ENVIRONMENTAL PROTECTION AGENCY
NORTHWEST REGION, PACIFIC NORTHWEST WATER LABORATORY
MATHEMATICAL MODEL
OF THE COLUMBIA RIVER
FROM THE PACIFIC OCEAN
TO BONNEVILLE DAM
PART II
'• 11
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COLUMBIA Rivtft CnTAanCC
publmfcad monthly i« tha locil Mafic* to MtrllWt by
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UNITED STATES-WEST COAST
OREGON - WASHINGTON
COLUMBIA RIVER
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MATHEMATICAL MODEL OF THE COLUMBIA
RIVER FROM THE PACIFIC OCEAN TO
BONNEVILLE DAM
PART II
Input-Output and Initial Verification Procedures
Uhmy
p,trifle Nixthwest Water LAtxJratMJ
ioo s.'U'.h !j;!i Strsat
Crtrvalils. Oregon 37330
by
R.O. Callaway and K.V. Byram
ENVIRONMENTAL PROTECTION AGENCY
Water Quality Office, Northwest Region
Pacific Northwest Water Laboratory
200 S.W. Thirty-fifth Street
Corvallis, Oregon 97330
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CONTENTS
Pa^e
INTRODUCTION 1
BOUNDARY AND INITIAL CONDITIONS-GENERAL 3
HYDRAULIC PROGRAM 7
Test Situation 7
Boundary and Initial Conditions 7
Control of Time 10
Control of Output 10
Flow and Velocity Sign Convention 10
Compatability Checks 11
Examples of Output 11
QUALITY PROGRAM 15
Boundary and Initial Conditions 15
Decay and Reoxygenation Coefficients 17
Inputting the Meteorological Data 18
Test Channel Run-Temperature 19
COLUMBIA RIVER DATA AND TEST RUNS 21
Flow Data and Hydraulics Verification 21
Columbia River Run 34
Reducing Errors 38
DISCUSSION 41
ACKNOWLEDGEMENT 45
REFERENCES 47
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LIST OF FIGURES
Figure Page
1 Test Channel Dimensions 8
2 Time-series of Tailwater and Outflow Records.
Bonneville Dam 23
3 Tailwater Elevations Versus Outflow.
Bonneville Dam 24
4 Computed and Observed Tidal Ranges, Columbia
River, Mile 0-30 25
5 Computed and Observed Tidal Ranges, Columbia
River, Mile 0-146 27
6 Computed Stage Elevations Versus Time,
Mile 27-146 28
7 Computed Tidal Elevation, Current Velocity and
Flow. Columbia River at about River Mile 70
for Low Flow Conditions 30
8 Computed Tidal Elevation, Velocity, Flow -
River Mile 0-68, Columbia River Low Flow Run. . 32
9 Computed Tidal Elevation, Velocity, Flow -
River Mile 24-134, Columbia River Low Flow Run. 33
10 Computed Temperature (°C) Versus Time (Days)
Columbia River 35
11 Computed Temperature (°C) Versus Time (Days)
Columbia River 36
12 Computed Temperatures (Summary) 37
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LIST OF TABLES
Table Page
1 Input Format - HYDRA, HYDEX, QUALTEMP, METDTA ... 51
2 Input Listing for Output Given in Appendix 1. . . . 57
3 Input Listing for Output Given in Appendix 7. . . . 59
4 Columbia River Flows - 1959, 1968 65
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LIST OF EXAMPLES
Example Page
1 HYDRA-HYDEX Output, Manning Coefficient =
0.02, No Inflow 68
2 HYDRA-HYDEX Output, Manning Coefficient =
0-03, No Inflow 80
3 HYDRA-HYDEX Output, 100 cfs Inflow 92
4 Junction-Channel Compatability Error Check. ... 104
5 HYDEX Output, Channel Length 2500 Feet 105
6 HYDEX Output, Channel Length 5000 Feet 110
7 QUAL Temperature Output Test Channel Run 115
8 QUAL Output, Continuing Check 126
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INTRODUCTION
Part I of this report discussed the general model features,
and presented program listings. In this part, examples of model
usage are given, as well as specific examples of input-output on
test cases. Preliminary verification of the model is discussed
and recommendations and conclusions for future work are outlined.
This report was originally undertaken as part of an effort
to model the entire Columbia River, as stated in Part I. Report
writing being what it is, the putting together of this document
has lagged behind implementation of the model. Thus, several
runs have already been made by Northwest Regional Office personnel
of EPA who learned how to use the model without benefit of this
writeup. They should be contacted if additional information on
model flows and, in particular, real-life conditions on the
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BOUNDARY AND INITIAL CONDITIONS - GENERAL
Boundary conditions for the hydraulic and quality models
must be carefully specified if the models are to make realistic
predictions. For the hydraulic model the boundary conditions
will usually consist of a fairly simple tide wave at the ocean
end and steady mainstream and tributary inflows upstream of the
ocean end.
Tide and river flow data are usually available from state
or federal agencies, but water quality data adequate for specifi-
cation of boundary conditions may be hard to find. While automatic
tide and stage recorders are inexpensive, easy to install and
maintain, automatic water sampling devices and chemical monitoring
equipment definitely are not. Furthermore, if a boundary water
quality parameter is to be correctly estimated it should be
measured throughout the water column and across a given stream-
restrictions that rarely apply to stage and tidal measurements.
As a result, the usual procedure is to find a point where
the parameter is constant over time and space (or nearly so,
compared to other fluctuations of interest), and specify a
constant boundary condition there. Otherwise, if the input load
is large enough or if the source is near the boundary, one has
the situation of having to specify what is to be predicted; the
only solution is thus to extend the boundaries of the model to a
distance where source loads will not significantly affect the
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4
Initial conditions are specified at each junction for both
programs in order to start the solutions. In the hydraulic model
the accumulation of errors due to poor guesses at initial conditions
is unimportant due to the presence of strong forcing functions. The
guesses are made (more simply, head and velocity are taken as zero -
hence not punched), the program is run for several tidal cycles, and
the output from HYDEX is examined to see whether the solution has been
carried far enough to achieve convergence (see appendices).
Poor guesses at quality initial conditions are another matter.
Convergence is generally slower because the amounts of quality
constituents are small in relation to the tidal and river flows.
Considerable amounts of time may be required, for instance, for a
substance to come to equilibrium starting from zero initial and/or
boundary concentrations in response to a point source load. Indeed,
a clear indication of an equilibrium state may not be obvious at all.
If the initial concentrations are set too high (with respect to the
simulated input loads) then loss of concentration is indicated; this
can only be accomplished by flushing out of the system. The latter
will proceed at a rate determined by the flows present in a particular
segment of the model. Conversely, a set of 'low' initial conditions
can approach higher concentrations only by allowing sufficient running
time for convergence.
The boundary value problem, as we have shown, is less troublesome
if the model is extended to a point where the boundary conditions are
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5
to run it than is necessary for the area of interest. If it is
desired to run only a section of the model, one can run the full
model to achieve convergence, and then use the hydraulic information
at the ends of the section for boundary conditions on a smaller
model. Tide guages, i.e., real boundary data, could achieve the
same thing in the absence of a larger model.
Instead of the mixed tide or constant flow options which
the program currently allows for as hydraulic boundary conditions,
it would generally be easier to input the data as equally spaced
points. We have programed one version of HYDRA in which up to
ten variable inputs (tributaries) can be substituted. The program
is not listed here and has not been extensively tested but is avail-
able on request.
In summary, the boundary-initial value problem is fairly
straightforward in the hydraulic case if constant inflow at the
upper end of the model is assumed, but can be troublesome, and
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HYDRAULIC PROGRAM
Test Situation
A many-junctioned and channeled model can produce lots of
computer output, and to keep down the weight of this publication
most of our examples are shown for a test system, which is
essentially a rectangular channel with five junctions and four
channels. The channel-junction numbering identification and
dimensions are shown in Figure 1. General format specifications
are given in Table 1. Card input format for a test run is shown
in Table 2. The output generated by these cards is shown in
Appendix 1.
Boundary and Initial Conditions
The boundary conditions for the hydraulic program are specified
as a function of time at the ocean end of the model and as constants
at the upper end. In the test system examples, a wave with a range
of two feet and period of 12 hours is input at the ocean end,
junction 1.
The Fourier series expression for head, y, at time t is then:
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AREAS (J).
CLPN(N)
AREA(N)
CHANNEL DIMENSIONS
FIXED
B(N)S 1,000 FT. - WIDTH
CLEN(N)= 5,000 FT. = LENGTH
VARIABLE
AREA (N) ¦ 10,000 FT.2- CROSS-SECTIONAL AREA(INITIAL)
R(N) - 10 FT * AREA(N)/B(N)- HYDRAULIC RADIUS
JUNCTION DIMENSIONS
AREAS(J)" 5x!06 FT2»SURFACE AREA (FIXED)
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9
The program will accept two harmonics as:
y = aQ + ai sin (tot + ^) + a2 s i n (2cot + (|>2)
where,
a = A datum level or constant stage elevation
with reference to the datum.
+ L%
a. = Amplitude of i harmonic,
a) = A speed number or frequency.
j. t_
<{>. = Phase angle of i harmonic,
t = Time.
If a more complicated wave form is required for input, i.e., one
requiring more than two harmonics, or if it is desired to utilize
known tidal coefficients, then program modifications can easily
be made.
If there are two junctions at the ocean with the same input wave
then YT(2) = YT(1) and Y(2) = Y(1) can be employed and the loops
changed from J=2, NJ to J=3, NJ. (See sequence numbers 160-161,
189-190 in program HYDRA, Part I)
No tributary or mainstream inflow will be allowed. This is the
condition that would exist in an embayment with no runoff entering
the system. For initial conditions, heads and velocities will be set
to zero and the Manning coefficient will be set to 0.02 for all
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10
Control of Time
For all cases, a time step of two minutes (DELT=120 seconds)
is used and the simulation run for a period of 18 hours. Then,
nrvr - 18 hrs x 60 min hr"1 n
NCYC " 2 min cycle-' = 540 Mraulic cycles.
HYDEX is called and an averaging period of 30 minutes used.
Then NODYN . '80° % (30^1;)- . ,5 (c^_,. Refern.„g t0
sequence numbers 34 and 35 in HYDEX, it will be seen that NST0P =
540 and NSTART = 540 - ^ = 180 > so the total averaging
period consists of 360 dynamic cycles or 12 hours.
Control of Output
The input data is listed (INPSUP=Q), printout begins with the
first cycle (IPRT = 1) and the binary record is written starting at
hydraulic cycle 180 (IWRTE = 180). Output is made at all junctions,
hence N0PRT = 5 and JPRT = 1, 2, 3, 4, and 5. A 'restart' deck is
written after cycle 540. If it is found that convergence has not
been achieved, this data may be used as initial conditions and the
program run again or extended.
For each example, the running time was about 24 seconds and
there were 493 lines of printed output.
Flow and Velocity Sign Convention
The sign convention for direction of flow from channels to
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11
This is carried in the "system status" printouts, and in the input
when it is necessary to use QIN to show tributary inflow (negative
QIN) or non-system outflow (positive QIN).
When a flow or velocity is printed for association only with
a channel, such as in the "channel data" or the channel summary in
HYDEX, a positive flow/velocity means a flow from junction number
NJUiNC (x,l) to junction number NJUNC (x,2). Since, on input of
channel data, the NJUNC (x,l) appears on the card to the left of
NJUNC (x,2), it may help to consider that positive flow is from
"left" to "right" (but only for this simple example!).
