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IKST.
SEP 141914
4I8R A
AN
IN V
WA0
T H R-0 U G
S T I G A T ION
91Q
A
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N T U RI
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Thesis of
Signature redacted
Submitted to M. I. DEPT., M.I.T.
1 9 1 4.
.1
HE
T
R
Acknowledgement.
This is to thank Professor C. W. Berry for
his general interest in my work, and for his kind
suggestions and assistance given to me from time
to time in completing the thesis.
I
Introduction.
Long since the investigation of the Venturi Meter
by Herschel in 1887, it
was experimented upon by the
inventor himself on large size meters fitted- to 12 and
as large as 108 inch pipes.
accurate.
The results were fairly
However, experiments made by Professor Cokes
on a small meter showed very variable results.
So in
hydraulic work, the meter is more advantageously used to
measure large quantities of water flowing in pipes.
While in gas and air measurements, though there is
not much data fream which to draw any conclusions, it
seems so far that in measuring large quantities of gas
and air the Venturi meter gives fairly accurate results.
Experiments made by E. P. Coleman in 1906, and by K.
Bush and I. U. Guilford in 1908, all
C.
showed that the
Venturi meter is valuable for measuring large quantities
of air.
At present the meter is manufactured by the Builders'
Iron Foundry in Providence, R.I. in large sizes.
These
are used as air and gas meters.
But for small quantities of fluids (air or steam) flowirig in pipes, the use of a Venturi meter has not yet been
experimented on; although in injector works and in Carburettor works for gas engines the principle of the Venturi
99 3.4
2
meter has been already employed.
So this investigation
is made to test the accuracy of the Venturi meter in
measuring small quanities of air flcwing in pipes.
To make the investigation a successful one, the following conditions were imposed at first:
1) That the drop in pressure shall not exceed one
pound.
2) That the moisture in air shall be considered.
3) That the results shall agree closely with Fliegner's
equations.
3.
EIEENOES.
The only published reference that has direct bearing
on the subject is an article entitled 'The Flow of Fluids
in a Venturi Tube*.
It
was written by Mr. E. P. Coleman
and published in the A.8.M.E. Transactions, Nov., 1906,
page 391, and Mar., 1907, page 1207.
I was given the privilege also to use the thesis work
of K. 0. Bush and I. IL
Guilford in 1908.
By kindness of
Prof. C. W. Berry I was allowed to use a special paper
which he has written on the thermodynamics of the Venturi
Meter.
In designing the meter the following were consulted:
1) 'The Venturi Air and Gas Meter', published by the Builders' Iron Foundry in Providence, Rhode Island; 2) Pitot
Tubes for Gas Measurements' written by V. C. Rowse in
A.S.M.E. Journal, Sept.1913.
Other books which have some
general relation to the matter are: 'Thennodynamics of the
Steam Engine' by Prof. 0. H. Peabody, 'Engineering Thermodynamics" by Prof.O. E. Lucke; 'Flow of Steam Through
Nozzles" by Rateau.
4
Object of Investigation.
The main object of the investigation was to test
the accuracy of the Venturi meter in measuring smell
quantities of air flowing in pipes.
It
is claimed by
the G and A Carburettor makers that a Venturi meter
having angles of convergence and divergence of 300 and
70 respectively will give the maximum flow.
While
Wimperis in his vInternal Combustion Engines* asserted
that a Venturi meter of 130 convergence and Sodivergence
will have the maximum flow.
It was my first intention
to make a series of tests with different angles of convergence and divergence, keeping the throat areathe same.
For if
the best angles would be more favorable that those
above quoted, or a few degrees deviation from them would
not make much difference in the maximum flow, the commercial difficulties in making these long slender tapering
nozzles would be much diminished.
However, it
is too long
and expensive a task to be performed at the present.
I hope that my experiments may be the first
of the
series; other students may finish the task later on.
6
Desian of the Meter.
A considerable time has been used in the design of
the meter in attaining arrangements for accurate measurements and in obtaining simplicity for machine work.
Though the meter is to be used for measuring small quantities of air, it was found that a throat area of less
than one square inch has no commercial value.
By recommendation of Mr. Hopwell experienced in the
use of the Venturi meter in carburetors of gasoline
engines, the angle of convergence and divergence was
made thirty degrees and seven degrees respectively. By
referring to Mr. W. 0. Rowsels experiments on pitot tubes
for gas measurementsthe holes in the piezometer rings
were drilled with 450 inclination.
A set of radial holes
were also drilled at the throat section to check the reading.
A set of tracings of the design are inserted at the
back of the thesis, the computations though simple are
given as follows:
Diameter of the 8 inch pipe with which the meter
will be used is 3.08655.
Diameter of I sq.inch circle = 1.12849
Use angle of convergence = 300.
8
..
the length of the converging portion
(3.0665 -
S---------
1.1284)
.98861
------
tan 150
=3.814
.28795
The length of the cylindrical portion is made as
short as possible.
so tbAt it
It
is made half an inch in this case
can accomodate the two sets of piezometer holes.
Use angle of divergence = TO
. The length of the diverging portion
} (3.0655
=--------------
- 1.1284)
tan Sij
.98851
= ------ = 15.836Y
.06116
7
TMEUJIYNAMIOS OF THE
VENTURI 32TER FOR AIR )MAUREMENT.
In establishing the theoretical equations for the
operation of the meter, great assistance has been given
by Prof. 0. W. Berry.
