Transactions A.S.M.E.

656 TRANSACTIONS OF THE A.S.M.E. NOVEMBER, 1940
the injection station was below that indicated in these tests as
being necessary for proper mixing. Thus, it is believed that the
factors concerning the critical mixing velocity which have been
discussed only apply to the measurement of flow in long straight
pipes with very low velocities.
S u m m a r y
The following conclusions may be drawn from these saltvelocity
measurements at low pipe velocities:
1 The low-velocity effects discussed in this paper are found
at velocities below those normally encountered in practice.
2 The critical mixing velocity is a very definite limiting
velocity below which proper mixing of the injected brine is not
secured.
3 The force of gravity does not have any influence upon the
accuracy of the salt-velocity measurement as long as the injected
brine is readily mixed with the water flowing in the pipe.
A c k n o w l e d g m e n t
The author gratefully acknowledges the assistance given by
Dr. Th. von K&rm&n who suggested the mechanics of the
mixing process and thereby contributed greatly to the value of
this investigation.
B IB LIO G R A PH Y
1 Basic description of the salt-velocity m ethod: “ The Salt-
Velocity M ethod of W ater M easurem ent,” by Charles M. Allen and
Edwin A. Taylor, Trans. A.S.M .E., vol. 45, 1923, pp. 285-341.
2 Study of the mixing process: “ How W ater Flows in a Pipe
Line,” by Charles M. Allen, Mechanical Engineering, vol. 56, Feb.,
1934, pp. 81-84.
3 Low-velocity study in open flumes: “ Contribution k l’Etude
de la Mesure des D ebits d ’E au par la M ethode Allen,” by M artin
Mason, Thesis at the U niversity of Grenoble, Revue GirUrale de
VHydraulique, Paris, 14.
4 Theoretical discussion of turbulence: “ Fluid Mechanics for
Hydraulic Engineers,” by H unter Rouse, McGraw-Hill Book Company,
Inc., New York, N. Y., 1938.
5 M easurem ents of turbulence in w ater: “ Investigation of
Errors of P ito t Tubes,” by C. W. H ubbard, Trans. A.S.M .E., vol. 61,
1939, pp. 477—492.
D iscussion
D. P. B a r n e s .2 Referring to this and the paper3 by O. H.
Dodkin, it is begining to be recognized that, for the salt-velocity
method to yield ideally correct results, it would be necessary
that all the small elementary volumes of salt solution spend
statistically equal periods of time in each of the different velocity
zones from the center line to the outer radius in passing between
electrode stations. This is to say that turbulent mixing should
be continuous and complete transversely across the pipe throughout
the passage. Any deviation from this continuous symmetry
and uniformity of mixing would mean that part of the salt cloud
must lag behind the mean flow, the center of gravity of the salt
cloud, therefore, with it.
The natural tendency of a dense solution to settle downward
and to underflow a lighter liquid as an integral body is now a well-
established experimental fact. In the salt-velocity test, if this
tendency is not completely countered by the turbulent mixing, it
would be expected that in time the salt cloud would become progressively
less symmetrical or less uniform with respect to the
pipe.
In a sloping pipe, the effect of the tendency for the denser
2 California In stitu te of Technology, Pasadena, Calif.
3 This is a joint discussion of the L. J. Hooper paper, and the paper
“ Field Checks of the Salt-Velocity M ethod,” by O. H . Dodkin, published
on page 663 of this issue of the Transactions.
liquid to assume an asymmetrical distribution is compounded
with the effect of the component of underflow in the downhill direction.
In any case the asymmetry or nonuniformity alone
would tend to produce a velocity reading smaller than the true
mean, and this effect would be increased in the case of pumps with
uphill flow or decreased in the case of turbines with downhill flow
by the downhill component of the underflow.
The numerous field checks would appear to establish that the
errors introduced by these tendencies are slight and, that where
the method is used with full recognition of the possible sources of
error and where a proper allowance is made for them, the results
may be supposed accurate within perhaps 0.5 per cent, at least
for downhill flow. This is a view to be accepted with caution,
however, for bends, obstructions, steep slopes, low velocities, or
abnormal velocity distributions in the penstocks must continue
to introduce uncertainties wherever their effects are not subject
to calibration. It would seem that each proposed application of
the method should therefore be considered largely on its own
merits.
A n d r e w F e j e r 4 a n d J. W. D a il y .5 During the last few years,
it has become more and more desirable to determine large rates of
flow with great accuracy. In the case of large-scale field tests the
salt-velocity method has been found particularly suited for such
measurements because of its simplicity and convenience in application.
Very little is known, however, about the performance of
the method at low velocities, and this paper furnishes useful experimental
information in that range.
In connection with investigations conducted at the hydraulicmachinery
laboratory of the California Institute of Technology
on the design, operation, and testing of large-capacity pumps and
especially in connection with the question of extrapolation of
model results to prototype results, it has been of considerable interest
for the Institute to subject the salt-velocity method to experimental
study. The experimentation was assigned to the
writers, who present the following summary of results with the
approval of the laboratory directors.
E x p e r im e n t a l W o r k
Following Dr. von ICdrmdn’s suggestion that a salt cloud would
tend to settle downward in water due to its higher density whenever
the turbulent forces were inadequate to keep the cloud in
suspension, it was decided to obtain qualitative information about
shape and character of salt clouds under different flow conditions.
The tests undertaken were made in a straight, transparent,
lucite pipe 20 ft long and 5'A in. inside diam, mounted in such a
way that it was possible to change its inclination from 0 to 13 deg.
Solutions of sodium nitrate deeply colored with potassium permanganate
were injected into the flow through pop valves under
compressed-air pressure, and visual, photographic and cinematographic
observations of the behavior of the cloud on its path
through the pipe were made. Two types of injection nozzles
were used, i.e., a single central pop valve in the pipe axis and a
combination of six pop valves distributed uniformly over the
cross section. Solutions of five different densities (1.2,1.15,1.10,
1.05, 1.025) were injected into flows of velocities, covering a range
of 0.1 to 1.5 fps. This range corresponds to a range of 0.5 to 7.5
fps for geometrically similar flow in a pipe 10 ft in diam.
D is c u s s io n o f R e s u l t s
It was found that the salt cloud retained its symmetrical shape
only at considerable flow velocities. This can happen only if the
4 Research Assistant, Hydraulic M achinery Laboratory, California
In stitu te of Technology, Pasadena, Calif.
6 Research Fellow, H ydraulic M achinery Laboratory, California
In stitu te of Technology, Pasadena, Calif. Jun. A.S.M.E.