3
ft.9
11.4
8.70
2.3
• .090
18.2
8.0
12.5
0.70
3.0
.090
27.3
8.5
1 l.S
8.70
2.5
. 107
27.3
2.7
12.3
6.30
7.3
.0 75
36.4
2.6
12. 1
5. 10
6.5
.070
27.3
2.7
12.3
6.20
6.2
.063
36.4
2.7
12. 1
5.80
6.8
.065
27.3
2.7
12.4
6.00
6.8
.063
36.4
2.7
12.2
6.00
6.2
.064
27.3
8.0
12.2
8.70
¦3.5
.094
36 • 4
9.6
11.5
8.70
2.7
.096
27.3
8.8
12.3
8. 70
3.4
. 100
36.4
9.6
11.5
8. 70
2.7
.093
36.4
2.7
12.6
6.30
6.0
.064
54.S
2.8
12.3
6.90
6.7
.053
36.4
2.7
12.6
6.50
6.2
.059
54.5
2.8
12.4
6.90
6.0
.048
36.4
2.7
12.6
6.40
6.0
.064
54,5
8.7
11.8
8.70
3.6
.078
36.4
7.7
12.4
8.70
3.3
.084
54.5
7.7
11.9
8.70
3.0
.085
36.4
7.7
12.5
8. 70
3.2
.078
54.5
7.4
12.0
8.70
3.0
.091
54.5
2.7
12.2
7.60
5.6
.057
81.8-
2.8
12.6
8. 20
6.2
.038
54.5
2.6
12.2
7.9.0
6.2
. 043
.81.8
2.8
12.7
8.20
5.6
.044
54.5
2.7
12.3
7.80
5.8
.050
81. 8
8.0
11.3
8.70
3.6
.068
54.5
8.7
12.3
8.70
4-. 3
.076
81.8
8.8
11.4
8.70
3.6
.068
54.5
8.8
12.3
8.70
4.0
'.083
9. 1
4.5
34.9
3.50
4.0
.174
81.8
2.7
12.3
8.40
5.0
.044
9.1
3.2
35.2
3.80
4.0
• 164
. 81.8
2.7
12.4
8.20
5.3
.038
9. 1
8.6
34. 1
7.90
6.3
.268
81.8
2.7
12.4
8.60
5.5 .
.044
9. 1
8.6
34.3 .
8.20
6.4
.269
81.8
8.7
12.3
8.70
4.5
.on
9. 1
8.6
34.6
8.20
6.0
.244
91.8
8.3
12.5
8.70
4.0
.065
18.2
3.1
35.7
3.90
5;5
.127
9. 1
3.2
36.4
3.60
4.9
. 149
18.2
3.2
35.»
4". 90
5.0
.133
9. 1
3.2
36.6
4.30
5.2
.156
18.2
3.3
36.0
4.40
5.4
.122
9. 1
3.2
36.9
4.30
5. 1
.127
1 8.2
8.6
33.9
8.70
5.7
.193
9. 1
9. 1
35.5
8.70
4.0
.174
1 8. 2
8.6
34. 1
8.70
5.3
.173
9.1
8.3
35.3
8.70
4.2
.178
11.2
8.6
34.2
8.70
4.5
.180
18.2
3.2
37.2
4.90
4.6
.096
?7.3
3.0
34.8
5.10
6.2
.110
18.2
3.2
37.5
4.50
4.6
.104
^ r. j
J.l>
3i>.0
5.10
5.8
.105
Id.2
3.2
J7.8
4.50
3. J
. 1 Ob
27.3
3.0
35.2
5.00
5. v
.097
. 18.2
8.6
34.0
8.70
3.5
.087
27. 3
a. 1
35.3
8.70
4.7
.130
l».2
8.6
34.4
8.70
<•.1
.084
27.3
H.3 -
35.4
8.70
4.4
.119
18.2
8.5
34.6
8.70
4.0
.084
3ft. 4
3.1
35.7
5.60
6.5
.091
2 7.3
3.2
36.6
5.50
6.7
.075
3ft • *+
3.0
36.0
5.80
6.4
.085
27.3
3.J
36.8
5.20
6. 1
.076
3ft.4
3.0
36.2
5.90
6.4
.0 74
27.3
3. 1
37. 1
4.90
6.5
.065
?ft.4
8.4
34.7
8. 70
3.6
.103
27.3
8.6
35.0
8.70
4.0
.080
3ft.4
8.4
34.9
8.70
3.6
.998
27.3
8.6
35.3
8.70
3.3 .
