Transactions A.S.M.E.

HOOPER—SALT-VELOCITY MEASUREMENTS AT LOW VELOCITIES IN PIPES 659
rate of diffusion of the solution throughout a cross section due to
turbulent mixing. The percentage of turbulence is certainly
one of the components of the criterion, and includes not only the
velocity, but also the roughness characteristics of the waterway.
Obviously, a size factor of the conduit must also be included
injthe criterion; for a closed channel the area, and for an open
channel, either the wetted area or the hydraulic radius might be
considered.
A third factor, time, must be included. Considering percentage
turbulence as a measure of the spatial rate of transport of
solution throughout the water, it is evident that a certain time
must elapse for the transport of a salt particle from, say, the center
of the conduit to the wall, or vice versa. The time factor
might then be expressed as the ratio of water depth or pipe diameter
to the radial component of the turbulence fluctuations.
The fractional portion of the linear dimension to be employed in
this expression will, of course, depend upon the injection pattern.
If a standard pattern of injection can be adopted the influence
of injection procedure may be eliminated, and more important,
the time factor may be very considerably reduced by the use of
a well-distributed injection pattern.
Assuming the foregoing analysis to be applicable and letting ut
be the mean turbulence fluctuation; A the cross-sectional area
of the channel; and T the time factor; the form of the mixing
criterion might be
M = u, A T ...................................... [1]
having the dimensions L 3 of a volume.
Because of the practical difficulty of measuring u„ it may be
desirable to substitute for u, the expression11 lv, where I is the
Prandtl mixing length, and v is the kinematic viscosity of the
water. Experiment alone will determine the most satisfactory
term to be used as a measure of the turbulent diffusion, the suggestions
given herein being intended principally to indicate the
nature of the term.
The results of the author’s tests to determine the effect of
gravity on the operation of the salt-velocity method are a further
corroboration of the writer’s thesis1 that turbulence in the stream
is the chief factor governing the accuracy of the method.
E. A. T a y l o r .12 The author has described a study which
gives a laboratory answer to a salt-velocity question which has
arisen several times in the field. This question was: “When salt
is introduced into a penstock does the higher specific gravity of
the salt solution drive the salt through the water and toward the
bottom of the penstock, thus changing the time of passage of the
salt solution through the test section, and introducing an error
in salt-velocity measurements”
At many of the high-head power plants, where salt-velocity
tests have been made, the penstocks have very steep slopes and,
at some of them, the penstocks approach the vertical for considerable
distances. If this difference in the specific-gravity question
were important, then the computations for turbine efficiency
at those plants might be appreciably in error.
The results of the laboratory studies described by the author
indicate that the effect of gravity on the salt-velocity method of
water measurement is negligible, when proper salt mixing and
distribution are secured.
In 1939, the salt-velocity method of water measurement was
used in making efficiency tests on the Colorado River Aqueduct
pumps for the Metropolitan Water District of Southern California.
During those tests, a field answer was found to the
specific-gravity question. The question was raised at the Iron
11 “ Modern Developments in Fluid Dynam ics,” edited by S.
Goldstein, Oxford University Press, New York, N. Y., 1938, chapter 5.
I! Consulting Engineer, Worcester, Mass.
Mountain Pumping Station and the district engineers agreed to
turn that plant into a field laboratory to study the subject.
The regular salt-velocity test section, used for pump-efficiency
tests at this plant, was 200 ft long, 100 ft from salt injection to
the first set of electrodes, and another 100 ft to the second set of
electrodes. For this specific-gravity study, two additional pairs
of electrodes were installed in the 10-ft delivery pipe.
These additional electrodes were called spot electrodes and
consisted of small steel plates, 4 in. square and spaced 2 in. apart.
These spot electrodes were fastened 5 ft beyond the regular second
set of electrodes, making the length of test section used for the
spot electrodes 105 instead of 100 ft. One pair of spot electrodes
was located at the top of the pipe and the other pair at the bottom.
During the study, the ammeter connections were alternated,
shot by shot, between the two sets of spot electrodes.
A total of 74 salt shots were made and computed in this study.
Averaging the results of these shots showed that the passage time
to the top spot electrodes was 0.04 sec less than the passage time
to the bottom electrodes. This was regarded as a perfect check
and a conclusive field answer to the gravity question.
As further assurance of the accuracy of the salt-velocity method
of water measurement and confirming the belief that any specificgravity
error was too small to be seriously considered, two volumetric
check tests have been made at Pacific Coast plants, one of
them being a high-head plant with a steep slope in the penstock.
For those check tests, a 3-acre forebay, 20 ft deep, and a 10-
acre reservoir, 10 ft deep, were used as basins for the volumetric
measurements. The volumetric results checked salt velocity,
by 0.75 per cent at one plant and by 0.5 per cent at the other
plant. The latter was the high-head steep-penstock plant where
any gravity effect would be expected to be most apparent.
The author’s conclusion, from laboratory tests, th at “for velocities
lower than those normally found in practice, there exists a
critical mixing velocity below which good mixing of the injected
brine does not occur” is confirmed by some field tests recently
made.
Field efficiency tests were made on the Colorado River Aqueduct
pumps in May and June, 1939. At Intake, the first station
tested, the discharge values for single pumps checked the discharges
when two or three pumps were operating together.
At the second station tested, Gene, the results of the preliminary
tests, comparing single- and multiple-pump discharges, did
not check.
At all five Colorado River Aqueduct pumping stations, one 10-ft
delivery pipe carries the discharge from the three pumps now installed
at each station. When only one pump is operating, the
velocity in the delivery pipe is comparatively slow, about 2 fps.
The inside of these delivery pipes is coated with an enamel finish,
as smooth as glazed porcelain, and there are no rivet heads or
other projections into the inside of the pipe.
This combination of extremely smooth pipe and low velocities
created a condition of low turbulence, too low for satisfactory
salt mixing, during the passage of a shot. This accounted for
the failure of the discharge values to check between single and
multiple pumps.
To provide more turbulence, an artificial agitator, called a “tur-
bulator” was installed beyond the salt-injection station. This
so-called turbulator was a steel disk, 6 ft in diam, fastened in the
center of the delivery pipe and normal to the axis of the pipe.
This disk had an 18 X 24-in. hole in the center and was located
40 ft beyond the pop valves. The turbulator was used
during the remainder of the pump tests and single-pump-discharge
results checked the multiple-pump values.
No artificial turbulator was required at Intake, because the
salt-injection station was just above the manifold where the three