The following equations are based
almost entirely on a special paper written by him some
time ago.
The action of air in expanding through the throat is
assuled to be adiabatic, as the flow of fluids through
orifices and nozzles.
The air is flowing from the lar-
ger pipe into the throat, and there will be a drop in
pressure and increase in velocity.
As the velocities
are different in the two sections there will be a change
in kinetic energy.
So, the equation expressing the first
law of thermodynamics, with an additional term taking care
of the change in kinetic energy, suffices to express the
change of air in the meter.
The oquation in its general
way may be written dQ = A (d E + dW + dK), where dK is the
change in kinetic energy.
Por further development of the equation the following
notations are employed:
8.
V = velocity in feet per sec.
v = volume in cubic feet
a = area in square I5e4
^
P = pressure in pounds per sq.inch.
E = internal energy in foot pound.,units.
T
-
temperature absolute in OF.
subscript 1 concerns section I.
subscript 2 concerns section 2.
T = weight of air passing through per sec.
Since there is no heat added to or radiated from the
air the sum of the external work, intrinsic energy, and
kinetic energy must be the same at section 1 as at section 2, so that
= P 2 v2 + E2
+
PIv1 + E, + -P4
2 g
also for adiabatic expansion, p:vIj
and
U
ajiv.
P2
'
2
---
-m----
.......
............
..
...
Combining (1) & (2)
2
2
V1 .- 2g
The intrinsic energy of a unit weight of air is
P V
=
+ constant,
---
(2)
ap, VR'
K-i
2g K
so the above reduces to
....
(3)
s.
Using the relation PV - RT
2g RK
2
2
V
V2
K-i
Pp V 1
Pa
- -Pi
(
29 KR
a2
2
a2
a1
a1
(4)
kJ
vi
I---
V2
-
" =
P2
a2
I
PJL
2
P2
2
K- I
P1
Combining (2) & (3), V:
V,2 =
2
P2
F
K-i
I
(2)
-
2g R
- ----K-1
P 2 vY 2
k
PI
0'' ''.'
''..... ''* * e
(5)
Combining (4) & (5)
2.
P 2 --k
)p)(---)P
a
V2.2
PI
a1
L
-
P2
K-i
P1
K-)Z
P1
Ik RTj (1
2g XR
(--)
P1
e 0 0 0 (a)
...........-
a
a2
P1
Oombining (2) (a)
and (8)
V1
2
T 1 k-
X-1
iR
-
L
2
P,
a 2 (2)2
1
I
7 2.-
-(
a1
P2
-- )
(---)
Pj
2
k
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lvi
P1
T1
10.
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P1
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I2
- a-k
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4
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(K-1)R
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P
-3 10L
EFIMOT OF MOISTURE IN THE AIR.
If there is any moisture in the air, the ratio of the
specific heats of air will not hold good.
The proper value
to be used should be the ratio of the specific heats Of the
mixture of water vapor and air
.
Since air always contains
some moisture, it was decided in the following experiments
to determine a new Nn' to fit the particular case.
It is accurate enough to take Yny of the mixture as
equal to
p
T vO,
,
which is equal to Wax .2375 + V3 X
Wa X.1890 + To X
0 pe
0
y8
where Va is the weight of air and W. is the weight of water
vapor..
The water vapor being compressed to a high pressure
will remain superheated after expansion in the receiver.
11
The matter now simplifies to the determination of
the specific heats of superheated steam and the weight
of water vapor and dry air in a cubic foot of mixture.
As there is no way to determine the specific heats of
superheated steam readily without going into a hard task,
these constants were extrapolated from Mollier's total
heat pressure diagram.
The weight of a cubic foot of
moist air was obtained from a chart in Professor Miller's
"Notes on Heating and Ventilation3 .
A numerical example
for finding Yn* is given on Page
TJS 7ESTIN
APPAATUSAN Mi HR
AMRANGE
NTS.
The apparatus at my command was a Norwalk three-stage
Air Compressor driven by Tandem Qompound Engine, ten storage tubes, and a big steel receiver.
A throttling valve
letting air into the receiver keeps the pressure constant
in the latter.
Three-inch discharge pipe leading out from
the receiver turns around the storage tubes; the Venturi
meter comes next to the pipe and a standard orifice cut in
a bolting flange comes at the end of the pipe line.
Diam-
eter of orifice = .6005m.
The measuring device consisted mainly of getting the
drop in pressure in the throat by a differential gage.
Water was used for it gives more accurate readings in small
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drop of pressure.
1/4N pipe was used to communicate
pressure to the differential gage or U-tube.
Valves were
used for p2 and p3 so that only one could be connected at
a time with pl.
S
Three gages were calibrated to get the pressure P1 and
P 4 and pressure in the receiver.
used to indicate t1 and t4 .
Two thermometers were
A sling psychometer was used
to serve the purpose of a wet and dry bulb thermometer.
EITHOD OF MAKING A TEST.
It is only after a day's hard work that things went
apparently right at low pressures.
In making the test,
two fellow students kindly helped me as it needed three
to run the test.
One man had to stay at the throttling
valve to keep the pressure constant in the receiver. One
of the remaining two took care of the readings of the
,
differential gage, and the last one took readings of P1
P4 , tj and t4 .
The tests lasted about five minutes and
as many readings as time allowed were taken in each test.
dED
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