3,251,226
`v. J. CUSHING
`May 17, 1966
`APPARATUS FOR MEASURING MASS FLOW AND DENSITY
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`3,251,226
`v. J. CUSHING
`may W, W66
`APPARATUS FOR MEASURING MASS FLOW AND DENSITY
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`3,251,226
`v. J. CUSHING
`May 17, 1966
`APPARATUS FOR MEASURING MASS FLOW AND DENSITY
`Filed March 12, 1963
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`United States Patent 0
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`cc
`
`3,251,226
`Patented May 17, 1966
`
`1
`
`3,251,226
`APPARATUS FOR MEASURING MASS
`FLOW AND DENSITY
`Vincent J. Cushing, 9804 Hillridge Drive,
`Kensington, Md.
`Filed Mar. 12, 1963, Ser. No. 264,604
`14 Claims. (Cl. 73—205)
`
`where
`
`2
`
`15
`
`20
`
`25
`
`(6)
`
`40
`
`The present invention relates to new and_novel ap
`paratus for measuring a mass transport property of a
`moving ?uid, and more particularly to measuring the
`density and mass ?ow of a moving ?uid employing an
`arrangement which establishes axial acceleration in the
`?uid to be measured.
`It has been a long-standing problem in the art to pro
`vide a simple and effective means for accurately measur
`ing the mass ?ow and density of ?uids, and the require
`ment for such apparatus has increased sharply in the
`recent past with the advent of high-powered engines
`and propulsion systems wherein horse power and/or
`thrust are measured and controlled in terms of propellant
`mass ?ow. There are, of course, many applications
`wherein it is essential to accurately measure the amount
`of ?uid ?ow as in pipe lines and the like.
`Flow meters now in use ‘and known in the prior art,
`and which fundamentally respond to mass-?ow rate gen
`erally make use of some sort of induced acceleration in
`the ?ow. ‘Radial ?ow types of existing ?ow meters make
`use of Coriolis acceleration, while axial ?ow types make
`use of torsional acceleration. On the other hand, gyro
`scopic types of ?ow meters now in use make use of angu
`lar acceleration. The radial and gyroscopic ?ow types
`now in use are quite bulky and require considerable dis
`turbance to the ?owing ?uid which is, of course, very
`undesirable. The axial ?ow type of ?ow meter causes
`a very de?nite internal obstruction to the ?ow and further
`requires the use of rotating parts. The novel apparatus
`of the present invention utilizes a completely new concept
`in this ?eld wherein an axial acceleration is established
`in the ?owing ?uid Without requiring the ?uid to change
`direction, the arrangement of the present invention super
`imposing a sinusoidal axial ?ow oscillation on the other
`wise steady ?ow as it passes through a measuring portion
`of the apparatus. This ‘sinusoidal'oscillation in the flow
`couples with the steady ?ow of the ?uid in such a manner
`so as to produce an alternating pressure which is pro
`portional to the steady mass ?ow rate, and means is
`provided for measuring this alternating pressure and in
`dicating the rate of mass ?ow as a function of the chang
`ing pressure.
`The basic concept upon which the invention is based
`is developed in the theoretical discussion set ‘forth here
`inbelowv.
`As a ?rst approach to the concept let us consider
`incompressible quasi-steady ?ow in one dimension. Ber
`noulli’s equation for such ?ow has the well known form
`
`45
`
`where P is the pressure where the flow velocity is U;
`P, is the pressure in the ?iud where the ?ow velocity
`is U1; p is the ?uid density.
`Now, if U, is the ?ow velocity due to the steady ?ow U
`with a superposed oscillatory ?ow u, we have
`U1: U-rt cos wt
`(2)
`where w is the angular frequency of the superposed ?ow
`oscillation. Substitution of Eq. 2 into Eq. 1 yields
`
`60
`
`65
`
`70
`
`(3a)
`
`(3b)
`
`(4a)
`pu=P-—pu2/ 4
`(4b)
`PFPUL!
`(46)
`P2=Pll2/4
`Clearly, then, pc is ‘the steady component of the meas
`ured pres-sure p1; p1 is the fundamental (i.e., at angular
`frequency to) component of ‘the measured pressure; p2 is
`the second harmonic of the measured pressure.
`Now, the pass ?ow Fm is de?ned by:
`(5)
`Fm=PUA
`where A is the cross-sectional area of the ?ow system.
