Abstract:
An apparatus for measuring the flow rate of a fluid flowing through a minimal flow pipeline with a Coriolis effect mass flowmeter. The flowmeter has a single flow tube with two loops. The loops are connected by a cross-over section. A driver oscillates the loops and the phase difference between the ends of the loops is measured. The measured phase difference is then used to find the flow rate of the fluid. The flow tube is fixedly attached to an anchor which is, in turn, attached to a housing. The anchor separate the vibrating, dynamic portion of the flowmeter from the non-vibrating portion of the flowmeter.

Description:
FIELD OF THE INVENTION 
     This invention relates to an apparatus for using a Coriolis mass flowmeter what a serial, dual loop, flow tube for measuring the flow rate of a fluid through a pipeline. More particularly, the invention relates to the element used to connect the two loops of the flow tube. Still more particularly, the invention relates to an anchor which connects a flow tube to a flow tube housing 
     PROBLEM 
     It is known to use Coriolis effect mass flowmeters to measure mass flow and other information of materials flowing through a pipeline as disclosed in U.S. Pat. No. 4,491,025 issued to J. E. Smith, et al. of Jan. 1, 1985 and U.S. Pat. No. Re. 31,450 to J. E. Smith of Feb. 11, 1982. These flowmeters have one or more flow tubes of a curved configuration. Each flow tube configuration in a Coriolis mass flowmeter has a set of natural vibration modes, which may be of a simple bending torsional, or coupled type. Each flow tube is driven to oscillate at resonance in one of these natural modes. The natural vibration modes of the vibrating, material filled system are defined in part by the combined mass of the flow tubes and the material within the flow tubes. Material flows into the flowmeter from a connected pipeline on the inlet side of the flowmeter. The material is then directed through the flow tube or flow tubes and exits the flowmeter to a pipeline connected on the outlet side. 
     A driver applies force to oscillate the flow tube. When there is no flow through the flowmeter, all points along a flow tube oscillate with an identical phase. As the material begins to flow, Coriolis accelerations cause each point along the flow tube to have a different phase with respect to other points along the flow tube. The phase on the inlet side of the flow tube lags the driver, while the phase on the outlet side leads the driver. Sensors are placed on the flow tube to produce sinusoidal signals representative of the motion of the flow tube. The phase difference between the two sensor signals is proportional to the mass flow rate of the material flowing through the flow tube or flow tubes. 
     Material flow though a flow tube creates only a slight phase difference on the order of several degrees between the inlet and outlet ends of an oscillating flow tube. When expressed in terms of a time difference measurement, the phase difference induced by material flow is on the order of tens of microseconds down to nanoseconds. Typically, a commercial flow rate measurement should have an error of less the 1%. Therefore, a Coriolis flowmeter must be uniquely designed to accurately measure these slight phase differences. 
     It is known to use a single loop, serial path flow tube to measure the rate of fluid flowing through a pipeline. However, the single loop, serial flow tube design has a disadvantage in that it is inherently unbalanced. A single loop, serial flow Coriolis flowmeter has a single curved tube or loop extending in cantilever fashion from a solid mount. Dual loop Coriolis flowmeters are balanced. A dual loop Coriolis flowmeter has two parallel, curved tubes or loops extending from a solid mount. The parallel flow tubes are driven to oscillate in opposition to one another with the vibrating force of one flow tube canceling out the vibration force of the other flow tube. The result is that in a properly constructed dual loop Coriolis flowmeter there are no flowmeter induced vibrations at the points of attachment between the flowmeter and the pipeline. This is called a “balanced” flowmeter. The absence of vibrations allows dual looped Coriolis flowmeter to be attached free standing to a pipeline. A single loop, serial path Coriolis flowmeter must be secured firmly to a support against which the flow tube can vibrate. The use of a support renders the use of a single loop, serial flow tube design impractical in most industrial applications because the serial flow tube requires that the pipeline be near an object that could be used as a support. Therefore, the dual loop flowmeter designs are desirable. 
     It is a particular problem to measure minimal flow rates of materials flowing through a pipeline. A mass flow rate through a pipeline of less than or substantially equal to 4 lbs. per minute is considered minimal for commercial applications. A Coriolis mass flowmeter measuring such small flow rates must be formed of relatively small components including tubes and manifolds. These relatively small components present a variety of challenges in the manufacturing process including but not limited to difficult welding processes. 