Compatability Checks
Junction numbers are listed on channel cards to designate the
junctions which are at the end of the channel. Channels are listed
on the junction cards to designate which channels enter the junction.
If an error in coding from the schematization results in an incon-
sistency, an error message is printed, and the program terminates.
Appendix 4 is such a case. The channel data show channel 1 ends at
junction 1 and 3, but the junction 3 data show only channel 4 as
connecting to it.
Examples of Output
Output for Appendix 1 is shown on pages 68 to 79. Junction,
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12
be seen that initial heads and speeds are set to zero. Output for
every thirtieth cycle is given on pages 70 to 72. Intermediate output
is not shown; cycle 511 and the final cycle output is shown on pages
73 and 74- Output from subroutine HYDEX is shown on pages 77 to 79..
In Appendix 2 (pp 80 to 91) conditions are the same as in
Appendix 1 except that the Manning coefficient is increased to 0.03.
Differences in head, velocity and flow compared with Appendix 1 begin
appearing at cycle 31 (page 83) and are most apparent in the HYDEX
output (pp 89 to 91). In both examples it can be seen that there is
a slight net flow (pp 77 and 89) in each channel. Flow is seaward
(-) in Appendix 1, and landward (+) in Appendix 2, a consequence of
the roughness coefficient, the duration of the run, and the averaging
period (1/2 hour).
As a third example, 100 cfs is input at the upstream junction
(QIN 5 = -100), other conditions being the same as Appendix 1 in order
to show the influence of inflow on the solution. Output is shown on
pages 92 to 103. As can be seen on page 101 the net flow is approxi-
mately 100 cfs seaward. Comparison with Appendix 1 shows a slight
difference in the channel cross-sectional areas; there is a general
increase seaward and decrease landward in velocities and flows as
would be expected because of the river input.
Subroutine HYDEX provides a means of determining whether
convergence has been achieved and indicates the magnitude of water
accumulation or loss (if any). Two additional cases of this are
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13
which only the HYDEX output is shown. The only difference in input
conditions is that all channel lengths for example 5 are 2500 feet
and for example 6 are 5000 feet. A flow of 1000 cfs is input at
junction 5. In each case only the junction and channel restart decks
at the end of 540 cycles are listed from program HYDRA, while print-
out from HYDEX is shown that for the 'short-channel' example net
flows in each channel are very close to the river input of 1000 cfs
while for the 'long-channel' example (p!12) there is a more serious
discrepancy. Differences are also apparent in the cross-sectional
area data, tidal ranges (ppl08 and 113), and the flows in the first
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QUALITY PROGRAM
Boundary and Initial Conditions
If the boundary conditions for BOD, for instance, are known
to be 0 or some constant value, regardless of the fluctuations in
head or velocity, or are specified, then the problems of convergence
iri the water quality program concern initial conditions specified
within the boundaries. If "too much" constituent is initially
specified, then so much computer time will be expended in removing
the excess; likewise, if "too little" is specified, then a certain
amount of time will be expended in reaching steady-state by addition
from the sources.
Experience in applying the convergence factor, FACTR (I,K),
to one or more groups, NGROUP (I), consisting of the junctions
numbered NJSTRT up to and including NJSTOP for any constituent, K,
can diminish the time required for convergence. If, after a certain
amount of time it is found that concentrations have not achieved
steady-state, the FACTR can be applied as some value >1 depending
on the constituent state at the time. The program then can be
restarted from the restart deck or from scratch.
Boundary conditions consist of those from tributaries or waste
flows at a given junction and those at the ocean (lower) end of the
model. Constituent mass is added to the system by either of two
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16
water of concentration CSPEC and flow rate QINWQ is assumed to come
from outside the system. Situations like these are tributary inflow
(where the flow of water is significant and has been allowed for in
HYDRA), or a sewage plant effluent (where the flow of water may not
be significant, but where the constituent is). The second mechanism
is a diversion return, where the water is to come out of and then be
returned to the system. Constituent is added to the system during
the diversion by specifying a mass-concentration (CONST, mg/l-cubic
foot/delta-t) independent of flow in the diversion. Constituent
originally in the water as it was diverted is transported by the
diversion, but if not all water removed is returned (RETRNF^l),
some constituent is lost to the system also. Only one of the two
mechanisms should be used at any particular junction.
The final quality boundary condition to be considered is at
the ocean or lower end. The simplest case occurs if the concen-
tration is some constant value. If it varies with tide stage, then
enough (NSPEC) varying concentration values must be input to cover
a tidal cycle. If the lower end is not large enough to be considered
an infinite source or sink or if a concentration is significantly
different from the specified boundary value (CIN) when the substance
reaches a boundary, then the resulting gradient will be forced to
conform to the boundary value.
In the specific case of the temperature initial and boundary
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17
set of conditions, preferably real data, is on hand at the outset.
If meteorological data are used, several trends of different duration
(days) may exist and there is no real approach to steady-state, so
that it may be difficult to detect subtle errors. If no large
gradients exist (e.g., in the absence of a large heat input at a
junction) the dispersion errors can be shown negligible by making
all initial and boundary conditions constant, removing the meteoro-
logical input and noting the accumulation of values different from
those initialized when the dispersion coefficient is set to zero.
Decay and Reoxygenation Coefficients
Decay and reoxygenation rates are usually given in units of
day"^. (If base 10 is employed the usual convention is to use
small k, i.e., ka and k2 for the first order decay and reoxygenation
rates, respectively. Base e goes with a capital: Ki, K2.) In
order to input these rates into the program, conversion to the time
unit employed (sec~^) must be made. No provision is made to vary
k2 with velocity or kj with flow or temperature here although these
options could be incorporated.
For the decay rate for BOD, or any substance, the dimensionless
quantity
l^c = 10 klAt (or = e"KicAt, if base e is employed)
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18
kt = Decay rate converted to sec
At = quality time step in seconds
K = Quantity input (klComputer) as DECAY(K), F10.0,
* th
(See sequence number 74; (K) here refers to the K
constituent.)
A different procedure is used for the reoxygenation coefficient
and
K2i = K2, or k2. = k2
is input, where K2 is the reoxygenation coefficient in sec , and
K is the quantity input as REOXK(K), F10.0, with dimensions of
2c
-1
sec .
For example with a quality time step of 30 minutes (At = 1800
seconds), and K, = 0.1 day"', KjC would be input as 0.997919; for
x2 = 0 1 day"1, K c would be input as 0.00000115. The program
assumes both rates to be uniform throughout the estuary. As always,
be wary of which base is being employed and be consistent, i.e.,
don't use base e for ^ while using base 10 for k2. Future versions
of the model will allow for automatic computation of these coefficients.
Inputting the Meteorological Data
It has been stated that the temperature independent terms were
assumed known or could be computed independently. The development
of program MIFP (Meteorologic Input File Program) for the FWQA (see
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19
writing a separate subroutine during the later development stages
of the Columbia River program. MIFP can be modified as a standard
subroutine to this estuary model.
We will assume the net radiation values (QRNETA) are available
in a table, as are winds, air temperature, wet bulb temperature and
air pressure. The interval between data points, INT, (usually three
hours are used in ESSA weather reports) the number of points, NPTS,
and the time of starting in relation to the quality program, NQCSM,
are all that are required. Data is then linearly interpolated
compatible with time step used in the quality program.
Test Channel Run-Temperature
Appendix 7 (pp 1 "15 to 125) shows temperature calculation output
using the 5 junction test channel. Here the initial and boundary
temperatures are taken as 10°C. No driving force is provided (heads
are zero) and no input flow is assumed, hence the "channel" acts as
a dormant slough, rto dispersion, waste water, or multiplication
factors were input.
The input meteorological data are shown on page 119; these data
were also used in the Columbia River run discussed below. Net in-
-2 -1
coming radiation (kcal m sec ) is input directly as is wind speed,
wet and dry bulb temperature, and atmospheric pressure. There are
24 hourly observations; the program assumes that these values are
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20
(or other interval) variations from day to day can, of course,
also be used as input.
Output from the program for several cycles is shown on
ppl20tol25as are the computed radiation terms and equilibrium
temperatures; normally these terms will be suppressed.
Format specifications for QUALTEMP and METDTA are given in
Table 1. The input list for the QUALTEMP listing in Appendix 7
is shown in Table 3. The output for HYDRA-HYDEX (required for
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COLUMBIA RIVER DATA AND TEST RUNS
Feigner and Harris (1970) have presented results of the
San Francisco Bay-Delta model. They show the influence of
varying the magnitude of the dispersion coefficient on output
concentrations as well as several other examples of model use.
Although temperature is not discussed, the reader is referred
to their work as it presents some types of examples which will
not be reported here, and provides further insight as to model
use.
Flow Data and Hydraulics Verification
The next few paragraphs deal with verification attempts in
the Columbia. We were not overwhelmed with actual field data and
relied mainly on USC&GS tide tables (U.S. Department of Commerce,
1970) for verification of the hydraulics. Stage elevations at
Bonneville Dam were taken from a report by Bonneville Power
Administration (1966).
Because of the volume of water contained in the Columbia,
the response of the system to hourly heat fluxes will not be as
dramatic as in the case of wide, shallow streams. This shows up
in real life and is reflected in the computations since a large
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22
A typical record of outflow and tailwater elevation at
Bonneville is shown in Figure 2. Data from these graphs were
picked off at several flows in order to obtain the correlation
shown in Figure 3, a plot of tailwater elevation versus flow.
The two flows and elevations used in the runs to be described
are also shown in this figure.
Although the actual records indicate rather wide diurnal
fluctuations, steady flows were assumed in our runs in order to
obtain (and be able to observe) dynamic steady-state as rapidly
as possible.
At the upper boundary condition the flow from the junction
representing Bonneville Dam was input. Water elevation above
datum was then approached as the channel depths responded to the
amount of discharge. At the outset of this study, we were not
sure just what the elevations should be and it was pleasurable
to find that the computed elevations fell within 1-2 inches of
observed, even when the difference in tailwater elevations for
two flows was about seven feet. The flows referred to are shown
in Table 4 and the remainder of this section deals with verification
using these flows.
In Figure 4, computed and observed co-range lines are given.
The computed tide range is output in subroutine HYDEX, the values
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20 r
S 15
U-l
10
15
o
10
CO
>4-1
o
0 ¦
Day A
Day 5
Day 6
Day 7
Day 2
Day 3
Day 1
-------
25-
0)
>-l
0)
AJ
eg
&
CO
H
20-
15-
10-
5 +
1968 Run
I
J.
10
1959 Run (see text)
_L
15
20 25
30
FIGURE 3.
10 n c.f.s.
TAILWATER ELEVATIONS VERSUS OUTFLOW.
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5r
r*
Ui
o
o
Vj
u:
Cj
51
STATUTE MILES
— CO-Range Line (Computed, ft.)
-0 Mean Diurnal Range, ft.
USC ft 6 S "Tide Tables
RM283,
&
V63
/ \;£fp Astoria
Jim Crow Point
i * / i • « \* V* I
^\ js.9
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ranges. Also shown in the figures are "observed" ranges as taken
from the C&GS tide tables. In general, the agreement between
computed and observed values is excellent.
