Environmental Engineering Reference
In-Depth Information
float, such as wooden disks, bottles partially filled with water, or even oranges. Two
cross sections are selected along a reach of straight channel, so that the time the
float takes to pass from one cross section to the other can be measured accurately.
Distance from the upstream to the downstream cross sections needs to be measured
and floats should be applied far enough upstream of the upper cross section that they
are travelling at the same speed as the surface current when they pass the upper
cross section. For best estimates of discharge, a number of floats are distributed
uniformly across the stream width, and the position of each with respect to distance
from the bank is noted. The stream-channel width can be segmented just as with
the velocity-area method described above, depth for each channel section can be
measured, and discharge calculated as the sum of each velocity-area product. This
method will over-estimate discharge because the surface velocity is faster than the
depth-integrated velocity. Therefore, a coefficient of 0.85 is commonly used to
convert the surface velocity to mean velocity (Rantz 1982 :262).
3.6.5 Stage-Discharge Rating Curve
Rating curves for discharge gaging stations are normally determined empirically
with periodic measurements of stage and discharge made over the full range of
stage at a particular station. Thereafter, only periodic measurements (commonly a
minimum of 10 per year) are needed if it has been demonstrated that the rating
curve does not vary with time (Rantz 1982 :285). However, shifts in rating curves
are common at gaging stations with natural control due to changing channel
conditions, including scour and fill, vegetation growth, boulder movements, and
ice formation. Rating curves are created by plotting the stage-discharge data and
fitting a suitable mathematical function to the entire data set, or fitting a set of
functions to separate segments of the data. Power functions are commonly used to
fit the data:
m
Q
¼
ah
ð
h 0
Þ
(3.26)
where Q (m 3 s 1 ) is discharge, a (m 3- m s 1 ) is a scaling constant, h (m) is stream
stage (i.e., water level), h 0 (m) is the stage at zero flow, and m is a dimensionless
constant. This function generates a straight line when Q and h
h 0 are plotted on
logarithmic axes. For gaging stations with no control or natural control, a and m are
determined by minimizing the difference between the measured discharge and the
predicted discharge using Eq. 3.26 .
For gaging stations with an artificial control structure, a formula developed in the
laboratory is provided with the device. For example, a rectangular thin-plate weir
has a rating curve in the form:
32
=
Q
¼
Cb h
ð
h 0
Þ
(3.27)
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