.075
3ft. <•
8.3
35. 1
0. 7U
3.5
.099
35.4
"3.1
37.3
5.60
6.1
.065
5<*.5
3.1
35.4
ft.70
7.3
.059
36.4
3.1' .
37.5
6.20
6.3
.065
5*».5
3.0 '
35.5
6.70
6.9
.060
36.4
3.0 "
37.7
5.50
6.o
.066
54.5
3.0
35.6
h.90
7.1
.066
36.^
8.4
35.3
8.70
4.5
; 058
5^.5
5.7
36.4
8.71>
4.0
.075
36.4
8. 3
35.4
8.70
4. 1
.053
54.5
8.5
36.6
8.70
3.7
.088
36.4
8.3
35.5 .
8.70
3.5
.053
5»*. 5
8.4
36. 7
8.70
3.8
• 0«8
54.5
3.0
35.8
- o . 7 0
6.3
. O'sS
81.8
3.0
3ft. 1
7.10
. 7.3
.043
54.5
3.0
36.0
5.90
6.3
.043
8 1.8
3.0
36.5
7.90
6.9 . .
.050
54.5
8.3
35. 1
8.70
4. it
.052
Hi. a
3.0
3b.8
8.00
6.5
.038
54.5
8. 3
35.3
8.70
4.4
.046
HI .8
8.4
35.0
8.70
5.4
.053
"1.3
3.0
36.3
b. 90
6.6
.038
H. J .fl
8.4
35.3
b. 70
5.4
.053
81.8
8.3
35.5
6. 70
4.£
.041
Ml .8
8.3
35.5
b. 70
5'. 0
.0*2
81.8
£. 3
2b. 7
£¦-. 70
4 . 7
.047
-------
APPENDIX B
Table B-l Correlations, Deep
Table B-2 Correlations, Shallow, No Turbulence
Table B-3 Correlations, Shallow, With Turbulence
33
-------
Table B-l
Correlations for Deeply Submerged Discharge Data
Z ATC W _ pa b kc Fd f
J5 'AT' D 6 n K r mod
o
1 2
6 Plume Characteristics a b c d f R
0,30,60,90
AT /AT
c 0
-5.79
-0.82
-0.10
0.04
1.28
0.910
W/D
2.40
0.35
0.37
0.04
-0.45
0.814
30,60,90
Z/D
3.72
0.37
0.89
-0.10
-0.79
0.908
0
Z/D
-1.22
CO
CO
•
0.99
-1.72
0.819
ATC/AT0
W/D
-1 .47
-0.29
-1.04
0.50
0.10
0.28
0
b
0.979
0.912
30
Z/D
-0.39
0.47
0.62
-0.05
0.872
AT /AT
C 0
W/D
0.69
-0.06
-0.86
0.40
0
0.30
0
0.09
0.950
0.906
60
Z/D.