`Thus, if we measure the pressure perturbation due to the
`superposed sinusoidal ?ow perturbation, we ?nd that the
`mass-?ow can be determined by tuning our pressure
`detection system to the fundamental ‘frequency w; the
`?ow signal p, at this frequency is
`p1=Fml£/A
`where Fm is the mass ?ow;
`u is the ?xed amplitude of the superposed sinusoidal
`?ow oscillation in the region where the pressure meas
`urement p1 is made;
`-
`A is the ?xed cross-sectional area of the ?ow system in
`‘the region where the steady flow velocity U exists.
`The above analysis is directed to an arrangment where
`in the system provides an indication of the mass ?ow of
`the ?uid. On the other hand, it is also possible to readily
`modify the system so as to provide an indication of the
`density of the ?uid.
`From an inspection of Eq. 3b and Eq. 40, it is ap
`parent that by tuning the pressure detection system to
`2w, the second harmonic of the fundamental frequency,
`an indication can be obtained of the density of the ?uid.
`It is apparent from the foregoing that the present in
`vention is directed to_ an arrangement for measuring
`either density or mass ?ow of a moving ?uid. Both
`density and mass ?ow may be designated as mass trans
`port properties‘ of a moving ?uid, and accordingly, this
`terminology is used throughout the speci?cation and
`claims to indicate generically both the density and the
`mass ?ow of the moving ?uid. It should be understood
`‘that the present invention may be employed for measur
`ing either of the two mass transport properties discussed
`above, independently of one another, or if desired, these
`two mass transport properties may be measured simul
`taneously.
`In the present invention, the ?owing ?uid is passed
`through a measuring Zone provided at a suitable portion
`of a ?uid conduit means, the ?uid to be measured pass
`ing through this measuring zone or portion at a sub
`stantially steady ?ow rate. The means for establishing
`an independent, known axial sinusoidal oscillation on the
`?uid passing through the measuring zone may take a num
`ber of different forms, and ‘several different con?gurations
`have been illustrated for carrying out this function. It
`will be understood that many other possible alternative
`means of developing these oscillations will occur to one
`skilled in the art, and the examples shown are for the
`purpose of illustration only.
`As mentioned previously, the axial oscillation super
`imposed on the ?ow couples with the steady flow to pro
`duce an alternating pressure. Suitable means is provided
`for measuring this pressure within one or more points in
`the measuring portion of the ?uid conduit means‘, and
`the measuring means preferably generates an electrical
`signal proportional to the pressure changes sensed by the
`measuring device.
`The output of the pressure measuring apparatus is con
`
`4
`
`

`

`10
`
`40
`
`Ii
`nected with suitable detector indicating means, the indi
`cating means taking any conventional form for indicating
`mass flow. The purpose of ‘the detector means is primari
`ly to remove undesired signals and to pass only those
`signals which are indicative of the pressure changes oc
`curring in the measuring zone due to the superimposed
`sinusoidal oscillations. For this purpose, a relatively con
`ventional ?lter means may be employed which is tuned
`either to the fundamental frequency or the second har
`monic of the fundamental ‘frequency of the means gen~
`crating the sinusoidal oscillations depending on whether
`it is desired to measure the mass ?ow or the density re
`spectively, the ?lter means serving to pass signals at these
`frequencies and to ?lter out different signals at other fre
`quencies.
`In addition, phase-sensitive means may be employed in
`the detector mechanism to assure that only those signals
`will be passed to the indicator which are in phase with the
`oscillations of the means producing the sinusoidal oscil
`lations thereby providing a relatively fool-proof means of
`preventing any spurious signals from reaching the indi
`cator mechanism.
`The present invention is particularly designed to pro
`vide excellent linearity over a very wide dynamic range,
`and a minimum pressure drop and substantially obstruc
`tionless con?guration is provided. The arrangement fur
`ther provides a rapid response time and is quite simple, in
`expensive and compact in construction, and yet e?cient
`and reliable in operation. The present invention may be
`carried out in many different ways with widely varying
`con?gurations utilizing readily available components of
`an inexpensive nature.
`An object of the present invention is to provide new
`and novel apparatus for measuring mass flow which has
`excellent linearity over a wide dynamic range.
`Another object of the invention is the provision of
`apparatus for measuring mass ?ow which provides a min
`imum pressure drop and which employs a substantially
`obstructionless physical con?guration.
