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INCORPORATED 1887.
ADVANCE PROOF— (Subject to revision)
N.B.— This Society, as a body, does not hold itself responsible for
tlie stiitoments ;iu(l opinions attvancod in any of its puhlications.
ON THE measurp:ment of water by a small
VENTURI METER.
By E. G. Coker, M.A., Cantab., D.Sc, Edix,, and
T. P. Strickland, M.Sc, McGill.
INTRODUCTION.
The problem of accurately measuring the continuous flow of
water is one that has received a large amount of attention, and
many forms of meters have been devised for attaining this object.
A form of meter, which has come into general use within the last
few years, is that liuown as the Venturi meter.
This form of meter is especially applicable to water-mains, as
the head necessary to operate tlie meter is small and the quan-
tities may be extremely large.
Herschel (1) has shown that, iu meters applicable to mains of 1
foot and 9 feet diameter respectively, the flow is proportional to
the square root of the difference of head between the two sections
of the cone forming the essential part of the meter, and this holds
through the wliole range.
In the present paper the meter used was a very small one, and
the principal object of the experiments was to determine the range
of the law
quantity = n ^JJg
and, as a consequence, the variation, of the "constant" in the equa-
tion connecting the flow with the dimensions of the meter and the
head.
The meter used was especially designed and constructed for the
experiments, and had several advantages over the ordina-y form.
(1.) The Venturi water meter. Trans. Am. Soc. C.E., 1887.
1
DESCRIPTION OF APPARATUS.
Id its simplest and more usual form, the Venturi meter con-
sists of two frustra oonuectod at their smaller ends bj'^ a short cylin-
drical tube or "throat," their outer ends being fitted to the pipe
through which the water it is desired to measure is passing, and
provided with means for attaching pressure gauges at the throat
and at the outer ends of the cones.
At the points Avhero it is desired to measure the pressure in the
meter a pressure-chamber encircles the pipe and (;ommuuicates with
the interior by a number of small lioles drilled as nearly radially
as possible. It is essential for accuracy that the holes should be
truly radial and the edges without burr, llie attainment of which is
a matter of considerable difficulty, especially in a small meter.
The meter used in these experiments overcomes the olijections
mentioned above.
Fig. 1 is a longitudinal section of the meter consisting of a
short "up stream" cone, A, and a "down stream" cone, B, connec-
ted by a combined coupling and pressure chamber, 0, which forms
the throat.
The Venturi is connected to the pipe by two other couplings of
the same form. The combined pressure cliamber and coupling is the
peculiar feature of the meter, and is shown clearly to an enlarged
scale by Fig. 2.
DISSCltll'llON OF I'KESSUBE CHAMBEB.
It consists Of three sopurate pieces, tlie outer one, A, of which
couples the parts B, C, together, leaving u continuous opening, D,
around the bore, which n^ay be of any required width. The part B
is recessed to form a pressure chamber connected to the guage by
an opening, K. The parts B and C are faced, so that when drawn
together by the coupling A they form a watertight joint at F, and
the ends of cones are screwed into corresponding recesses in B ami
C.
This form of throat possesses several advantages. The con-
tinuous •>pening gives a more accurate value of the pressure than, a
serh-s of holes; it can be faced without any burr, and Its width can
be adjusted with accuracy. Also, the diameter of the throat at thi-
i.oint where the pressure is measured can be determined with the
greatest possible accuracy, and, moreover, is open to Inspection.
The parts can be rotated relatively to tiie others without des-
troying tile joint, an advantage in setting up the apparatus.
It should be pointed out that the measurement of the pressure
at the down stream end of the cone is not essential for practical
measurements; it was merely used for determining tlie total loss of
head in the instrument. The down-stream pressure chamber can,
therefore, be dlspensetl with in ordinary, use,
/
GAUGES.
The gauges used for measuring the pressure of the water In. the
pipes are of unusual pattern.
