Method and structure for flow measurement

Abstract

Apparatus and method for mass flow measurement utilizing a substantially "U" shaped conduit mounted in a cantilever manner at the legs thereof, means for oscillating the conduit, and means for measuring so that, when the conduit is oscillated, sensors mounted on the conduit can measure the Coriolis force by measurement of the force moment or the angular motion of the conduit around an axis substantially symmetrical to the legs of the conduit. The force moment is measured by sensing incipient movement around the axis, and generating and measuring a nulling force. In preferred embodiments, the oscillating means are mounted on a spring arm having a natural frequency substantially equal to that of the "U" shaped conduit, and in a particularly preferred displacement embodiment the measuring means are sensors sensors are mounted on the "U" shaped conduit and adapted to measure, with proper direction sense, the time differential between the leading and trailing portions of the "U" shaped conduit passing through the plane of the "U" shaped conduit at substantially midpoint of the oscillation thereof.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to a flow measuring device, and more particularly to a flow measuring device in the form of a "U" shaped conduit mounted in beamlike, cantilevered, fashion and arranged to determine the density of a fluid material in the conduit, the mass flow rate therethrough, and accordingly other dependent flow parameters.

2. Description of the Prior Art

Heretofore, flow meters of the general type with which the present invention is concerned have been known as gyroscopic mass flow meters, or Coriolis force mass flow meters. In essence, the function of both types of flow meters is based upon the same resonentthus,. Thus, the time period (T₁) of the conduit can be expressed ##EQU2## Where: K₁ K₂ and K₃ are fixed constants and

D_fm =mass density of the fluid

Therefore, by counting a fixed frequency oscillation, i.e., oscillator 84, density factor d_f can be generated; ##EQU3## Where: d_f =density factor

f_o =oscillator frequency

MASS FLOW RATE

The Coriolis force on a particle on a revolving plane can be expressed by:

F_c =2M_p W×V_p

Where:

F_c =force on particle due to Coriolis acceleration

M_p =particle mass

V_p =radial velocity of particle

W=Angular velocity of plane

In the case of the "U" shaped conduit, two forces, F_c1 and F_c2 are produced around axis O--O, which generate an oscillating moment ΔM, expressed as:

ΔM=F_c1 r +F_c2 r₂

Where:

r₁ and r₂ =distance from axis O--O to each leg Assuming symmetry, ΔM=2F_c1 r₁ =4M₁ V₁ Wr₁

Where:

V₁ =particle velocity

M₁ =particle mass

W=angular velocity ##EQU4##

Thus ΔM=4Wr₁ 3Δ_q

M=∫ΔM=4Wr₁q

Thus ΔM=4Wr₁ ΔQ

M=∫ΔM=4Wr₁ Q

Where: ΔQ=incremental mass flow rate

Where: Q=Total mass flow rate in conduit

The deflection of conduit around axis O--O can be expressed as:

Torque=K_s ⊖

Where:

⊖=deflection angle

K_s =Angular spring constant

thus Q=K_s ⊖/4Wr₁, i.e., Q is directly proportional to ⊖ and K_s are , and inversely proportional to W.

Considering the time period Δt between outputs of sensors 43 and 44:

V_p Δt=.Badd.2r⊖.Baddend. 2r₁ ⊖ ##EQU5## Where: V_p =conduit velocity

Δt=time interval between outputs 43 and 44

V_p =LW

Where:

L=length of conduit ##EQU6##

Thus, mass flow is a function of pipe geometry constants and Δt. Accordingly, only Δt need be determined in that the constants are, in effect, a scale factor.

Another embodiment of the invention is shown in FIG. 9, whereat wherein mass flow meter 100, which is similar an in many respects to flow meter device 10, is illustrated. As shown, flow meter 100 includes a base 102 and "U" shaped conduit 104 extending therefrom in a substantially solidly mounted, i.e., free of pivoting devices, manner. "U" shaped conduit 104 includes inlet 105 and outlet 106 which communicate with inlet leg 108 and outleg leg 109, respectively. Legs 108 and 109 are arranged to pivot at points 112 and 114 along axis W'--W' to permit oscillation of "U" shaped conduit 104 around axis W"--W". This may be facilitated by, for instance, a thinning in the walls of "U" shaped conduit 104 at pivots 112 and 114, but such pivot points are continuous areas of "U" shaped conduit 104 and may be unaltered tubes. Base leg 116 connects inlet leg 108 and outlet leg 109 thus completing "U" shaped conduit 104.

Contrary to the preferred arrangement of flow meter 10, "U" shaped conduit 104 may advantageously have less resistance to bending around the Coriolis force distortion axis than around oscillation axis W'--W' since Coriolis force distortion is nulled. Magnets 118 carried on base leg 116 by supports 119 interact with drive coil 120 to oscillate "U" shaped conduit 104. Preferably, drive coil 120 is carried on cantilevered spring leaf 122 which is pivotally mounted adjacent axis W'--W' and of a natural frequency substantially equivalent to that of "U" shaped conduit 104 carrying the contemplated fluid therein. Of course, the mounting of magnet 118 and force coil 120 may be reversed, i.e., on conduit 104 and leaf spring 122, respectively. Also, leaf spring 122 may be dispensed with entirely when base 102 is of substantial mass compared to the mass of "U" shaped conduit 104 and the fluidized material flowed therethrough. However, in most instances, it is preferred to oscillate "U" shaped conduit 104 and leaf spring 122 at a common frequency but 180° out of phase to internally balance the forces within flow meter 100 and avoid vibration of base 102.

