PCWA-L 467.pdf - PCWA Middle Fork American River Project ...

7. DlSCHARGE-TRACER-DlLUTION METHOD 217
mixing is considered to have occurred when the area under the
concentration-time curve, shown in figure 117, has the same value at
all points in the downstream sampling section.
For a reach ofchannel of given geometry and stream discharge, the
length ofreach required for adequate mixing ofthe tracer is the same
for either of the two methods oftracer injection. Several formulas are
available for estimating the required mixing length for a particular
set of conditions, but these formulas, while useful as guides, are too
simplistic to give adequate consideration to the degree of mixing desired.
Perfect mixing is seldom the optimum goal (see below) because
perfect mixing usually requires an extremely long reach of channel,
along with a correspondingly long period of injection in the constantrate-injection
(CRn method and a correspondingly long period of
sampling in the sudden-injection (81) method.
Figures 116 and 117 are only rudimentary illustrations of the two
methods. For either method to be successful an understanding is
needed of the interrelations among mixing length and injection and
sampling times. Figure 118 attempts to illustrate those interrelations
for both types of injection. It is important to realize that unless
adequate mixing is known to exist at a given sampling site, the tracer
cloud in the Sl method must be sampled for its entire time of passage
at several locations laterally in the channel, such as at A, B, and C in
figur.$' 118. Similarly, in the cm method the plateau concentr.ation
must be sampled at several locations laterally in the channeL Experience
indicates that regardless of method or stream size, at least three
lateral sampling points should be used at each sampling site.
Figure 118 indicates that there is an optimum mixing length for a
given stream reach and discharge. Use of too short a distance will
result in an inaccurate accounting of the tracer mass passing the
sampling site. Use oftoo great a distance will yield excellent results,
but only if it is feasible to inject the tracer for a long enough period
(Cm method) or to sample for a long enough period (81 method). An
optimum mixing length is one that produces mixing adequate for an
accurate discharge measurement but does not require an excessively
long duration of injection or sampling.
As mentioned earlier, figure 118 shows that the tracer cloud resulting
from a sudden injection must be sampled at the sampling site
from the time of its first appearance there until the time (T,J of its
disappearance at all points in the sampling cross section. For the
same mixing reach and discharge, if the em method is used, a
plateau will first be reached at all points in the sampling cross section
at time T r after injection starts at the injection site. Thus, it is seen
that for the CRI method the duration of injection must at least be
equal to Tr and injection should continue long enough thereafter to