     One solution for measuring minimal flow rates has been to use a single loop, serial flow tube Coriolis effect mass flowmeter. Single loop, serial flow tube Coriolis flowmeters have certain advantages. The flow tube has a larger diameter which reduces pressure drop across the flowmeter. No manifold is necessary to split the flow into two tubes. The larger flow tube is easier to draw and weld. There are also other advantages. The problem is that single loop, serial flow tube flowmeters cannot be mounted free standing into the pipeline since they are not balanced flowmeters. 
     Dual loop, parallel flow tube flowmeters can be mounted freestanding into the pipeline. However, the small size necessary for measuring minimal flow rates creates design and manufacture problems for use of the dual loop, parallel flow tube design. These problems limit the industrial applications of dual loop, dual tube Coriolis flowmeters for measuring minimal flow rates. 
     A particular problem with dual loop, parallel flow tube design is that a manifold must be used to direct the flow entering the inlet end of the flowmeter in order to divide the flow so that it enters the two flow tubes. It is difficult to produce a manifold, by casting or otherwise, in the small dimensions necessary to measure a minimal flow rate. Also, the manifold increases pressure drop across the flowmeter. Further, the flow tubes must be welded or brazed onto the manifold. It is difficult too weld very thin walled tubing. The welds and joints do not provide the smooth surface needed for sanitary applications of the flowmeter. Sanitary applications demand a continuous, smooth flow tube surface that does not promote adhesion of material to the walls of the flow tube. Further, the additional welds that are necessary reduce the manufacturing yield. Therefore, the use of a manifold is not desired in flowmeters designed for measuring minimal flow rates. 
     The smaller diameters of the dual flow tubes make the tubes more prone to plugging. The smaller diameter is needed to assure a sufficient flow rate through the flow tubes. Material is more likely to plug the flow path through these flow tubes because smaller particles in the material can obstruct the smaller flow path. These obstructions can cause inaccurate readings of the flow rate and breakage of the flow tube. Therefore, the dual flow tube design does not offer a satisfactory solution for measuring minimal flow rates. 
     A further problem is that sometimes a Coriolis flowmeter is used to measure flow through a pipeline where the flowing material is pressurized. If a flow tube cracks, the pressured material will rapidly spray from the highly pressurized flow tube to the outside surroundings which have a lower pressure than the flow tube. The pressurized material spraying from the flow tube can damage the pipeline or surrounding structures. 
     SOLUTION 
     The above and other problems are solved by the apparatus of the present invention that comprises a dual loop, serial path flow tube. Each of the loops is oriented in a plane parallel to the plane containing the other loop. The flow tube is enclosed in a housing to which the flow tube is connected through an anchor. The housing can be configured to contain the leakage of pressurized materials from a break in the flow tube. These advantages allow the present invention to be used to measure the flow rates, including minimal flow rates, of material flowing through the pipeline. 
     In the present invention, the dual loops in the serial flow tube are connected by a crossover section. The outlet end of the first loop connects to an inlet end of the crossover section in the plane containing the first loop. The inlet end of the second loop connects to an outlet end of the crossover section in the plane of the second loop. The crossover section of the flow tube allows the present invention to have the advantages of both serial and parallel flow tube designs for measuring minimal flow rates. 
     The present invention has a serial flow tube. Serial flow tube and parallel flow tube flowmeters each have advantages and disadvantages. For the same tube parameters, i.e. inside tube diameter, tube wall thickness, and tube geometry, an oscillating serial flow tube generates more Coriolis force than an oscillating parallel flow tube since all the flow passes through each portion of a serial flow tube instead of only half of the flow passing through each portion of a parallel flow tube. The disadvantage of a serial flow tube is that the pressure drop through a serial flow tube is higher than for a parallel flow tube with the same tube parameters. To reduce pressure drop, a sensor with a serial flow tube typically uses a larger diameter and proportionally thicker flow tube wall to achieve substantially the same pressure drop of a parallel flow tube flowmeter. Therefore, serial path Coriolis flowmeters are inherently larger than parallel path flowmeters. Generally this is a disadvantage for Coriolis flowmeters. However, for minimal flow rate sensors it is an advantage. A flow tube with a greater diameter reduces the probability of particles plugging the flow tube. The joining, by welding or brazing, of a relatively larger diameter, heavier wall flow tube make the flowmeter design of the present invention easier to produce and better suited for sanitary applications. Therefore the flowmeter of the present invention can be used for industrial applications in which a typical dual loop, parallel flow flowmeter cannot be used. 