Fig. 3 Is a section, in which A is an iron base plate about %
inch thick, provided with three brass levelling screws, B. On a
ring of india-rubber on the plate stands a cylindrical glass vessel,
C, or reservoir, about 2V2 inches in diameter, vv^ith an aluminium
cover, D. Four rods, not shown, screwed Into the base plate and
passing through the cover, have screwed ends and nuts at the top,
by which tlie reservoir is pressed down on the rubber ring. Near
the centre of the aluminium top is a tap, E, and a nipple, into which
is screwed a T piece, the upper part of which is provided with an
air cock, wiiile the liorizontal brancli Is connected with the pressure
chamber by means of a piece of rubber tubing.
Beneath the Iron base is a pipe, F, connecting the reservoir with
n vertical glass tube. G. of ;■, inch bore and Ti.j inches in length.
Behind tills tube is a scale reading up to 32 inches, and movable
relatively to the tube and reservoir.
At the lower end of the scale a spindle, H, is attached to the
l)ack, and passes through a glnnd into the reservoir. The bottom of
Pressure Column
Srde Elevation
Scale
finely graduahd
Top Plan
thiH spindle Is of alumiuiuui. with a poiut ou tlie same level us the
zero of the scale. On the top of the spindle Is a luilleU head, I, by
meaus of which the spindle and scale can be moved up or dowtt
until the point reaches the surface of the mercury in the reservoir.
The'reading of the scale is then evidently the height of the mercury
column above the level of the mercury in the reservoir. There is a
email steel auxiliary scale, with .01 inch divisions, which measures
the displaceiiieut. fi-om a datum, of the zero of the main scale, when
the latter is moved until the point touches the surface of the mer-
cury. The zeros of the small auxiliary scales of the two gauges are
set on the same level.
It is easily seen that the displacement of the main scale, or,
rather, the difference of the displacements of the main scales from
the same level, is a correction in pressure of water to be applied to
the difference of the readings of the mercury colunms. The read-
ings (»f the mercury columns were made ui)on steel scales, gradua-
ted to .01 inches, and tixed with their zeros on the same level as
the surface of the mercury in tlie glass tube, when the pointer
touciies tlie surface of the mercui-y in the reservoir before the water
is admitted. In this way there is no error due to difference, in capil-
larity due to small differences of diameter In the glass tubes of the
two gauges. I<:acli gauge is read l)y means of a Marten's telescope,
^^'hi(•h is fixed up at alwut 6 feet from the gauge and adjusted to
tlie level of tlie meniscus. With a good light and steady pressure
the readings can be taken to .001 inch.
For measuring the vacuum at the throat, the pressure chamber
was connected to a long glass tube running up parallel to the tube
of the pressure gauge, to which it was connected at the top, where
it was provided with an air tap. One of the difficulties to be con-
r(<nded with is leakage of air into the vacuum, and several trial
runs were made to detect and remedy this akage before commenc-*
lug accurate work. All pipe joints were covered with tallow and
wrapped with telegrapher's tape, and, it is believed, there is no
error from this source.
GENERAL DESCRIPTION OF THE APPARATUS.
The water was drawn frcm the experimental tank in the hy-
draulic laboratory, and passed by a 1% inch pipe, 12 feet long, to
tho Venturi; tlie outflow pipe Avas feet long and of the same dia-
meter.
The tank was pi'ovided witli means for setting and regulating
the hend, and no difficulty was exiierienced in keeping the head prac-
tically constant.
Instead of the pipe discharging under water, an artlticlal head
was created by screwing a nozzle of % Inch diameter on the end of
;
the outflow I |t.'. The function ul' this was lo ensure limt the pipe
ran full belo the Venluri.
Through his nozzle th*- wiitcr (list'linr^ed into ji birurcutiTl MJioot
supported oi. a wooden frame and pivoted in sueli a manner that
either lej? could be brouKJit in front of the nozzle, the instant Of
change beiiig recorded on a clirouograpli. One leg discharged to
waste and the other to the measuring tank. ,
The tanli, one of a s.'ries of Uve, was benealli the lloor level,
and was J) feet by feet by 3 feet (J Indies, cast irou'cneased in con-
crete, and experiment showed that there was no leakage whatevt-r.
