Abstract
A magnetic-inductive flow meter includes: a housing; a first and a second measurement electrode in galvanic contact with a flowing medium in a pipe; a magnetic field-generating device positioned in the housing and including a measurement circuit configured to determine a first measurement variable, and wherein measurement values of the first measurement variable are measured between two measurement electrodes or at a measurement electrode in relation to a reference potential; and an evaluation circuit configured to determine a Reynolds number and/or a kinematic viscosity value of the medium using measurement values of the first measurement variable and of a second measurement variable, which differs from the first measurement variable, wherein the measurement electrodes are positioned such that, during a test measurement, quotients of current measurement values of the first and of the second measurement variable correspond bijectively with the Reynolds number of the medium in the pipe.
Claims
1-15. (canceled)
16. A magnetic-inductive flow meter, which is configured to be introduced into a pipe adapted to convey a flowing medium, comprising: a housing, wherein the housing includes a housing wall; a first measurement electrode, a second measurement electrode and at least a third measurement electrode, which are each arranged on the housing wall such that each forms a galvanic contact with the medium when introduced into the pipe; a magnetic field-generating device configured to generate a magnetic field passing through the housing wall, wherein the magnetic field-generating device is disposed in the housing; and a measurement circuit configured to determine at least a first measurement variable, wherein measurement values of the first measurement variable are measured between two of the first, second and third measurement electrodes or at one of the first, second and third measurement electrodes in relation to a reference potential; and an evaluation circuit configured to determine a Reynolds number and/or a kinematic viscosity value of the medium in the pipe using measurement values of the first measurement variable and a second measurement variable, which differs from the first measurement variable, wherein measurement values of the second measurement variable are determined between two of the first, second and third measurement electrodes or at one of the first, second and third measurement electrodes in relation to a reference potential, wherein at least one measurement electrode of the first, second and third measurement electrodes used to determine the measurement values of the second measurement variable differs from the measurement electrodes used to determine the measurement values of the first measurement variable.
17. The flow meter of claim 16, wherein the first, second and third measurement electrodes are arranged on the housing wall such that, during a test measurement, quotients of current measurement values of the first and second measurement variable bijectively correspond to the Reynolds number of the medium in the pipe, at least in a Reynolds number range of 1,000≤Re≤1,000,000.
18. The flow meter of claim 16, wherein the measurement circuit is configured to determine the measurement values of the first measurement variable between the first and the second measurement electrodes, and wherein the measurement circuit is configured to determine measurement values of the second measurement variable between the first and third measurement electrodes or between the second and third measurement electrodes.
19. The flow meter of claim 16, further comprising a fourth measurement electrode, wherein the measurement circuit is configured to determine the measurement values of the first measurement variable between the first and second measurement electrodes, and wherein the measurement circuit is configured to determine measurement values of the second measurement variable between the third and fourth measurement electrodes.
20. The flow meter of claim 16, wherein the housing is cylindrical at least in sections and includes a lateral surface, and wherein the third measurement electrode is disposed on the lateral surface as to form a galvanic contact with the medium in operation.
21. The flow meter of claim 16, wherein the first, second and third measurement electrodes are disposed on an end face of the housing.
22. The flow meter of claim 21, wherein the first and second measurement electrodes lie on a first circumference on the end face and are arranged coaxially to the housing, wherein the first circumference defines an area in which the third measurement electrode is disposed.
23. The flow meter of claim 22, further comprising a fourth measurement electrode, wherein both the third and the fourth measurement electrodes are disposed within the defined area.
24. The flow meter of claim 21, further comprising a fourth measurement electrode, wherein the first and second measurement electrodes are arranged on a straight line on the end face, and wherein the third and fourth measurement electrodes are arranged on the straight line between the first and second measurement electrodes.
25. The flow meter of claim 22, further comprising a fourth measurement electrode, wherein the first and second measurement electrodes are arranged on a straight line on the end face, and wherein the third and fourth measurement electrodes are arranged on the straight line between the first and second measurement electrodes.
26. The flow meter of claim 22, further comprising a fourth measurement electrode, wherein the first, second, third and fourth measurement electrodes lie on circumferences of concentric circles, wherein the first and second measurement electrodes lie on the first circumference having a first radius R.sub.12, wherein the third and fourth measurement electrodes lie on a second circumference having a second radius R.sub.34, and wherein a ratio of the first and second radii satisfies 0.2≤R.sub.34/R.sub.12≤0.9.