-0.11
0.35
1.06
-0.13
0.948
AT /AT
C 0
0.26
-0.79
-0.21
0.05
0.946
W/D
0.53
0.28
0.48
0.926
90
Z/D
0.21
0.32
0.95
-0.10
0.957
ATc/ATo
-0.47
-0.62
-0.32
0.07
0.916
W/D
0.59
0.21
0.50
0.05
0.904
34
-------
Table B-2
Correlations for Shallow Sumberged Discharge Data, No Turbulence
Z AJr W a b „c cd
D> D " e * K r mod
1 2
0 Plume Characteristics a b c d f R
0,15,45,90 AT /AT -8.71 -0.77 -0.13 0.T4 1.80 0.922
C V
15,45,90 Z/D 3.80 0.34 0.69 -0.06 -0.82 0.869
Z/D -5.85 2.22 0.73 -1.48 0.755
ATc/ATq 0.82 -0.81 -0.10 0.17 0.975
W/D 0.34 0.43 0.32 -0.29 0.954
15 Z/D -0.89 0.51 0.66 -0.11 0.937
ATc/ATq 0.48 -0.81 0.10 0.968
45 Z/D -0.10 0.27 0.73 0.938
AT /AT -0,19 -0.66 -0.16 0.08 0.924
CO
90 Z/D 0.30 0.21 0.69 0.901
AT /AT -0.42 -0.74 -0.38 0.16 0.888
C O
erod = 180° - e
35
-------
Table B-3
Correlations for Shallow Submerged Discharge Data, With Turbulence
1 AEc. K = ea nb.i^c Fd flf
D' AT^' D e n K r mod
1 2
8 Plume Characteristics a be d f R
0,15,45,90 AT /AT -6.05 0.73 0.16 1.25 0.892
C O
15,45,90 Z/D 2.78 0.26 0.41 -0.10 -0.45 0.729
0 Z/D -1.49 ,1.28 0.35 -1.49 0.817
AT /AT 0.95 -0.89 0.12 0.974
C O
W/D 0.50 0.45 0.22 -0.30 0.956
15 Z/D -0.14 0.47 0.48 -0.16 0.894
AT /AT 0.40 -0.90 0.24 0.09 0.982
CO
45 Z/D 0.67 0.18 0.40 0.777
AT /AT -0.85 -0.64 0.31 0.06 0.947
C O
90 Z/D 1.18 0.16 0.39 -0.12 0.787
AT /AT -0.70 -0.53 0.12 -0.09 0.871
C O
'• 0rod = 18O°-e
36
-------
APPENDIX C
Figures C-l to C-24 Deep Submergence
Figures C-25 to C-35 Shallow, No Turbulence
Figures C-35- to C-46 Shallow, With turbulence
37
-------
_ 18
s
>
o
z 12
<
S 10
<
o
i-
a:
UJ
>
TEMPERATURE-TRAJECTORY
K « 2 . Ff • 10
0.03
oT'0.2
—90
__ 60*-
—30* —
Q07J
V
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-I. Temperature-Trajectory Chart, Deep Discharge, K*2, Fr = IO.
90"
a 03
30
^ 16
UJ 14
o
2 12
0.075.
0.1
TEMPERATURE - TRAJECTORY
20
40
80
60
ilOO
HORIZONTAL DISTANCE (X/D)
FIGURE C-2. Temperature-Trajectory Chart, Deep [Discharge, K°8, Fr°IO.
38
-------
18
o
N
16
14
lii
O
Z 12
<
H
2
WIDTH-TRAJECTORY
K«2, ^ ¦ 10
W/0*8
_ —8d-
—«o-
——r— -—30*-
20 40 60 80 nOO
HORIZONTAL DISTANCE (X/D)
FIGURE G- 3. Width-Trajectory Chart, Deep Discharge, Ka2, Fr«IO.
18
Q
N
Z 14
in 10
8
WIDTH-TRAJECTORW
K-8, -10
6
4
2
20
40 60
HORIZONTAL DISTANCE (X/D)
80
1100
FIGURE G-4. Width-Trajectory Chart, Deep Discharge, K= 8, Fr »10.
39
-------
_ 18
Q
N 16
U14
O
z 12
<
co 10
TEMPERATURE - TRAJECTORY
K-2, Fr - 50
<
O
h-
cr
UJ
>
8
6
4
2
a 075
02
\
Ql v
\ -N
-9
-------
~'8
§'6
ui'4
o
I12
fe 10
O
8
3 6
ir 4
UI
> 1
WIDTH-TRAJECTORY
K-2. ff «50
90*—
W/O-8
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-7. Width-Trajectory Chart, Deep Discharge, K-2, Fr
o
\
90
u 14
O
5 12
w io
WIDTH-TRAJECTORY
K"8, ^-50
20
' 40 60
HORIZONTAL DISTANCE (X/D)
80
100
FIGURE C-8, Width-Trajectory Chart, Deep Discharge, K«8, Fr
41
-------
o
10
\
N
w
111
o
8
z
<
H
cn
6
Q
_i
<
4
o
h
oc
liJ
2
>
/
TEMPERATURE- TRAJECTORY
0-0°, K » 4
If -10
/
/
AT-0.05
I /
/1 0.073
Q2 / ai
.20'
40—
—eo—
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-9. Temperature-Trajectory Chart, Deep Discharge, 0 = 0°, K = 4.