To the tank was connected a 4 in(;h vertical brass pipe forming a
float chamber. The tloat was attaclied to a vertical
Inch l)ras8
rod with a pointer at tiie upper end indicating on a brass scale the
quantity of water in the tank. A fine cord fastened to the top of the
rod rose vertically, passed over a frlctioidess jtulley and carried a;
balance weight, which kep*^ tlie cord taut and prevented I lie pointer
from rubbing against the scalo.
SETTING OF (iAU(;i:8.
The gauges stood on a firm slab of slate, and were accurately
levelled. The zeros of the auxiliary scales were set on the same
level, and referred to the scale on the supply tank, and also to the
axis of the Venturi, by means of a Dumpy level.
THE CHARACTER OK THE MOTION.
In order to study the motion by aid of colour bands, a glass
pipe, Fig. 4, was draAvn out to form a Venturi meter of approxi-
mately one-half the linear size of the meter under experiment.
Fig. 4
with a head of about three feet of watei- upon this meter a
colour band was introduced, and the aiotion studied by its aid.
The water was always found to be stable in tlie up-slream cone
as long as the water coming to it was stable; whereas, after passing
the neck it immediately broke down into eddies as shown. On
Increasing the head the coloured band in the up-stream cone stUi
remained clearly defined until swept out by the water breaking
dow^n in the supply pipe above.
It, therefore, appears that the motion in tlie up-stream cone may
be taken as stable until the limit for the up-stream pipe Is reached,
6
uud tbls lluilt, for a i)li>f of unUonn biisi', has beeu sUowu by 08-
borue Key Holds to bo glvfu by the (oiiuula:—
r, := 0.039 tSIl
where F,. = critical velocity.
/ ( r) = (I + .WMi T + .U0U221 2'-) -'
T rr temperature centigrade,
D — diaiiieu' of the pipe in inches.
lu ussuiulug Ik'riiouilli'a Theorom \v(? are luaUiug the assuiuy-
tiou that the lluid is t'rii-tiouk's.s, or else tluit the luotiou is such
that tile ioss due to tlui(i I'rletlou luay l)e disregardeii. In the ures-
eiit ease tiie loss in I'rietiou is large, being given l>y the values l\ I^^
Table 1. and siiown for different disdiarges in the curve Klg. lU.
This loss will be divideii uneciually between the two coues.
The loss in tiie up-stream cone will l)e niiuli smaller than in the
down-stream, partly because of its short ii'ugth, but principalij be-
cause the How is in general stable, while in tiie down-stream cone
the divergence of the walls causes eddy motion.
NOTATION.
Let Q = total quantity in galionp.
q = discharge in cubic feet per second.
Jii, ^o> A:! = ^^^ readings of the gausses.
(Jj, fjg, (5., = the readings on auxiliary scales.
2 z„ z — hei<'hts of the zeros of the auxiliary scales above the axis of
the Venturi
T = total time of run in seconds
r =: tetnperature of water.
IIo pressure of atmosphere.
7
Pitpt))Pz = prfHHures at the ptensure ciminber.s in feet of watiT.
a I, Uu, 02 = areas of the tliroatH.
•i» "o* ^i -• velociiiefl at tlie lliroatH.
C =r coenicient of Venluri.
g =r 32.170 tor Montreal.
r = (lennity of in<'rcury.
If wt' ciiii iiHsiuiic tliiil Hcniouiin's Tln'omii liolds tiHU> for llie
motion ill I ho Vcuturl liio tiicoiy is I'xtrem.'ly 8liu[th', and ii sluiiile
expri-wsloii can be olttaliu'd for tlu; diHcIiargi,'.
Vakiii),' the axis of tho i)li)«' as levi'l, and in the datum plane, we
bavo:--
Now
P^
PjL
+ 2g
Pi f'o
- ■ - ss:
U) (4)
+ ■
ah^ + f!, +2,
12
' 12
12
//")
+ 12
.*. »(,- •
- "r'
= 2g H
Now V ,
da
a
1
H aav
I
1
"0
«,
Oi - — a" ■' 2.(7 H
q = a„ i\ =
"(I "I ,
J~r- -"= y 2g U
To allow for friction, etc., we may put
a a
C' -.