Figure 5 shows a longitudinal section of computed and observed
ranges. Note the agreement in the lower river which shows an
increase in mean diurnal range with distance upstream, passing
through 6 feet about mile 5 and again at mile 25. The agreement
is rather good along the entire river stretch with the exception
of from about mile 70 to 100. The reasons for the discrepancy
here are not known at this time, but could be due to channel
modifications made after the USC&GS computations base data were
collected, but which are incorporated on the charts from which
the input data was taken.
The 1959 flow data (Table 4) were chosen as representative
of a "normal" low flow period. Starting at river mile 27, a wave
i>
with 6 foot range, Manning coefficient of 0.02 ft'6 and 12.5
hour period was input at a river level of 3.8 feet (as determined
from Corps of Engineers data for the flows used). It was assumed
that 25 hours would be sufficient for convergence, hence these
output data (first 25 hours) were discarded. Figure 6 shows the
progression of the wave with distance upstream. Agreement between
computed and Tide Table phase lags and amplitudes was on the order
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4-
O
Ul O
t— CO UJ
=> => 5»
Q.ZK
7" i—• Ll/
O S on
o 00
O
+ 1.0
- 1.0
© © Computed
0 Q USC & GS Tide Tables
RIVER MILES FROM NORTH JETTY
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18
16
14
12
10
8
6
4
2
0
; 6
River Mile 146
130
Input (y = 3.8 + 3.0(SINu)t +
, 4.712389))
25 27 29 31 33 35 37 39
HOURS
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29
Clark and Snyder (1969) published a note on their observations
of current reversal 70 miles (113 km) upstream from the mouth of the
Columbia River, near the proposed site of two thermal electric power
plants. The particular river stretch was chosen because heated cooling
water returned to the stream might interfere with the endemic and
anadromous fishery, especially if there were to be periods of low
current speeds as during a current reversal. The purpose of their
study was thus to determine if reversal occurred, and if so, to measure
its duration during a very low flow period of less than half the
river's mean annual discharge (of 84,500 cfs at Astoria). A rather
extensive field study using dye dumps and fluorometry was reported;
in summary, they found that reversal occurred over a four-hour period
from about 3:50 a.m. to 8:00 a.m. on April 16-17, 1968.
The low flow occurring during their study was the result of
filling the then just-completed John Day Reservoir. Such events
are not recurrent; the flow magnitudes occurring, however, have been
projected as future possibilities.
A sine wave with a period of 12.5 hours and range of 7.5 feet,
the diurnal range at the North Jetty, was Input at the ocean end
of the model. A Manning coefficient of 0.02 ft /6 was employed and
conditions simulated for two tidal cycles.
Figure 7 1s a computer plot of tidal elevations, velocities
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6
4
2
0
~
o
3 2
Convergence
River Mile 67 *
5,
H 1 1 1 1 1 1 1 (-
H 1 1 1 1 1 1 1 1 1 1 1 1
(• adjusted from Clark and Snyder (1969))
^RM 71
^—i—i—i—)
HOURS AFTER LWS, ENTRANCE
| t | | | I I I I I I I ! I I I I I I I I I I
5 10 15 20
25
RM 68
(
RM 7
2.5 t
4RM 73
FIGURE 7. COMPUTED TIDAL ELEVATION, CURRENT VELOCITY AND FLOW.
COLUMBIA RIVER AT ABOUT RIVER MILE 70 FOR LOW FLOW
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31
the first few hours of simulation are due to the convergence of the
numerical solution from the given set of initial conditions. In this
case, convergence was complete in about 10 hours. The open circles on
the figure are tidal elevations as taken from Figure 2 of Clark and
Snyder and adjusted so that the computed second high water maximum is
in phase with the observed.
Even though no attempt was made to input the existing mixed
tide at the entrance (although it could easily have been at the
expense of more computer time) the computed curve is in good agree-
ment with the observed. It can be seen that the frictional and non-
linear terms in the equation of motion have distorted the ocean input
sine wave to the output shown near Prescott. Computed tide reversal
(middle figure) occurs for about three hours as compared with four
hours observed. Closer agreement could be accomplished by adjusting
the friction coefficient. Computed maximum flood velocity was 1.2 fps;
maximum ebb velocity was 2.1 fps. These velocities are integreated
vertically across channel and will generally be lower than observed
peak velocities in mid-channel.
Computed transport through the channels is shown in the lower
part of the figure. Net flow in the Columbia channels for the last
12.5 hours of the run was 78,606 cfs; the remaining flow being
diverted north through another channel. For the low flow period of
1968, Figures 8 and 9 show computer plots of head, velocity, and
volume of flow with river mile upstream for the tidal cycles. These
results have not been "verified" as such but are given here as additional
examples of output. u^f„y
fv.m,: Njrthwett Water Uboraton
iiOO South stiwt
-------
Convergence
River Mile
J,0V^C
RM 38,
CM
RM 12
RM 0.0
CM
«/>
RM 31
u.
OQ
00 CM
TIME, HRS AFTER LWS AT ENTRANCE
'\RM 0.0
in
o
u-
o
00
o
in
FIGURE 8 COMPUTED TIDAL ELEVATION, VELOCITY, FLOW - RIVER MILE
-------
River Mile 134
Convergence
'RM 86
RM 71
RM 2
RM 85
RM 125-135
TIME, HRS AFTER LWS AT ENTRANCE
RM 125-135
FIGURE
9.
COMPUTED TIDAL ELEVATION, VELOCITY, FLOW - RIVER MILE
-------
34
Columbia River Run
Temperatures on the Columbia were computed from Jim Crow
Point to the Dam. Hydraulic output from HYDRA-HYDEX is input
to QUAL; initial conditions are taken from Sylvester (1958) and
range from 17.5°C at the lower end to 18.2°C below the dam.
Figures 10 and 11 show examples of computed values at selected
river miles. The 'error' and 'corrected' values are discussed
later.
Computations were made for 10 days assuming that the
initial 24 hour meteorological data repeated itself for each
day. The computations were made using 1/2 hourly hydraulic
output averages; computed values are shown only for the beginning
of every second day.
The largest variations in computed temperatures occur at
mile 100 which is the confluence of the Willamette and Columbia
Rivers. Although verification data are lacking, this fluctuation
appears realistic given that mixing of the Columbia and Willamette
will result in relatively large temperature fluctuations when
Willamette temperatures are different from those of the mainstream.
Figure 12 summarizes 10-day temperature at all four locations.
It can be seen that in the absence of any large temperature gradients
under the assumed meteorological Input data that temperatures will
-------
-a Computer
+ +
18.4 +4.0
18.2 +2.0
18.0 0.0
17.8 -2,0
River Mile 35
4 6
DAYS —
8 10
T(°C) %E
18.4 +4.0
18.2 +2.0
18.0 0.0
River Mile 75
% Error
Corrected
0 2 4 6 8 10
DAYS ~
FIGURE 10.
COMPUTED TEMPERATURE (°C) VS TIME (DAYS)
-------
C)
0
8
%E
6 +6.1
4 +4.i
,2 +2J
,0 O.i
,8 -2.
6 -4.1
4
/
RIVER MILE 100
(Wi11amette-Columbi a)
%E
18.6 +6.0
18.4 +4.0
18.2 +2.0
RIVER MILE 130
°——° Computer
* •" % Error
~~~~° Corrected
17.4
8 10
8 10
FIGURE 11.
COMPUTED TEMPERATURE (°C) VS TIME (DAYS)
-------
18.4
River Mile 100
18.2 " A
18.0
17.8
17.6
17.4
17.2
0 2 4 6 8 10
DAYS
FIGURE 12.
-------
38
Reducing Errors
In this section a discussion is given on means of controlling
¦pseudo-dispersion' errors. As a first step in evaluating a particular
schematization a "continuity check" should be made. This is illus-
trated in Appendix 8 (pp 126 to 130), where the initial boundary values
are taken as 15.0 arbitrary units (pi28). An inflow of 100 cfs of
pollutant with concentrations of 15.0 is assumed. As discussed
earlier, any numerical 'leakage' will show up as differences from
15.0 over so many cycles. The output for the first quality cycles
is shown on p."130 . All further cycles showed no deviation from 15.0.
Checks as above should be made to determine the magnitude of
the error (if it exists). The time step should be reduced if
large errors occur. If the time step cannot be adjusted to minimize
this error, the following "brute force" correction can be tried.
A running account of the error is made by inputting a second
constituent with initial and boundary conditions equal to 100.00
arbitrary units. If instabilities occur, they will be reflected
as a certain percent error at each junction for each time step.
This error can then be subtracted from the constituent of interest,
reset to 100.00, and reapplied at each time step.
Figures 10 and 11 show the percent errors and the corrected
-------
39
suggested will work for any constituent in the absence of any large
gradients. Where errors associated with large gradients occur, the
quarter-point method discussed in Part I will minimize, but not
completely eliminate, the associated pseudo-dispersion error (which
-------
DISCUSSION
The model discussed here is of the 'macro' variety in that
small scale detail is neglected. So-called 'micro' models deal with
conditions in the immediate vicinity of outfalls, hence must be
capable of treating entrainment and jet-flow in terms of the depth
and angle of discharge and prevailing Reynolds and Froude numbers.
The equations relating to buoyancy dependent flows such as heated
discharges are at least two-dimensional in nature and somewhat
more involved than the wave equations solved for in this report.
As stated before, then, the model presented does not purport to
treat discharges in the near vicinity of an outfall, whether it be
heat or any other substance.
It is felt that the greatest use of this type of model is as a
descriptor of currents and water levels at given points in the
system and as an indicator of space averaged concentration profiles.
In a system as complex as the Columbia the use of the model in
predicting currents under different river and tidal inputs seems
justification enough in undertaking the work. The hydraulic portion
of the model is relatively simple to use and trouble free or trouble
obvious as far as numerical problems are concerned. Predicting
effluent concentrations and salinity intrusion should be attempted
only with an attentive eye to the problems associated with explicit
-------
42
Extension of the model to a treatment of phytoplankton dynamics
is somewhat obvious for the well-mixed case. Certain assumptions
would be required regarding the penetration of light, etc., but
computation of relatively simple predator-prey relationships would
not be a major problem.
Use of the model in shallow lakes and reservoirs has not been
attempted by us; in certain cases the model could be so used, such
as in treating dye releases on a short term (order of days) basis.
Provisions could be made to provide for bottom uptake of material
through the decay coefficient.
Obvious modifications of the program would be to include wind
stress as a forcing function, to provide for graphical output, to
include tidal flat areas, etc. We have displayed the data (see
Figures 8 and 9) but have not attempted to include this as part of
the package. Inclusion of wind would require a simple bookkeeping
scheme for orienting the channels with the wind; in this regard
several wind regimes could be employed as could several meteorological
systems. In particular this would be more realistic than assuming the
same weather over as diverse a climatological setting as the lower
Columbia; it was felt, however, at the beginning stages that this
would amount to lily gilding.
In summary, it is felt that the model is as good as any of the
one-dimensional models on the market, especially in those cases where
-------
43
broad embayment is to be treated then by all means employ a two-
dimensional scheme such as Leendertse's - keeping in mind that one
should, in the final analysis, employ the simplest tool possible.
If a slide rule will do the work don't use this model or anyone
-------
ACKNOWLEDGEMENT
Thanks are due K. Feigner, D. Fitzgerald, and J. Yearsley,
-------
REFERENCES
Bonneville Power Administration, 1966, Summary Report on
hourly operation studies including 600 MW units at Grand
Coulee. BPA, Branch of Power Resources. Unpaginated
MS dated Nov. 16, 1966.