o
\
10
N
LlI
O
8
Z
<
f—
CO
6
o
_J
<
4
o
h*
a:
UJ
2
>
/
WIDTH - TRAJECTORY
G-O", K»4
y* o
W/D-12
/
/
6 /
.20'
-40
—eo-
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-10. Width-Trajectory Chart, Deep Discharge, 0=0°, K = 4
42
-------
v 10
N
U1
O
Z
<
H
8
<
o
H
OC
UJ
>
TEMPERATURE- TRAJECTORY
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C- 11. Temperature-Trajectory Chart, Deep Discharge, 0*0% Fr = 20.
o
\
10
N
UJ
8
o
z
<
h
ir>
6
Q
<
4
o
h-
a:
ui
2
>
WIDTH - TRAJECTORY
6- 0°, «20
K«I2
VV/D-12 /
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-12. Width-Trajectory Chart, Deep Discharge, 0=0°, Ff «20
43
-------
V 10
N
U ft
O O
z
<
,10 ,. 20.
..40'
;,.Fr-ao
AT-0.1 /
! ^
I
0.2'
0.03
Q07S
TEMPERATURE-TRAJECTORY
6-30°, K ¦ 4
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C- 13. Temperature-Trajectory Chart, Deep Discharge, 0=30°, K°4
W/D-6 X
A
WIDTH - TRAJECTORY
e»30°, K«4
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-14. Width-Trajectory Chart, Deep Discharge, £ =30? K = 4
44
-------
o
£25
uj
o 20
z
<
S 15
Q
2 'o
h
QT
s5
TEMPERATURE - TRAJECTORY
0-30°. Fr ¦ 20
K»I2
02
__l
AT-0.03
— 2 —
0.1
0
075
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C -15. Temperature - Trajectory Chart, Deep Discharge, 0=30? f' = 20.
5 25
N
y 2oi-
z
<
<2 I
a
< 10
o
H
£ 5
>
WIDTH-TRAJECTORY
6-30°, Fr -20
w/D-l;
12
"20 40 60 "80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-16. Width-Trajectory Chart, Deep Discharge, 0«30°, Fr » 20.
45
-------
10
N
W o
O °
z
<
I-
c/) 6
/
0.073
40
^•eo
AT'0 05
< 4
o
h
q;
lu
>
TEMPERATURE - TRAJECTORY
9-60°, K • 4
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C- 17. Temperature -Trajectory Chart, Deep Discharge, 0 = 60, K =4.
< 4
o
IS 2
>
W/0«I2
WIDTH-TRAJECTORY
0-60°, K-4
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C- 18. Width - Tra jectory Chart, Deep Discharge, 0 = 60°, K = 4
46
-------
"7
TEMPERATURE - TRAJECTORY
<1075
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-19. Temperature - Trajectory Chart, Deep Discharge, 0=60® =20.
/"
wo-s
WIDTH-TRAJECTORY
0 • 60°, Ff - 20
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-20. Width-Trajectory Chart, Deep Discharge, 0=60, fy. ° 20.
47
-------
S 12
\
N
UJ
O
10
<8
V)
<
4
h-
cc
Ul O
> *
0.073
AT-0^3
/ -
5V ^
7\
10
20
40"
,Fr-eo
\
TEMPERATURE-TRAJECTORY
0-90°, K-4-
20 40 60 80 100
HORIZONTAL DISTANCE (X/D5
FIGURE C-21. Temperature - Trajectory Chart, Deep Discharge, 0 = 90, K =4.
3 12
N
N
UJ
10
O
z
<
8
K
co
Q
6
_J
<
o
4
h
CC
UJ
2
>
40
.60
WIDTH - TRAJECTORY
20 40 60 80 100
HORIZONTAL DISTANCE (X/D3
FIGURE C-22. Width-Trajectory Chart, Deep Discharge, 0=90°, K = 4.