^T-_:-7 '^2gH
LIMITS OF EKROR.
Total disciiarge, Q.~ln the gauging tank one gallon corresponch^d
to .087 Inch, and the position of tho pointer could be read to 005
Inch, or about .06 of a gallon. Q varied from 04 to 330 gallons so
that the error of reading varied from ,„',, to -,5',,;.
As Q was measured by differences, the greatest probable error
would be twice the above. All tlie readings were taken indepen-
dently by two observers.
t
I
I
1
Time.-Tlw (•liioii..Kni|.li wun oi.t'mt.'d tn.ni n 8taii*lanl clock
In tho liilK)iutor.v, tlH' M..(k hcliiK conipMivd with the .Mh;||! Observ-
atory i|„ok nich >Uiy Thi. ,list!iiKt- on tln« r.'cord (•nrii-8,...ii(llnK to 1
■ecoiul was 0.4 lucht'8. ami r.'aaiMjrs ooKid i... made to .(Kjr. lucbt-a,
BO fhiit tlj»' Kr.-at.'st |H.8slblt' error In a roadinw wiia ,'„ seconds,
or tlw combiiH'd .mtop .,r tbo roadbiKs at start and llnlsh was ,'
■e('(iu<ls.
Th»' total time was always Mbout l.UUO seconds, so tbat tbe error
wonid not exceed 1 in KiOJKMl.
Tile only pobu to be noted in eonn.'etion with tbe chrono^rnph
was the nse of two pens. or. liitluT. one |)en and a kIiiss stylus fol-
l(»wiiiK in Its tnick. the former leaving c on^h ink for the stylus.
Thes.. two pens ree<MNled in opiM)slte directions, so that there could
be no eoiifnslon between tlie seconds' ui.'irk and the mark recording
the instiint of tlnowiufc' over tiie sboot.
MEASUHEME.VT OF DIAMEXEBS OF VENTURI.
This was done on ii dlvidiii>r mjK->dne readlnj? to .0001 Inches;
tlie djjinieter of tiie tiirojit w;is (t.;5T!>S Irches: area^,- .OOOTST sq. ft;
the diameter of the up-stream tliroat wiis 1 .CLiT Inches and the dia-
meter of the down-stream tliroat was 1.020 inches.
Mejin area .014411 acjuare feet.
I
I
MEASLKEMENT (JF I'KESSUKES.
In all except runs 7r> to H."^ inclusive, mercury wrs used in the
pressure and vacuum fiMiiKes. .-nid readings were taken to .001 in.
Tlio accuracy with which pressures are obtained depends not
only on the reading of tln' fe'auj,'e. but on the settings of the zeros
and of the pointers. The ievelling of the gauges could be done to
within .01 inches of wat«>r. or say, .001 inches of mercury. The
error of setting the pointer would not probal»ly Iv." more than .002
inches, so that the combined error of any single reading is not likely
to he more than .005 inches. As the pressure readings were gener-
ally very constant thioughout a run, the probable error of the mean
would not be as large as this, and the error of 7', - jr. is probably
not more than .003 inches, since ten readings were taken for each
run. The vacuum, however, generally varied a good deal, and an
error of .01 inches in the reading of /•^ + ]\ Is very probable. The
greatest value of P, - 1\ is aliout 2.1 inches of mercury, giving an
error of, say. 1 in S.OOO. Tlu> least reading for mercury was about
.72 inch, giving an error of 1 in 240.
The greatest value of 1\ + P„ Avas about 50 inches, giving an error
of, say. 1 in 5,000, nnd tlie least about 1.2 inehe-;. giving 1 In 120.
lu tile iVv,' exiterimeuts iu wUicii water Was used iu the gaugtsi
lusteutl of uiei'cury, llio readiugb were only lakeu to tlie ueurest
,100 oi! an in, ii, and the order of the error Is iibout the fcame na
glveu above.
METHOD OF EXPElUii-L'-NT.
