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Патент USA US3071011

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Jan. 1, 1963
Filed Feb. 16, 1960
Herbert Goldsmith
i fan/W
Fatented Jan. 1, 1983
Herbert Goldsmith, Washington, D.C., assignor to Na
tional Instrument Laboratories, inc, Washington, D.C.,
a corporation of Maryland
Filed Feb. 16, 1960, Ser. No. 9,114
'7 Claims. {£1 73--211)
This invention relates to measuring ‘the rate of ?ow
(or viscosity) of a ?uid, whether gaseous or liquid, and
more particularly to an improved linear flow meter.
Brie?y, a linear ?ow meter comprises: an elongated
housing through which ?uid flows. Inside the housing
Essentially the instant invention improves a linear
?ow meter by positioning on each side of the flow re
strictor a specially constructed pressure tap; the pres
sure taps kinematically correct for the channel entrance
and exit nonlinearities of the flow restrictor.
An advantage of the preferred mode of the instant in
vention lies in its provision of a simple technique for
assembling the meter in a manner which most accurately
corrects for ?ow non-linearities.
The actual practice of the instant invention can best
be described With reference to the attached drawing,
is a viscous resistance element, that is to say a flow re
FIGURE 1 diagrammatically illustrates a ?ow meter
strictor or ?ow pack comprising one or more elongated
constructed according to the teachings of the instant in
narrow passageways which serve as ?ow channels. Each 15 vention.
passageway is so proportioned that under normal work
ing conditions the resistance to ?ow through the restrictor
FIGURE 2 is a sectional view along the line 2—2 of
FIG. 1.
as a whole is substantially proportional to the rate of
FIGURE 3 is a sectional view along the line 3—3
flow. A manometer or other device for measuring pres
of FIG. 1.
sure difference is connected to the housing across the two 20
FIGURE 4 is a graphic representation of the pressure
sides of the ?ow restrictor so as to measure the pressure
distribution formed by flow of an ideal ?uid about a
difference caused by flow therethrough.
The advantages of the linear type flow meter over
‘those which operate on the Bernoulli principle, i.e., ?xed
FIG. 5 diagrammatically illustrates an alternate con
struction for the ?ow meter.
Referring more particularly to FIGURE 1 of the draw
ing where ?ow meter 10 is illustrated, the numeral 12
ori?ces, nozzles, venturi tubes, variable ori?ces, etc., are
well known to those skilled in the art. However, the
linear type ?ow meters are still characterized by certain
generally designates a tubular housing having reduced
disadvantages, including inaccuracies, which will be spe
ci?cally referred to as the accompanying description pro
ends 13 and 14 which are, in turn, connected with the
inlet and outlet connections 16 and 17, respectively, for
the ?uid whose ?ow (or viscosity) is to be measured.
Thus, despite the linear or laminar ?ow through a well
The ?ow restrictor 15 packing the main body portion
of housing 12 is annularly disposed around an elongated
designed ?ow restrictor, it'has been established experi
mentally and theoretically that a non-linear pressure
closed arbor 18 which constitutes the core element. The
leading and trailing pressure taps of the ?ow meter are
indicated at 20 and 22, respectively. Taps 20, 22 lead
drop occurs across the entrance as well as across the exit
of the individual flow channels of the ?ow restrictor.
In magnitude, this nonlinear pressure drop is proportional
to the product of the ?uid density and the square of
_the volume ?ow, and is much greater at the entrance
than at the exit. It has been found that downstream
of the flow channel entrance a distance equal to about 4-0
twenty times the depth of the channel, ?ow approaches
a laminar distribution and remains laminar until a short
to an indicating instrument which may take any one of
a number of well-known forms, but which as such, form
no part of the present invention, and accordingly is
neither shown herein nor speci?cally referred to here
While the details of the ?ow restrictor or flow pack
15 do not form a part of the instant invention, a par
distance from the channel exit, at which point the exit
nonlinearity appears. It has also been found that if the
pressure measuring taps are both disposed within the
truly laminar ?ow region of the ?ow restrictor or pack,
the pressure drop across these taps is proportional to the
ticularly advantageous shape is the spiral wound rectan
gular channel construction disclosed and claimed in co
pending application S.N. 824,423 of Joseph Weichbrod,
?led July 1, 1959.
Inside the linear ?ow element illustrated in FIGURE
mean volume flow rate between these taps to a very high
1, the pressure difference Ap between two cross sections,
degree of linearity. Unfortunately such a construction
e.g., between (the exteriors of) taps 20, 22, is related to
is difficult and expensive.