Base leg 116 carries magnets 125 and 126 which depend downwardly therefrom. Magnet 125 is disposed within sense coil 128 mounted to base 102, while magnet 126 is similarly disposed within sense coil 129 also mounted on base 102. Magnet 125 extends within force coil 131 arranged symmetrically with sense coil 128, while magnet 126 extends within force coil 132 similarly mounted relative to sense coil 129. Deflection sensing means 133 and 134, which are shown in a simplified manner in FIG. 9, but in more detail in FIGS. 11 through 13, are positioned adjacent the intersection of inlet legs 108 and 109 and base leg 116.

Turning now to FIG. 10 which sets forth the circuit details not shown in FIG. 9, it should be noted that sense coils 128 and 129 are connected in series in such a manner that the movement of magnets 125 and 126 into sense coils 128 and 129 will generate a sinuosoidal sinusoidal signal "A" with an amplitude proportional to the velocity of "U" shaped conduit 104. This signal, the magnitude of which is proportional to the speed of movement of magnets 125 and 126, and accordingly a function of the amplitude of oscillation of "U" shaped conduit 104, is provided to AC amplifier 135, and to diode 136 which permits only the positive portion of the sinusodial sinusoidsal signal to charge capacitor 137. Accordingly, the input from diode 136 and capacitor 137 to differential amplifier 138 is determined by the magnitude of the sinusoidal signal. Differential amplifier 138 compares such input with reference voltage VR₁. Thus, if the voltage of capacitor 137 exceeds VR₁, amplifier 138 outputs a stronger signal. The output from AC amplifier 135, which is of course a sinuosoidal sinusoidal signal in phase with the oscillation of "U" shaped tube 104 and of a magnitude determined by the gain control outputed outputted by differential amplifier 138, drives coil 120 to maintain the desired oscillation of "U" shaped tube 104. Signal A is also supplied to a bridge formed of resistors 140, 141, 142 and photoresistor 143. Resistor 144 is included in a feedback loop between resistors 140 and 142, and the output from the interconnection of resistors 140, 142 and 144 is connected to, for instance, the minus input of differential amplifier 145. A variable light source, such as LED 147, is connected through resistor 148 to the output of servo amplifier 150. Servo compensator 152 is a conventional expedient in servo systems as described in Feedback Control Systems, Analysis And Synthesis, by D+Azo D'Azo and Hopuis, published by McGraw Hill, 1966, forms the feedback loop between one input of servo amplifier 150 and the output therefrom. Signal B, which is a DC signal porportions proportional to the small, unnulled distortion of "U" shaped conduit 104 generated as described below with regard to FIGS. 11, 12 and 13, is connected through resistor 153 to an input of servo amplifier 150. The output of servo amplifier 150 is referenced to voltage VR₂ and connected through resistor 148 to LED 147. Thus, as a function of the magnitude of signal B with respect to VR₂ driving servo amplifier 150, the intensity of LED 147 is regulated. For instance, the resistivity of photoresistor 143 decreases upon an increase in intensity of LED 147, thereby decreasing the signal supplied to the positive input of differential amplifier 145 relative to that through resistors 140 and 142 to the negative input thereof. Thus, the output of differential amplifier 145 is 180° out of phase with signal A, since the positive input thereto is decreased while the negative input is not. In summary, as signal B increases, LED 147 is dimmed and the resistance of photoresistor 143 increases. This causes the Signal A phase output of differential amplifier 145 to increase. The output of differential amplifier 145 is connected to force coils 131 and 132 which, as described above, are supported on base 102 and connected in series and out of phase. Thus, current through force coils 131 and 132 creates, with reference to FIG. 9, a torque by attracting, for instance, magnet 125 and repelling magnet 126, both of which are connected to base leg 116. This torque across base leg 116 nulls distortion of base leg 116 as a result of Coriolis forces generated by flow through "U" shaped conduit 104.

Resistors 155, 156 or 157 are connectable, by means of switch 159 and, to force coils 131 and 132 thereby providing a selectable load to adjust the scale factor and provide for greater or lesser torque on base leg 116. The output from series connected force coils 131 and 132 are also connected as one input to synchronous demodulator 162, which will be described in more detail with reference to FIG. 14. The output of synchronous demodulator 162 is a DC signal proportional to mass flow rate, and accordingly provides a measurement of mass flow rate. A DC volt meter (not shown) may be connected to the output of synchronous demodulator 162 to provide a visual reading of mass flow rate through "U" shaped conduit 104, or the DC signal may be directly employed in, for instance, a control loop to other equipment.