Clark, Shirley M. and G. R. Snyder, 1969, Timing and extent
of a flow reversal in the lower Columbia River. Limn,
and Ocean. 1£(6), pp. 960-965.
Feigner, K. D. and H. S. Harris, 1970, Documentation Report:
FWQA dynamic estuary model. U.S. Gov't. Printing Office,
Washington, D. C. 181 pp + 67 pp Appendix.
Sylvester, R. 0., 1958, Water quality studies in the Columbia
River basin. U.S. Fish and Wildlife Serv. SSR #239. 134 pp.
U.S. Dept. of Commerce, 1970, Tide tables, West Coast North and
South America including the Hawaiian Islands. Envir. Sci.
-------
Input Card Preparation
Table 1 shows the cards required for input to HYDRA,
HVDEX and QUALTEMP in addition to format specifications and
sequence number location in the Part I program listings.
Table 2 shows the input listing for the output given
in Appendix 1, a HYDRA-HYDEX run.
In Table 3 the input list for the QUALTEMP output shown
in Appendix 7 is given. Output for the HYDRA-HYDEX is not
-------
TABLE 1
Input Card Preparation
-------
TABLE 1A
INPUT FORMAT - HYDRA, HYDEX
U1
ro
Reference
Information
Card Content
Format
Number of
Cards
Always
Required?
19 (HYDRA) Identification ALPHA
20 Control
22 Output Control
35 Junction Data
49 Channel Data
18A4
5I5,2F10,3I5
62 Junction No's
where output
is desired
63 Ocean Boundary
Conditions;
Fourier Series
24 (HYDEX) Identification ALPHA
25 Number of NODYN
dynamic cycles
NJ,NC,NCYC,NPRT,
NOPRT,DELT,TZERO,
NETFLW.ISTART.INSUP
IPRT,IWRTE,KPNCHI
JJ,AREAS(J),(NCHAN
(J,K),K=1,5),Y(J)
QIN(J)»YT(J)
NN,CLEN(N),(NJUNC(N, 15,F8,2I3,F6.1
K),K=1,2),R(N),CN(N), F5.3.F5,5X,F10.3
B(N),V(N)
(JPRT(J),I=1,N0PRT) 1415
315
I5,F10,5X,
5I3.F10.5.F10,
F10.5
A1,A2,A3,PH12,PH13, 6F10
PERIOD
18A4
515
2
1
1
NJ
NC
NOPRT+13 2/
T5
2
1
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes-7
Yes—7
Note:
1. Reference # refers to numbers on the right-hand side of the program listings in Part I.
2. Truncated value.
-------
TABLE IB
INPUT FORMAT - QUALTEMP, METDTA
Reference # — Information
Card Content
Format
Number of
Cards
36
37
38
54
62
65
67
71
74
84
Control
Control
Output
Identification
Number of
Constituents
Identification
Concentration
Upper Limits
Constituent with
a reaction rate?
Reaction rates &
saturation values
Diversion-return
pairs
NJ,NC,NSTART,NSTOP,
NODYN.NOJ,ITEMP,
IEQTEM
NRSTRT,INCYC,N0CYC,
N0EXT,CDIFFK,NTAG
IPRT,NQPRT,NEXTPR,
INTBIG,IWRITE,NEXTWR,
IWRINT
ALPHA
NUMCON
ALPHA
CLIMIT
DECAY(K),RE0XK(K)
CSAT(K)
NUNITS
815
4I5,F10,I5
715
18A4
15
18A4
5F10
{NCQNDK(K),NC0N0X(K), 1015
K=1,NUMCON)
3F10
15
1
1
1
2
1
NUMCON
1
1
NUMCON
1
Always
Required?
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
-------
TABLE IB (Cont'd)
INPUT FORMAT - QUALTEMP, METDTA
Reference # —
Information
Card Content
Format
Number of
Cards
Always
Required?
on
-P»
90 Diversion-return
junctions and
factors
101 Waste inflows &
concentration
109 Waste inflows &
concentration
118 Convergence
factor groups
121 Convergence
factor and
junctions where
applied
143 Number of Ocean
boundary values
to be read
145 Boundary con-
centrations or
values
148 Number of
junctions' data
to be output
JDIVl(I),JDIV2(I)
JRET1(I),JRET2(J)
(RETRNF( I,M),C0NST(I,M),
M=1,NUMCON)
JJ,QINWQ(J),(C(0,K),
CSPEC(J,K),K=1 ,NFIRST)
JJ,(C(J,K),CSPEC(J,K),
K=NFIRST,NUMCON)
NGROUP(I)
(FACTR(I,K),NO STRT
(I,K),NJST0P(I,k),
K=1,NG)
NSPEC
(CIN(M,I),1=1,
NSPEC)
NOPRT
13,314,5(F5,
E8.2)
I5,7F10
I5.7F10
15
5(F5,I5,I5)
15
NUNITS
NO
NJ
NUMCON
NUMCON
7F10
15
NUMCON x (NSPEC+6)
7
No
Yes
No
Yes
No
Yes
Yes
-------
TABLE IB (Cont'd)
INPUT FORMAT - QUALTEMP, METDTA
1J
Reference ¥-
Information
Card Content
Format
Number of
Cards
Always
Reaui red?
149
Junction numbers
where output is
to be made
(JPRT(I),1=1,
NOPRT)
14 j 5
(NOPRT+13)-/
14
Yes
629
(METDTA)
Meteorological
interpolation
& evaporation
coefficients
INT,NPTS,NQCSM,
A,BB
3110,F5.2,
E9.2
1
No
632
Meteorologi cal
data
QRNETA(I),UWINDA(I),
TAA(I),TAWA(I),APA(I)
F4.4,3F3.1 ,
F4 NPTS
No
~ Reference # refers to numbers on the right-hand side of the program listings in Part I.
2/
— Trancated value.
in
-------
TABLE 2
-------
TABLE 2
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-------
TABLE 3
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80 COLUMN PUNCHED CARD LAYOUT
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9
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.10
.1 o
. o.
10.0
,vo
,1 ,0,
1 0 . 0
I'll"''
10 .
1 o . Q
1 ''T '
0.0.
¦ i ...i
10 I
i—M
¦ ¦ » i '• 1 '»l»f >' l»:IHWiHl»
1 0
.,0.
iH.
10.0
' 1 I
.1 o
¦'0- • 1
• »-«»i«4i W4|4T|«I—.volai
-------
80 COLUMN PUNCHED CARD LAYOUT
« i r , • i • i -o
<> | 9 < >1| 14 | 19
"I"!*'"!'9
KUllHllt
hi r»'»
* T
X i» . 11 !»,* ,M •<=
; 1 ! 1 ; 1
, 1 ' .
1 , ¦ I
!
— | : . j .
! . . ! . 14 8' i
J
i < l i
,
i !
l . l 1
lilt
1 1 1
1 I 1 \
! ¦
! i i !
.(fJW'
I,), 1=1.
N ! 1
. « ,2,4
1 1 : I
1 1 . I^i ! , . .0
1 . 5 6:E - 0 9
. i i s . • i t . . . ( , ,
-i. 1 1 1
1 1 1 1
f
I i i I | 1 1 I t
> ' 1 1 . 1
i ' , j : 1 ! t
T^i i i
i
!
. . , ,
h—
' '
es —
^ i
§¦
1 1 1 1
j i
i • i , ' . i i 1 ! i j i
¦ .63.2
, .
OH
. , "P.
jc 3
=r, f-,
< a.
1 1 1 1
1 i 1 1
1111
i. i !
I
i i > 1 1 1 I : i
III!
. , ,
-M-
-M-
•4- -W-
0.6 40 0
041 80
17,8.1 LC
15, , ,
0,6.4.0.0
0 41 80
1,7,71,0
1 5
1 1 1 1
1 1 I 1
1 1 I •
0640 0
0 41 83
17 810
1 5
1
till
¦ I i i
1-1.1 1
4 111
1 1 1 1
1 1 1 I
! 1 1 1
1111
lilt
1 1 1 1
I ! I :
1 i I 1
/
, , :K
¦r,,,
. 1 i ¦
06 4 00
0 41 78
17 510
1 5
1 1 1 i
1 1 1
1 1 1 1
l 1 1 I
¦ ill
l 1 i ~
i : i _l_
i . » >
. , . ,
. 1 J 1 1
i i j i
J—i. .111
1 1 1 = j i ' ' ¦
;
¦ 1 ; j | ; i i i.
I |
i i ; j iJ—i—;—:—
ii i>9iun«»i»
¦VltTtMlttiK
KitriHiitiH
»lttlU.M.»
*1 , t|lWlMi«
MitMiiti to
Hil'.IIW PO!»" • »• •i"l« ft §4'
-------
TABLE 4
-------
TABLE 4
COLUMBIA RIVER FLOWS - 1959, 1968
River Name
Mile
km
cfs, 1959
m3sec-1, 1959
cfs, 1968
m3sec_1, 1968
(Bonneville Dam)
146
235
147160
4167
65014
1841
Sandy
122
196
1250
35
1250
35
Washougal
121
195
600
17
600
17
Willamette
102
164
9910
280
15150
429
Lewi s
90
144
2430
69
4238
120
Kal ama
73
118
670
19
670
19
Coweeman
70
113
150
4.2
150
4.2
Cowl i tz
68
109
4500
127
0
0
Abe rn a thy Cr.
55
88
60
1.7
60
1.7
Mill Cr.
54
87
70
2.0
70
2.0
Elochman
36
58
240
6.8
240
6.8
Grays
22
35
180
5.1
180
5.1
Note: Data for 1959 sumnarized by FWQA from USA Corps of Engineers Records for September 1959.
-------
OUTPUT OF APPENDICES
-------
-------
•• CHANNEL DATA ••
channel
LENGTH
WIDTH
A«EA
-MANN I No..
VELCCUJC
HYD RADIUS
JUNCTIONS at
1
5030
looo
10000*0
• 020
0
10.0
L
2
5000
1000
10000*0
• 020
0
10.0
2
3
5000
looo
10000*0
^02Q
0
3-
4
5000
1000
10000.0
,020
0
10.0
••CCEFFICTFWTS FCR TIQA1 INPUT**
A1 A2 A3 PHI2 PHI3 PEWlCD
0 2.000000 0 0 0 12.00
WHEfiE
Y(l>« A1*A2»SIM(WT*PHI2)»A3«SIN(WT*PHT^>
EXAMPLE 1_(Cont'd)
01
-------
SYSTEM STATUS AFTER
CYCLE 1
~03 HOURS
JUNCTION head channel VELOCITY FLOW
NUMRER (FT) NUMBER (CFS>
.0317
.0032
*01348 134*9
1 -0.01348 -134.9
2 0 0
2 -0 -0
3 0 0
3 -0 -0
4 0 0
-0 -0
-------
SYSTEM STATUS AFTER CYCLE 31
1.03 dCURS
JUNCTION
NUMREH
MCAO
-------
ro
SYSTEM STATUS AFTER CxCLE. £1
2«-03 HOURS
JUNCTION
NUMBER
1
2
HEAD
(FT)
1•59S1
1.7786
1.7744
1.7841
1.7901
CHANNIfJL
NUMBER
1
2
2
3
3
4
VELOCITY
iFPS)
*54672
-0.54672
.44829
-0*44829
156
•0.31756
.1643£
flow
(CPS)
6422.4
-6422.4
5269.8
"5269*8
-3734 »5
-3734.5
1933.2
4 -0.16432 -1933.2
RESTART DECK TAPE WAS LAST WRITTEN AFTFR CYCLE 90 TZERC FOR RESTARTING a
3.0000
-------
SYSTEM STATUS AFTE» CYCLE 511
17.03 HOURS
JUNCTION
NUMBER
1
HEAD
(FT)
1,0900
.9843
I-.0QJJ3
1.0073
1.0100
CHANNEL
NUM8FR
1
2
2
3
3
4.