50 the mean volumetric flow Qm by the equation:
Commonly the pressure taps are both placed outside
the ?ow restrictor, but the ?ow restrictor must then be
made relatively long in order to have the linear pressure
where a, b are constants, hm, pm are, respectively, the
drop at the laminar ?ow central portion swamp out the
mean viscosity and the mean density (the term mean is
effect of nonlinearities at the ends thereof. This is usual 55 here de?ned as the arithmetic mean of the ?uid proper
ly not practical for commercial devices in which the
ties at the two sections for well designed flow meters
shortest and most compact device and a least possible
having small pressure drops; little change in tempera
pressure drop is desired.
ture or density occurs between these sections).
Thus as a practical matter the prior art linear flow
The ?rst expression on the right of Equation 1 is the
meters, even those with highly improved ?ow restrictors, 60 linear term, and arises from the viscous flow in the flow
are faced with the existence of errors due to non-linearity
restrictor 15. The second term is non-linear, and arises
of ?ow. Strictly speaking the instant invention relates
from the effect of abrupt changes in cross-sectional area
to an arrangement which eliminates or at least minimizes
together with conversion of velocity pro?les from non
such errors.
The principal object of the present invention is to pro
vide a practical linear ?ow meter of an accuracy hitherto
equilibriurn to equilibrium distributions. (Experimental
65 ly it has been found that the second term is a function of,
Another object is to provide a novel technique for
assembling and calibrating an acurate linear ?ow meter.
Further objects and the advantages of the instant in
vention will be apparent from the description which fol 70
and increases with the Reynolds number.)
If it were
possible to apply a non-linear correction to the observed
pressure differences (Ap) of Equation 1, only the ?rst
term would remain, and the resulting ?ow meter would
be truly linear.
Such a correction is used in the practice of this inven
tion. The correction utilizes the pressure distribution at
the outside surface of a cylinder immersed in a uniform
?uid ?owing uniformly at right angles to the cylinder
axis. Theoretically and experimentally it has been found
that the pressure distribution is a function of po and qo,
ond term is the conventional pressure drop experienced by
the linear ?ow element of FIG. 1, and is expressed by
Equation 1. Combining all of these terms into Equation
7, there is obtained
the pressure and velocity head of the undisturbed stream.
The usual de?nition of this velocity head is given by:
By a suitable choice of K1 and K2 the second expression
on the right may be made to vanish for all values of Qm
where p0, V0 are the density and velocity of the undis
turbed stream and g is the acceleration of gravity. The 10 and there is left only the linear relation
relation between the local pressure p at the outside sur
face of the cylinder and p0 and go is
From Equation 8 it is clear that K2 should be a positive
maximum, a condition which requires that the tap open
where K is a function of both the geometry and the 15 ing be oriented to point directly into the stream. K1, on
the other hand, should be negative, which requires that it
Reynolds number. A simple solution for K has been ob
be oriented at an angle (0) of from 40° to 80° to the
tained for the ideal or non viscous ?uid and this is depicted
in FIG. ‘4. For this case, K turns out to be independent
direction of ?ow.
It is noteworthy that the pressure distribution about
the outside surface of the cylinder as described above is
20 rarely encountered in the ?ow of real ?uids. As a result
of viscosity, there is a ?ow separation that develops about
where 0 is depicted in FIG. 4. Note that at the impact
the trailing edge of the cylinder, and produces a pressure
point, where 0:0, as well as where 0=180°, K takes on
distribution markedly dilferent from the idealized case
the value of 1 and the local pressure at the outside surface
of the cylinder is greater than the undisturbed stream 25 illustrated in FIG. 4. However, the leading edge distri
bution is‘ unchanged, while that situated at 90° to the
pressure by an amount go. At angles of 30°, 150°, 210°,
direction of ?ow is modi?ed somewhat. (The distribu
330°, the factor K becomes zero, and accordingly the
tion in a real ?uid depends upon Reynolds number in
local pressure is equal to the undisturbed stream pressure.
the manner shown in FIGS. 152, 153 and 159 of “Modern
At angles of 90° and 270°, K takes on the value —3,
Developments in Fluid Dynamics”—vol. II by Gold
and the local pressure is less than the free stream pressure
stein-—-Clarendon Press 1952.) Up to 45° the pressure
by an amount 3q0.
distribution is independent of Reynolds number, but
If a hollow cylinder is provided with a very small hole
beyond this angle the pressure maximum varies from
that communicates with the exterior space surrounding
-—qo to —-3.5 :10 at locations from 70° to 82° over a range
the cylinder, the pressure within the cylinder may be made
of Reynolds number from 2800 to 40,000. Generally,
to differ from the external free stream pressure by an
the greater the Reynolds number, the greater the value
amount that may be varied from qo to —~3q0, for a total
of the negative maximum.
range of 4%, by simply rotating the cylinder about its
EIn actual linear ?ow meters, the usual value of q is
own axis. This basically is the compensation scheme
about 0.4 in. of water pressure. Therefore, with the
that is used to add or subtract a non-linear pressure incre
ment to the linear pressure drop produced by ?uid ?ow 4.0 optimum con?guration of taps 20, 22 (K1=1, K2=~3)
the maximum correction that can be obtained is 4q or
through ?ow restrictor 15.