As shown in FIG. 11, deflection sensors 133 and 134 may comprise, for instance, left flag 164 and right flag 165 which depend from conduit 104. Fixed left flag 166 and fixed right flag 167 are mounted on base 102. Accordingly, as base leg 116 oscillates, flags 164 and 165 will preclude light from light sources 169 and 170 from reaching photosensors 181 and 182, respectively. Preferably, the point at which flags 164 and 166, and 165 and 167 intersect to block light is about at the midpoint of oscillation of base leg 116, but one set of flags may be offset somewhat from the other with regard to the interference point. It will be recognized that in the event of distortion of base leg 116 angularly relative to base 102 as a result of Coriolis forces generated by flow through "U" shaped conduit 104, a change in time lapse will exist between the occulting by flags 164 and 166 and flags 165 and 167. The time difference, and sense, will be dependent upon, at At a fixed oscillating rate of base leg 116, the time difference and sense thereof will be dependent upon the Coriolis forces generated and the direction of oscillation. Photosensor 181 is connected to flip-flop 185 at the reset side and 186 at the reset side, with the connection to flipflop 186 being through inverter 188. Differentiating capacitors 191 and 192 are included in reset input. Similarly, photosensor 182 is connected to the set side of flip-flop 185 and, through inverter 189 to the set side of flip-flop 186 with differentiating capacitors 193 and 194 similarly included in the inputs. Thus, as flags 164 and 166 close, a positive signal is generated by photosensor 181 which activates the reset side of flip-flop 185 and as flags 165 and 167 close, a positive signal is similarly generated by photosensor 182 to activate the set side of flip-flop 185. Accordingly, flipflop 185 is activated for the period between the closing of such sets of flags. On the other hand, the opening of flags 164 and 166, and 165 and 167, during the upstroke of base leg 116, generates a falling edge, or negative signal, from photosensors 181 and 182, respectively, which similarly activates flip-flop 186 through inverters 188 and 189. Accordingly, flip-flop 186 is activated for the period between the opening of one set of such flags and the other set. The outputs from flip-flop 185 and 186 are provided, through resistors 195 and 196, respectively, to the inputs of differential integrator 198. Integrating capacitor 200 is provided in association with resistor 195, while integrating capacitor 201 is provided in association with resistor 196 at such inputs to provide integrating capacity.

Output signal B from differential integrator 198 thus depends on the periods of activation of flip-flops 185 and 186. In the event that base leg 116 is merely oscillating without distortion, the time differences between the opening and closing of the flags will be substantially constant and the inputs to differential integrator 198 essentially identical, thereby providing no signal B. On the other hand, in the event Coriolis forces are generated, base leg 116 will be distorted in a clockwise direction on one stroke of the oscillation, and in a counter clockwise direction on the other stroke. Thus, the closing on one side of the flags will be early on one stroke and late on the other, while the other set of flags will be late on the first stroke and early on the other. The activation of flipflops 185 and 186 therefore will not be for equal lengths of time, and differential integrator 198 will output an appropriate DC signal B of a desired plus or minus sense depending upon the phase of the distortion of base leg 116 relative to the up/down stroke.

Another arrangement to provide the same result is shown in FIG. 12. As shown, strain gages 204 and 205 are mounted adjacent the intersection of inlet leg 108 and base leg 116, and outlet leg 109 and base leg 116, respectively. Strain gages 204 and 205, which may be viewed as variable resistors dependent upon the distortion of the adjacent portion of "U" shaped conduits 104, are connected with resistors 207 and 208 to form a bridge circuit communicating with a voltage source as indicated, and connected to AC differential amplifier 210. In the case of simple oscillation of "U" shaped conduit 104, the resistivity of strain gages 204 and 205 vary equally thereby providing essentially identical inputs to AC differential amplifier 210. However, in the event of distortion due to Coriolis forces, one of strain gages 204 and 205 will increase in resistivity while the other decreases thereby providing different inputs to AC differential amplifier 210 and providing an output in the form of an AC signal proportional in magnitude and sense to the different strains imposed upon strain gages 204 and 205.

The output from AC differential amplifier 210 is provided to synchronous demodulator 211, which, in conjunction with signal A, provides a DC output proportional in magnitude and sense to the distortion of "U" shaped conduit 104 as a result of Coriolis forces. Synchronous demodulator 211 is similar to above-described synchronous demodulator 162, which will be described in more detail with reference to FIG. 14.

A somewhat similar arrangement for generating signal B is illustrated in FIG. 13. In this instance, however, pivot member 215 is mounted centrally on base leg 116 and carries inertia bar 217 which is free to rotate around pivot member 215 and balanced thereon. Crystals 219 and 220 are connected between inertia bar 217 and base leg 116. Thus, if base leg 116 undergoes simple oscillation, inertia bar 217 merely follows the oscillation without a tendency to rotate around pivot member 215. However, in the event of distortion of "U" shaped conduit 104 as a result of Coriolis forces, base leg 116 tends to rotate relative to inertia bar 217, thereby imposing forces in opposite directions upon crystal crystals 219 and 220 and thus generating, as a result of piezoelectric effect, signals from crystals 219 and 220. The outputs from crystals 219 and 220 are connected to AC differential amplifier 222, which in turn is connected to synchronous demodulator 224 to provide, in conjunction with signal A, a DC signal B of a magnitude and sense proportional to the distortion of "U" shaped conduit 104. It is to be understood, of course, that a voltage source and strain gages could be conveniently employed in place of crystals 219 and 220.