27. The flow meter of claim 26, wherein the ratio of the first and second radii satisfies 0.4≤R.sub.34/R.sub.12≤0.6.
28. The flow meter of claim 17, wherein current measurement values of the first measurement variable during the test measurement in a Reynolds number range of 10,000≤Re≤100,000 are substantially proportional to the flow rate of the medium, wherein a change in current measurement values of the second measurement variable is not constant as the Reynolds number increases during the test measurement in a Reynolds number range of 10,000≤Re≤100,000.
29. The flow meter of claim 17, wherein, during the test measurement, the flowing medium is a Newtonian fluid, and wherein, for the test measurement, the flow meter is disposed in a pipe having a straight inlet section of at least DN 20 such that a substantially symmetrical flow profile is present in the medium, wherein the pipe otherwise has a diameter DN 80, wherein a distance between an end face of the housing and an opening of the pipe in which the flow meter is disposed defines the installation depth D, and wherein the installation depth satisfies 0.05≤D/DN≤0.4.
30. The flow meter of claim 17, wherein the first, second and third measurement electrodes are arranged on the housing wall such that, during a test measurement, quotients of current measurement values of the first and second measurement variable bijectively correspond to the Reynolds number of the medium in the pipe, at least in a Reynolds number range of 10,000≤Re≤100,000.
31. The flow meter of claim 16, wherein to the reference potential is a ground potential.
32. A method for operating the magnetic-inductive flow meter according to claim 16, the method comprising: detecting a measurement value of the first measurement variable and a measurement value of the second measurement variable that differs from the first measurement variable, wherein the measurement values of the respective measurement variables are determined between two of the first, second and third measurement electrodes or at one of the first, second and third measurement electrodes in relation to a reference potential; and determining a Reynolds number that depends on the first and the second measurement variable.
33. The method of claim 32, further comprising: defining a reference value from the measurement values of the first and the second measurement variable, wherein the reference value is proportional to the quotient of the measurement values of the first and the second measurement variable; and determining the Reynolds number as a function of the reference value.
34. The method of claim 33, further comprising: defining a corrected flow rate and/or a corrected volumetric flow using a correction factor dependent on the Reynolds number; and/or determining the kinematic viscosity value of the medium in the pipe using the measurement values of the first or second measurement variable and the determined Reynolds number.
35. The method of claim 32, further comprising: defining a corrected flow rate and/or a corrected volumetric flow using a correction factor dependent on the Reynolds number; and/or determining the kinematic viscosity value of the medium in the pipe using the measurement values of the first or second measurement variable and the determined Reynolds number.
36. A flow measuring point, comprising: a pipe having a diameter DN and an opening; and a magnetic-inductive flow meter according to claim 16, wherein the magnetic-inductive flow meter is disposed in the opening at an installation depth D, which satisfies 0.05≤D/DN≤0.4.
Description
[0087] The invention is explained in greater detail with reference to the following figures. The following are shown:
[0088] FIG. 1: a perspective and partially sectional illustration of a magnetic-inductive flow meter according to the prior art;
[0089] FIG. 2: a longitudinal sectional view of a magnetic-inductive flow meter according to the prior art installed in a pipeline;
[0090] FIG. 3: a front view of a first embodiment of the magnetic-inductive flow meter according to the invention;
[0091] FIG. 4: a front view of a second embodiment of the magnetic-inductive flow meter according to the invention;
[0092] FIG. 5: a longitudinal sectional view of the first embodiment of the magnetic-inductive flow meter according to the invention with an additional paddle;
[0093] FIG. 6: a longitudinal sectional view of a third embodiment of the magnetic-inductive flow meter according to the invention;
[0094] FIG. 7: a longitudinal sectional view of a fourth embodiment of the magnetic-inductive flow meter according to the invention;
[0095] FIG. 8: two diagrams, wherein the first diagram depicts the functions ƒ.sub.1(Re) and ƒ.sub.2(Re) as a function of the Reynolds number, and the second diagram depicts the quotient g of the two functions ƒ.sub.1(Re) and ƒ.sub.2(Re) as a function of the Reynolds number;
[0096] FIG. 9: a diagram showing the error as a function of the flow rate of the medium for various electrode arrangements; and
[0097] FIG. 10: a flow chart of an embodiment of the method for operating a magnetic-inductive flow meter.
