Publication NumberUS 3952577
Assignees
  • Canadian Patents and Development Limited
StatusIssued Patent
Application Number05/547607
AvailabilityUnknown
Filing Date1975-02-06
Publication Date1976-04-27

Abstract

An apparatus for measuring the flow rate and/or viscous characteristics of a fluid comprising a casing having a fluid passage, a fluid inlet cavity and a fluid outlet cavity, fluid pressure detecting means preferably at spaced positions along the passage, and fluid pressure indicating means for indicating the or each characteristic to be measured in terms of the fluid pressure differential between the detecting means positions. The fluid inlet cavity provides a substantially unobstructed flow path to the fluid passage and the fluid outlet cavity provides a substantially unobstructed flow path therefrom. The fluid passage cross-sectional area decreases in the fluid flow direction in order to maintain laminar flow of the fluid therealong and wall boundary induced viscous shear therealong, over an extended range of Reynolds number within the fluid passage and formulae are given, using substantially pure water as a standard fluid, from which the limits of fluid passage geometry can be defined. In one embodiment the fluid passage is annular in shape and the fluid flow radially inward. The fluid passage may be divided into a plurality of substantially identical fluid passages to increase the flow rate capacity of the apparatus.

Claims

  • 1. Apparatus for measuring the flow rate and/or the viscous characteristics of a fluid, comprising: a. a casing having a fluid passage, a fluid inlet cavity for connection to a source of pressurized fluid and forming a substantially unobstructed flow path for fluid to the whole area of an inlet end of the fluid passage, normal to the direction for flow of fluid in the fluid passage, and a fluid outlet cavity for the escape of fluid from the casing and forming a substantially unobstructed flow path for fluid from substantially the whole area of an outlet end of the fluid passage, normal to the direction for flow of fluid in the fluid passage, b. fluid pressure detecting means in the casing for detecting a fluid pressure differential between spaced positions in the fluid passage in the direction for flow of fluid therein, and c. fluid pressure indicating means, connected to the fluid pressure detecting means, from which the fluid pressure differential in the fluid passage can be deduced, and wherein, d. the ratio of the mean breadth to the mean width of the fluid passare area, normal to the direction for flow of fluid therein, is at least ten to one for at least the portion of the fluid passage which extends between the said spaced positions, e. the area of the fluid passage, normal to the direction for flow of fluid in the fluid passage, and for at least the portion of the fluid passage which extends between the said spaced positions, continuously reduces in size in the direction for flow of the fluid such that laminar flow will be maintained of the fluid flowing in the passage, and such that when using substantially pure water at 70°F as a standard, the static pressure differential at said spaced locations is dependant upon the mass flow rate G of the substantially pure water through the fluid passage and satisfies the relationship in consistent units: Δp = K.sub.1 (G).sup.2 + K.sub.2 (G), and ii. the total pressure differential at said spaced locations is linearily dependant upon the mass flow rate G of the substantially pure water in the fluid passage, and the above pressure differential relationships for static and total pressure differential (Δp and ΔP respectively) are over a range of flow rates for the substantially pure water for which the difference between the maximum Reynolds numbers in the fluid passage between the said spaced positions therein is within the range 0 and 8000, where the Reynolds number R.sub.e is defined, in consistent units, by: R.sub.e = hρU/μ, where h = the mean width of the fluid passage at the position between the said spaced positions for which the Reynolds number is a maximum, ρ = the fluid density of the substantially pure water, U = the means velocity of the substantially pure water at the position between the said spaced positions for which the Reynolds number is a maximum, and μ = the absolute viscosity of the substantially pure water, and where in the case of static pressure differential the ratio K.sub.1 /k.sub.2 is greater than 0.01, where K.sub.1 and K.sub.2 are constants for a given fluid passage geometry and are determined from the relationships: ##EQU9## and ##EQU10## where Δp.sub.1 = static pressure differential between the said spaced positions when the maximum Reynolds number in the fluid passage between the said spaced positions is 8000, G.sub.1 = the fluid mass flow rate of the substantially pure water through the fluid passage when the maximum Reynolds number in the fluid passage between the said spaced positions is 8000, Δp.sub.2 = static pressure differential between the said spaced positions when the maximum Reynolds number in the fluid passage between the said spaced positions is 3500, G.sub.2 = the fluid mass flow rate of the substantially pure water through the fluid passage when the maximum Reynolds number in the fluid passage between the said spaced positions is 3500, so that f. the fluid characteristic to be measured is related to the pressure differential, indicated by the fluid pressure differential indicating means, and is deducible therefrom in a consistent manner for different fluids.