Synchronous demodulator 162, described above with reference to FIG. 10, and accordingly, similar to synchronous demodulators 211 and 224, is described in more detail at FIG. 14. As shown, input signal in the form of an AC signal is provided at input line 225 to the primary winding 227 of a transformer. Secondary windings 228, having a common ground, are, as indicated by the polarity, wound in opposite directions. Thus, the output from the opposed ends of secondary windings 228 will be out of phase by 180°. Switching means, in the form of FET transistors 230 and 231 are provided in the outputs from secondary windings 228. Comparator 233, which is connected to signal A, outputs positive or negative signals depending upon the relationship of signal A to reference voltage VR₃. The output of comparator 233 thus is a square wave signal of positive or negative sense, and is provided to inverter 235 which inverts the signal. Thus, one portion of the square wave signal turns on switching means 230 while switching means 231 is turned off, and the other portion turns on switching means 231 while switching means 230 is off. Accordingly, the portion of input signal 225 which is in phase with signal A is provided to RC circuit 237 formed of resistor 238 and capacitor 239 which outputs a DC signal which is proportional to the root mean square of the input to filter 237. This DC output constitutes the readout as described above, i.e., a DC signal proportional to the mass flow through "U" shaped conduit 104.

In summary, flow meter 100 described above, utilizes deflection sensors 133 and 134 to detect the magnitude and sense of small, incipient deflections of "U" shaped conduit 104 due to Coriolis force and generate a DC signal of a sense and magnitude proportional to such deflection. The DC signal, signal B, is in essence a feedback signal which regulates the nulling force generated by force coils 131 and 132 to produce a counterforce thus preventing appreciable distortion beyond the incipient sensed distortion. Sense coils 128 and 129, in addition to maintaining the frequency of oscillation of "U" shaped conduit 104 through the drive circuit described above, also provides signal A, a signal in phase with the Coriolis forces thus providing for proper modulation of force coils 131 and 132, proper synchronization of the output of AC amplifier 135 to drive "U" shaped conduit 104 and proper demodulation of the synchronous signal of force coils 131 and 132 to produce a DC output proportional to mass flow rate.

Though the two generally preferred means for measuring the Coriolis forces are described in detail above, i.e., allowing resilient deflection of the conduit and measuring the deflection, or nulling the force to preclude deflection and measuring the nulling force, numerous other generally less desirable means exist. In any event, by using a solidly mounted "U" shaped conduit essentially free of pressure sensitive joints or pivot means, oscillation and deflection may be readily accomplished and mass flow determined over wide pressure ranges.

Although only limited preferred embodiments of the invention have been illustrated and described, it is anticipated that various changes and modifications will be apparent to those skilled in the art, and that such changes may be made without departing from the scope of the invention as defined by the following claims.

Claims

1. A flow meter for flowable materials comprising:

(1) a support;

(2) a "U" shaped, continuous conduit which

(i) is free of pressure sensitive joints,

(ii) is solidly mounted at the open end ends of the "U" to the support,

(iii) and extending therefrom in a nonarticulated, extends from the support in a cantilevered fashion;,

(iv) has an oscillation axis, passing through the side legs thereof substantially at the points of solid mounting and parallel to the support, about which the conduit may be rotated relative to the support and a deflection axis positioned in the plane of the conduit substantially equidistant between and parallel to the side legs of said conduit and extending perpendicularly through the oscillation axis,

(v) exhibits a different resonant frequency about each of the respective axes;

(3) means for oscillating the conduit relative to the support on either side of the static plane of the "U" shaped conduit and about a first said oscillation axis; and

(4) means to measure the magnitude of Coriolis forces tending to elastically distort the "U" shaped conduit around a second about the deflection axis positioned substantially equidistant between the side legs of the "U" shaped conduit and through the oscillation axis thereof;

whereby the rate of mass flow of the flowable material may be is determined by from the magnitude of the said Coriolis forces tending to deflect the "U" shaped conduit around the second deflection axis.

2. A flow meter as set forth in claim 1 5 in which the "U" shaped conduit is oscillated about its oscillation axis at constant frequency and the means to measure the magnitude of Coriolis forces comprise means to measure the angular deflection of the "U" shaped conduit as a result of elastic deformation of the "U" shaped conduit around a second about the deflection axis positioned substantially equidistant between the conduit side legs;

whereby the rate of mass flow of the flowable material may be is determined by the degree of deflection of the "U" shaped conduit around the second axis about the deflection axis.

3. A flow meter as set forth in claim 2 1 in which the resonant frequency of the "U" shaped conduit around about the first oscillation axis is lower than the resonant frequency of the "U" shaped conduit around about the second deflection axis.

4. A flow meter as set forth in claim 2 1 in which the means for oscillating the conduit comprise a magnet mounted on the "U" shaped conduit, a sensor coil mounted adjacent the magnet, a force coil mounted adjacent the magnet, and means to supply an electrical current to the force coil in response to a signal from the sensor coil.