[0098] The measuring principle on which the invention is based is first explained on the basis of the perspective and partially sectional illustration of FIG. 1. A flow meter 1 comprises a generally circular cylindrical housing 3 having a predetermined outer diameter. Said housing is adapted to the diameter of a bore, which is situated in a wall of a pipeline 13 that is not shown in FIG. 1 but is shown in FIG. 2, and into which the flow meter 1 is inserted in a fluid-tight manner. A medium to be measured flows in the pipeline 13 and the flow meter 1 is immersed into said medium essentially perpendicularly to the direction of flow of the medium, which is indicated by the wavy arrows 12. A front end 2 of the housing 3 that projects into the medium is sealed in a fluid-tight manner with a front part 6 made of insulating material. By means of a coil arrangement 9 arranged in the housing 2, a magnetic field 8 can be generated, which extends through the front end into the medium. A coil core 7, which is at least partially made of a soft magnetic material and is arranged in the housing 2, terminates at or near the front end. A return 10 that surrounds the coil arrangement 9 and the coil core 7 is configured to return, into the housing 2, the magnetic field 8 extending through from the front end. The coil core 7, the coil arrangement 9 and a return 10 form a magnetic field-generating device. A first and a second galvanic measurement electrode 4, 5 are arranged in the front part 6 and contact the medium. An electrical voltage induced on the basis of Faraday's law of induction can be tapped at the measurement electrodes 4, 5 by means of a measurement and/or evaluation unit 11. This is at a maximum if the flow meter is installed in the pipeline 13 such that a plane spanned by a straight line intersecting the two measurement electrodes 4, 5 and by a longitudinal axis of the flow meter runs in a manner perpendicular to the direction of flow 12 or to the longitudinal axis of the pipeline 21.
[0099] FIG. 2 shows a longitudinal section of a flow meter 1 installed in a pipeline. The flow meter 1 is fastened in the pipeline 13 in a fluid-tight manner by means of a screw-in connection 14, which is inserted into the wall of the pipeline 13 and is welded thereto, for example. This structure of the measuring point is particularly suitable since the screw-in connection 14 can initially be inserted into the pipeline 13 and welded therein and only then does the flow meter 1 have to be inserted into the screw-in connection 14, in turn screwed therein, and sealed by means of a seal 15. This results in an unknown installation angle due to the installation. The first, second, third and fourth measurement electrodes 4, 5, 19, 20 are arranged on the front end 2 symmetrically to a center 6 of the front end 2. All four measurement electrodes 4, 5, 19, 20 lie on a straight line. The installation depth D indicates how deep the flow meter is inserted into the medium or projects into the pipe.
[0100] FIGS. 3 to 7 show different embodiments of the magnetic-inductive flow meter according to the invention. The embodiments differ in that the positioning of the measurement electrodes varies. In order to ensure the clarity of the figures, the illustration of the magnetic field-generating device is omitted. FIGS. 1 and 2 each disclose a magnet system that discloses a coil, a coil core, and a return body. However, other magnetic field-generating devices that are installed in magnetic-inductive flow meters are also known. The exact arrangement of the measurement electrodes depends upon the geometry and arrangement of the magnetic field-generating device. This must therefore be taken into account when optimizing the ideal arrangement of the measurement electrodes.
[0101] FIG. 3 shows a schematic front view of a first exemplary embodiment of the flow meter according to the invention. An arrow indicates the direction of flow 12 of the flowing medium. The ideal installation orientation requires a straight reference line 21 intersecting the measurement electrode pair to run perpendicularly to the direction of flow 12 of the medium. The first and the second measurement electrode 3, 4 are arranged, lying on the front face 22, on the straight reference line, and their positioning is adapted to the magnetic field-generating device such that the induced measurement voltage applied to the two measurement electrodes 3, 4 is linear over the specified Reynolds number range. In addition to the first and second measurement electrodes 3, 4, a third and fourth measurement electrode 19, 20 are arranged on the front face 22. The third and fourth measurement electrodes 19, 20 also lie on the straight reference line 21 and are arranged between the first and second measurement electrodes 4, 5. The first and second measurement electrodes 4, 5 lie on a circumference with radius R.sub.12 and the third and fourth measurement electrodes lie on a circumference with radius R.sub.34. According to this embodiment, R.sub.34<R.sub.12.