  • 2. Apparatus according to claim 1, wherein the fluid pressure means comprises two static pressure taps in the casing and each is in communication with one of the said spaced positions within the fluid passage.
  • 3. Apparatus according to claim 1, wherein the fluid pressure detecting means comprises one static pressure tap and one total pressure probe and each is in communication with one of the said spaced positions.
  • 4. Apparatus according to claim 1, wherein the fluid pressure detecting means comprises one static pressure tap and one total pressure probe each located at one of the said spaced positions.
  • 5. Apparatus according to claim 1, wherein the fluid pressure detecting means comprises two detectors in the form of a static pressure tap and a total pressure probe, and one detector is in communication with one of the said spaced positions and the other detector is located at the other of the said spaced positions.
  • 6. Apparatus according to claim 1, wherein one of the said spaced positions is located between the inlet and the outlet of the fluid passage at a position such that the detected pressure differential is measurably sensitive to variations of fluid viscosity, and the fluid detection means comprises static pressure taps.
  • 7. Apparatus according to claim 1, wherein the fluid pressure detecting means comprises at least three static pressure taps at spaced locations between the said spaced positions, and the fluid pressure indicating means comprises a plurality of pressure measuring instruments each connected to one of the static pressure taps so that the static pressure distribution between the said spaced positions can be deduced.
  • 8. Apparatus according to claim 1, wherein the fluid pressure detecting means comprises two total pressure probes in the casing and located at the said spaced positions.
  • 9. Apparatus according to claim 1, wherein one of the said spaced positions is located between the inlet and the outlet of the fluid passage such that the detected pressure differential is measurably sensitive to variations of fluid viscosity and the fluid detection means comprises total pressure probes.
  • 10. Apparatus according to claim 1, wherein the fluid pressure detecting means comprises at least three total pressure probes at spaced locations between the said spaced positions, and the fluid pressure indicating means comprises a plurality of pressure measuring instruments each connected to one of the total pressure probes so that the total pressure distribution between the said spaced positions can be deduced.
  • 11. Apparatus according to claim 1, wherein the casing is a cylindrical casing containing an outer, annular shaped fluid inlet cavity, an intemediate, annular shaped fluid passage for radial inward flow of fluid therethrough, and an inner, fluid outlet cavity, and wherein the outer annular shaped fluid inlet cavity forms the substantially unobstructed flow path to the whole outer periphery of the intermediate annular shaped fluid passage and the inner, fluid outlet cavity forms the substantially unobstructed flow path from the whole inner periphery of the intermediate, annular shaped fluid passage for the escape of fluid from the casing, and the fluid pressure detecting means in the casing is for detecting a fluid pressure differential between radially spaced positions in the fluid passage.
  • 12. Apparatus according to claim 11, which includes a conical center body attached to one side of the cylindrical casing, and a conical outer shell surrounding and spaced from the conical center body, the conical outer shell being attached to the casing so that the space between the conical center body and the conical outer shell is a conical inlet passage extending around the whole of the fluid inlet cavity, for delivering the pressurized fluid thereto from the pressurized fluid source.
  • 13. Apparatus according to claim 1, which includes a flexible member in the casing forming one wall of the fluid passage and attached to the casing around the edge of the flexible member to space a portion of the said member from the casing, and deflection transducers forming the fluid pressure detecting means are attached to the flexible member to detect the fluid pressure differential by measuring deflections of the flexible member.
  • 14. Apparatus according to claim 1, which includes a flexible member in the casing and attached thereto around the edge of the flexible member to space a portion of the said member from the casing and deflecting means for deflecting the flexible member to adjust the distance between the walls of the passage to define the said area of the fluid passage.
