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

7. DISCHARGE-TRACER-DILUTION METHOD 255
ionic wave. The ratio ofdilution for the sample of injection solution is
1:10,000, because 1 mL of injection solution was mixed witb 10 L of
river water.
COMPUTATION OF DISCHARGE
The simplest way to describe the computation of discharge from
salt-dilution data is by means of an example. Assume that in the
preceding discussion of methodology, the stream discharge had been
estimated to be about 4.5 mats. The unit quantity of salt to be used
was 2 kg/m 3 /s of discharge; consequently about 9 kg of salt was prepared.
Water was added to the salt at the rate of 10 L per 3 kg ofsalt.
As a result, 30 L (0.03 m 3 ) of injection solution was prepared. This
value is shown on line 1 on the left-hand side ofthe computation sheet
in figure 127. At the sampling site, 10 L of river water (line 2) was
mixed with 1 mL of injection solution (line 3), giving a dilution ratio
of 10,000 (line 4). The resistance of the river water was found to be
969 ohms (lines 5 and 6), and the resistance of the sample of diluted
(1:10,000) injection solution was found to be 691 ohms (line 7)_ The
relative conductance of that sample, as read on the rheochord in
tenths ofa percent, was 402 (line 8). On line 9, the rheochord reading
for the dilute sample of injection solution is checked mathematically
by use of the measured resistances. The equation used on line ,9 is
identical with equation 39. On line 10 the relative conductance ofthe
injected solution is computed by multiplying the relative conductance
of the diluted injection sample by the dilution ratio.
On the right-hand side offigure 127 are shown the relative conductance
values read on the rheochord scale at 15-s intervals during the
15-min passage of the ionic wave. Subtotals are shown for the three
columns of relative conductance values; the grand total is 1,933. The
data are presented graphically in figure 128, where relative conductance
is plotted against time.
Discharge is computed from equation 40, the denominator of which
is the area under the curve of relative conductance versus time:
where
Q
V,
P"
F
Q= V,P"
F ± AF
(40)
is discharge, in cubic meters per second,
.Is volume of the injected solution, in cubic meters,
is relative conductance ofthe injected solution, in tenths of
a percent,
is the product of the sampling interval, in seconds, multiplied
by the sum of the observed values of relative
conductance, and
is a correction factor for any change in reading of the rela