4
velocity
(FPS;
-Q«45632
.45632
.0.34151
.34151
.0.22748
.22748
•0 *.11-371
11371
FLOW
ICFS)
-5017.3
5017.3
•3760.3
3760*3
-2506.7
2506.7
-1253.5
1253.5
-------
-u
4S
SYSTEM STATUS AFTER CYCLE 540
18.00 HSURS
JUNCTION
NUMBER
1
2
head
(FT)
.1395
.0207
.0388
,0450
.3473
CHANNEL
NUMBER
1
2
2
3.
3
4
VELOCITY
(FPS)
-Q.57963
.57963
-0.43421
•43421
-0-2B937
.28937
-0.1446-9
FLOW
(CFS)
-5814.1
5814.1
-4363.0
4363*8
¦2910*8
2910.8
-1456.1
4 .14469 1456.1
RESTART DECK TAPE WAS LAST WRITTEN AFTER CYCLE 540 TZERC FOR RESTARTING ¦ 18.0000
END OF FILE WAS WRITTEN CN TAPE 10.
-------
JUNCTION DATA FOR RESTART DECK
JUNCTION INITIAL HEAD SUfiPACE- AREA UiWJT-OUTPUT
1 #1395 5000000 0
?. #0207 5000000 0
3 ,0388 5000000 0
4 .0450 5000000 0
5 ,0473 5000000 0
EXAMPLE. 1 (Cont'd)
CHANNELS entering juncticm
1
1
2
1
0
2
3
4
0
0
0
0
0
0
0
0
3
D
3
-------
CHANNEL DATA FOR RESTART DECK
channel length width
AREA
m&nnins velocity
1
2
3
4
5030
5000
5000
5000
1000
1000
1000
1000
100«0*1
10029.7
100*1.9
100*6.1
• 020
.020
.020
.020
-0*57963
-0.43421
-0.20937
-0.14469
TAPE 10 WAS WRITTEN FROM CYCLE
180 TO CYCLE
540
end cf two-dimensional Explicit program. 540 cycles.
EXAMPLE 1 (Cont'd)
. -vl
(Jl
HYO RADIUS JUNCTIOMS At ENDS
10.03
1
?.
10.05
?
3
10.06
3
4
10.06
4
-------
FXAM»LE 1
FIVF JUNCTIOMS.FOUH CHANNELS.CONSTANT FRICTION
CX*m«>L€ I C5MTIMUE0
SUBftCUriNE HYDE* OUTPUT
FEDERAL. WAT£s PCLLUTICM CSNTrOl - ADH-LSlSiaiTiiM
PACIFIC wsIIhwEST wATM LAH2«AT-e»r
•••••••• From HYDRAULICS PROGRAM •••••••• HYDRAULIC CYCLES PER TIME INTERVAL IN
START cycle STCP CYCLE time INTERVAL QUALITY CYCLE QUALITY PRCG9A*
180 540 120 5EC5N0S IS .50 HOU'S
CHANNEL
NUMAFR
NET FLC«
(CFS|
« • • • FLCW • • • • • • • VELOCITY • •
MIH. MAX. "In. MA*.
(CfS) «CFS> (CFS) (CFS)
• • » cR5SS-SFcrrr:NAL a»f/> • • •
MIN. <1A*. ivE.
(SO. FT) (S3. FT) (Si. FTI
1
2
1
4
-0.36
.0.40
.0.38
-0,23
•5716.05
.4287,44
.2872,27
• 1441^25
5876.48
4422,65
2955.26
1V79.45
-0.625
.0,473
.1.317
-O.159
.599
,450
,300
.150
7990.fl
7974.4
7962.5
7955*3
l?HS.4
12n22.«.
I2i2iu6
moo?.?
I'W3*,#9
lOOU7*q
EXAMPLE 1 (Cont'd)
-------
JUNCTION MIMIMIJM HEAD OCCURS AT MAXIMUM HEAD
NUMRER (FT) CYCLE (FT)
1 -2.01 274 2.00
2 -2.02 270 2,01
3 -2.03 27o 2.02
A -2.04 270 2.03
5 -2.05 270 £.03
EXAMPLE 1 (Cont'd)
CCURS AT AVERAGE HEAD TIDAL 3AMGE
CYCLE (FT) (FT)
454 .00 4,01
450 .01 4.03
450 .01 4.05
450 .01 4.07
-------
«~«* OUTPUT FOR CHECKING DATA CN EXTRACTED TAPE #***
HYDRAULIC HEAD Aj #FLCW In CHANNFL*
CYCLE .JUNCTION NO a NO. I- NO. 2
1 BO
195
210
2?5
240
?55
270
285
300
315
330
345
360
375
390
405
420
435
450
465
480
405
510
525
.13
-0*38
"0*87
-1.31
-1.65
-1 .39
-2.00
-1.97
-1.80
-1.51
-1.12
-0.65
-0*14
• 38
• 88
1-31
1*66
1.89
2.00
1.97
1.80
1-51
1.12
.65
5671.30
5663-47
4702-56
3765.51
2539-96
-*92-50
787.25
2184.11
3486.86
4697.05
5434.64
5810.66
5876-48
5428-57
4666*59
36lR«48
2254.45
«19.00
-710.55
'2156-87
3434.56
'4531.67
'5287.85
'57_L6_»_Q5
-4248.18
-4283.36
-3531-69
-2844.41
-1935-26
-680.48
595.96
1633.43
2606.34
3530.98
4083.18
4363.21
4422-65
4081*34
3508.98
2726-48
1696.15
621.88
-528.45
-1613-26
-2568.69
-3395.99
-3962.95
-42B7144,
END OF NET FLOW PROGRAM,
-------
00
o
EXAMPLE S
FIVE jUNCTlCNS.rO** CHANNELS'*CONSTANT FRICTION
FEOERAL' WATER POLLUTION CONTROL ADMINIST«*TI5N
pacific northwest water laboratory
JUNCTIONS CHANNELS CYCLES OUTPUT INTERVAL
5 * 5*0 30 CTCLES
TIME INTERVAL INITIAL TIME WRITE BINARY TAPE RESTART INTERVAL START PRINT
120 SEC. 0 MRS, CYCLES 160 TO 5*0 90 CYCLES CYCLE 1
•• JUNCTION DATA ••
JUNCTION INITIAL HEAD SURFACE AREA INPUTISUTPUT
CHANNELS ENTERtNS JUNCTION
1
2
3
*
5
0
0
0
0
0
5000000
sonoooo
5000000
5000000
soooooo
0
0
0
0
0
I
1
2
3
4
0
2
3
*
0
0
0
0
0
0
0
0
0
0
0
o
9
9
0
0
-------
*• CHANNEL data ••
channel
LENGTH
WlnTH
area
manning
VELOCITY
HYD OAOIUS
JUNCTIONS AT
1
5000
looo
10000.0
.030
0
10.0
1
2
5000
looo
10000*0
•030
0
10«0
2
3
5000
looo
10000*0
.030
0
10.0
3
4
5000
1000
10000.0
.030
0
10.0
4-
••COEFFICIENTS for tidal input**
A1 A2 A3 PHtz PHI3 PERIOD
0 2.000000 000 12*00
WHERE
VC1)« Al*A2#SlM
-------
SYSTEM STATUS AFTER CYCLE 1
•03 HOURS
JUNCTION
NUMBER
1
2
HEAD
(FT)
• 0317
• 0032
CHANNEL
numrer
1
2
VELOCITY
(FPS)
•01348
•0,01348
0
FLOW
(CFS)
134.9
-134.9
0
2
3
-0
0
¦o
0
3
4
-0
0
-0
0
-0
-0
-------
SYSTEM STATUS AFTER
JUNCTION HEAD
NUMRER (FT)
X .8986
2 1.0868
3 1.1159
4 1.1523
5 1.1738
CYCLE 31 1.03 HOURS
channel velocity flow
number (FPS) (CFS)
1 *49626 5478*1
1 -0.49626 -5478.1
2 .38460 4262.0
2 -0.38460 -4262.0
3 .26160 2908.6
3 -0.26160 -2908.6
4 ,13247 1476.6
4 -0*13247 -1476-6
-------
SYSTEM STATUS AFTER CYCLE 61
2*03 HOURS
00
JUNCTION
NUMBER
1
4
HEAD
(FT)
1.6352
1.7625
1.7538
1.7569
1.7595
CHANNEL
NUMBER
1
2
2
3
3
4
velocity
(FPS)
.40456
-0.40456
.32375
-0-32375
.22570
-0.22570
.11575
flow
(CFSJ
4750*3
-4750.3
3801.4
"3801*4
2650.0
-2650.0
1359.2
4 -0.11575 -1359.2
RESTART OECK TAPE WAS LAST WRITTEN AFTER CyCLE 90 TZERC FOR RESTARTING
3,0000
-------
SYSTEM STATUS AFTER
JUNCTION HEAD
NUMBER (FT)
1 1.0884
2 .9915
3 1.0136
4 1.0219
5 1.0251
CYCLE 511 17*03 HOURS
CHANNEL VELOCITY FLOW
NUMBER (FPS) (CFS)
1 -0.45002 -4949.6
1 .45002 4949.6
2 -0.33596 -3702.4
2 .33596 3702.4
3 -0.22349 -2465.6
3 .22349 2465.6
4 "0*11166 "1232*5
4 .11166 1232.5
-------
00
SYSTEM STATUS AFTER CYCLE 540
JUNCTION HEAD CHANNEL
(FT)
NUMBER
I
.1380
.0344
.0620
.0722
.0756
number
1
1
2
2
3
3
4
4
18.00 HOURS
VELOCITY FLOW
(FPS) (CFS)
-0.57319
.57319
-0.4P829
•42829
-0.2*502
.28502
.0.14244
-5753.3
5753.3
-4312.1
43l2»l
•2874.2
2874.2
-1437.4
•14244 1437*4
RESTART DECK TAPE WAS LAST WRITTEN AFTER CYCLE 540 TZERS FOR RESTARTINS
end cf file written cn tape lo.
IS.0000
-------
JUNCTION DATA FOR RESTART DECK
JUNCTION INITIAL HEAD SURFACE AREA INPUT-CUTPUT CHANNELS ENTERING JUNCTION
1 .1380 5000000 0 10 0 0 0
2 .0344 5000000 0 12 0 0 0
3 .0620 5000000 0 2 3 0 0 0
4 .0722 5000000 0 3 4 0 0 0
5 .0756 5000000 0 4 0 0 0 0
-------
00
oo
CHANNEL DATA FOR RESTART DECK
channel
LEN3TH
width
AREA
manning
VELOCITY
HYD RADIUS
junctions at
ends
1
5000
1000
10086.2
.030
-0.57319
10.04
1
2
2
5000
1000
10048.2
.030
-0.42829
10.07
2
3
3
5000
1000
10067.1
.030
-0.28502
10.08
3
4
4
5000
1000
10073.9
.030
-0.14244
10.09
4
5
TAPE 10 WAS WRITTEN FROM CYCLE 180 TO CYCLE 540
END CF TWO-DIMENSIONAL EXPLICIT PROGRAM. 540 CYCLES*
-------
EXAMPLE 2
FIVE JUNCTICHS.FCUR CHANNELS.CCNSTANT FRICTION
est ample 2 CCMTIMliED
SUBRCUTINE HYDE* OUTPUT
FEDERAL WATER POLLUTION C&NTRCL A0*I*tI5T«ATICM
PACIFIC W50THWE5T WATER lABORATSRy
•••••••• FROM HYDRAULICS PROGRAM ••••••••
START CYCLE STOP CYCLE TIME INTERVAL
ISO
S40
120 SECONDS
HYDRAULIC CYCLES PER
ouM-ity cycle
15
TIME INTERVAL' IN
quality PROGRAM
.50 HOURS
channel
NUMBER
I
?