5. A flow meter as set forth in claim 4 in which the oscillation means further comprise means to identify the peak amplitude of the signal generated by the sensor coil as a result of relative movement between the sensor coil and the magnet and to output current to the force coil such that a preselected amplitude of oscillation is maintained.

6. A flow meter as set forth in claim 2 in which the "U" shaped conduit has attached thereto at the oscillation axis a 1 wherein the oscillation means includes a suitably mounted spring arm having a natural resonant frequency substantially equal to that of the "U" shaped conduit.

7. A flow meter as set forth in claim 6 in which a sensor coil and force coil are carried on the spring arm or the conduit, and a magnet positioned adjacent both the sensor coil and force coil is carried on the other, with whereby the magnet, sensor coil and force coil in conjunction with amplifying and peak detector means comprising comprise the means for oscillating the conduit around the first and spring arm out of phase with each other about the oscillation axis.

8. A flow meter as set forth in claim 2 1 in which the means to measure the mass flow rate comprise first and second sensors are mounted adjacent the "U" shaped conduit at symmetrical positions relative to the second deflection axis and substantially at the mid-point midpoint of oscillation of the conduit, each sensor being adapted to output a signal as the adjacent portion of the "U" shaped conduit passes through the mid-plane of oscillation, and further including means for measuring the time lag between signal outputs by the sensors may be thereby establishing the degree of deflection of the "U" shaped conduit whereby the rate of mass flow is determined as a directly proportional function of said time lag.

9. A flow meter as set forth in claim 8 in which time lag measurement means subtracts subtract the time lags lag in one direction of conduit oscillation from that of in the other direction of conduit oscillation.

10. A flow meter as set forth in claim 8 in which the output outputs from the first and second sensors are each electrically connected to a pair of inverters in series, the outputs of the first inverters in each series being are connected one each to the set and reset inputs of a first flip-flip flip-flop and the outputs of the second inverters in each series being are connected one each to the set and reset inputs of a second flip-flop, first and second logic gates, the output from the first flip-flop being is connected to an one input of the a first logic gate and the output of the second flip-flop being is connected to an one input of the a second logic gate, an oscillator connected to inputs of both the first and second logic gates, the other inputs of both the first and second logic gates are connected to an oscillator, the output of the first logic gate being is connected to one clock input of an up-down counter, and the output of the second logic gate being is connected to the other input of the up-down counter, whereby the up-down counter is activated as a function of the time differential of activation of the first and second sensors with upcount up-count being provided in one direction of the conduit oscillation and downcount the down-count being provided in the opposite direction of conduit oscillation, thereby providing a determination of the deflection of the "U" shaped conduit as a function of the absolute count therein .

11. A flow meter as set forth in claim 10 further including means for transferring and displaying the output from the up-down counter to a display register upon the occurrence of "N" oscillations of the "U" shaped conduit as a readout of the mass flow rate therethrough and also including means for resetting the up-down counter after transfer to of the up-down counter output to the display register.

12. A flow meter as set forth in claim 10 further including a fixed frequency oscillator and in which wherein the output of the updown up-down counter is connected to a digital integrator, the digital integrator also being connected to the output of the fixed frequency oscillator, the integrated output of the integrator being derives a time base from a fixed frequency oscillator, and the output of the digital integrator is connected to a display readout of total mass flow, and further including means for resetting, latching and displaying the output from the digital integrator upon the occurrence of the "N" oscillations of the conduit.

13. A flow meter as set forth in claim 2 8 including means for measuring the time period of oscillation of the "U" shaped conduit and displaying the time period as a related function of the density of a fluid flowing through the "U" shaped conduit.

14. A flow meter as set forth in claim 1 in which the means for oscillating the conduit cause oscillation at constant frequency and amplitude and the means to measure the magnitude of Coriolis forces comprise:

means to sense distortion of the "U" shaped conduit around about the second deflection axis positioned substantially equidistant between the side legs of the "U" shaped conduit;

means responsive to the distortion sensing means to generate a counter force to limit the distortion to but a small, an incipient distortion; and

means to measure the counter force;

whereby the rate of mass flow of the flowable material may be is determined by the magnitude of the counterforce.

15. A flow meter as set forth in claim 14 in which the means to sense distortion of the "U" shaped conduit around a second about the deflection axis comprise centerline crossing sensors positioned one each adjacent the side legs of the "U" shaped conduit at substantially the midpoint of the oscillation around the first about the oscillation axis.

16. A flow meter as set forth in claims claim 15 in which the centerline crossing sensors each comprise a pair of flags, one fixedly mounted and the other attached to the a side leg of the "U" shaped conduit and adapted to overlap the fixed flag at about the midpoint of the oscillation, a light source mounted on one side of the flags, and a photosensitive detector mounted on the other side of the flags whereby the centerline crossing may be detected by blocking the light source from the photosensitive detector by the flags.

17. A flow meter as set forth in claim 14 in which the means to detect distortion of the "U" shaped conduit about the deflection axis comprise a pair of strain gages attached one each to the "U" shaped conduit adjacent each intersection of the side legs and base leg of the "U" shaped conduit, the strain gages forming a bridge circuit means having a signal output proportional to the distortion of the "U" shaped conduit around the second about the deflection axis.