`A further object of the invention is to provide appara
`tus for measuring mass flow which has rapid response
`time, which is simple, inexpensive and compact in con
`struction; and yet which is quite e?icient and reliable in
`operation.
`Other objects and many attendant advantages of the in
`vention will become more apparent when considered in
`connection with the speci?cation and accompanying draw
`ings, wherein:
`FIG. 1 is a longitudinal section through one form of
`the apparatus illustrating rather schematically the elec
`trical network associated with ‘the physical structure for
`carrying out the invention;
`‘FIG. 2 is a View similar to FIG. 1 illustrating a modi
`?ed form of the apparatus;
`‘
`FIG. 3 is a view similar to FIG. 1 illustrating a still
`further modi?ed form of the apparatus;
`FIG. 4 is a view similar to FIG. 1 illustrating still an
`other modi?cation of the present invention;
`FIG. 5 is a longitudinal section through a modi?ed
`form of pressure sensing means;
`FIG. 6 is a cross-sectional view taken substantially
`along line 6--6 of FIG. 5 looking in the direction of the
`arrows;
`FIG. 7 illustrates a further modi?ed form of the inven
`tion wherein a plurality of devices for measuring mass
`flow are connected in series with one another; and
`FIG. 8 illustrates a further modi?ed form of the in
`vention wherein a plurality of devices for measuring mass
`?ow are connected in parallel with one another.
`In the ?rst three modi?cations illustrated in the draw
`ings as seen in FIGS. 1, 2 and 3, the means for producing
`the desired ?ow perturbations on the ?uid ?ow takes the
`familiar con?guration of a Venturi which has one or
`more portions thereof connected so as to oscillate to and
`fro along its axis of symmetry. In applying the fore
`
`3,251,226
`
`going technical discussion to this type of physical con
`?guration, we shall assume that there is one~dimensional
`quasi-steady ?ow. The one-dimensional assumption im
`plies that all ?uid-dynamic variables are functions of only
`one space coordinate, and in this case, the coordinate
`would be measured along the axis of the ?uid conduit
`means and the Venturi.
`The quasi-steady ?ow assumption implies that the
`equations derived for steady ?ow conditions can be used
`to represent conditions in the ?owmeter. To determine
`the condition under which a quasi-steady analysis is
`valid we note the following. If 0 is the velocity of
`sound in the metered ?uid and w is the angular fre
`quency of the oscillating Venturi, the wavelength of this
`disturbance is >\=2¢rc/w. If the length of the ?uid ele
`ment we are. investigating, i.e., the length of the ?ow
`meter, is very small compared with the wavelength, then
`the time derivatives of the ?uid-dynamic variables can be
`neglected. For example, c in water is about 5000 ft./sec.,
`so if the frequency of the oscillation of the Venturi were
`60 c.p.s., the Wave length would be about 83 feet, and
`the quasi-steady ?ow assumption would be valid if the
`?owmeter length were on the order of one foot, as ex
`pected.
`A second consideration bearing on the frequency of
`oscillation, is that the axial acceleration ?owmeter can
`resolve variations in flow and density which take place
`at a rate slow compared with the frequency of oscillation.
`For such quasi-steady flow conditions We have from
`the equation of continuity
`(7)
`F m=pUA
`where Fm is the mass-?ow rate;
`U is the average (throughout any cross ‘section of the
`?ow pipe) velocity of the metered ?uid;
`p is the density of the metered ?uid;
`A is the cross sectional area of the ?ow pipe. We
`emphasize that U is the ?uid velocity relative to the ?xed
`plumbing system (i.e., to a ?xed reference frame).
`If Ut is the ?uid velocity (averaged across the throat
`area) in the Venturi’s throat-and again we emphasize
`velocity relative to the ?xed plumbing system—then the
`quasi~steady equation of continuity in the frame of refer
`ence moving with the Venturi throat yields
`(8)
`(U-u cos wt) A=(Ut—u cos 0:1)pAt
`where 14 cos wt is the velocity of the Venturi throat rela
`tive to the ?xed plumbing system;
`At is the cross-sectional area of the Venturi throat.