[0102] The measurement circuit is designed in such a way that it taps a first potential difference U.sub.1 between the first and the second measurement electrode 4, 5 and a second potential difference U.sub.2 between the third and fourth measurement electrodes 19, 20, where U.sub.1=ƒ.sub.1(Re).Math.S.sub.1.Math.u and U.sub.2=ƒ.sub.2 (Re).Math.S.sub.2.Math.u, wherein ƒ.sub.1(Re) and ƒ.sub.2(Re) each describe a Reynolds number-dependent correction factor. The positioning of the third and fourth measurement electrodes 19, 20 is optimized in such a way that the quotient of the first and second potential differences U.sub.1/U.sub.2 behaves bijectively to the Reynolds number of the flowing medium in the pipe or that a mathematical function which is dependent on the first and second potential differences and which maps the Reynolds number onto the quotient is bijective. The arrangement can be optimized experimentally or by means of a simulation method, for example, by means of finite element simulations.
[0103] For the quotient U.sub.1/U.sub.2 the following results:
[00004]
[0104] In the case that gRe is invertible,
[00005]
[0105] also applies, wherein g.sup.−1 is the inverse function of g. The bijectivity of the quotient can most easily be realized in that the first and the second measurement electrode are attached in the housing such that the first correction factor ƒ.sub.1(Re) is independent of the Reynolds number over the Reynolds number range. In this case, the second correction factor ƒ.sub.2 must bijectively correspond to the Reynolds number.
[0106] The measurement circuit is configured to tap a potential difference between the first and the second measurement electrode 3, 4 and a potential difference at the third and fourth measurement electrodes 19, 20 or to measure a potential in relation to a reference potential at the respective measurement electrode. The measurement data are forwarded to an evaluation unit which comprises a memory unit in which reference values and Reynolds numbers are stored. An evaluation circuit is configured to determine the Reynolds number of the medium in the pipe from the measured measurement data and the stored reference data. If the Reynolds number is known, the kinematic viscosity can be calculated using the measurement values of the first or the second measurement variable or of the already determined flow rate or of the volumetric flow. The measurement circuit, evaluation circuit, and the memory unit can be arranged on an electronic unit in a different way than is depicted in the schematic illustration.
[0107] According to the first embodiment, the measurement electrodes at which an optimally Reynolds number-independent measurement voltage is tapped lie on a circumference which surrounds a region in which the two measurement electrodes, at which a Reynolds number-dependent measurement voltage is tapped, are arranged. However, with an adaptation of the magnet system, the measurement voltage applied to the internal measurement electrodes can also be linearly correlated with the flow rate and the measurement voltage applied to the external measurement electrodes can be Reynolds number-dependent. According to the invention, it must only be fulfilled that the quotient of the two induced and measured measurement voltages must be bijective over a defined Reynolds number range.
[0108] FIG. 4 shows a front view of a second embodiment of the magnetic-inductive flow meter according to the invention. In this embodiment, four measurement electrodes 4, 5, 19, 20 are arranged on the front end 2 of the flow meter. A first measurement electrode axis 24 intersects the second measurement electrode pair 19, 20, and a second measurement electrode axis 25 intersects the first measurement electrode pair 4, 5. The two measurement electrode axes 24, 25 run substantially in parallel to each other. A straight reference line 21 which divides the front face into two equally large faces and runs in parallel to the first or second measurement electrode axis 24, 25 runs through the center point 23 of the front end 2. One of the two measurement electrodes 19, 20 forming the second measurement electrode pair and the center point 23 are intersected by a second radius. One of the two measurement electrodes 4, 5 forming the first measurement electrode pair and the center point 23 of the front face 2 are intersected by a first straight line such that the straight reference line 21 and the first straight line span an angle β. A first straight line, which intersects the center point 23 and one of the two measurement electrodes 4, 5 forming the first measurement electrode pair, spans an angle α together with the straight reference line 21. If the angles are selected such that α=β=0° applies, one arrives at the first embodiment. Starting from the magnet system, the angles α and β can be optimized such that a Reynolds number-independent measurement voltage is induced at one measurement electrode pair and a Reynolds number-dependent measurement voltage is induced at the other measurement electrode pair, wherein the respective dependence applies to a limited Reynolds number range. The straight reference line 21 is additionally also oriented perpendicularly to the direction of flow of the medium. The flow meter is installed in the pipe such that the direction of flow of the medium runs perpendicularly to the straight reference line 21.