18. A flow meter as set forth in claim 14 in which the means to sense distortion of the "U" shaped conduit about the deflection axis comprise an enertia inertia bar symetrically symmetrically and pivotally mounted at about the mid-point midpoint of the base leg of the "U" shaped conduit, and a pair of force sensing means connected one each between each end of the inertia bar and the adjacent portions of the base leg of the "U" shaped conduit.

19. A flow meter as set forth in claim 18 in which the force sensing means comprise crystals adapted to output an electrical signal when a force is imposed thereon.

20. A flow meter as set forth in claim 18 19 in which the crystals are included in a bridge circuit adapted to output a signal of magnitude and sense proportional to the strain imposed on the crystals by the inertia bar and adjacent "U" shaped conduit.

21. A flow meter as set forth in claim 14 in which the means responsive to the distortion sensing means comprise a pair of force coils and a pair of associated magnets, one pair being mounted fixedly and the other pair being mounted to the "U" shaped conduit, and means to provide a signal to the force coils to induce a torque around the second about the deflection axis of the "U" shaped conduit as one force coil attracts an associated magnet and the other force coil repels the associated magnet.

22. A flow meter as set forth in claim 21 in which the force coils are connected in series but with opposite polarity and the signal thereto is generated by a differential amplifier responsive to the magnitude of the distortion sensed by the distortion sensing means.

23. A flow meter as set forth in claim 21 in which a synchronous demodulator is included with one input thereto being the signal provided to the force coils and a second signal input thereto being a signal varying with generated by the oscillation of the "U" shaped conduit, and the output being the portion of the two input signals in phase with one another is a direct current signal proportional to mass flow rate.

24. A flow meter for flowable materials comprising:

(1) a support;

(2) a continuous joint-free conduit fixedly attached to the support at the inlet and outlet ends of the conduit and extending directly from the support in a cantilevered, nonarticulated manner around an axis of symmetry substantially midway between the inlet and outlet of the conduit and in the plane of the conduit; a continuous conduit which

(i) is free of pressure sensitive joints,

(i) is fixedly attached to the support at the inlet and outlet ends of the conduit,

(iii) extends from the support in a cantilevered fashion,

(iv) is mounted about an axis of symmetry located substantially midway between the inlet and outlet ends of the conduit and transverse to an oscillation axis, said oscillation axis passing through the side legs of the conduit substantially at the points of solid mounting and parallel to the support, and both axes being in the plane of the conduit, and

(v) exhibits a different resonant frequency about each of the respective axes;

(3) means for oscillating the conduit around an about the oscillation axis transverse to the axis of symmetry; and

(4) means for measuring the angular displacement of the conduit as a result of elastic deformation of the conduit around the axis of symmetry thereof upon oscillation of the conduit with fluid flow therethrough;

whereby the rate of mass flow through the conduit may be is determined as a function of the angular displacement of the conduit around about the axis of symmetry.

25. A flow meter as set forth in claim 24 in which said continuous conduit is oscillated about the oscillation axis at constant frequency and amplitude and the means to measure angular deflection of the conduit comprise first and second sensors positioned adjacent opposite sides of the conduit at a plane positioned at the mid-point midpoint of oscillation thereof, and further includes means for measuring the time differential of passage of the corresponding portions of the conduit past the first sensor and the second sensor.

26. A flow meter as set forth in claim 24 in which a spring arm having a resonant frequency substantially the same as the resonant frequency of the conduit around about the oscillation axis thereof is attached to the conduit between the inlet and outlet ends thereof adjacent the support.

27. A flow meter as set forth in claim 24 in which the resonant frequency of the conduit around about the oscillation axis is lower than the resonant frequency of the conduit around about the axis of symmetry thereof.

28. A flow meter for flowable materials comprising;:

(1) a support;

a continuous joint-free conduit fixedly attached to the support at the inlet and outlet ends of the conduit and extending directly from the support in a cantilevered, nonarticulated manner around an axis of symmetry substantially midway between the inlet and outlet of the conduit and in the plane of the conduit;

(2) a continous conduit which

(i) is free of pressure sensitive joints,

(ii) is fixedly attached to the support at the inlet and outlet ends of the conduit,

(iii) extends from the support in a cantilevered fashion,

(iv) is mounted about an axis of symmetry located substantially midway between the inlet and outlet ends of the conduit and transverse to an oscillation axis, said oscillation axis passing through the side legs of the conduit substantially at the points of solid mounting and parallel to the support, and both axes being in the plane of the conduit, and

(v) exhibits a different resonant frequency about each of the respective axes;

(3) means for oscillating the conduit around an about the oscillation axis transverse to the axis of symmetry, the oscillation being at a predetermined frequency; at a constant frequency and amplitude;

(4) means to sense incipient angular displacement of the conduit around about the axis of symmetry thereof upon oscillation of the conduit with fluid flow therethrough;

(5) means responsive to the incipient angular displacement sensing means to generate a nulling force to limit elastic deformation of the conduit around about the axis of symmetry to small increments; and

(6) means to measure the nulling force;

whereby mass flow to rate through the conduit may be is determined as a function of the magnitude of the nulling force.