3
4
met flow
ccfsj
.T3
.61
.*2
.21
• •
MIN
ICFS>
• • FLCW
-56B4.69
.4259.19
-2B3B.2T
-1*19.27
• • • • •
MAX.
(CFSI
5916.32
4456,07
7978.39
1491.0*
~ • VELOCITY • •
mIn. MAX.
CCFS) (CFS)
-0.597
-0.447
•0.298
-0.1*9
.604
.454
.304
.152
f • • CROSS-SECTIJNAL AREA • • •
Ml*. MA*. AvE.
(SQ. FT) ISO. FTI (S3. Ft)
79B9.9
7972.0
795B.8
7950.9
12005.5
12nl5.2
12022.2
12026.3
10003.3
10006.9
10007.7
10008.3
EXAMPLE 2 (Cont'd)
CO
-------
1
-2.00
275
2.00
454
-0.00
4.01
2
-2.02
27o
2.01
45o
.01
4.03
3
-2.0^
271
2.02
45o
.01
4,06
4
-2.OS
271
2.02
45o
.01
4.07
5
-2.05
271
2.03
450
.01
4.OB
-------
«»*• OUTPUT FOR CHECKING DATA CN EXTRACTED TAPE
HYDRAULIC
CYCLE
HEAD AT
JUMCTICN NO.1
«FLCW IN CHAMNFL»
NC.l NC.2
lflO
195
210
225
240
255
270
2*5
300
315
330
345
360
375
390
405
420
435
450
465
4fl0
495
510
525
.14
—0* 38
-0.88
-1.31
-1.65
-1.89
-2.00
-1.97
-1 .80
-1.51
-1.12
"0*^5
-0*14
.38
.88
1.31
1.66
1.89
2.00
1.97
1.80
1.51
1,12
*65
•5684.69
¦5480*52
¦4820,81
¦3873.17
•2614.75
•1023.20
775.41
2170.75
3322.11
4591.76
5445-90
5846*15
5916.32
5521.45
4730.57
3654,21
2305.46
816.11
-708.20
•2122.09
-3400.62
-4471.28
,5224.16
.5655.24
-4259.19
-4123.92
-3635.26
-2935.66
-1997.77
-793.35
586.04
1624.31
2464.37
3439.21
<~092.44
4393*60
4456*07
4161.29
3564.43
2756.85
1740.51
619.34
-526.70
-1583.26
-2539.88
-3344.32
.3908.73
.4235,78
PNO OF NET FLOW PRCGRaM,
-------
<£>
ro
FXA«PLF 3
riVP j ;
-------
•• CHANNEL data ••
CHANNEL LEN3TH WIDTH
1
Z
3
4
5030
5000
5300
5000
lOf'O
1000
1000
1000
ahea
10000.0
roooo.o
10000-0
10000.0
MANNING VELOCITY HYD RADIUS
<020
• 02f>
• 020
• 020
0
0
0
0
10.0
10.0
10.0
10.0
JUNCTIONS At ENDS
1
2
3
A
2
3
4
5
••COEFFICIENTS FOR TIDAI INPUT**
A1 A2
0 2.OO000D
A3
PHI2
0
PHI 3
0
PERIOD
12.00
WHERE
¥(!>¦ A1*A2»SIN(WT*PHI2)*A3»SIN(WT-»PHI3)
EXAMPLE 3 (Cont'd)
ID
-------
SYSTEM STATUS AFTER CYCLE
•03 HOURS
JUNCTION
numrer
HEAD
(FT)
.0317
.0032
CHANNEL
NUMBER
1
2
VELOCITY
(FPS)
• 0134-8
•0.01348
0
flow
(CFS)
134.9
•134.9
0
.0002
.0022
2
3
3
4
•0
0
»0
¦0.00093
.00093
'0
0
-0
-9-.3
9.3
-------
SYSTEM STATUS AFTER CYCLE 31
1.03 HOURS
JUNCTION
NUMBER
HEAD
fFTJ
•VT20
1.1179
1,1783
1.2362
1.2689
CHANNEL
NUMBER
1
2
2
3
3
4
VELOCITY
(FPS1
•44517
.0.44517
.34171
•0.34I7I
•23001
'0#23001
•11283
-0.11283
flow
(CFS)
4921*5
-4921.5
3803.3
-3003.3
2574.6
'2574*6
1267-9
-1267.9
EXAMPLE 3 (Cont'd)
10
-------
SYSTEM STATUS AFTER CYCLE 61
2.03 HOURS
U3
O"!
JUNCTION
NUMBER
1
2
HEAD
(FT)
1.5989
1.7781
1.7746
1.7844
1.7905
CHANNEL
NUMBER
1
2
3
3
4
VELOCITY
(FPS)
.53321
-0.53321
.43529
•0,43529
.30560
-0.30560
.15393
Flow
(CFS)
6263.7
-*>263.7
5117.0
-5117.0
3594.0
-3594.0
1811.0
4 -0.15393 -1811.0
RESTART DECK TAPE WAS LAST WRITTEN AFTFR CYCLE 90 TZERC FOR RESTARTING »
3.0000
-------
SYSTEM STATUS AFTER
JUNCTION HEAD
NUMBER rFTl
1 1.0^23
2 .9847
3 1.D022
4 1,008^
5 1,0113
CYCLE 511 17.03 HCIJRS
CHANNEL VELOCITY FLOW
NUMRER (FPS) (CFS)
1 ~0»46515 ""5114*5
1 .46515 5114.5
2 -0.35036 -3858.0
2 .35036 3858.0
3 -0.23638 -2605.0
3 ,23638 26o5.0
4 .0.12269 -1352.6
4 *12269 1352*6
-------
<£>
00
SYSTEM STATUS AFTER CYCLE 540
1R*00 HOURS
JUNCTIOM
NUMBER
HFAO
(FT)
.1418
.0214
.0*00
.0465
.0491
CHANNFL
NUMRFR
1
2
2
3
3
4
VELOCITY
(FPS)
.58922
.0.44381
•44381
-0*20905
.29905
-0.15449
FLOW
(CFS)
-0.58922 -5910.5
5910.5
-4460.7
4460*7
-3008*6
3008*6
-1555.0
4 .15449 1555.0
RESTART DECK TAPE: WAS LAST WRITTEN AFTFR CYCLE 540 TZERC FOR RESTARTING
END Of FTLF *aS WR-jT-I-^m on Ta»E 10.
18.0000
-------
JUNCTION nATft fop restart dfck
JUNCTION INITIAL HEAD SURFACE AREA INPUT-OUTPUT CHANNELS ENTERING JUNCTION
1 .1418 5000000 0 10 0 0 3
2 .021* 5000000 0 12 0 0 0
3 .0400 5000000 0 2 3 0 0 3
4 .0465 5000000 0 3 4 0 0 0
5 .0491 5000000 -100.00 4 0 0 0 0
-------
o
o
CHANNEL DATA POP RESTART DECK
channel lemsth width
AREA
MANNING
VELOCITY HYO RADIUS
JUNCTIONS AT ends
1
2
3
A
5000
5000
5000
5000
1000
1000
1000
1000
100*1.*
10030.7
100*3.3
100*7.8
TApE lO XAS WRITTEN FRO* CYCLE
.020
.020
.020
.020
-0.56922
-0.443R1
-0.29905
-0.15449
180 TO CYCLE
540
10.03
10.05
10.06
10.07
1
2
3
4
2
3
4
5
ENO CF TWC-DIMFMSICNAL EXPLICIT PRC6RA". 540 CYCLES.
-------
»5*A»«>I.e3 FEOFRAL water POLLUTION CONTROL AOHMlSTftATl
FlVF JlWCH:-rt»rC'l» CrtAMMELS.CONSTANT FHICTICN.IOO CFS IMFlSW PACIFIC NS^HWEST HATE» LABORATORY
exauole * cs^Ti'i'jfn
SURRS>m*E HYO£* C«ITP|IT
•••••••• Fo;>4 4YI.RAULICS PHCGRAM •••••••• HYDRAULIC CTCLES PER TIME INTERVAL IN
START CYCLF ST3P CrCLE TIME INTERVAL OijAlJTY CvCl.E 0U*LITY PROOFS
ISO 5*0 l?0 SECONDS 15 .50 H0U*S
CHANNFC
wwnrn
I
7
3
A
Nrr Ft. ex
(CFS)
-1<»C.V»
-100.37
-103.36
•100.22
Miri.
(CFSJ
-Wi.33
-4315,J4
-2964,45
-1537.11
MAX.
CCFS)
5772.09
*318.65
2852.30
1377.92
• • VELOCITY • •
'4lM. MAX.
(CFs) (CFS)
-0.63*
-0.492
-0.327
-0.169
> • • CRSSS-SECTISNAL AREA • • •
MIN. MAX. AVE.
ISO. FT) (SO. FT) (S3. FT)
.589
.439
.290
.140
7990.8
7974.5
7962.6
7955.5
12005.5
12015.?
12022.2
12026.4
1O003.*
11)007.J
10008.5
10009.2
-------
JUNCTION MIVTMt»M MEAD SCCtJRS AT MAXIMUM HEAD
NUMRER (FT) CYCLE (FT)
1 -2.00 274 2.01
2 -2.02 270 2.01
3 -2.03 270 2.02
h -2.04 270 2.02
5 -2.OS 270 2.03
EXAMPLE 3 (Cont'd)
CC'JRS AT AVERA0E HEAD TIDAL RANSE
CYCLE (FT) (FT)
454. .00 4.01
450 .01 *.03
45o *01 4.05
45o .01 4.07
-------
•••* OUTPUT FS* CHECKING DATA ON EXTRACTED TAPE
HYDRAULIC
CYCLE
HEAD AT
JUNCTION NC.l
•PLOW IN CHANNEL*
NC.l NO.2
1BO
IPS
210
225
240
255
270
2*5
300
315
330
345
3&0
375
390
405
4?0
435
450
465
48o
405
510
5?5
.13
-0.37
¦0.&7
-1.31
¦1.05
¦1.89
¦2.00
-1.97
¦ItftO
-1.51
-1.12
*0»65
*0-14
• 38
.49
1.32
1.06
1.90
2.00
1.97
1.8U
1.51
1.12
•65
-5771.66
"5751.33
-4808.35
-38*9.39
•2641.11
-1004.II
6B0.31
2098.96
3305.15
4589.56
5342.02
5707-04
5772*09
5333.36
4561-76
3519.07
2156.07
71S.29
-H05.69
-2254.76
-3533.72
-4627.02
-5386.29
-5813«33
-4350.24
•4372.75
-3636.79
-2947.67
•2036.08
-790.47
490.06
1546.62
2505.14
3424.41
3989.65
4260.14
4318.65
3985.49
3404.71
2626.83
1597.52
518.50
-624.29
-1711.48
-2668.06
-3492.01
-4061.70
¦4385-14
END CF NET FLOW PROGRAM,
-------
STEADY STATE eitvPLE.eHtiMCI. LfNOTM BEQUCE4 H* TWO
£«»«IE sr HIKE! C^iUSEL-JlMCtlCM MMIWMNfc SCHC4P
fEI>E»«L ><«TE* JSU.UTT3N CSNToCt. IB*1VISTa«TISN
P-ACIR1C. .Ma<«rMWEST. JIATtt LABSR*T£]IV
JUNCTIONS
4
CHANNELS
4
cycle*
s*o
aiTWIT INTPWAL
SO CYCLES
TIM? INTfPVAL TNTTTAL TINE WPITE TtPC PrST»»T 1«|TE»V»L *T«»T »OIsT
ISO *EC. 0 MRS. CYCLE* l»l> TS 940 i«o cyclm c*n« 1
•• JUNCTION. MIA »•
JUNCT
ON INITIAL NEW. SURFACE **E* 1MPUTISUTPUT
2500000
25ooono
a*onooo
zsonooo
Z500000.