[0109] FIG. 5 shows a longitudinal sectional view of a modification of the first embodiment of the flow meter according to the invention. In contrast to FIG. 1, the front end 2 has a paddle 26. The front end 2 is thus not formed by a single front face but by several front faces which are partially perpendicular to one another or run in parallel. This also means that the measurement electrodes can be arranged on the side faces or on the front face of the paddle 26. According to the first embodiment, however, the measurement electrodes are not attached to the paddle 26. The measurement electrodes 4, 5, 19, 20 are located in the region between the paddle 26 and the edge region of the front end 2. The first and second measurement electrodes 4, 5 each have a distance R.sub.12 from the center point of the front end. The position of the two measurement electrodes 4, 5 is optimized in such a way that the correction factor for determining the flow rate is independent of the Reynolds number. The center point of the front end lies on a longitudinal plane of the flow meter, which is also simultaneously a mirror plane. The third and fourth measurement electrodes 19, 20 lie on the perimeter of a circumference with radius R.sub.34 to the center point. The position of the two measurement electrodes 19, 20 is optimized in such a way that the correction factor for determining the flow rate depends on the Reynolds number. To the embodiment depicted in FIG. 5, R.sub.34<R.sub.12 applies.
[0110] FIG. 6 shows a longitudinal sectional view of a second embodiment, in which the third and fourth measurement electrodes 19, 20 are arranged on the lateral surface (28) of the housing and the first and second measurement electrodes 4, 5 are arranged on the front end 2. In this embodiment, the arrangement of the measurement electrodes 4, 5 arranged on the front face is adapted to the magnetic field-generating device in such a way that the flow measurement value correlates linearly with the determined measurement voltage over as large a Reynolds number range as possible. The positioning of the measurement electrodes 19, 20 arranged on the sheath in correlation with the magnet system is selected such that the measurement voltage induced on the two measurement electrodes is Reynolds number-dependent over as large a Reynolds number range as possible. The optimization of these two measurement electrodes 19, 20 takes place such that the slope of the correction factor ƒ (Re) becomes as large as possible with a varying Reynolds number.
[0111] Magnetic-inductive flow meters are known in the prior art which have measurement electrodes which are attached exclusively to the lateral surface (28) of the housing. Accordingly, the magnetic field-generating device is also adapted such that the induced measurement voltage correlates linearly with the flow rate. Starting from such flow meters, the arrangement of the first and second measurement electrodes (4, 5) is selected depending on the magnet system such that the induced measurement voltage is Reynolds number-dependent over as large a Reynolds number range as possible, or that the gradient of the correction factor is as large as possible as the Reynolds number increases.
[0112] FIG. 7 shows a longitudinal section of a fourth embodiment. In addition to the first and second measurement electrodes 4, 5, which are both arranged on the front end 2, a third measurement electrode 19 is also positioned on the front face. The distance between the first and second measurement electrodes 4, 5 defines the diameter of a circle. The third measurement electrode 19 is located outside the circular area. According to the fourth embodiment, the measurement circuit is configured such that a measurement voltage at the first and second measurement electrodes 4, 5 and an electrical potential at the third measurement electrode 19 in relation to a ground potential or a measurement voltage between the third and the first or second measurement electrodes 19, 4 or 19, 5, respectively, are tapped.
[0113] It applies to all embodiments that the positioning of the measurement electrodes in relation to the magnetic field-generating device must be selected such that a first measurement variable, which is Reynolds number-independent over a Reynolds number range, and a second measurement variable, which is Reynolds number-dependent over the same Reynolds number range, can be determined. It must especially be true that the quotient of the two measurement variables describes a bijective mathematical function for different Reynolds numbers.