As a general rule three runs were made at each head, iu a few
cases four. The water was always turned on andallowod to how to
waste for half-an-hour or lougt-r before lonuneucin^j: a series of runs,
as it was found that tile vacuum did not reath i steady condition un-
til some tiui^ alter the water was turned on. ^toy watches were em-
ployed as a rougn checli on the chronograph aud for determining
time of readings.
DISCUSSION Ol' Tin: (JI!SERVAT10>'S.
The observations are given, o-i Table I, and the value of C
has been deduced from tlie mean values of each set of experiments,
on the assumption that Bernouilli's !aw liolds for tlie cone.
It will be noticed that c is in general less than unity, and Is
least for the highest values of H gradually increasing with the
diminution of head until a head of about 8 feet is reached, when It
passes through the value unity. With still lower heads the increase
in (• is iiiuch more morlved, rising to a value of l.;]58 for a head of
0.972 f<^ot.
I'tO
ng. 6
l'«9
1 40
I'M
ISO
K* 1 2B
,
Id l'20
Hh,
\
\
5? los
V
100
s
Vj
tB
~~^
K>_.
_--
— -«
=a=s
to
■
1
1
'K
i
,
HEAD IN FEET
10
I
The relation of c to H is plotted In Fig. (5, and the wide vari-
ation in tlie valne of c is clearly aijparent.
It is noticeable that Herschel* found much lower values of c,
but none of bis experiments give such a high value as l.iiGS.
For moderate heads the experiments bear out the usual assuitip-
tion, for this form of meter, that the constant does not dlfftr much
from unity.
P'or low heads, however, this does not hold, ariW a cdinpMratlvoJy
large error is introduced by assuming a coefficient of unity.
The variation in the value of c appears to have an Intimate con-
nection with the question of the stability of flow in the up-stream
cone, and on plotting the discharges as ordl nates witli the heads aa
abscissae, Fig. 7,
Fig. 7
OA
^
■^
-»-
^
^
Ojg
,^
^
I
To
^
>
z
03
j(^
X^'
o
UI
it
y
y^
y
y
t
K
UI
Q.
. 02.
1
i«_.
y
/
.^
^
/
r
^
^
0flr-
Ui
UI
IL
■018
lA
/
1 1
^-
:^
i
A
1
.^
K
o
5
/
_iiL--^
i^''
7
/
,^
^
^
3_
,,^
^
1
00>
A
...
,^
1
f
3i
:
4
6
Q
t
'
a
1
A
1
f
1'
1 Lo
1 H
I:: ,
1
)
1
>
2
3
H
2
EA
5
D 1
N
FE
ET
4^
D
4
t
5
«
3
5
S _
It was seen that the upper part of the curve was of a noinewhiait
different character to the lower part. This becomes more evident
when logarithmic oo-ordinatos are used, for If the law concerning
Q and H be taken to bo represented by the equation
log q — log A- -f n log F
and the slope of the line gives the value of n.
* loc cit.
il
Ihis has been done iu Fig. 7, in which the line A B has a slopt
whoB^ tangent is approximately 0.341, while B O has an inclin-
a.^n whose tangent is 0.478. It. therefore, appears that In this
me tr for low velocities the discharge is proportional to a root of H
higher than the square and less than the cube, while for higher
velocities it varie.s nearly as the square root of the head
This rt^sult affords a clue to the rise in the value of c for low
heads, for since its value has been deduced from the formula
q = k H^
k being some constant, while the law for the lower part of the scale
is represented by
Where
n > 2 < 'A
it is clear that the value of c, being a factor of k, will necessarily
Increase. ^
It is instructive to compare these results with those obtained
by Herschel on a meter for a pipe of one foot diameter and on one
for a nine foot pipe.
These results are tabulateil in his paper, and from his Table I
the values of q and H have been plotted logarithmically.
For various reasons, which are fully stated in the paper, a num-
ber Of the results were of doubtful accuracy, and, in consequence,
are not considered here.