0
0
-looo.oo
0
0
CHANNELS ENTCfttNA JUNCTIS*
i a
t 3
A D
» 4
? 1
A 3
o ¦»
0 9
0 It
a a
•• CHANNEL 0»T« ••
CHANNEL LEW* WIDTH
AHEA
MiNtlNS VELOCITY HY1 BtPIUS
JUNCTIONS »T ENOS
1
1W
lNWCUO
•P 7.11
0
in.O
1
3
9
Ipnn
lAOt^.Q
ft
in a
t
%
f
MM
low
10000*0
0
10*0
2
3
.4
looo
IOOAO»0
0
10.0
4-
%
••CItrriCIt"" f-« TIOAt INPUT**
A1
>r
A3
P*I?
0
PHIS
0
WRTSn
12.00
WW
rni« •i»A>*si*(<. CH*'»lEL 4. JUNCTION 5
CC»ATI«ItTtY C**C«. CH*'«CL 1. J-INCTION t
eSM*4Ti«TLtTT rxrrx.' C>l4tMfC *. JiwrTISs 1
-------
JUNCTION DAT A FOR RESTART DECK
JUNCTION INITIAL HEAD SURFACE AREA INPUT-CUTPUT
1 .0480 2500000 0
2 -0.0153 2500000 0
3 .0053 2500000 0
4 -O.OOlO 2500000 0
5 .0011 2500000 -1000,00
CHANNELS ENTERING JUNCTI
10 0 0
12 0 0
2 3 0 0
3 4 0 0
4 0 0 0
-------
CHANNEL DATA FOR RESTART DECK
channel length width
AREA
MANNING VELOCITY
1
2
3
4
2500
2500
2500
2500
1000
1000
lOGO
1000
10016.3
9995.0
10002*2
10000*1
.020
.020
.020
.020
-0.10000
-0.10000
-0.10000
-0.09999
TAPE 10 WAS WRITTEN FROM CYCLE 180 TO CYCLE
540
END OF TWO-DIMENSIONAL EXPLICIT PROGRAM. 540 CYCLES*
EXAMPLE 5 (Cont'd)
HYD RADIUS
junctions at ENDS
10.00 1 2
10.00 2 3
10*00 3 *
-------
STEADY "STATE EXAMPLEtCHANNEL LENGTH REDUCED BV TUC
FIVE Ji|NCT!5'IS,FCl|k CH4MNCLS.CONSTANT F«ICTICN, 1000 CFS INFLO*
STEADY STATE EXAMPLE CONTINuro
SUBROUTINE MYOE* OUTPUT
federal water pollution control administration
PACIFIC NORThwCST WATE« LABORATORY
••••«••• FROM HYDRAULICS PROGRAM ••••••••
START CYCLE STOP CYCLE TIME INTERVAL
190
5«0
120 SECCNOS
HYDRAULIC CYCLES PER
OUALITf CYCLE
15
TIM£ INTERVAL IN
QUALITY PROSRA*
.SO HOURS
CHANNEL
number
1
8
3
4
NET FLOW
-1003.47
-1003.1*
-1002.34
-1001.24
FLOW
• • • • •
MAX.
-995.70
-496.70
-997.43
-498.67
» • VELOCITY • •
MIn. max.
•0.102
-0.102
-0.101
-0.101
-0.09H
•0.099
-0.099
-0.099
~ • • CROSS-SECT13NAL AREA • • •
MIN. MAX. AVE.
(SO. FT» (SO. FT) (S3. FT)
9999.9
9999.8
9999.7
9999.S
10000.?
10000.7
10001.1
10001.4
10000.1
10000.3
10000.s
10000.7
-------
JUNCTION! MIMIMUM HEAD OCCURS AT MAXIMUM HEAD
NUMBER (FT) CYCLE (FT)
1 .05 189 .05
2 -0.02 182 -0.01
3 .00 184 .01
4 -0.00 184 -0.00
5 .00 184 .00
EXAMPLE 5 (Cont'd)
CCURS AT AVERAGE HEAD TIDAL RANGE
CYCLE (FT) (FT)
180 .05 .00
192 -0.02 .00
195 .01 .00
194 -0*00 .00
-------
OUTPUT FCP CHECKING DATA ON EXTRACTED TAPE ****
HYORAUL1C HEAP AJ
CYCLE JUNCTION NC.l
lflO
.05
195
.05
210
.05
225
.05
240
.05
255
.05
270
.05
?R5
.05
300
.05
115
.05
330
.05
345
.05
360
.05
375
.05
390
.05
405
.05
420
.05
435
.05
450
.05
'*65
.05
480
.05
4Q5
.05
510
.05
525
.05
end OF net FLOW PROGRAM,
~flow in
CHANNEL*
NC.l
NO.2
-995.70
-996.70
-1003.47
-1003.14
-1001.03
-1000.64
-997.93
-998.23
-1000.15
-1000.25
-1000.99
-1000.81
-999.61
-999,61
-999.63
-999.72
-1000.32
-1000.28
-1000.09
-1000.05
-999.82
-999.84
-1000.02
-1000.03
-1000.09
-1000.07
-999.96
-999.96
-999.97
-999.98
-1000.03
-1000.03
-1000.01
-1000.00
-999.98
-999.99
-1000.00
-1000.00
-1000.01
-1000.01
-1000.00
-1000.00
-1000.00
-1000.00
-1000.00
-1000.00
-1000.00
-1000.00
-------
JUNCTION DATA FOR RESTART DECK
JUNCTION INITIAL HEAD
1 .0239
2 -0.0007
3 *0009
* .0012
S .0016
SURFACE aREa
5000000
5000000
5000000
5000000
5000000
EXAMPLE 6
INPUT-OUTPUT
0
0
0
0
-1000.00
CHANNELS ENTERING JlJNCTI
10 0 0
12 0 0
2 3 0 0
3*00
-------
CHANNEL DATA FOR RESTART DECK
CHANNEL LENGTH WIDTH AREA MANNING VELOCITY HYD sAOIUS JUNCTIONS AT ENDS
1
5000
looo
10011.6
. 020
•0.09970
If). 00
1
2
2
5000
1000
10000.1
.020
-0.09974
lo.oo
2
3
a
5000
1000
10001.0
.020
-0.09980
10.00
3
-------
STEADY STATE fKAMptE
riVE JUNCTIONS.FOUR CHANNELS.CONSTANT FHICTISN
STEADY STATE EXAMPLE CONTINUED
SUBROUTINE HYDE* OUTPUT
FEDERAL WATEk P5LLUTJCN C3NI»£l ia!USl«allO
PACIFIC NORTHWEST «»TE« lARORATSRY
FR5t HYDRAULICS PflJGBAN ••••••••
START CYCLE STOP CYCLE TIME INTERVAL
]«0
5*0
120 SECONDS
HYDRAULIC cycles PER
OUALITY CYCLE
IS
time interval in
QUALITY PRC63A*
.50 HCU3S
CHANNEL
NUMBER
1
*
3
*
NET FL5W
cCsi
-100*.0*
-1003.5*
-1002.65
•1901.41
MIN.
ICFSI
-H50.oa
-1131.58
-1097.67
•1051.9*
MAX.
(CF 51
» • » crcss-sfcti-nal »or»
-0.119
-0.117
•0.113
-0.107
—0.08*
-0.086
-0.090
-0.095
WJN,
(SO. FTl
999R.6
9996.0
9*93.6
9952.5
MA*.
(SJ. FTl
10*02.3
10906.&
I0MO.1
1Q?12.5
• » »
(S3, fl,
1.1000,3
JOflOO.B
l*noi.?
J 000) »«•
-------
JUNCTION MINIMUM HEAD OCCURS AT
NUMBER (FT) CYCLE
1 .02 210
2 -0.00 199
3 -0.01 200
4 -0.01 200
5 -0.01 200
MAXIMUM HEAD
fFT)
,03
.00
.01
.01
.01
OCCURS AT
cycle
189
18n
180
180
180
average HEAD
IFT)
.02
-0.00
.00
.00
• 00
tidal range
(FT)
.01
.01
.01
.02
.02
-------
OUTPUT FOR CHECKING OATA ON EXTRACTED TAPE #•••
>RAUUC
HEAD AT
»F|_3W IN
CHANNFL*
:ycle
JUNCTION NC.l
NC.l
NC.2
ISO
.02
-1150.08
-1131.58
195
.03
-955.98
-9ft?.10
210
.02
-935.52
-94?.72
225
.03
-1101.95
-1089.65
240
.02
-938.90
-946.69
255
.02
-989.58
-990.39
270
.03
-1056.74
-1050.06
285
.02
-947.00
-953.55
300
.02
-1014.53
-1012.49
315
.03
-1023.95
-1021.25
330
.02
-963.52
-967.93
345
.02
-1021.24
-1018.53
360
.02
-1004.43
-1004.06
375
.02
-979.42
-981.85
390
.02
-1018,74
-1016.42
405
.02
-995.26
-995.93
4?0
.02
-991.12
-992.12
435
.02
1013.05
-1011.47
450
.02
-992. t>4
-993.58
465
.02
-998.16
-998.33
480
.02
-1007.45
-1006.57
495
.02
-993.38
-994.20
510
.02
-1001.53
-1001.31
525
.02
-1003.29
-1002.91
END OF NET FLOW PROGRAM.
-------
OCWNSTREaM ftSl'-jOARY CONSTANT
MS FLOW AT THP UPSTREAM ROUUDARY.
TEMPERATURE TtST.HYDfAULICSlW" T»IB Cfl MAINSTREAM FLOW.
NC DRIVING FO^CEtNO INPUT TIDE.
FEDERAL WATER PCLLUTTOM CONTROL ADMINISTRATIS*
PACIFIC VS9TMVEST WATFB LABORATORY
•••••••• FOJvi HYDRAULICS PRJRPAM •*»«••••
START CYCLF STOP CYCLE TIME interval
1 BO 5«0 120 SECONDS
STAOT1W Cycle initial QUALITY total DUALITY ••• SUToUT INTERVALS »•» TT TWTERVAL in . CONSTANT for
on hyo, extract tape cycle cycles cycles hours quality program diffusion coefficients
1«0 l 120 so 2.00 1.000 HOURS 0
PRINTOUT is to *fgin at CYCLF 1
ouality ta»e for extracting is TO HEGIn at cycle
i constituents being, ccwsioerfo in this run
temperature is the only constituent.