48
-------
TEMPERATURE - TRAJECTORY
0073
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-23. Temperature-Trajectory Chart, Deep Discharge, 0» 90°, Fy°20.
° 25
N
uj 20
o
z
<
CO 15
<10
o
H
£ 5
>
/
WIDTH-TRAJECTORY
©•90°, Fr «20
W/D* 9
— 2
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-24. Width-Trajectory Chart, Deep Discharge, 9 ° 90°, Fr«20.
49
-------
o
\
N
UJ
6
o
z
<
1—
(£>
a
4
-j
<
o
h
2
cr
Hi
>
TEMPERATURE -TRAJECTORY
K-2, Fr -10
,6Cf-
n m
— 7
^30*
X"
/
AT> 0.2
\
/
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C- 25 Temperature-Trajectory Chart, Shallow Discharge,
No Turbulence, K°2t 10.
*
/
AT* 0.075
TEMPERATURE-TRAJECTORY
K • 8, Fr - 10
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-26. Temperature-Trajectory Chart, Shallow Discharge,
No Turbulence, K*8, F^ »IO.
50
-------
8
o
\
N
111
6
O
z
<
>—
V)
a
4
_i
<
o
f—
?
TEMPERATURE - TRAJECTORY
K - 2 , Fr "50
-90*
,60-
-OQi.
. QQ7S
-309 "
AT" 0.1
02
__ —or—
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-27. Temperature-Trajectory Chart, Shallow Discharge,
No Turbulence, K ¦ 2 , Fr » 50.
_ 8
o
\
N
W e
O ©
Z
£
(/)
5 4-
<
o
2
a: 41
Ixl
>
AT-0.1
TEMPERATURE - TRAJECTORY
K"8, Fr -50
0.075
\
\
.0^
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-28. Temperature- Trajectory Chart, Shallow Discharge,
No Turbulence, K°8 , Fr °50.
51
-------
_ 8
Q
\
N
w 6
o
z
<
H
in
5 4
<
o
i- 2
a:
LU
>
TEMPERATURE-TRAJECTORY
6-0°, K-4
0.2
F. -tO
oT* 0.075
20 40 60 80
HORIZONTAL DISTANCE (X/D)
FIGURE C-29 Temperature - Trajectory Chart, Shal low Discharge,
No Turbulence, © ¦ 0°, K»4.
8
Q
s
N
W c
O o
<
h-
V)
Q 4
<
O
2
ce c
LU
>
WIDTH-TRAJECTORY
0- 0°, K = 4
W/D • 6 -
-10
/
20
_40-
— 80-
kfta '
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-30r Width-Trajectory Chart, Shallow Discharge,
No Turbulence , 0 = 0*, Kc 4.
52
-------
8"
Q
\
N
¦
lii
6
O
z
<
.
H
to
O
4-
<
-
o
h-
2
a.
UJ
>
TEMPERATURE - TRAJECTORY
e-ov Fr • 20
K • 12
/
/ .
0.2
acre
AT*ar
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C- 31. Temperature-Trajectory Chart, Shallow Discharge,
No Turbulence, 0« 0°, Fr « 20.
8
a
v
N
w
UJ
o
6
z
<
h
V)
o
4
_1
<
o
h-
2
QL
LJ
>
WIDTH-TRAJECTORY
e-06, ^ '20
W/U'fl
20 40 60 80 1100
HORIZONTAL DISTANCE (X/DJ
FIGURE C-32, Width-Trajectory Chart, Shalllkw Discharge,
No Turbulence, $= Cf, Fr«20.
53
-------
/
8
a
\
N
'
UJ
6
o
z-
<
h-
o
4
<
o
h-
2
cr
LU
>
12
/
/ /
/ AT-0.1
/
02 /
/
0.075
0.05
TEMPERATURE-TRAJECTORY
e-158, Fr ' 20
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-33. Temperature - Trajectory Chart, Shallow Discharge,
No Turbulence, 0=15° F 3 20.
8
Q
\
fsl
W fi
a o
z
<
j—
V)
o 4
<
o
2
cc £
LU
>
/
K"0
\
\ -
Ql
£IT«0.05
0.075
TEMPERATURE - TRAJECTORY
6 - 45°Fr » 20
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-34. Temperature-Trajectory Chart, Shallow Discharge,
No Turbulence, 0 = 45, Fr *20.