     The present invention is also an improvement over the dual loop, parallel flow tube flowmeters because the present invention does not need a manifold. Manifolds are needed in dual flow tube designs to divide the flow entering the flowmeter into the two flow tubes. Since the present invention has a serial flow tube, a manifold is not needed to divide the flow. Thus, the flow tube of the present invention is easier to weld as there are fewer welds. 
     The two loops of the flow tube of the present invention are oscillated in opposition to one another. Vibrations caused by the oscillation of the loops are canceled out and do not affect the ends of the flowmeter. Therefore, the flowmeter of the present invention is balanced and does not have to be attached to a support. Thus, the flowmeter of the present invention may be attached freestanding in a pipeline without mounting the flowmeter to a support. 
     The flow tube of the present invention is secured, near the crossover section, by an anchor. The anchor is the solid mounting from which the dual loops of the flow tube extend in cantilever fashion. The anchor is fixed to a flowmeter housing. The inlet and outlet of the flow tube are connected to the housing through an adapter which transitions the fluid from the flow tube to a process connection. The process connections are flanges or the like for connecting the flow tube to the process pipeline. Therefore the flow tube, anchor, and housing share a common physical reference. The housing can be designed to contain the leakage of a pressurized fluid in the case breakage of the flow tube. The anchor connected to the housing and flow tube holds the flow tube securely in place with enough room to oscillate freely inside the housing. The anchor is used to attach the flow tube to the housing to minimize the effect of distortions of the flow tube that would be caused if the flow tube were attached directly to the housing with welds. Also the anchor decouples the vibrating portion of the flowmeter, above the anchor, from the non-vibrating portion of the flowmeter where the flowmeter attaches to the pipeline. 
     The inlet and outlet portions of the flow tube of the present invention can be formed to any desirable configuration. For example the inlet and outlet portions of the flow tube can be formed in-line with each other or the meter can be made self-draining by forming them in a spiral, off-set configuration. 
     The modular design of the flowmeter of the present invention makes it relatively easy for the designer to make changes to the wetted components of the flow tube. Since the fluid only contacts the flow tube and the adapters, the housing and anchor can be used with flow tubes and adapters of different materials without necessarily making any further design changes. 
     The apparatus of the present invention has the above described and other advantages in measuring the flow rate of material flowing through pipelines. Unlike traditional Coriolis flowmeters, the present invention has a serial, balanced flow tube. A crossover section in the flow tube connects two loops in the flow tube. The configuration of the serial flow tube allows the present invention to behave like a dual flow tube flowmeter, while having serial flow tube characteristics. The anchor and housing configuration provide support for the flow tube and minimize distortion of the flow tube. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 discloses a flow tube with a crossover section of the present invention; 
     FIG. 2 discloses a flow tube with the shape of the preferred embodiment of the invention; 
     FIG. 3 discloses a top-side view the flow tube of the present invention; 
     FIG. 4 discloses a top-side view of the complete flowmeter of the present invention with the top housing removed to expose the interior; 
     FIG. 5 discloses a flow tube of the present invention with b-shaped loops; 
     FIG. 6 discloses a flow tube of the invention with circular loops; and 
     FIG. 7 discloses an assembly view of the preferred embodiment of the Coriolis flowmeter of the present invention. 
     FIG. 8 is a process flow chart illustrating the steps for manufacturing a flowmeter according to the present invention. 
     FIG. 9 depicts a brace bar half. 
     FIG. 10 depicts a portion of two flow tube loops and interconnecting brace bar halves. 
    
    
     DETAILED DESCRIPTION 
     Flow Tube Geometry—FIGS. 1-4 
     A basic embodiment of the flow tube  101  of the present invention is illustrated in FIG.  1 . Inlet  103  of serial flow tube  101  attaches to a pipeline and receives a flowing material from the pipeline. Outlet  104  attaches to the pipeline to return the flowing material to the pipeline. Serial flow tube  101  has two loops  151  and  152 . Crossover section  115  joins loops  151  and  152  to form one continuous flow tube  101 . 