ALL CONSTITUENTS TPEATEO AS CONSERVATIVE IN THIS RUN
MS WASTE WATER RETURN FACTORS APPLIED
-------
~~~~~MULTIPLICATION factors applied to obtain starting CONCENTRATIONS
CONSTITUENT GROUP FACTOR JUNCTION NUMBERS
NO MULTIPLICATION FACTOR APPLIED TO CONSTITUENT NO. 1
-------
yaTCQ QUALITY OAfA
• F1PST CONSTITUENT • SFC5HO CONSTITUENT • TulftO CONSTITUENT • FOURTH CONSTITUENT • FIFTH CCWTITl'CNT •
I'll! IAL INFLOW INITIAL INFLOW JMlTl AL INFLOW INITIAL INFLO* INITIAL IVLOw
JVNC. INFLOW COnC. CONC. CONC. CCNCt cSNC. CCNC. CONC. CONC. CSNC> CCNC.
0
10.0
0
0
10.0
0
0
m.o
0
0
10.0
0
0
10.0
0
SWCIFIEn C-FAGTOftS *T J>INCTION 1 FOB CONSTTTIIMT *0. I
10.no 10.00 10.00 10.00 10*00 10.00 10.00
10.00 10.00 10.00 10.00 10.00 10.00 ln.oo
10.00 10.00 10.00 10.00 10.00 10.00 10.00
10.00 10.00 10.00
-------
CM*N. LPNQT>4 KlOTH aPf«
CHANMCl DATA ••••••••••••••«••••••••»•••••
hanntna nft flow hvd. radios junc. at ends
JONC. HFAO
JUNCTTSN *>aTa
CHANNFLS ENlfPl*8 JIINCTISM
1
2500
1000
lOOOrt
.020
0
10.0
1
2
1
0
1
0
0
0
2
?Sr>0
JOOO
10000
.020
0
10>0
z
3
2
0
1
¦»
o
0
S
1000
10000
.020
0
to.o
3
A
3
0
2
fl
0
*
2S00
1000
10000
.020
0
10«0
A
s
A
0
3
•
0
0
5
0
A
0
0
0
-------
••••#••••••••••••••«•••••••• 7ahi.f zf wnrcQScsncAi oat a ••••••••••••••••••••••••••••
tin o*v «tt
4T** "lit* Rill A ATMS^t»wpPTC
«Af)IATTCM S»£€f>
tKe/«?/SECl<«/*ECl
TE--P Tf*p
to ici
PHf55UHE
1MB)
6.400C-02
•4
18.00 lT.no
1015.0
6.430F-32
*4
18.00 IT.TO
1018.0
4.400C-02
.4
18.30 1T.H0
1015.0
A.4«Of-C2
• 4
18.40 18.30
1018.0
• 4
18.60 18.30
1018.0
T.iWOZ
• 4
it.«h> ln.io
1015.0
(I.3W-32
• 4
18.SO 17.80
1C18.0
l.OW-Ol
• 4
IT.00 IT.00
1015.0
1.I70C-01
• 4
14.00 18.00
1015.0
l.lS0f-3l
*5
19.?0 18.00
1015.0
1.450C-01
•4
22.30 20.00
1015.0
I•4*0t*?1
.$
22.5c 18.TO
1015.0
1.4WT.01
• 4
24.40 29.80
1018.0
l«*4or-ni
• T
24.50 22.00
101*.0
i.sw-oi
• 4
26.00 21.50
1015.0
1.2?Of-Ol
*5
2S.no 23.00
IPI«.0
1-0
22.50 19.00
1015.0
1.000C-01
•5
19.30 18.00
1015.0
7.MMK-92
•6
20.30 19.20
1015.0
••5A0£-C2
.5
19.10 18.T0
1015.0
6.400C-02
18.40 IT.TO
1015.0
4.40M-42
.4
IT.SO 17.00
lOin.O
A.4A0T*0I
.4
17.60 1T.40
1015.0
*.*ooe«o2
•4
17.80 IT,50
1015.0
HAPKI It)}
¦ 1
-------
SYSTEM STATUS AFTER QUALITY CYCLE \ 0 RAYS. 1.00 HOURS
••••••*«••***»•••••••«•••* Concentration factors
JUNCTION head 1ST. CCNSTIT. 2ND* CSNSTIT. 3RD. COMSTIT. 4TH. C5NSTIT. 5TH. CSmSTIT.
NUMBER (FT) (MOD < <*3L> (HGl)
1 0 10.00
2 0 9.98
3 0 9.98
4 0 9.98
5 0 9.98
-------
••••••••»•••••• UAf>t*TtCN TfflMS ANO PWTLIBRIU* TEMPERATURES •••••••••••••••
IKCAL IMPLIES 4.947
8.S3E-0Z
113.214
OE
00
0
-1.B0F-03
-2.390
.25
1.9M-12
-25.881
6.4DC-0?
S4.«47
8.53F-02
113.21*
or
00
0
-l.BOr-OJ
-2.^93
.29
1. W-02
-?5.881
6.*o€-0i
•4.947
8.53E-02
113.21*
OE
00
0
-t.BOC-03
•2.390
1.956-02
-25. Ml
t.tAC-OZ
*4.947
8.53E-02
113.218
OC
00
0
-l.B0f-O3
•2.940
-------
K>
IV)
SYSTEM STATUS AFTER QUALITY CYCLE 3 0 DAYS* 3.00 HOURS
»••••«»•••««•••«•••••••»»• concentration factors «»»«»••«»•»••••«•»«»«••»••
JUNCTION HEAD 1ST- CONSTAT. 2ND, CCNSTlT. 3RD. C5MSTIT. 4TH. CONS"!-!!. «>Th, COmSTJT.
NUHRER (FT) (MGL> (MSL) (M^L)
-------
••••••••••••••• HADIfcTTON TFBMS ANO EQUILIBRIUM TEMPf ft»Tl»ft£S ••••••••*••••••
KCAL IMPLIES 2
-?S.M7
6.4OC-0?
•4.Q47
B.52C-02
113.146
oe
oo
A
-1.MP-03
-2.S83
.so
-»«617
•4.947
H.S2F>02
113.14*
OE
oo
0
-1.9SF-03
-e.*B3
•so
-I. -02
-2S.617
6.40E-05!
B4.947
8.526-02
113.146
oe
00
0
-l.WE-03
-2.SB3
.so
-------
SVSTFM status after oiiality cycle 12o
S DAYS* 0 MCUqs
•••••••••••••»•••••••••••• CCMCEnTRAtISN factors
JWCTI8N HEAD 1ST. CCNSTtT. 2ND, CONSTlT. *RO. CCNSTIT. *Th. CtJNSTlT. 5TH. CS**STIT.
number rrT> (Hod mgli <«sl» (*gi)
1 0 10.00
2 o 11.62
3 o 11.62
* 0 11.62
* 0 11.62
-------
•••••••••••••~• PAD1AT1CN TFRMS AND F3U1L1BRIUM TEMPERATURES •••••••••••••••
IKCAL IMOCIE5 "< IL CfiR AM-C A(.OR IES PFR SO* I ARE METER PER SECOND. BTU IMPLIES BTU PER SOU*Rf FC-T PE» HCUR)
NET RAOIAT13M INCCHIN6 SOLAR BACK RAOIaTTON
EVAP0RATI5N
CONDUCTION EQUIL' TF*f>
KCAL BTU
KCAL
BTU KCAL
9TU
KCAL BTU
KC*L
BTU
CENTlSRAOE
OE 00
0
6.4OE-02
8*.9*7
OF 00
0
OF
00
0
OF 00
0
0
-2.1BE-02
-28.939
6.A0E-0?
84.9*7
B.72E-02
115.779
OE
00
0
-1.A3F-03
-1.89*
.93
•7.1W-0?
-28.939
6.40T-0?
84.4*7
B.72C-02
115.770
OE
00
0
—I.43F-03
-1.89*
.93
-2.1BE-02
28.939
6.4OE-0?
8*.9*7
B.72E-02
115.779
OE
00
0
-1.43E-03
-1.89*
.93
-S.lBE-92
-28.939
b.*0C-0?
8*.9*7
B.72E-02
115.779
OE
00
0
-1.43F-03
—1.89*
.93
QUALITY TAPE <»5 WRITTEN FROM CYCLE 1 TO CYCLE 25
OUAtlTY tape rfAS WRITTEN from cycle 50 TO CYCLE 7*
QUALITY TAPE rfAS WRITTEN FROM CYCLE 96 T5 CYCLE 180
cm CT QUALITY RUM. 120 CYCLES.
-------
ETUm»LF g FEDER*L WATER POLLUTION CvNTnOL ADMINISTRATION
Fivr jM'irTTc-i<;.Fr,iin channels.constajt friction,100 cfs inflow pacific ns^thwest water laboratory
example *—C5MTIMIITV TEST
MYORAULICS FR3M FXAkPlE I
•••••••• F35X HYDRAULICS PRCRPAM ••••••••
START erCL* STOP CYCLE TIME interval
180
¦><~0
120 SECONDS
$r#8Tinr. cvCLE „ I'HTIAL OUALITV TOTAl OUALITY
¦C* HrO. ExTOACt TAp€ CyT(.E C*ClEs
1«>0
• •• yyfOI
Cycles
UT°UT INTERVALS •••
H;UPS
240
50
1.00
TI«E INTERVAL in CONSTANT FOR
QuA^lTV PRC®RAm DIFFUSION COEFFICIENTS
.*00 HOl'ftS
PRINTOUT IS T5 «EGI« AT CYCLF 1
QUALITY TAPE *0" EXTRACTING TS TO BEGIN AT CYCLE
I CONSTITUENTS HElrtG CONSIDERED IN THIS RUN
CXAMBLE^i CONTINUED
ALL CC*
-------
#*#»«mwltiplicatiom factors applied to obtain starting concentrations
CONSTITUENT GaC'JP FACTOP JUNCTION NUMRE^S
NO MULTIPLICATION KACjO^ APPLIED to constituent NO. 1
-------
••••*••»••••••**•••«••»»•••«••««•«•«••••<>•«••« rikTER QUALITY DATA ••••••••••••••••••••••••••••»••••••»•••*••••••
• FI:
-------
••«•••••••••••••¦•••••••«•••
CHAN, LEWT" *I0IM AH£A
CH&W1FI DATA »••»••••••«•»••••••»»••••••••
MANNING NFT FLCM HYO. RADIUS JUNC. AT ENDS
1
sooo
1000
9947
.0?0
-100.34
10.0
1
2
sooo
loo 0
10018
.020
-100.3T
10*0
2
3
•SOnO
IOC
1001*
.020
-100.36
10.0
3
4
5000
looc
roo3s
.020
-100.22
10.0
4
MASK f 1.1> * 1
EXAMPLE 8 (Cont'd)
lUtlMtH
JUNC. head
JUNCTTSN ftata ••••••••••
CHAmnFLS ENTEfttN* JU*CT13*
1
0
1
0
0
0
0
2
0
1
S»
0
0
0
3
0
2
S
0
©
0
4
0
3
4
0
0
0
5
0
4
0
0
0
0
-------
KT*TrM-<;T*T.** 15.00
------- |