54
-------
T §"
AT> 0.03
_K-2- -
0.078
TEMPERATURE- TRAJECTORY
e - 90°. Fr -20
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-35. Temperature-Trajectory Chart, Shallow Discharge,
No Turbulence, 0- 90°, Fr « 20.
55
-------
_ 8
o
\
N
B 6
z
<
H
a A
<
o
»- 2
q:
IU
>
TEMPERATURE-TRAJECTORY
K ¦ 2 , Ff « 10
_90*—'
-0 05
_60°-
-30°-
AT- 0.075
0*'
0.1
0.2
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-36. Temperature - Trajectory Chart, Shal low Discharge,
With Turbulence, K ¦ 2 , Fr = 10 .
AT«0.
0.075
TEMPERATURE-TRAJECTORY
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-37. Temperature-Trajectory Chart, Shal low Discharge,
With Turbulence, K ® 8 , Fr = 10.
56
-------
TEMPERATURE-TRAJECTORY
Fr - 50
•30
ftT-0.073
•- 2
or
UJ
0.2
100
80
40 60
HORIZONTAL DISTANCE (X/D)
20
FIGURE C-38. Temperature-Trajectory Chart, Shallow Discharge,
With Turbulence; K ¦ 2 , Fr » 50.
20 40 ~60~ 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-39l Temperature-Trajectory Chart, Shallow Discharge,
With Turbulence, K »8, Fr »50.
57
-------
_ 8
Q
\
N
S 6
Z
<
(/>
5 4
<
o
UJ
>
TEMPERATURE-TRAJECTORY
*
6 - 0# , K « 4
0.2
\.
0.075
0.4-
4T-0.I
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-40. Temperature - Trajectory Chart, Shallow Discharge,
With Turbulence, 0" 0°, K»4.
8
a
\
INI
UJ a
O O
z
<
I-
(f)
Q 4
<
o
2
DC. c~
UJ
>
WIDTH-TRAJECTORY
0 - 0°. K =¦ 4
W/D ¦ 6
F. . 10
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-41. Width-Trajectory Chart, Shallow Discharge,
With Turbulence, 9=0°, K = 4 .
58
-------
i ^ r
^ 8
Q
\
N
g 6
z
<
H
(O
5 4
<
o
P 2
a:
TEMPERATURE-TRAJECTORY
0»0\ Fr-20
0.073
AT-0.1
T
0.2
K-I2--
.—4 -
—2 —
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-42. Temperature-Trajectory Chart, Shallow Discharge,
With Turbulence, 0" 0°, Fr ° 20.
~ 8
a
\
N
u C
O 6
z
p
(0
5 4
_i
<
o
2
tr c
ui
>
*7
T ^ r
WIDTH-TRAJECTORY
0-0°, Fr-20
K-12
•4"
•2-
W/0-
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-43, Width-Trajectory Chart, Shallow Discharge,
With Turbulence, 0=0°, Fr»20.
59
-------
_ 8
Q
S
N
u 6
o
z
<
h-
cn
5 4
<
o
o:
LxJ
>
/
JZ.
V
AT »0.05
V
TEMPERATURE - TRAJECTORY
6-15°. F, -20
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-44. Temperature - Trajectory Chart, Shal low Discharge,
With Turbulence, 9 » 15°, Fr°20.
_ 8
a
\
is/
w a
O ©
z
<
H
uT'0.1
0.075
0.05
K- 2
7 /
TEMPERATURE- TRAJECTORY
6-45°. Fr « 20
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-45. Temperature-Trajectory Chart, Shallow Discharge,
With Turbulence, 0 = 45°, F =20.
GO
-------
AT«0.05
(X075-
TEMPERATURE -TRAJECTORY
0 » 90°, Fr = 20
20 40 60 80 100
HORIZONTAL DISTANCE (X/D)
FIGURE C-46. Temperature-Trajectory Chart, Shallow Discharge,
With Turbulence, 0 » 90°, Fr°20.
61
------- |