     FIG. 3 illustrates a top view of flow tube  101 . Elements common between any of the FIGS. are referenced by common reference numerals. Flow tube loop  151  is oriented in plane F 1  and flow tube loop  152  is oriented in plane F 2 . Planes F 1  and F 2  are parallel. Crossover section  115  has a first end in plane F 1 , where it is attached to loop  151 . The middle section of crossover section  115  traverses from plane F 1  to plane F 2 . Crossover section  115  then has a second end connected to loop  152  in plane F 2 . One continuous flow tube  101  is produced by the connection of loops  151  and  152  by crossover section  115 . 
     Crossover section  115  is an important element of continuous flow tube  101 . Crossover section  115  eliminates the need for the manifold by forming the flow tube itself to conduct the fluid from loop  151  to  152 . Serial flow tube  101  is continuous and provides a smooth tube surface required for sanitary applications. 
     A drive coil  131  is mounted at a midpoint region of flow tube loops  151  and  152  to oscillate loops  151  and  152  in opposition to each other. Left pick-off sensor  132  and right pick-off sensor  133  are mounted in the respective corners of the top sections of flow tube loops  151  and  152 . Sensor  132  and  133  sense the relative velocity of flow tube loops  151  and  152  during oscillations. 
     In the embodiment of FIG. 1, loops  151  and  152  are substantially triangular shaped. Loops  151  and  152  of the flow tube contain bends  111 ,  112 ,  121 , and  122 . Each of the bends  111 ,  112 ,  121 , and  122  is substantially 135-degrees. Straight sections  116 ,  117 ,  118 ,  126 ,  127 , and  128  connect to bends  111 ,  112 , and  121 , and  122 . Straight sections  116  and  118  of loop  151  and straight sections  126  and  128  of loop  152  are nonparallel and aligned substantially 90 degrees from each other along their longitudinal axis. Crossover section  115  connects straight section  118  on the right side of loop  151  to straight section  126  on the left side of loop  152 . The complex bend of crossover section  115  connects loops  151  and loops  152  so that material flows in the same direction through each loop. 
     FIG. 2 illustrates the shape of the serial flow tube  101  of the preferred embodiment of the present invention. Flow tube  101  has all of the elements depicted in FIG. 1 with the additional elements of inlet bend  201  and outlet bend  202 . Inlet  103  and outlet  104  are planar with a pipeline (not shown) and are not co-planar with either plane F 1  or F 2 . ( See FIG. 3) Inlet bend  201  attaches inlet  103  with loop  151  by crossing from inlet  103  to plane F 1  and connecting to section  118 . An outlet bend  202  joins outlet  104  and loop  152  by crossing from outlet  104  to plane F 2  and connecting with section  128 . The inlet and outlet bends allow Coriolis flowmeter  101  to be attached to the pipeline while the two loops are not planar with the pipeline. 
     FIG. 4 illustrates a flowmeter  400  including flow tube  101 , anchor  401  and housing base  450 . Flow tube  101  is fixedly attached to anchor  401  at a location near cross-over section  115  of flow tube  101 . Flow tube loops  151 - 152  extend from anchor  401  on one side of anchor  401 . Cross-over section  115  extends from anchor  401  on an opposite side of anchor  401 . One way to attach loops  151 - 152  to anchor  401  is with blocks  411  and  412 . Anchor  401  is formed with depressions corresponding to the outer diameter of flow tube  101 . Likewise, blocks  411  and  412  are formed with corresponding depressions. During assembly, anchor  401 , blocks  411 - 412  and flow tube  101  are brazed together to form a fixed, solid attachment between flow tube  101  and anchor  401  at the interfaces between anchor  401  and blocks  411 - 412 . Anchor  401  is then welded to housing base  450  using bosses (not shown) corresponding to and oppositely arranged from bosses  413 - 414 . During operation of flowmeter  400 , the non-vibrating portion of flow tube  101  extends from face  432  of anchor  401  and the vibrating portion of flow tube  101  extends from the opposite face of anchor  401 . 