1.6 in. of water. For a ?owmeter having a 10 in. of
Thus the pressure taps 20, 22 are small hollow cylinders
overall pressure drop, virtually complete compensa
which‘ extend cross-wise of ?uid ?ow (as shown in
tion can be obtained for non-linearities up to 16%, i.e._.
FIGURE 1) through the axis of the flow path (see FIG.
8.4 in. of linear drop and 1.6 in. of non-linear drop, and
2). Desirably, they are mounted adjacent the ends of an
partial compensation for non-linearities in excess of this
extended ?ow restrictor core 18. Each of the cylindrical
taps 20, 22 are provided with two holes 24, 26 which
Certain inherent characteristics of linear ?ow meters
communicate with the interior and are located at the mid
make practice of the instant invention highly advan
radius of the annular ?ow area 19 between core element
tageous. Thus, for example, the ability to correct for
18 and housing 12. One end of each cylindrical tap 20,
22 is capped while the other end communicates with the 50 the non-linearity of a vgiven meter permits a greater de
gree of latitude in placement of pressure taps 20, 22.
pressure measuring device. The tap cylinders are, of
Thus in linear flow meters constructed according to the
course, provided with seals at their points of entry through
practice of the aforementioned Weichbrod application,
the housing Wall of the ?ow meter.
greatest accuracy is attained when the pressure taps are
In practice, the flow meter is proportioned so that the
both disposed within the truly laminar ?ow region which
annular area 19 at taps 20, 22 is equal and the density at
exists only inside the ?ow restrictor and only at a con
the taps 20, 22 is very nearly equal to the mean density
siderable ‘distance from both the inlet and outlet thereof.
pm. Since the area obstruction caused by the tap cylinders
Placement of the taps outside the ?ow restrictor would
is small, the free stream velocity V0 at the taps is given
of Reynolds number and is given by
K=(1—4 sin2 0)
make the same instrument less accurate by reason of non
60 linearity at the entrance and exit. Since the non-linear
where Qm is the mean flow described previously.
expression for qo is then
pressure drop follows Equation 1, employment of cy
lindrical pressure taps 20, 22 permits their placement
outside the ?ow restrictor because their compensation can
be made to substantially balance out the non-linearity.
In addition to the predictable phenomena of linearity
If we use the subscript t to describe conditions within the
tap, and the subscript 1 and 2 for the upstream and down
stream tap, respectively, the pressure difference App“
that is measured by the pressure measuring device con
nected to the taps may be Written as
The ?rst and last terms on the right are the pressure incre
and non-linearity which can be allowed for by proper
construction of the flow meters, there always exists cer
tain unpredictable errors which are, in e?ect, a charac
teristic of each individual ?ow meter. One example of
each is the roughness of channel walls (in the ?ow re-_
strictor). Every little obstruction in the ?ow stream
causes formation of a vortex wave, which will either
propagate downstream or be ‘damped out (depending on
ments developed by the upstream and downstream taps,
respectively, and are expressed by Equation 3. The sec 75 the local value of the Reynolds number). In vany event
there will be a local velocity change which can only in
crease the magnitude of the non-linear term of Equation
1, and whose eifect will be felt all the way down the
sulting pressure drop through the ?ow meter is 10 inches
of water at a full ?ow of 300 liters per minute of air.
While I have shown and described certain speci?c em
bodiments of the present invention, it will be readily
channel. Both predictable and unpredictable deviations
from linearity can be compensated for by constructing
the preferred mode of ?ow meter illustrated in the draw
understood by those skilled in the art that I do not wish
to be limited exactly thereto, since various modi?ca
tions may be made without departing from the scope of
ing, and by assembling same according to the following
the invention as de?ned in the appended claims.
What is claimed is:
form of ?ow meter where an elongated core 18 extends 10
1. A linear ?ow meter comprising an elongated hous
axially upstream and downstream from any conventional
ing having a ?uid inlet and a ?uid outlet at the ends
FIGURE 1 diagrammatically illustrates the preferred
?ow restrictor; preferably, the annular or spiral wrapped
?ow restrictors disclosed in the aforementioned Weichbrod
thereof, an elongated ?ow restrictor positioned inside
said housing, and a pair of spaced apart pressure taps
positioned on said housing intermediate the ends there
application ‘are employed. Cylindrical taps 20, 22 pierc
ing the core member as shown, are each made turnable 15 of, said taps being adapted for connection to an indicat
or rotatable about its own axis of symmetry. A set screw
ing instrument between said taps, said taps being dis
or other suitable locking element 30‘ is built into each
end of arbor 18 to releasably hold each cylinder with its
posed entirely outside the ?ow restrictor one on each
side thereof, each tap being in the form of a hollow cyl
inder extending cross-wise or" the ?uid ?ow path through
tap opening 24, 26 ‘at predetermined angles to the direc
tion of ?ow.
said housing, each cylinder having therein at least one
small hole providing communication between the hol
low cylinder and the ?uid ?ow path.