The most reliable results appear to be those numbered 37 to 60,
and these were plotted logarltlimically, and are shown on Fig. 8.
i-ogq
Fig. 8
r—
^
yA
r
^
r^'
\ —
^
^
4^
—^
^
X"
^
y^
/
X
-^
^
^.
y^
In this case, the value of n for the higher velocities came out
as .49, while the low velocities of experiments 58, 59 and 60 gave a
value of n — 0.6.
1-2
The reason foe this discrepancy is not cledr, but It may be poin-
ted out that this first series of expenmeuts was conducted under
great disadvantages, in spite of the care taken to ensure accurate
results.
The second set of experiments was made upon a meter for a pipe
» feet in diameter, all the linear dimensions being approximately 9
times greater than those of the first meter.
The observations were massed into groups, which an inspection
of Table II. shows to be justifiable, and the mean results plotted in
Fig. 9. .
to
•
Fig
9
^
\
»0
->^
^^
^
.^
^
^
^^
^
^f^
-^
l^
10
::d
.__„^
AH the points were found to lie on a straight line, uaving an
inclination tan-' \ almost exactly, and, tlierefore, verifying the theo
retical law in the ease of large meters.
These results point to the conclusion that in large Venturi
meters the discharge is very approximately proportional to the
square root of the head throughout the whole range, while in small
meters the discharge does not apparently follow this law for low
heads, but does so approximately for high heads.
It appears, therefore, that a small meter would require special
oalebration for use when di^icharging small quantities of water,
since it does not follow the square i-oot law, and this renders the
meter unsuitable for use in the measurement of, say, a domestic
supply, where it is important that small quantities should be accur-
ately measured, as well as lasses due to leakage in pipes, defective
taps and the like. Moreover, there is a considerable loss of head in
such small meters, as can be seen from the Table, Fig. 10, and this
is a further disadvantage.
On the other hand, its gi-eat advantage for the measurement of
large quantities of water is manifest, in fact, it is the only practic-
able method of measuring the water passine through a nmin. and it
has been shown repeatedly that the loss of head in this case Is
small.
Fig. 10
CUBIC FEET PER SECOND
No.
of
Expt.
IIKAnS IN FKET OF WATER.
Total
time
seconds.
Total
quantity
gallons.
Cubic
feet
per sec.
Coeffct.
C
Up
stream
gauge.
Po
Centre
vacuum
gauge.
P.
Down
stream
gauge.
18
19
20
10.120
16.122
16.128
14.142
14.138
14.141
32.898
32.886
32.910
4.918
4.918
4.924
1,205.3
1,205.0
1,205.3
313.95
314.02
314.76
.0418 i
.0418 >
.0419 S
.9494
21
22
23
33.098
33.047
33.040
4.838
4.841
4.839
1,205.6
1,204.7
' ■ 15.3
310.46
311.09
311.30
306.44
307.36
.307.60
.0413
.0414
.0415
.9578
.9567
.9564
2;5b
24
25
13.174
13.101
13.100
33.002
.32.992
32.987
4.70G
4.708
4.714
1,205.0
1,205.0
1,205.5
.0408
.0409
.0409
25a
20
27
12.175
12.170
12.174
11.224
11.224
11.224
32.540
32.487
32.490
4.568
4.563
4.565
1,205.2
1,205.4
l,-'05.3
:-^01.84
302.47
303.85
.0402
.0101
.0403
2cS
29
30
.30.776
30.781
30.785
4.272
4 375
4.281
1,205.2
1,205.4
1,205.7
292.44
293.36
292.90
.0389
.0391
.0390
.9566
.9569
31
32
33
10.314
I0.30li
10.. 302
28.266
28.239
28.228
3.s^96
3.921
3.920
1,205.7
1,205 2
1,206.0
280.12
281.49
281.28
.0373
.0375
.0374
L4
No.
of
Expt.
Head in feet of vater.
34
36
36
H7
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
50
58
59
00
61
02
03
04
65
06
07
08
71
72
73
Up
stream
guajie.
9.362
9.300
9.300
8 440
8.424
8.420
>M.417
Centre
vacuum
image.