[0114] FIG. 8 shows two diagrams, wherein the first diagram shows a relationship between the individual correction factors ƒ.sub.1, ƒ.sub.2 and the Reynolds number of the flowing medium in the pipe, and the second diagram shows a relationship between the quotients of the correction factors g and the Reynolds number of the flowing medium in the pipe. The two diagrams are limited to a Reynolds number range of approximately 10.sup.3 to 10.sup.7. The correction factors ƒ.sub.1 and ƒ.sub.2 are each linked to one of the two potential differences tapped by different measurement electrode pairs. The curve of the functions ƒ.sub.1 and ƒ.sub.2 has three ranges I, II, III. In the first and third ranges I, III, the curve of ƒ.sub.1 is not constant. In this example, the curve has a negative slope in the first range I and a positive slope in the third range III. In contrast, the curve of ƒ.sub.1 is constant in the second range II. The flow meter is linear for this Reynolds number range. The second function ƒ.sub.2 is bijective at least in the second range. In the example shown, the curve of ƒ.sub.2 is also bijective in the first and third ranges I, III. This results in the quotient g being bijective in the ranges one to three I, II, III. A Reynolds number can thus be clearly assigned to each quotient of the measurement data of the two measurement variables. This means that if a value of g can be determined, the corresponding Reynolds number can be derived. For the ranges in which the flow rate is sensitive to Reynolds number changes, see ranges I and III, measuring deviations can be corrected taking into account the Reynolds number-dependent correction function.
[0115] FIG. 9 shows a diagram describing the influence of the position of the measurement electrodes on the front end on the Reynolds number dependence of the induced measurement voltage. The diagram maps the Reynolds number-related measurement error onto the flow rate. The Reynolds number depends on the flow rate. Five different measurement electrode positions (5; 7; 9; 9.5; and 11 millimeters of distance from the center point) were measured and the deviation from the actual flow value was determined (curves A-E). The value after the symbol “e” indicates the radius of an imaginary circumference in millimeters on which the measurement electrodes are located. It can be seen from the measurement data that, at a distance of 9.5 mm, the deviation of the flow measurement value over the entire depicted Reynolds number range is substantially independent of the Reynolds number, or that the error is always less than 2.5% (see dotted curve B). However, if the measurement electrodes are arranged on a circumference with a radius of 5 mm, a correction factor independent of the Reynolds number can no longer be assumed. Measurement deviations of up to 20% are present (see curve E). With the aid of a flow meter that has a measurement electrode pair which lies on a circumference with 9.5 mm and that has an additional measurement electrode pair which lies on a circumference with a radius of 5 mm, the Reynolds number can now be determined or a Reynolds number-dependent correction of one of the two measurement voltages can now be carried out, taking into account the measurement voltage applied to each of the measurement electrode pairs.
[0116] FIG. 10 shows a flow diagram of an embodiment of the method for operating a magnetic-inductive flow meter. In a first step, the first potential difference U.sub.1 is measured at the first measurement electrode pair. In a second step, the second potential difference U.sub.2 is measured at the second measurement electrode pair. As an alternative to measuring the potential difference, the potentials at the respective measurement electrodes in relation to the reference potential can also be measured in both aforementioned steps, and the difference can be formed, for example, in the evaluation circuit. The two first steps do not have to take place in succession but can also take place simultaneously. The second potential difference U.sub.2 may also be measured first and then the first potential difference U.sub.1. However, measurement voltages of two measuring phases, in which different, especially, opposite, DC voltages are applied to each of the coils and in which the magnetic field has been adjusted, are usually taken into account for determining the flow rate or the volumetric flow. An offset at the zero point can thereby be compensated. The measurement of the potential difference or of the potentials takes place via a measurement circuit. The evaluation circuit forms a quotient of the two measured measurement values, especially, potential differences, and compares this quotient with a Reynolds number assigned to this determined quotient. The Reynolds number is stored in a memory. Alternatively, a mathematical equation or a mathematical function which assigns a Reynolds number or a Reynolds number range to a quotient may also be stored in the memory. Alternatively, data that have been determined in a calibration method may also be stored in the memory. The data can be the reference values measured in the calibration method but also interpolated or extrapolated values or values of, for example, a smoothed characteristic curve or fit function of the measurement data. The reference values can be determined in a calibration method experimentally and/or by means of a simulation program.
TABLE-US-00001 List of reference signs 1 Flow meter 2 Front end 3 Housing 4 First measurement electrode 5 Second measurement electrode 6 Front part 7 Coil core 8 Magnetic field lines 9 Coil arrangement 10 Return 11 Measurement, operation and/or evaluation unit 12 Direction of flow 13 Pipeline 14 Screw-in connection 15 Seal 16 Measurement electrode 17 Radius R.sub.12 18 Radius R.sub.34 19 Third measurement electrode 20 Fourth measurement electrode 21 Straight reference line 22 Front face 23 Center point 24 First measurement electrode axis 25 Second measurement electrode axis 26 Paddle 27 Longitudinal axis 28 Lateral surface