29. A flow meter as set forth in claim 28 in which the conduit is "U" shaped and the deflection measuring means comprise centerline crossing detectors positioned one each adjacent the intersections of the side legs and base leg of the "U" shaped conduit.

30. A flow meter as set forth in claim 28 in which a spring arm having a resonant frequency substantially the same as the resonant frequency of the conduit around about the oscillation axis thereof is attached to the conduit between the inlet and outlet ends at the oscillation axis and the means for oscillating the conduit around and spring arm about the oscillation axis transverse to the axis of symmetry are carried on the spring arm and the adjacent portion of the "U" shaped conduit.

31. A flow meter as set forth in claim 28 in which the resonant frequency of the conduit around about the oscillation axis is higher than the resonant frequency of the conduit around about the axis of symmetry thereof.

32. A flow meter for flowable materials comprising:

a support;

a "U" shaped conduit mounted at the open end ends of the "U" to the support and extending therefrom in a cantilevered fashion;

means for oscillating the conduit relative to the support on either side of the static plane of the "U" shaped conduit and about a first oscillation axis;

first and second sensors mounted adjacent the "U" shaped conduit at symmetrical positions relative to a second deflection axis positioned substantially equidistant between the side legs of, and in the same plane as, the "U" shaped conduit and through the oscillation axis thereof, the sensors being positioned substantially at the midpoint of oscillation of the "U" shaped conduit and each sensor being adapted to output a signal as the adjacent portion of the "U" shaped conduit passes the sensor; and

means for measuring the time lag between the signal outputs by the sensors thereby establishing the degree of deflection of the "U" shaped conduit. mass flow rate through the "U" shaped conduit.

33. A flow meter as set forth in claim 32 in which time lag measurement means subtracts the time lags in one direction of conduit oscillation from that of in the other direction of conduit oscillation.

34. A flow meter as set forth in claim 32 in which the output from the first and second sensors are each electrically connected to a pair of invertors inverters in series, the outputs of the first invertors inverters in each series being are connected one each to the set and reset inputs of a first flip-flop and the outputs of the second inverters in each series being are connected one each ot to the set and reset inputs of a second flip-flop, first and second logic gates, the output from the first flip-flop being is connected to an one input of the a first logic gate and the output of the second flip-flop being is connected to inputs of both the first and second logic gates, one input of a second logic gate, the other inputs of both the first and second logic gates are connected to an oscillator, the output of the first logic gate being is connected to one clock input of an up-down counter, and the output of the second logic gate being is connected to the other input of the up-down counter, whereby the up-down counter is activated as a function of the time differential of activation of the first and second sensors with upcount up-count being provided in one direction of the conduit oscillation and the downcount down-count being provided in the opposite direction of conduit oscillation, thereby providing a determination of the deflection of the "U" shaped conduit as a function of the absolute count therein.

35. A flow meter as set forth in claim 34 further including means for transferring and displaying the output from the up-down counter to a display register upon the occurrence of "N" oscillations of the "U" shaped conduit as a readout of the mass flow rate therethrough and also including means for resetting the updown up-down counter after transfer of the updown up-down counter output from to the display register.

36. A flow meter as set forth in claim 34 further including a fixed frequency oscillator and in which wherein the output of the updown up-down counter is connected to a digital integrator, the digital integrator also being connected to the output of the fixed frequency oscillator, the integrated output of the integrator being derives a time base from a fixed frequency oscillator, and the output of the digital integrator is connected to a display for readout of total mass flow, and further including means for resetting, latching and displaying the output from the digital integrator upon the occurence of "N" oscillations of the conduit.

37. A flow meter as set forth in claim 32 in which the means for oscillating the conduit cause oscillation at constant frequency and amplitude and means are present for generating a counterforce in response to the force generating the Coriolis force-generated deflection of the "U" shaped conduit are indicated to limit the such deflection to a small, unapparent an incipient deflection, and the mass flow rate is measured by determining the magnitude of the counterforce.

38. A flow meter for flowable materials comprising:

a support;

a continuous conduit attached to the support at the inlet and outlet ends of the conduit and extending from the support in a cantilevered manner around an axis of symmetry substantially midway between the inlet and outlet of the conduit and in the plane of the conduit;

means for oscillating the conduit around an oscillation axis substantially transverse to the axis of symmetry; first and second sensors positioned adjacent opposite sides of the conduit at a point positioned at the midpoint of oscillation thereof; and

further means for measuring the time differential of passage of the corresponding symmetrically opposite portions of the conduit past the first sensor and the second sensor.

39. A flow meter as set forth in claim 38 in which time differential measurement means subtracts the time differentials in one direction of conduit oscillation from the time differentials in the other direction of conduit oscillation.

40. A flow meter as set forth in claim 39 in which the means for oscillating the conduit cause oscillation at constant frequency and amplitude and means are present to produce a nulling force to limit the time differential of passage of the opposite sides of the conduit through the midpoint of oscillation to that having a minimum deviation from the time differential of passage of an undistorted "U" shaped conduit, are included of a conduit free from deflection about the axis of symmetry caused by Coriolis forces, and the mass flow rate is measured by determining the magnitude of the nulling force.