With the angle 6 preset at or near a the
oretical optimum, e.g., 01=30°; 02:0“, the assembled
?ow meter is then calibrated against an accurate meter
2. The linear flow meter of claim 1 wherein the ?ow re
over its entire intended ?ow range. An angular adjust
ment in either or both tap cylinders is thereafter made
to compensate for what has been discovered to be the
instrument error, and the tap cylinders locked in this
stricting pack is annularly disposed around an arbor
which extends beyond the pack on both the upstream
and the downstream end thereof, the cylindrical taps
being mounted adjacent the ends of said arbor.
angular position. Invariably the tap openings of 20, 22
3. The linear flow meter of claim 2 wherein each cy
are at least 30° apart, mostly being 40°~80° apart, with
lindrical tap is provided with a small hole at the upper
the correction being almost always entirely in 01. Once
the taps are permanently locked in optimum position, the 30 and at the lower mid radius of the resultingly annular
?uid ?ow area between the arbor and the housing.
instrument is ready for use.
4. The linear ?ow meter of claim 2 wherein each cy
In order to allow as great a qo velocity head com
lindrical tap is mounted directly adjacent the ?ow restric
tor, thereby serving as structural elements which maintain
(thereby insuring a relatively high velocity at the taps). 35 the ?ow restrictor in ?xed position.
pensation as is reasonably possible, the annular ?ow
area 19 at the taps should be made relatively small
5. The linear ?ow meter of claim 1 wherein the hole
To this eifect, a relatively large sized bulbous core can
in the upstream cylindrical tap is angularly offset from the
be employed in the ?ow restrictor. Also the taps should
hole in the downstream cylindrical tap, and wherein the
be placed in regions where housing 12 is most restricted
downstream tap hole looks directly into the ?uid ?ow.
in size, as for example, where the housing has been
necked down at 13, 14 to allow insertion of the meter 40 I 6. A linear ?ow meter comprising an elongated hous—
mg having a ?uid entranceway and a ?uid exit passage
into a conduit. This latter expedient is illustrated in
FIG. 1. FIGURE 2 illustrates the extent to which the
at the ends thereof, an elongated ?ow restrictor inside
resulting annular flow area 19 can be constricted with
said housing, and a pair of spaced apart pressure taps po
in the normal sizes .and proportions for linear ?ow
sitloned on said housing intermediate the ends thereof
45 adapted for connection to an indicating instrument, said
Another advantageous mode of the instant invention
taps being positioned entirely outside the ?ow restrictor
is particularly adapted for use on meters where the
housing 12 need not be necked down for insertion of
the meter into the ?uid ?ow line. With such a hous
one on each side thereof, and at least one tap being in
the form of a hollow cylinder extending cross-wise of the
?uid ?ow path through said housing and having at least
ing, as shown in FIGURE 5, the cylindrical taps 20, 22 50 one small hole therein for providing communication be
tween the hollow cylinder and the ?uid ?ow path.
are placed on arbor 18 directly adjacent the ?ow re
strictor 15 and are then relied upon as structural ele
7. The linear flow meter of claim 6 wherein the ?ow
ments which maintain the flow restrictor 15 in the de
restricting pack is ‘annularly disposed around a bulbous
sired ?xed position.
arbor which extends into the ?ow path beyond the pack
In a typical 300 liters per minute air flow meter con 55 and on which the said cylindrical tap is mounted, said tap
structed according to the practice of the instant inven
further being positioned at a relatively narrow region of
tion, the housing is 5 inches long and is 1% inches in
the elongated housing, whereby the resultingly annular
diameter with a 1/16" wall. The core is 31/2 inches long
?ow area at the cylindrical tap is restricted.
by 34 inch in diameter and is provided with two No.
References Cited in the ?le of this patent
10 set screws in each end. The ?ow restrictor is 21/2 60
inches long and ?lls the annulus between the 1%" CD.
of the core and the 1%" ID. of the housing. The
two cylindrical taps are 1A," in diameter with 1A6" walls
and are provided with two %4" holes located 1" on
centers, the locations being at the mid radius of the 65
annulus. The tap spacings are 2%” so that each tap
cylinder properly restrains the ?ow restrictor. The re
Greve ______________ __. Sept. 9, 1924
Schmidt ____________ -._ Feb. 19, 1929
Goetzl _____________ __ June 27', 1939
Skoldberg ___________ .._ July 16, 1940
Cornell _____________ __ Aug. 9, 1960
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