`From Eq.- 8 we ?nd that the fluid velocity in the throat,
`U{;, is
`
`Next, since we are assuming quasi-steady ?ow, we can
`use Bernoulli’s equation:
`
`where Pt is the ?uid pressure in the Venturi throat;
`P is the pressure of the metered ?uid (i.e., an ambient
`pressure undisturbed by the oscillating Venturi); ‘
`p is the ?uid density (which is allowed to vary quasi
`steadily) of the metered ?uid;
`U is the ?ow velocity of the metered ?uid;
`U; is the ?ow velocity in the Venturi throat.
`Of the variables in Eq. 10, Pt and U1, may be expected to
`have a steady component plus alternating components;
`the remainder are steady in time.
`If we now substitute Eq. 9 into Eq. 10, we can set up
`three equations: the ?rst is established by equating the
`steady terms; the second equation is established by equat
`mg those terms which vary as cos wt; and the third equa
`tion is established by equating those terms which vary as
`cos Zwt. We observe that the throat pressure, Pt, must
`have corresponding frequency components, i.e.,
`
`70
`
`5
`
`

`

`3,251,226
`
`(12b)
`
`5
`(11)
`Pt=Pto+p1 cos wt-I-PZ cos 2w!
`Consequently, making use of Eq. 11, the three equations
`are:
`The Steady Component:
`Pto=P— (p/2) ([A/At]2— 1 ) U2
`— (p/4) ([A/At]—1)2u2 (12a)
`The Fundamental Component:
`P1‘=PUA(u/At)([A/At]—~1)
`The Second Harmonic Component:
`(120)
`P2: —-(pu2/4) ([A/At] ~1)2
`We now tune our pressure sensing system in the throat to
`the fundamental frequency, i.e., we selectively detect the
`alternating pressure 121.
`If we substitute Eq. 7 into Eq. 12b, we ?nd as the ex
`pression for the alternating pressure
`P1_(”/A.t) ([A/At] —1)Fm
`where u is the alternating velocity of the Venturi;
`At is the cross sectional area of the Venturi throat;
`A is the cross sectional area of the ?ow pipe;
`Fm is the mass ?ow rate in the ?ow pipe.
`If We express the cross sectional areas in Eq. 13 in terms
`of pipe diameter, D, and Venturi throat diameter, Db;
`and if the alternating motion of the Venturi is simple
`harmonic with (full) stroke, S, and angular frequency,
`211-)‘, we have
`
`(13)
`
`25
`
`30
`
`6
`tion 31. An electric motor indicated schematically by
`reference numeral 40 is indicated as having an output
`shaft schematically indicated by line 41 which in turn
`has an eccentric member 42 connected thereto. Mem
`ber 42 is slidably mounted within slot 37 of the actuating
`means 30. As the motor 40 is driven at a substantially
`constant speed during operation of the apparatus, eccen
`tric portion 42 will travel in a circular orbit as indicated
`by dotted line 44, member 42 sliding up and down within
`the slot 37 thereby generating a sinusoidal oscillation of
`the actuating means 30 and the attached measuring por
`tion 11.
`It will be understood that various means may be em
`ployed for obtainind the desired reciprocatory movement
`of the measuring portion, and the provision of an elec
`tric motor 40 and the illustrated attachment to the actuat
`ing means 30 is a most simple and and effective means
`for obtaining the desired movement.
`It is anticipated that motor 40 will generally be oper
`ated off of conventionally available 60-cycle electrical
`energy such that the measuring portion 11 may oscillate
`at a fundamental frequency of 60 cycles per second. In
`such a case, the line voltage may be utilized for obtaining
`a reference signal for operating the phase-sensitive de
`tector hereinafter described.
`It should be understood that the actuating means 30
`can be reciprocated at any desired frequency and in
`this case suitable means is provided for providing a
`reference voltage, this means being illustrated in FIG. 1
`as comprising a permanent magnet 50 which may be
`embedded or supported within arm portion 34, a ?xed
`coil 51 being disposed in surrounding relationship to the
`permanent magnet such that upon reciprocation of the
`actuating means 30, the permanent magnet will generate
`an electrical voltage in coil 51 which in turn may be
`utilized as a reference signal for actuating the phase
`sensitive detector means hereinafter described.
`A ?rst presure tap 55 is threaded into a suitable open
`ing in the measuring portion 11 and is in communication
`with the central portion of the Venturi throat 27. Tap
`55 is connected through a suitable ?exible tube 56 to a
`differential pressure gauge 57. A second pressure tap
`60 is also threaded into a suitable opening in the measur
`ing portion 11, and is in communication with the ?uid
`conduit means immediately to one side of the Venturi ,
`tube section. It should be understood further that the
`?uid may ?ow through the ?uid conduit means in either
`direction and the apparatus will operate equally as well.
