Method and structure for flow measurement

• US RE31,450 E
• Filed: 02/11/1982
• Issued: 11/29/1983
• Est. Priority Date: 07/25/1977
• Status: Expired due to Term

• Current Assignee: Micro Motion Incorporated (Emerson Electric Company)
• Original Assignee: Micro Motion Incorporated (Emerson Electric Company)
• Inventors: Smith, James E.
• Primary Examiner(s): MYRACLE, JERRY
• Application Number:
  US06/348,071
• Time in Patent Office: 656 Days
• Field of Search: 73/32 A, 73/434, 73/505, 73/861.18, 73/861.35, 73/861.37, 73/861.38
• US Class Current: 73/861.356
• CPC Class Codes: G01F 1/8413 means for influencing the flowmeter's motional or vibrational behaviour, e.g., conduit support or fixing means, or conduit attachments
• CPC Class Codes: G01F 1/8431 electronic circuits
• CPC Class Codes: G01F 1/8472 having curved measuring conduits, i.e. whereby the measuring conduits' curved center line lies within a plane G01F1/8481 takes precedence

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.]. .Iadd.so that, when the conduit is oscillated, sensors mounted on the conduit can measure .Iaddend.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.]. .Iadd.embodiment .Iaddend.the measuring .[.means are sensors.]. .Iadd.sensors are .Iaddend.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.

Claims

1. A flow meter for flowable materials comprising:

(.Iadd.1.Iaddend.) a support;

(.Iadd.2.Iaddend.) a "U" shaped, continuous conduit .Iadd.which

(i) is free of pressure sensitive joints,

(ii) is .Iaddend.solidly mounted at the open .[.end.]. .Iadd.ends .Iaddend.of the "U" to the support.Iadd.,

(iii.Iaddend.) .[.and extending therefrom in a nonarticulated,.]. .Iadd.extends from the support in a .Iaddend.cantilevered fashion.[.;

.]..Iadd.,

(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.Iaddend.) 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.]. .Iadd.said .Iaddend.oscillation axis; and

(.Iadd.4.Iaddend.) means to measure the .Iadd.magnitude of .Iaddend.Coriolis forces tending to elastically distort the "U" shaped conduit .[.around a second.]. .Iadd.about the .Iaddend. 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.]. .Iadd.is .Iaddend.determined .[.by.]. .Iadd.from .Iaddend.the magnitude of .[.the.]. .Iadd.said Coriolis .Iaddend.forces .[.tending to deflect the "U" shaped conduit around the second deflection axis.]..

2. A flow meter as set forth in claim .[.1.]. .Iadd.5 .Iaddend.in which the .Iadd."U" shaped conduit is oscillated about its oscillation axis at constant frequency and the .Iaddend.means to measure .Iadd.the magnitude of .Iaddend.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.]. .Iadd.about the .Iaddend.deflection axis .[.positioned substantially equidistant between the conduit side legs.].;

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

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

4. A flow meter as set forth in claim .[.2.]. .Iadd.1 .Iaddend.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.]. .Iadd.1 wherein the oscillation means includes a suitably mounted .Iaddend.spring arm having a natural resonant frequency substantially .Iadd.equal to .Iaddend.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.]. .Iadd.whereby .Iaddend.the magnet, sensor coil and force coil in conjunction with amplifying and peak detector means .[.comprising.]. .Iadd.comprise .Iaddend.the means for oscillating the conduit .[.around the first.]. .Iadd.and spring arm out of phase with each other about the .Iaddend.oscillation axis.

8. A flow meter as set forth in claim .[.2.]. .Iadd.1 .Iaddend.in which .Iadd.the means to measure the mass flow rate comprise .Iaddend.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.]. .Iadd.midpoint .Iaddend.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.]. .Iadd.whereby the rate of mass flow is determined as a directly proportional function of said time lag.Iaddend..

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

10. A flow meter as set forth in claim 8 in which the .[.output.]. .Iadd.outputs .Iaddend.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.]. .Iadd.are .Iaddend.connected one each to the set and reset inputs of a first .[.flip-flip.]. .Iadd.flip-flop .Iaddend.and the outputs of the second inverters in each series .[.being.]. .Iadd.are .Iaddend.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.]. .Iadd.is .Iaddend.connected to .[.an.]. .Iadd.one .Iaddend.input of .[.the.]. .Iadd.a .Iaddend.first logic gate and the output of the second flip-flop .[.being.]. .Iadd.is .Iaddend.connected to .[. an.]. .Iadd.one .Iaddend.input of .[.the.]. .Iadd.a .Iaddend.second logic gate, .[.an oscillator connected to inputs of both the first and second logic gates,.]. .Iadd.the other inputs of both the first and second logic gates are connected to an oscillator, .Iaddend.the output of the first logic gate .[.being.]. .Iadd.is .Iaddend.connected to one clock input of an up-down counter, and the output of the second logic gate .[.being.]. .Iadd.is .Iaddend.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.]. .Iadd.up-count .Iaddend.being provided in one direction of .[.the.]. .Iadd.conduit .Iaddend.oscillation and .[.downcount.]. .Iadd.the down-count .Iaddend.being provided in the opposite direction of .Iadd.conduit .Iaddend.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 .Iadd.rate .Iaddend.therethrough and also including means for resetting the up-down counter after transfer .[.to.]. .Iadd.of .Iaddend.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.]. .Iadd.wherein .Iaddend.the output of the .[.updown.]. .Iadd.up-down .Iaddend.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.]. .Iadd.derives a time base from a fixed frequency oscillator, and the output of the digital integrator is .Iaddend.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.]. .Iadd.8 .Iaddend.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 .Iadd.for oscillating the conduit cause oscillation at constant frequency and amplitude and the means .Iaddend.to measure .Iadd.the magnitude of .Iaddend.Coriolis forces comprise:

means to sense distortion of the "U" shaped conduit .[.around.]. .Iadd.about .Iaddend.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,.]. .Iadd.an .Iaddend.incipient distortion; and

means to measure the counter force;

whereby the rate of mass flow of the flowable material .[.may be.]. .Iadd.is .Iaddend.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.]. .Iadd.about the .Iaddend.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.]. .Iadd.about the .Iaddend.oscillation axis.

17. A flow meter as set forth in claim 14 in which the means to detect distortion of the "U" shaped conduit .Iadd.about the deflection axis .Iaddend.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.]. .Iadd.about the .Iaddend.deflection axis.

18. A flow meter as set forth in claim 14 in which the means to sense distortion of the "U" shaped conduit .Iadd.about the deflection axis .Iaddend.comprise an .[.enertia.]. .Iadd.inertia .Iaddend.bar .[.symetrically.]. .Iadd.symmetrically .Iaddend.and pivotally mounted at about the .[.mid-point.]. .Iadd.midpoint .Iaddend.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.]. .Iadd.19 .Iaddend.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.]. .Iadd.about the .Iaddend.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 .Iadd.to .Iaddend.the force coils and a second .[.signal.]. .Iadd.input thereto .Iaddend.being a signal .[.varying with.]. .Iadd.generated by .Iaddend.the oscillation of the "U" shaped conduit, and the output .[.being the portion of the two input signals in phase with one another.]. .Iadd.is a direct current signal proportional to mass flow rate.Iaddend..

16. A flow meter as set forth in .[.claims.]. .Iadd.claim .Iaddend.15 in which the centerline crossing sensors each comprise a pair of flags, one fixedly mounted and the other attached to .[.the.]. .Iadd.a .Iaddend.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.

24. A flow meter for flowable materials comprising:

(.Iadd.1.Iaddend.) a support;

(.Iadd.2.Iaddend.) .[.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;

.]. .Iadd.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;

.Iaddend.

(.Iadd.3.Iaddend.) means for oscillating the conduit .[.around an.]. .Iadd.about the .Iaddend.oscillation axis .[.transverse to the axis of symmetry.].; and

(.Iadd.4.Iaddend.) 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 .Iadd.the rate of .Iaddend.mass flow through the conduit .[.may be.]. .Iadd.is .Iaddend.determined as a function of the angular displacement of the conduit .[.around.]. .Iadd.about .Iaddend.the axis of symmetry.

25. A flow meter as set forth in claim 24 in which .Iadd.said continuous conduit is oscillated about the oscillation axis at constant frequency and amplitude and .Iaddend.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.]. .Iadd.midpoint .Iaddend.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.]. .Iadd.about .Iaddend.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.]. .Iadd.about .Iaddend.the oscillation axis is lower than the resonant frequency of the conduit .[.around.]. .Iadd.about .Iaddend.the axis of symmetry .[.thereof.]..

28. A flow meter for flowable materials comprising.[.;

.]..Iadd.;

(1.Iaddend.) 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;

.].

(.Iadd.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) .Iaddend.means for oscillating the conduit .[.around an.]. .Iadd.about the .Iaddend.oscillation axis .[.transverse to the axis of symmetry, the oscillation being at a predetermined frequency;

.]. .Iadd.at a constant frequency and amplitude;

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

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

(.Iadd.6) .Iaddend.means to measure the nulling force;

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

29. A flow meter as set forth in claim 28 in which .Iadd.the conduit is "U" shaped and .Iaddend.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.]. .Iadd.about .Iaddend.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.]. .Iadd.and spring arm about .Iaddend.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.]. .Iadd.about .Iaddend.the oscillation axis is higher than the resonant frequency of the conduit .[.around.]. .Iadd.about .Iaddend.the axis of symmetry thereof.

32. A flow meter for flowable materials comprising:

a support;

a "U" shaped conduit mounted at the open .[.end.]. .Iadd.ends .Iaddend.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.Iadd., and in the same plane as, .Iaddend.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..]. .Iadd.mass flow rate through the "U" shaped conduit. .Iaddend.