41. A method of measuring flow of a material comprising:

(1) flowing the material through a continuous, joint-free curved conduit free of pressure-sensitive joints, with the inlet and outlet portions thereof solidly connected in a cantilevered, beamlike fashion to a support;, which conduit

(i) is mounted about an axis of symmetry located substantially midway between the inlet and outlet ends of the conduit and transverse to an oscillation axis, said oscillation axis passing through the side legs of the conduit substantially at the points of solid mounting and parallel to the support, and both axes being in the plane of the conduit, and

(ii) exhibits a different resonant frequency about each of the respective axes;

(2) oscillating the conduit substantially around an axis transverse to the inlet and outlet portions thereof; about the oscillation axis; (3) generating Coriolis forces in the curved conduit as a result of material flow through the oscillating conduit; and

(4) measuring the magnitude of the Coriolis forces tending to deform the conduit around an about the axis of symmetry substantially perpendicular to the oscillation axis of the conduit;

whereby the magnitude of the deforming Coriolis forces indicates the mass flow is a function of the mass flow rate through the conduit.

42. A method of measuring mass flow rate as set forth in claim 41 44 in which the magnitude of Coriolis deforming forces are measured by tending to elastically deforming deform the conduit along the length thereof and around the axis of symmetry substantially perpendicular to the oscillation axis of the conduit; and is determined by

measuring the angular deflection of the conduit around the axis of symmetry;

whereby the angle of deflection indicates the is a function of mass flow rate through the conduit.

43. A method of measuring mass flow rate as set forth in claim 42 in which the angle of deflection is determined by measuring the time differential between passage of one portion of the conduit through a plane substantially at the midpoint of the oscillation and the passage of a symmetrically opposite second portion of the conduit through such plane.

44. A method of measuring mass flow rate as set forth in claim 42 41 in which the conduit is oscillated at the resonant frequency of the conduit and material therein. and at constant amplitude.

45. A method of measuring mass flow rate as set forth in claim 42 41 in which a spring arm having a resonant frequency substantially identical to that of the conduit is attached to the conduit adjacent the inlet and outlet portions thereof and oscillated out of phase with the conduit.

46. A method of measuring mass flow rate as set forth in claim 42 in which the deforming magnitude of Coriolis forces are is measured by sensing incipient distortion of the conduit around about the axis of symmetry substantially perpendicular to the oscillation axis of the conduit;

generating a force opposing the deforming Coriolis forces in response to the sensed incipient distortion to limit the distortion to the incipient distortion; and

measuring the magnitude of opposing force to determine mass flow rate.

47. A method of measuring mass flow rate as set forth in claim 46 in which the incipient distortion is detected by measuring the time differential between passage of one portion of the conduit through a plane substantially at the midpoint of the oscillation and the passage of a symmetrically opposite second portion of a conduit through such plane.

48. A method for of measuring mass flow rate as set forth in claim 46 in which the incipient distortion is detected by strain gages mounted on the conduit at positions symmetrical relative to the axis of symmetry.

49. A method of measuring mass flow rate as set forth in claim 46 in which the incipient distortion of the conduit is detected by crystals mounted between the conduit and an inertia bar pivotally mounted to the conduit at the axis of symmetry, the crystals being positioned symmetrically relative to the axis of symmetry of the conduit.

50. A method of measuring mass flow set forth in claim 46 in which the conduit

is oscillated at a predetermined amplitude. 51. A method for measuring mass flow rate of a material comprising:

flowing the material through a "U" shaped conduit;

oscillating the conduit around about an axis of oscillation passing through the legs of the conduit at substantially equal right angles; and

measuring the forces tending to deflect the "U" shaped conduit around a deflection axis perpendicular to the oscillation axis and symmetrical to the conduit material mass flow rate by determining the time lag between the passage of one side of the conduit through a plane substantially at the midpoint of oscillation and the passage of the other

side of the conduit through such plane. 52. A method for measuring material mass flow rate as set forth in claim 51 in which the time lags are measured in both directions of conduit oscillation and time lags lag in one direction of conduit oscillation is subtracted from time lags lag in the opposite direction of conduit oscillation.

53. A method for measuring material flow as set forth in claim 52 in which the "U" shaped conduit deflects around the deflection axis and the material flow

is measured by determining the net time lags. 54. A method for measuring material mass flow rate as set forth in claim 52 in which the "U" shaped conduit is oscillated at a constant amplitude and frequency and the magnitude of forces, resulting from the conduit oscillation and fluid flow, tending to deflect the "U" shaped conduit are measured by generating counterforces thereto in response to the net time lags measured to minimize the time lags, and determining the magnitude of the counterforces to establish the material mass flow

rate. 55. A method for measuring material mass flow rate as set forth in claim 54 51 in which the "U" shaped conduit is oscillated at a substantially constant amplitude at resonant frequency.

56. A flow meter as set forth in claim 32 in which the resonant frequency of the "U" shaped conduit about said first oscillation axis is lower than the resonant frequency of the "U" shaped conduit about said second deflection axis.

57. A flow meter as set forth in claim 38 in which the resonant frequency of the continuous conduit about said oscillation axis is lower than the resonant frequency of the continuous conduit about said axis of symmetry.