`Pressure tap 60 is connected by means of a ?exible tube
`61 with the differential pressure gauge 57.
`The differential pressure gauge 57 may be of any con
`ventional construction, and may for example comprise
`a differential diaphragm type transducer such as manu
`tactur-ed by Dynisco, Division of American Brake Shoe
`Company, Cambridge, Mass, and identi?ed as Model PT
`69. The two tubes 56 and 61 communicate with op
`posite sides of the diaphragm of the gauge and an output
`electrical signal is provided proportional to the differ
`ences in the pressures operating on opposite sides of the
`diaphragm.
`The signal output from the gauge 57 is fed into a con
`ventional ‘ampli?er 65, the output of which is connected
`with a ?lter 66. This ?lter may be tuned to the funda
`mental frequency of ‘the actuating means 30 so‘ as to pass
`substantially only those pressure signals occurring as
`a result of the superimposed sinusoidal oscillations on
`the ?uid ?ow. For example, ?lter 66 may comprise a rela
`tively narrow band pass ?lter means having a center
`frequency the same as that of the fundamental frequency
`of the actuating means 30.
`The output of the ?lter means 66 is in turn connected
`with a phase-sensitive detector mechanism‘ 67. This
`phase-sensitive detector mechanism is connected by means
`of leads 68 and 69 with the coil 51 previously described
`such that the mechanism 67 receives a reference signal
`
`Referring now particularly to FIG. 1 of the drawings,
`two spaced portions of a ?uid conduit means or ?ow pipe
`are indicated'generally by reference numerals 10 and 10’,
`it being understood that ?uid will flow through this ?uid
`conduit means during operation of the apparatus at a sub
`stantially steady ?ow rate. An intermediate measuring
`portion of the ?uid conduit means is indicated generally
`by reference numeral 11, and includes opposite end plates
`12 and 13 which are connected with the adjacent end
`‘portions of the ?uid conduit means by means of ?exible
`bellows 16 and 17 respectively which enable the inter
`mediate measuring portion to freely oscillate during}
`operation of the apparatus while at the same time ensur
`ing that an effective ?uidtight seal is maintained.
`A pair of guide rods 20 and 21 have the opposite ends
`thereof supported within the walls of the conduit por~
`tions 10 and 10', the measuring portion 11 including out
`wardly projecting ?ange portions 12' and 13' to which
`the plates 12 and 13 are secured respectively, members
`12, 12’, 13 and 13' all having aligned openings formed
`therethrough for receiving the guide rods 20 and 21 such
`that‘the inter-mediate measuring portion of the apparatus
`will be guided for axial oscillation.
`It will be noted that the inner surface of the measur
`ing portion 11 de?nes a Venturi tube, the two inner sur
`faces 25 and 26 tapering inwardly from the outer ends of
`the measuring portion and joining with a Venturi throat
`portion 27 at the central part of the measuring portion.
`The actuating means for producing the desired oscil
`latory movement of the measuring portion 11 is indicated ‘
`generally by reference, numeral 30 and includes a central
`portion 31 from one side of which extends an arm 32
`which in turn is connected with an arm 33 connected
`with the portion 12' of the measuring portion. An arm
`34 extends from the opposite side of the central portion
`31 of the actuating means and joins with an arm 35 which
`in turn is connected with the portion 13’ of the measur
`ing portion, Suitable means is provided for providing
`a sinusoidal axial oscillation of means 30 which in turn
`will cause a corresponding oscillatory movement of the
`measuring portion 11. This means takes the form of
`a slot 37 extending vertically as seen in FIG. 1 in por
`
`35
`
`45
`
`50
`
`60
`
`70
`
`75
`
`6
`
`

`

`3,251,226
`
`10
`
`20
`
`7
`from the actuating mechanism 30. ‘The phase-sensitive
`detector and indicator 7t) may be combined in the form
`of a conventional wattmeter. Generally, this type of in
`strument is designed to indicate the product of electrical
`current and voltage taking into account phase angle.
`However, such instruments can and have been modi?ed
`in the past to indicate the product of two voltages includ
`ing consideration of phase angle, i.e., to provide phase
`sensitive voltage measurement.