     Inlet  103  of flow tube  101  is connected to adapter  402  with, preferably, an orbital weld at location  421 . Outlet  104  of flow tube  101  is connected to adapter  403  with preferably an orbital weld at location  422 . Since inlet  103  and outlet  104  are not part of the vibrating, dynamic portion of the flowmeter they can be arranged in any configuration. For example, inlet  103  and outlet  104  can be arranged so that planes F 1 -F 2 , with reference to FIG. 3, are perpendicular to the pipeline to which the flowmeter is connected. Another alternative is to arrange inlet  103  and outlet  104  so that flowmeter  400  is self-draining. Driver  131  and sensors  132 - 133  are arranged, and operate, as described with respect to FIG.  1 . Brace bars  425 - 426  are fixedly attached between loops  151 - 152  of flow tube  101 . 
     Brace Bars—FIGS. 9-10 
     FIGS. 9-10 depict the preferred embodiment of brace bars  425 - 426 . Each of brace bars  425 - 426  is comprised of two brace bar halves  900 . Each brace bar half  900  has a body  901  and an overlap tab  903 . In addition, each brace bar half  900  has a hole  902  through which flow tube  101  passes. FIG. 10 depicts the manner in which two brace bar halves  900  are connected to form a single brace bar  425  or  426 . Brace bar half  900 A having body  901 A and overlap tab  903 A is positioned on flow tube loop  151 . Likewise, brace bar half  900 B having body  901 B and overlap tab  903 B is positioned on flow tube loop  152 . Overlap tab  903 A and overlap tab  903 B overlap one another and are tack-welded in the region of their  15  overlap. This forms a solid, one piece brace bar between flow tube loops  151  and  152 . Brace bars  425 - 426  are each comprised from two brace bar halves  900 , as just described. 
     Forming each brace bar  425 - 426  from two brace bar halves  900  allows significant flexibility in assembly of the flowmeter of the present invention. The brace bar halves  900  are threaded onto flow tube  101  at any time prior to the attachment of flow tube  101  to adapters  402 - 403 . Flow tube  101  can be further processed before the brace bar half pairs are welded together to form complete, solid brace bars. 
     Flowmeter Assembly—FIGS. 7-8 
     FIG. 7 is an exploded view of the complete flowmeter  700  including housing cover  701 , housing base  450  and the remaining components as described below. Housing cover  701  has holes  721 - 722  which mate with bosses  414  and  413 , respectively. Housing cover  701  also has holes  724 - 723  through which bosses  703 - 704  extend. 
     Adapters  402 - 403  attach to flow tube  101  using preferably orbital welds at points  421 - 422 . Adaptor  403  has surface  727  that is welded to surface  728  on housing base  450  and housing cover  701 . Adaptor  402  has a similar surface (not shown) that is welded to surface  729  on housing base  450 . As described with respect to FIG. 9, brace bars  425 - 426  are each formed from two brace bar halves  900  which are welded to form a complete brace bar. Anchor  401  and anchor blocks  411 - 412  are brazed to flow tube  101  to form a solid attachment between flow tube  101  and anchor  401 . Depressions  730  in blocks  411 - 412  and depressions  731  in anchor  401  are formed to cooperate with the outer diameter of tube loops  151 - 152 . Anchor  401  has bottom bosses (not shown) which insert through holes  725 - 726  in housing base  450 . Anchor  401  is welded to housing base  450  where the bottom bosses pass through holes  725 - 726 . Bosses  413 - 414  and  703 - 704  are inserted through holes  722 - 721  and  723 - 724 , respectively. Housing cover  701  and bosses  413 - 414  and  703 - 704  are welded together. Finally, housing base  450  is welded to housing cover  701  around the entire circumference of the mating edge between housing base  450  and housing cover  701 . 
     Flow tube  101  is thereby coupled to the flowmeter housing and consequently the pipeline (not shown) through anchor  401  and adapters  402 - 403 . Any stresses induced by the pipeline on flowmeter  700  are seen only by the non-vibrating portion of flow tube  101  below anchor  401 . Thus the vibrating, active measurement portion of flow tube  101  is not effected by external forces, torques and vibrations. Anchor  401  is massive enough that it experiences minimal distortion when welded to housing base  450  and housing cover  701 . This in turn means that flow tube  101  experiences minimal distortion as a result of the welding operations. Any distortion that does occur to flow tube  101  at least occurs equally to both loops  151 - 152  thereby minimizing any impact on the measurement performance of flowmeter  700 . 