33. A flow meter as set forth in claim 32 in which time lag measurement means subtract.[.s.]. the time lag.[.s.]. in one direction of .Iadd.conduit .Iaddend.oscillation from that .[.of.]. .Iadd.in .Iaddend.the other direction of .Iadd.conduit .Iaddend.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.]. .Iadd.inverters .Iaddend.in series, the outputs of the first .[.invertors.]. .Iadd.inverters .Iaddend.in each series .[.being.]. .Iadd.are .Iaddend.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.]. .Iadd.are .Iaddend.connected one each .[.ot.]. .Iadd.to .Iaddend.the set and reset inputs of a second flip-flop, .[.first and second logic gates,.]. the output from the first flip-flop .[.being.]. .Iadd.is .Iaddend.connected to .[.an.]. .Iadd.one .Iaddend.input of .[.the.]. .Iadd.a .Iaddend.first logic gate and the output of the second flip-flop .[.being.]. .Iadd. is .Iaddend.connected to .[.inputs of both the first and second logic gates,.]. .Iadd.one input of a second logic gate, the other inputs of both the first and second logic gates are connected to an oscillator, .Iaddend.the output of the first logic gate .[.being.]. .Iadd.is .Iaddend.connected to one clock input of an up-down counter, and the output of the second logic gate .[.being.]. .Iadd.is .Iaddend.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.]. .Iadd.up-count .Iaddend.being provided in one direction of .[.the.]. .Iadd.conduit .Iaddend.oscillation and the .[.downcount.]. .Iadd.down-count .Iaddend.being provided in the opposite direction of .Iadd.conduit .Iaddend.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 .Iadd.a .Iaddend.display register upon the occurrence of "N" oscillations of the "U" shaped conduit as a readout of the mass flow .Iadd.rate .Iaddend.therethrough and also including means for resetting the .[.updown.]. .Iadd.up-down .Iaddend.counter after transfer of the .[.updown.]. .Iadd.up-down .Iaddend.counter output .[.from.]. .Iadd.to .Iaddend.the display register.

36. A flow meter as set forth in claim 34 .[.further including a fixed frequency oscillator and in which.]. .Iadd.wherein .Iaddend.the output of the .[.updown.]. .Iadd.up-down .Iaddend.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.]. .Iadd.derives a time base from a fixed frequency oscillator, and the output of the digital integrator is .Iaddend.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 .Iadd.the .Iaddend.means for .Iadd.oscillating the conduit cause oscillation at constant frequency and amplitude and means are present for .Iaddend.generating a counterforce in response to the .[.force generating the.]. .Iadd.Coriolis force-generated .Iaddend.deflection of the "U" shaped conduit .[.are indicated.]. to limit .[.the.]. .Iadd.such .Iaddend.deflection to .[.a small, unapparent.]. .Iadd.an incipient .Iaddend.deflection, and the .Iadd.mass .Iaddend.flow .Iadd.rate .Iaddend.is measured by determining the .Iadd.magnitude of the .Iaddend.counterforce.

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

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.]. .Iadd.symmetrically opposite .Iaddend.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 subtract.[.s.]. the time differential.[.s.]. in one direction of .Iadd.conduit .Iaddend.oscillation from the time differential.[.s.]. in the other direction of .Iadd.conduit .Iaddend.oscillation.

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

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

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

.]..Iadd., 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) .Iaddend.oscillating the conduit .[.substantially around an axis transverse to the inlet and outlet portions thereof;

.]. .Iadd.about the oscillation axis;

(3) .Iaddend.generating Coriolis forces in the curved conduit as a result of material flow through the oscillating conduit; and

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

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

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

.[.and.]. .Iadd.is determined by .Iaddend.

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

whereby the angle of deflection .[.indicates the.]. .Iadd.is a function of .Iaddend.mass flow .Iadd.rate .Iaddend.through the conduit.

43. A method of measuring mass flow .Iadd.rate .Iaddend.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 .Iadd.symmetrically opposite .Iaddend.second portion of the conduit through such plane.

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

45. A method of measuring mass flow .Iadd.rate .Iaddend.as set forth in claim .[.42.]. .Iadd.41 .Iaddend.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 .Iadd.the .Iaddend.conduit.

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

generating a force opposing the .[.deforming.]. .Iadd.Coriolis .Iaddend.forces in response to the sensed incipient distortion to limit the distortion to the incipient distortion; and

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

47. A method of measuring mass flow .Iadd.rate .Iaddend.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 .Iadd.symmetrically opposite .Iaddend.second portion of a conduit through such plane.

48. A method .[.for.]. .Iadd.of .Iaddend.measuring mass flow .Iadd.rate .Iaddend.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 .Iadd.rate .Iaddend.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

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

flowing the material through a "U" shaped conduit;

oscillating the conduit .[.around.]. .Iadd.about .Iaddend.an axis of oscillation passing through the legs of the conduit at substantially .[.equal.]. .Iadd.right .Iaddend.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.]. .Iadd.material mass flow rate .Iaddend.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

52. is measured by determining the net time lags..]. 54. A method for measuring material .Iadd.mass .Iaddend.flow .Iadd.rate .Iaddend.as set forth in claim 52 in which the .Iadd."U" shaped conduit is oscillated at a constant amplitude and frequency and the magnitude of .Iaddend.forces.Iadd., resulting from the conduit oscillation and fluid flow, .Iaddend.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 .Iadd.mass .Iaddend.flow

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