`Another form of phase-sensitive detector and indicator
`which can be made to operate at any selected frequency
`is a phase-angle voltmeter such as manufactured by North
`Atlantic Industries, Plainview, Long Island, New York,
`and identi?ed as their Model VM-202. A further form
`of phase-sensitive detector and indicator which may be
`employed is a lock-in ampli?er such as manufactured by
`Electronics, Missiles and Communications, Inc, Mount
`Vernon, New York, and identi?ed as Model RIB. It is
`accordingly apparent that any combination of readily
`avail-able components may be employed for providing the
`desired phase-sensitive detecting function and indicating
`function as indicated schematically by boxes 67 and 78
`in FIG. 1 of the drawings.
`It is apparent that the phase-sensitive detector means
`will assure that only those signals occurring in the meas
`uring portion as a result of the oscillation of the actuat
`ing means will affect the indicator means to thereby pre
`vent any signals not in phase with this frequency from
`‘causing a false reading.
`In the arrangement shown in FIG. 1, the pressure con
`nect-ions from the oscillating Venturi measuring portion
`to a capacitance type differential pressure gauge are
`such that one pressure lead measures the ambient pres
`sure while the other pressure lead measures the steady
`pressure plus signal pressure in the throat of the Venturi.
`In this manner, the sensitive elements of the differential
`pressure gauge may be subjected to relatively small dif
`ferential pressures which will give rise to a small steady
`displacement of the differential sensor.
`If- the steady differential pressure in an arrangement
`shown in FIG. 1 should prove excessive, a modi?ca
`tion as shown in FIG. 2 may be employed wherein similar
`parts ‘have been given the same reference numerals primed
`in FIG. 1.
`'
`The only difference in the construction shown in FIG.
`2 as compared to that shown in FIG. 1 is that a single
`pressure tap 55' is employed, pressure tap 60 as shown
`in FIG. 1 having been eliminated. The ?exible tubing
`75 leading from pressure tap 55' joins with a branch tube
`7 6 ‘which leads to the opposite side of the diaphragm of the
`gauge 57’ as does tube 75. A damping mechanism such
`as a porous plug 77 is disposed within tube 76 to block
`the pressure alternations on one side of the differential
`pressure transducer while permitting the pressure oscilla
`tions to act on the second side of the differential pressure
`transducer through tube 75.
`It is contemplated that sufficient accuracy may be ob
`tained with the apparatus in certain instances where the
`output of the pressure measuring means is ampli?ed and
`then simply passed through a ?lter tuned to the funda
`mental frequency of the actuating means. vWhere it is
`necessary on the other hand to detect a relatively small
`signal from a large noise background, it is anticipated
`that it will be necessary to also employ the phase-sensitive
`detector means or auto-correlated detection techniques.
`Referring now to FIG. 3 of the drawings, a further
`modi?ed form of the invention is illustrated wherein the
`?uid conduit means or flow pipe sections 80 and 81)’ are
`spaced from one another and support a pair of guide rods
`82 and 83. A Venturi arrangement is again employed
`wherein the central portion 85 having the Venturi throat
`86 therewithin is ?xed in the position shown in FIG. 3.
`On the other hand, portions 87 and 88 of the Venturi con
`?guration are freely axially reciprocable and are guided
`by the guide rods 82 and 83 in such reciprocatory move
`
`30
`
`35
`
`8
`ment, the guide rods extending through suitable openings
`provided in members 87 and 88.
`Suitable means such as a bellows 98 is connected be
`tween members 80 and 87 to provide a ?uid-tight seal.
`Bellows 91 and 82 provide a fluid—tight seal between the.
`?xed portion 85 and the reciprocable portions 87 and 88
`respectively. A further bellows means 93 is connected
`between members 88 and 80’ in order to assure a fluid
`tight seal at all times while permitting free axial oscilla
`tion of portions 87 and 88.
`Actuating means 96 includes a pair of oppositely ex
`tending arms 97 and 98, arm 97 being connected .through
`member 108 and 1011 wit-h the oscillating portion 87, and
`arm 98 of the actuating means being connected through
`members 182 and 103 with the portion 88. The actuating
`means includes an enlarged central portion 105 having a
`slot 106 formed therethrough which engages an eccentric
`107 connected with the motor 108 in the same manner
`previously described so as to provide sinusoidal oscilla
`tion of the actuating means upon constant speed rotation
`of the motor 108.
