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540
iij
APPENDICES
APPENDIX A
TRAVEL TIME CALCULATIONS.
The estimation of travel-times for the Clark Fork River from
below Milltown dam to above Thompson Falls was done using a
simple model. The model was developed by the following steps:
1. a field dye-study to measure travel-times for selected
reaches ;
2. comparison of the measured travel-times with ones
calculated; and
3. development of a procedure for estimating travel-times
at other flows and for other reaches of the river.
The field dye-study was performed on July 17-18, 1984.
Rhodamine WT was injected at three locations and the travel-time
over a total of about 86 river miles was measured. The arrival
of the dye at various monitoring points along each of the
reaches in the study was monitored using a fluorometer with a
chart recorder. The quantity of dye to inject was calculated
according to Hubbard, et. al.(1982) and was based on the maximum
concentration of dye being 0.5 ppb at the end of the reach.
Pertinent data used for each of the reaches and the results of
the study are given below. The r i v e r -m i I eag e s and elevation
changes were estimated from USGS topographic maps. The
mileages were compared with published values of U.S. EPA and the
Montana Dept. of Natural Resources and Conservation and in some
cases adjusted or remeasured until acceptable agreement was
reached. The measured travel-times are the times to the peak
concentration of dye at the monitoring point.
The flow at the time of the study was 4800 cfs as measured at
the USGS guage below Missoula (below the confluence witti the
Bitterroot River) Flows for the reach through Missoula and the
rach below St. Regis were estimated using regression equations.
Since 1981 seemed to be a year with similar flow conditions,
regressions were done using USGS daily flows at three stations
for the period July 11-31, 1981 during which the flow varied
from 6660 cfs to 3010 cfs at the station below Missoula. The
resulting regression equations are:
OCbel St Regis) = 1.260(bel Missoula) + 350 (r=.99)
QCabv Missoula) = .46 6Q(bel Missoula) + 710 Cr=.99)
where Q is flow at the indicated stations in cfs.
The flows at other locations were estimated using a rough
extrapolation from the above three stations.
Injection 1 :
Reserve St. Bridge to Harper Bridge: 12.8 river-miles;
97 foot elevation change; flow = 4800 cfs (2950 cfS (est)
above the Bitterroot R); measured travel-time = 5.9 hours;
calculated river velocity = 2.25 mph.
541
Appendix A. Continued
Harper Bridge to Champion: 3.5 r i v e r -m i I e s ; 20 foot
elevation change; flow = 4800 cfs (est); measured
travel-time = 1.4 hours; calculated river velocity = 2.50
mph .
Champion to Huson: 8.8 river-miles; 48 foot elevation
change; flow = 4800 cfs (est); measured travel-time = 3.5
hours; calculated river velocity = 2.43 mph.
Huson to Petty Creek: 10.5 rivei-miles; 35 foot
elevation change; flow = 5200 cfs (e'l; measured
travel-time = 4.9 hours; calculated river velocity = 2.14
mph .
Injection 2 :
Petty Creek to Forest Grove: 24 river-miles; 217 foot
elevation change; flow = 5400 cfs (est); measured
travel-time = 10.5 hours; calculated river velocity = 2 29
mph .
Forest Grove to LaVista: 16.5 riwer-'.iiles; 68 foot
elevation change; flow = 6000 cfs (est); measured
travel-time = 6.3 hours; calculated river velocity = 2.62
mp h .
Injection 3 :
Below St. Regis on highway 135 from mile-post 11 to
mile-post 20.5: 10.4 river-miles ; 55 foot elevation
change; flow = 6400 cfs (est); measured travel-time = 4.2
hours; calculated river velocity = 2.48 mph.
Theoretical calculations of velocities of the river for each
of the reaches were made using the equations of Boning (1974).
He gives separate equations for "channel-controlled" reaches and
for "pool and riffle" reaches. These equations are:
V = 2 . 69(Q)° ■^®(S)° " ^® (channe I -con t ro I I ed)
c c
V = 0.38(0)°' ^^(S)°-^° (pool and riffle)
pr
V is velocity in ft/sec, is discharge in cfs, and S
is slope in ft/ft. V was converted to mph by
multiplying by 0. 682 .
The results of the calculations were in good agreement with
the results of the dye-study and for the most part the two
velocities (channel-control and pool-riffle) calculated for
each reach bracketed the measured velocity (see table
b e I ow) .
A model was then conceived that consisted of using the two
equations above after determining for each reach whether the
channel-control equation, the pool-riffle equation, or a
combination of the two should be used To carry this out
542
Appendix A. Continued
a calibration procedure was used in which a weighted-average
of the channel-control and pool-riffle results was
calculated for the flows at which the dye-study was carried
out and the weighting factors were chosen so that the
weighted-average equalled the measured velocity. Or in
mathematical terms:
V = A(V ) + B(V )
m CO p r
V is the measured velocity, V and V are the
m c c D [
calculated channel-control and pool-riTTle results, and
A and B are the weighting factors.
The results are s umma rized in the following table.
Ca
c .
Use
d
Reach
V
m
V
cc
V
Pr
A
B
A
B
Res. St -Ha r pe r s
2.25
2 . 49
1 . 90
. 59
. 4 1
. 6
. 4
Harper s-Champ i on
2.50
2 . 46
1 .96
1 . 08
-.08
1 .0
0.0
Champ i on-Huson
2. 43
2 . 44
1 . 95
.98
.02
1 .
.0
Huson-Pe t t y Cr
2.14
2.15
1 . 82
. 97
.03
1 .
0.0
Petty Cr-F Grove
2.29
2 .86
2.24
.08
. 92
0.0
1 .
F Grove-LaVista
2 . 62
2 . 48
2 . 07
I .34
- .34
1 .34
-.34
Hwy mile 1 1-20 . 5
2 . 48
2 . 62
2.21
.66
.34
.66
.34
A high value for A indicates that the reach has a predominately
channel-control character, while a high value for B indicates a