     Housing base  450  and housing cover  701  can be formed of thick enough material such that flowmeter  700  is capable of withstanding significant pressures. This is advantageous if flowmeter  700  is utilized in a pipeline in which flows highly pressurized materials. Should flow tube  101  rupture, the flowmeter housing is capable of containing the pressurized fluid. In the preferred embodiment of the present invention, housing cover  701  and housing base  450  are formed from steel by casting and provide secondary containment (rated to 500 pounds per square inch) for flowmeter  700 . A feed-thru (not shown) is used to extend wiring from inside of flowmeter  700  to outside of flowmeter  700 . 
     FIG. 8 depicts a flow chart illustrating the steps for the preferred method of fabricating the flowmeter of the present invention. The assembly process begins with element  802 . During step  804  the brace bar halves are threaded onto the flow tube. The flow tube may already have been partially or completely bent prior to threading the brace bar halves onto the flow tube. 
     Once the brace bar halves are threaded on the flow tube the adapters are attached to the inlet and outlet of the flow tube during step  806 . During step  808  the flow tube inlet and outlet and attached adapters are bent, if necessary to achieve the final configuration of the flow tube. In the preferred embodiment, the flow tube inlet and outlet are in-line with one another and in-line with the pipeline to which the flowmeter is attached. Therefore during step  808  the flow tube inlet and outlet are bent so that the adapters are in-line. 
     During step  810  the brace bar half pairs are welded to form solid brace bars. The solid brace bars can also be welded to the flow tube during this step or, alternatively, the brace bars are brazed to the flow tube during step  812 . 
     A brazing operation is preferably performed during step  812 . All the remaining necessary attachments to the flow tube are made during this step. This includes the anchor, brace bar brackets, pick-off sensor brackets and driver attachments to the flow tube. Alternatively, one could perform multiple welding operations to complete the necessary attachments to the flow tube. The result of this step is a complete flow tube assembly. The flow tube assembly includes the flow tube and everything in the completed flowmeter that is attached to the flow tube including the anchor, brace bars, adapters, driver brackets and pick-off sensor brackets. 
     During step  814  the flow tube assembly is inserted into the housing base. The anchor is then welded to the housing base. Any necessary internal wiring for the flowmeter is also completed during step  814 . 
     During step  816  the flowmeter is completed by mating the housing cover to the housing base. The anchor is welded to the housing cover. The adapters are welded to the housing base and the housing cover. The housing base and housing cover are welded around the entire circumference of the housing to produce a housing providing secondary containment of pressure. Processing of the flowmeter then ends with element  818 . 
     Alternative Embodiments—FIGS. 5-6 
     FIG. 5 illustrates alternatively shaped flow tube  500 . Flow tube  500  has loops  501  and  502 . Loops  501  and  502  are substantially B-shaped and are each contained in respective parallel planes. Inlet  503  is connected to a pipeline (not shown) at one end and to loop  501  at its other end. Inlet  503  bends to direct the fluid flow from the plane of the pipeline to the plane of loop  501 . The fluid flowing through loop  501  is directed to loop  502  through crossover section  505 . Fluid is then directed through loop  502  where it is directed back to the plane of the pipeline by outlet  504 . Flow tube  500  shares the crossover section design of the flow tubes described with respect to FIGS. 1-4. 
     FIG. 6 illustrates a second alternatively shaped flow tube  600 . Loops  601  and  602  are substantially circular and contained in respective parallel planes. Inlet  603  is connected to a pipeline (not shown) at one end and to loop  601  at its other end. Fluid flowing through flow tube  600  is directed from the plane of the pipeline to the plane of loop  601 . The fluid then flows through loop  601  and is directed to loop  602  through crossover section  605 . The fluid then flows through loop  602 . Outlet  504  then returns the flowing fluid to the pipeline plane from plane of loop  152 . Flow tube  600  shares the crossover section of the designs described with respect to FIGS. 1-5. 
     The present invention includes a dual loop, serial flow tube utilizing a complex bend to direct flow from a first loop to a second loop. The present invention also includes an anchor for securing the flow tube to a housing. The present invention includes a two-piece brace bar design and a method for assembling a flowmeter incorporating the features of the present invention. Although specific embodiments of the present invention are disclosed herein, it is expected that persons skilled in the art can and will design alternative dual loop, serial flow tube Coriolis flowmeters that are within the scope of the following claim either literally or under the doctrine of equivalents.