`A permanent magnet 118 is supported in arm 98 of
`the actuating means, and a coil 111 is disposed there
`around for providing a reference voltage in this modi?
`cation. A pressure transducer indicated generally by
`reference numeral 115 is mounted in the ?xed portion
`85 and is in communication with the interior of the
`Venturi throat 86. This pressure transducer in con
`trast to the transducers previously described is not of
`the differential type. It should be understood that any
`suitable type of pressure measuring means may be em
`ployed according to the present invention and with any
`of the various modi?cations disclosed herein. This pres
`sure transducer may be of any conventional construc
`tion and may for example be of the type manufactured
`by Sensonics, Inc., Washington, DC. and identi?ed as
`their Model V7225. The pressure transducer is connected
`through connection 116 with a lock-in ampli?er and
`detector means 118. Means 118 may be of the type
`manufactured by Electronics, Missiles and Communica
`tions, Inc, Mount Vernon, New York, and identi?ed
`as their Model RIB.
`Means 118 receives a reference signal through leads‘
`119 and 128 which are connected with the coil 111
`previously described.
`Referring now to FIG. 4 of the drawings, the ?uid
`conduit means or flow pipe is indicated by reference
`numeral 125, and has a pair of spaced openings 128
`and 128 formed through the side wall thereof. Open
`ings 128 and 129 communicate with the interior of the
`chamber de?ned by the housing 131.
`_
`An elongated rod 135 extends through the chamber
`de?ned by housing 131 and has an enlarged piston
`member 136 formed in the intermediate portion there
`of, this piston member serving to separate the cavity
`within housing 131 into two separate chambers indi
`cated by reference numerals 137 and 137', these two
`chambers being respectively in communication with the
`openings 128 and 129 through the side wall of the ?uid
`conduit means.
`A ?exible sealing member 138 is ?xed to the outer
`end of member 135, and a ?exible sealing means 139
`is connected with an intermediate portion of member
`135 to ensure an eifective seal between member 135
`and the housing 131 as member 135 and its associated
`piston 136 reciprocate within housing 131.
`Outer end 140 of member 135 is connected with any
`suitable driving mechanism so as to provide the piston
`136 with a simple harmonic motion to thereby cause a
`?ow variation to take place in the sensing area illus
`trated in FIG. 4. It should be noted in connection with
`the modi?cation shown in FIG. 4 that the ?ow impedance
`of the fluid conduit means to the right and left of the
`portion shown in FIG. 4 is relatively high while the flow
`impedance through the ?owmeter portion between the
`
`7
`
`

`

`3,251,226
`
`10
`the fundamental frequency of the superimposed oscilla
`tion in order to determine mass ?ow, or the ?lter means
`may be tuned to, the second harmonic of the superim
`posed oscillation so as to determine the density, of the
`?uid. It is also obvious that both of these mass transport
`properties can be determined and indicated simultane
`ously if desired by providing from the output of the ampli~
`?er for example in the circuits illustrated a parallel path
`through a pair of ?lters to a pair of indicators as will be
`Well understood by one skilled in the art.
`A further possible modi?cation of the present invention
`is the employment of a plurality of the mass flow measur
`ing devices arranged either in a series or parrallel ar
`rangement with one another, such interconnection of the
`devices affording certain advantages as will hereinafter
`appear.
`Considering now the theoretical concept underlying the
`series or parallel operation, if two measuring devices ac
`cording to the present invention are placed in. series and
`mechanically operated such that the means for superim
`posing the sinusoidal axial ?ow oscillations on the ?uid
`are operated with a 180° phase difference, the analysis
`previously presented herein can be carried through.
`Eq. 2 applies for the ?rst measuring device, while the
`equation for the second measuring device will read
`U2=U+u cos wt
`(15)
`and therefore Eq. 31; becomes
`(16)
`P2=P0—P1 COS ot+p2 cos Zwt
`If now we take the pressure difference, AP, from our
`two pressure sensors, we obtain [subtracting Eq. 16 from
`
`10
`
`20
`
`25
`
`30
`
`9
`two ports 128, 129 is very low since the passage through '
`the ?owmeter is very short and virtually unobstructed. .
`Accordingly, essentially all of the generated ?ow velocity
`oscillation produced by piston 136 will appear in the
`measuring portion of the apparatus.
`'
`The pressure tap 145