25.813
25.791
■^5.707
P,
Down
stream
guage.
3 586
3. .58 7
3.587
Total
time
seconds,
1,205.0
1,204.9
1,205.2
23.519
23.090
23.527
23.438
7.516 J 20.525
7.509 1 20..')27
7.514 ' 20..544
0.549
0,660
6.571
5.03?
5.037
5.030
5.0;'-6
4.709
4.709
4.709
3.792
3.792
3.791
2.873
2.870
2.808
1.9i3
1.943
1.944
1.003
1.001
0.998
20 956
20.959
20.9000
11.471
1 474
1.479
17.726
17.026
17.029
15.154
15 165
15,146
15 138
I 12.325
j 12 223
12.138
8.955
8.916
8.879
5.879
5.853
5.843
3.382
3.324
3.288
1.012
.727
.759
33.183
33.197
33.079
2 524
2.494
2 438
3.220
3.267
3.263
3.258
2.821
2.820
2.825
2.4(;2
2.459
2 456
2.093
2.093
2.0itl
2 091
1.709
1.707
1.701
1.257
1 257
1.2.54
0.845
0.843
0.844
.506
.501
.498
.116
.127
.131
5.670
5.681
5.684
0,375
0.380
0.370
Total C»t)ic
quantity feet
gallons. ; per sec.
1,206.0
1,206.3
1,206.3
1,206.3
1,205.2
1,0.35.0
1,206.5
1,205.9
1,200.1
1,206.12
1,200.5
1,206.6
1,206.3
1,205.7
1,207.4
1,207.1
1 ,205 4
1.206.0
1,205.8
k,205.9
1,200.4
1,205.9
1,205.5
1,204 9
1,205.3
1.205.2
1,105.2
1,205.4
1 205.9
I
1,205.8
1,200 1
1,200.0
262.00
269.7'i
269.79
255.27
257.83
257,93
257.93
239.83
215,98
240.40
.0358
.0359
.0369
.0340
.0343
.0343
.0.343
.0319
.0319
.0319
227 40
225.46
225.72
.03fl3
.0300
.0300
209.89
208.85
209.66
209 54
.0278
.0278
.0279
0279
191.72
191.09
189.44
.0255
.0254
.0252
105.63
105.52
165.29
1,206.2
1 ,200 1
1.206.9
138.85
13S.59
138.62
111.70
111.32
110.97
74.46
74.23
74.00
335.00
335.90
336.15
.0220
.0220
.0220
.0185
.0184
.0185
99.89
99.89
99.32
.0149
.0148
.0149
.0099
.0099
.0098
.0447
.0447
.0447
.0133
,0133
.0132
Coeflf
C.
0.9619
0.9644
0.9587
0.9719
0.9704
0.9572
0.9800
0.9929
1.0296
1.1757
0.9537
1.0596
16
//
HKAI> IN KEKT OF
HATER.
Py
1\
P.
No.
Up
Centre
Down
Total
Total
Cubic
Coefft.
of
stream
vacuum
stream
time
qimntitv
feet
Expt.
Kauge.
gauge.
gauge.
secoudfj.
gallonss.
per sec.
C.
75
.941
.880
.552
1,206,9
75 12
.0010
7G
.945
.782
.579
1,205 2
74.93
.0010
77
.944
.677
.570
1 ,208.2
72.63
.0096
1.2021
78
.944
.642
569
1,206.2
72.08
.0096
79
.944
,034
.567
1,207.1
72.30
.0096
80
.775
.207
.459
1,207.2
63.39
.0084
81
.774
.195
.457
1,207.2
63.3.3
.0084
1.3583
82
.773 •
.195
.455
1,206.0
63.28
.0084
83
1.485
2.314
.538
1,205.85
96.26
.0128
84
1.571
2.228
.626
1,205.80
96.72
.0129
1.0491
85
1.570
2.204
.664
1,206.55
96.72
.0129
In conclusion, the authors desire to express their thanks to Pro-
fessor Bovey for the facilities afforded l)y liim for carrying out the
work in the Macdonald Engineering Building. McGill University,
16