The American Society of Mechanical Engineers

ANGUS—IM PROVED TEC H N IQ U E FO R C EN T R IFU G A L -PU M P-E FFIC IE N C Y M EA SUREM ENTS 27
W. M. W h i t e . 17 The 93 per cent efficiency obtained on one
of the pumps is not an impossible efficiency. The filtration
pumps in the City of Milwaukee also showed an efficiency of 93
per cent when the quantity of water was measured volumetrically.
A point of interest to the writer is the close adherence of the
actual performance of stepup to the theoretical performance of
step up by the Moody formula. In the case of the M etropolitan
W ater District pumps a stepup similar to th a t at Toronto was
not secured. We have as yet been unable to find the reason why
the large pumps on the M etropolitan did not give the high
efficiency which should have been shown.
One im portant point not entirely clarified in the paper is the
fact th at the coefficient of one of the venturi meters was found,
by volumetric measurement, to be in error by 3 per cent. T hat
is to say, when the m anufacturer’s coefficient was used, the
quantity was 3 per cent higher than when the coefficient was
corrected by means of volumetric measurement. This emphasizes
the necessity of careful calibration being made on venturi
meters for im portant centrifugal-pump tests.
A r t h u r R y n d e r s . 18 The w riter’s experience shows th a t the
data hardest to obtain accurately in a pump test concern the
volume of water pumped.
Some years ago, in testing centrifugal pumping units a t the
Menomonee Valley Booster Station, the w ater pumped was
measured volumetrically. A t this station there are no venturi
meters. The pumping units are used to pump water from a sixmillion-gallon
welded steel ground storage tank into the distribution
mains. Field measurements of the tank were determined
before filling the tank to find as nearly as possible its
exact size a t a known tem perature. During the test, various
levels of the water surface were measured by means of a hook
gage. The volume computed from these measurements was
corrected for the elastic volume change of the tank and the
temperature of the tank wall a t the time of test. The results of
the test were considered to be within satisfactory limits of
accuracy.
Recently the pumping units a t the W ater Purification Plant
were tested. The units tested consist of four 50-mgd and one
75-mgd low-level pumping units; and two 20-mgd washwater
pumping units. I t was decided to measure the w ater
volumetrically even though venturi meters were available in the
low-level discharge line. The tanks were underground reinforced-concrete
structures 297 X 372 ft in plan X 22.5 ft deep.
Hook gages were again used to determine the w ater levels.
The computed volume was used without any correction. The
test results obtained were considered to be very accurate. Calculation
made from these tests and motor tests indicated th at
some of our pumps have an efficiency slightly exceeding 93 per
cent.
A u t h o r ’s C l o s u r e
In his discussion Mr. Allan suggests that, for large differentials
on the venturi meters, one camera for each column would have
some advantage, but the author believes th at there would always
exist some question as to whether the cameras exactly synchronized.
The single camera for the two columns gave excellent results
and there was much less trouble in setting up the apparatus,
changing films, etc.
Mr. Allan mentions the use of motion-picture cameras. Much
thought was given the question, particularly in connection with
the electrical instruments. However, since the contractors were
17 Manager and Chief Engineer, Hydraulic Department, Allis-
Chalmers Manufacturing Company, Milwaukee, Wis. Mem.
A S.M.E.
l* Mechanical Engineer, City Engineer’s Office, City of Milwaukee,
Wis.
still working on the building and equipment, the facilities at
hand were far from perfect and precluded some methods which
might otherwise have been further considered. In work of this
kind, it is necessary to obtain the results of tests quickly, which
would scarcely have been possible w ith the motion-picture film.
In the actual test, films and plates exposed during one night were
developed and available within about 10 hr, so th a t the result of
each test was determined promptly.
The use of the Moody formula in comparing the results on the
model and prototype has been referred to several times in the discussion.
The author holds no brief for this formula and fully
realizes some, if not all, of its defects, although there appears to
be no reason why it should not apply to pumps as well as to
turbines. The exponents in the head-and-diam eter relation, as
given by Professor Pardoe m ay be closer than those given by
Professor Moody, and it would seem th a t experience alone would
be the safest guide in this direction. All th at the author can say
in his defense is th at the formula seemed to be well worth trying
and it has given quite satisfactory results on these pumps.
In order to compare the results of Professor Pardoe’s suggested
exponents for the head-and-diam eter ratios in the step-up
formula, the author recalculated the results on these pumps
which are given in Table 7 of this closure. The exponent of H /h
is 0.1 as suggested by Professor Moody and 0.125 by Professor
Pardoe, while the exponents of d/D are 0.25 and 0.2, respectively.
T A B L E 7
C O M P A R IS O N O F M O O D Y F O R M U L A A N D P A R D O E
M O D IF IC A T IO N
P u m p M easu red C a lc u la te d efficiency
cap a c ity ,
m illion gal
p e r 24 h r
m odel ✓------ E of p ro to ty p e ------ n M easu red
efficiency M oody P a rd o e efficiency
e fo rm u la m odificatio n on p u m p
12 0 .9 0 0 0 .9 0 8 0 .9 0 5 0 .9 0 2
24 0 .8 9 6 0 .9 1 0 0 .9 0 7 0 .9 1 5
48 0 .8 9 6 0 .9 2 0 0 .9 1 4 0 .9 3 0
30 0 .9 0 7 0 .9 2 4 0 .9 2 1 0 .9 1 8
It is seen th a t the two calculations give alm ost the same results
but, in this case, the maximum ratio D /d was only 2.63.
Since the values of H /h lie between 0.81 and 1.47 it will make
slight difference whether the exponent 0.125 or 0.1 is used.
In the cases quoted by Mr. Babb and D r. W hite the Moody
formula did not prove satisfactory, which shows th a t it is either
defective in construction or th at the exponents vary in different
cases. The scale of the models mentioned by Mr. Babb was
much smaller than those mentioned in the paper, and there may
be some little differences due to the method of discharge measurem
ent used.
Comments on the venturi-m eter coefficient are interesting, and
Mr. B abb’s statem ent th at he found differences in the coefficient
of 0.3 to 0.4 per cent between calibrations is striking and gives
reason for some concern, assuming, of course, th at the elapsed
time between the calibrations was not great. The variations
mentioned by Mr. M cDonald are so large th at one wonders
whether they are due to setting or to m anufacture or both. The
author has made a careful examination of Professor Pardoe’s
laboratory and the methods he has used in calibrating meters
and believes them to be fully as accurate as claimed. A t the same
time, the coefficient given by the Fluid M eters Committee, on
Professor Pardoe’s authority, was undoubtedly in error in the
meter discussed in the paper.
W hen opportunity offers, the author will try to follow Professor
Pardoe’s suggestion of traversing the pipe close to the meter. In
the meantime the author’s result rather shakes confidence in the
coefficients, undoubtedly accurate for the circumstances under
which they were obtained, but uncertain in some field installations.
Unfortunately, no suggestion is made as to how one is to know
whether or not the Fluid M eters Committee’s coefficients should
be corrected. The author primarily introduced this m atter in