Environmental Engineering Reference
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eastern U.S. and one laboratory flume involving 72
K
d
measurements confirmed this as they concluded
“for a wide range of flow regimes, so-called “bottle” estimates of
K
d
adequately reflect corresponding
rates that can be expected in receiving waters.”
Masters (1991) reports that for turbulent, shallow, rapidly moving streams, the use of the bottle estimate
of
K
d
is less valid because such streams have
K
d
values that can be significantly higher than the values
determined in the laboratory. For example, Hamdy and Jatinder (1972) reported that the value of
K
d
under
continuous mixing conditions is more than 10 times the value of
K
d
obtained under stagnant conditions.
Finally, Wright and McDonnell (1979) reported that for shallow, low flow streams
K
d
falls consistently in
the range 2.5 to 3.5 d
-1
reflecting the turbulence in such mountain streams of the eastern U.S. (values as
high as 4.24 d
-1
are included in their database). Thus, if working in streams where turbulent flows are
likely, field calibration of
K
d
based on in-stream CBOD measurements should be done.
Determination of the reaeration-rate coefficient,
K
a
—Reaeration is the physical absorption of oxygen
from the atmosphere by water. It is the most important natural means by which rivers affected by waste
inputs may recover DO. The reaeration-rate coefficient,
K
a
, typically is the dominant parameter affecting
the uncertainty in the simulation of DO concentrations in streams (Brown and Barnwell, 1987; Melching
and Yoon, 1996). Because the value of
K
a
can substantially affect waste load allocations derived with
computer models, the value of
K
a
utilized in simulation models must be carefully determined.
The value of
K
a
can be measured accurately utilizing tracer-gas methods (Kilpatrick et al. 1989) and
field measurement of
K
a
is strongly encouraged for reliable waste-load allocation (Melching and Flores,
1999). Extensive field measurements of
K
a
are, however, rarely done for waste-load allocation studies.
K
a
values typically are determined using one of three approaches for waste-load allocation studies.
(1) The concentrations of all key constituents in the river system are measured for a representative
low-flow period, a simulation model is calibrated for this period, and the
K
a
estimation equation from the
literature that results in the best fit to the data is used [e.g., New Jersey Department of Environmental
Protection (1987)].
(2) A limited number of
K
a
values are measured for the river system in question utilizing the tracer-gas
method, and the best
K
a
estimation equation from the literature for this river system is determined on the
basis of these measurements [e.g., Schmidt and Stamer (1987)]. The example presented by St. John et al.
(1984) illustrates an extrapolation problem with approach 2. St. John et al. (1984) applied 9 commonly used
K
a
estimation equations (listed in Table 9.2) to a hypothetical river for which the slope was 0.000985 and
Table 9.2
Summary of commonly used estimation equations for the reaeration-rate coefficient that were applied in the
e
xample of St. John et al. (1984)
Classification
Reference
Estimation equation
Velocity-depth
O'Connor and Dobbins (1958)
K
3.93
VD
0.5
/
1.5
a
0.67
1.85
Owens et al. (1964)
K
5.32
VD
/
a
1.33
Langbein and Durum (1967)
K
5.135
VD
/
a
0.97
1.67
Churchill et al. (1962)
K
5.05
VD
/
a
Bennett and Rathbun (1972) II
K
5.20
VD
0.61
/
1.69
a
Energy Dissipation
Tsivoglou and Neal (1976)
K
15, 244
SV
a
Shindala and Truax (1980)
K
16,976
SV
a
0.5
Others
Thackston and Krenkel (1969)
K
24.94(1
FuD
)
* /
a
0.413
0.273
1.408
K
Note:
V
= reach average velocity in meters per second,
D
= reach average depth in meters,
S
= energy slope for the
reach in meter per meter,
F
= the Froude number =
Bennett and Rathbun (1972) I
32.47V
S
/ D
0.5
VgD
,
g
= the acceleration of gravity,
u
* = the shear
/(
)
0.5
velocity =
gRS
, and
R
= the hydraulic radius, which approximately equals the reach average depth for a wide
channel (assumed in computing Fig. 9.3)
(
)
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