  • 15. Apparatus for measuring the flow rate and/or the viscous characteristics of a fluid, comprising: a. a casing having a plurality of substantially identical fluid passages, a fluid inlet cavity for connection to a source of pressurized fluid and forming a substantially unobstructed flow path for fluid to the whole area of the inlet end of each fluid passage, normal to the direction for flow of fluid in the fluid passage, and a fluid outlet cavity for the escape of fluid from the casing and forming a substantially unobstructed flow path for each fluid passage, b. fluid pressure detecting means in the casing for detecting a fluid pressure differential between spaced positions in at least one of the fluid passages in the direction for flow of fluid therein, and c. fluid pressure indicating means, connected to the fluid pressure detecting means, from which the fluid pressure differential in at least the said one of the fluid passages can be deduced, and wherein, d. the ratio of the mean breadth to the mean width of each fluid passage area, normal to the direction for flow of fluid therein, is at least ten to one for at least the portion of the fluid passages which extends between the said spaced positions, e. the area of each fluid passage, normal to the direction for flow of fluid in the fluid passage, and for at least the same portion of each fluid passage as that which extends between the said positions, continuously reduces in size in the direction for flow of the fluid such that laminar flow will be maintained of the fluid flowing in each fluid passage, and each fluid passage is such that when using substantially pure water at 70°F as a standard, and i. the static pressure differential a at said spaced locations is dependant upon the mass flow rate G of the substantially pure water through the fluid passage and satisifies the relationship in consistent units: Δp = K.sub.1 (G).sup.2 + K.sub.2 (G), and ii. the total pressure differential at said spaced locations is linearily dependant upon the mass flow rate G of the substantially pure water in the fluid passage, and the above pressure differential relationships for static and total pressure differential (Δp and ΔP respectively) are over a range of flow rates for the substantially pure water for which the difference between the maximum Reynolds numbers in the fluid passage between the said spaced positions therein is within the range 0 and 8000, where the Reynolds number R.sub.e is defined, in consistent units, by: R.sub.e = hρU/μ, where h = the mean width of the fluid passage at the position between the said spaced positions for which the Reynolds number is a maximum, ρ = the fluid density of the substantially pure water, U = the mean velocity of the substantially pure water at the position between the said spaced positions for which the Reynolds number is a maximum, μ = the absolute viscosity of the substantially pure water, and where in the case of static pressure differential the ratio K.sub.1 /k.sub.2 is greater than 0.01, and K.sub.1 and K.sub.2 are constants for given substantially identical fluid passage geometries and are determined from the relationships: ##EQU11## and ##EQU12## where Δp.sub.1 = static pressure differential between the said spaced positions when the maximum Reynolds number in the fluid passage between the said spaced positions is 8000, G.sub.1 = the fluid mass flow rate of the substantially pure water through the fluid passage when the maximum Reynolds number in the fluid passage between the said spaced positions is 8000, Δp.sub.2 = static pressure differential between the said spaced positions when the maximum Reynolds number in the fluid passage between the said spaced positions is 3500, G.sub.2 = the fluid mass flow rate of the substantially pure water through the fluid passage when the maximum Reynolds number in the fluid passage between the said spaced positions is 3500, so that f. the characteristic to be measured is related to the pressure differential, indicated by the fluid pressure differential indicating means, and is deducible therefrom in a consistent manner for different fluids.
  • 16. Apparatus according to claim 15, wherein the fluid pressure detecting means comprises two static pressure taps in the casing and each is in communication with one of the said spaced positions in a fluid passage.
  • 17. Apparatus according to claim 15, wherein the said spaced positions are in one fluid passage, and the two static pressure taps are located at the spaced positions.
  • 18. Apparatus according to claim 15, wherein the said spaced positions are in different fluid passages, and the two static pressure taps are located at the spaced positions.
  • 19. Apparatus according to claim 15, wherein the fluid pressure detecting means comprises two static pressure taps, one of which is in communication with one of the said spaced positions and the other of which is located at the other spaced position.
  • 20. Apparatus according to claim 15, wherein the fluid pressure detecting means comprises one static pressure tap and one total pressure probe and each is in communication with one of the said spaced positions.
  • 21. Apparatus according to claim 15, wherein the said spaced positions are in one fluid passage, and the fluid pressure detecting means comprises one static pressure tap and one total pressure probe each located at one of the said spaced positions.
  • 22. Apparatus according to claim 15, wherein the said spaced positions are in different fluid passages, and the fluid pressure detecting means comprises one static pressure tap and one total pressure probe each located at one of the said spaced positions.
  • 23. Apparatus according to claim 15, wherein the fluid pressure detecting means comprises two detectors in the form of a static pressure tap and a total pressue probe, and one detector is in communication with one of the said spaced positions and the other detector is located at the other of the said spaced positions.
  • 24. Apparatus according to claim 15, wherein one of the said spaced positions is located between the inlet and the outlet of one of the fluid passages at a position such that the detected pressure differential is measurably sensitive to variations of fluid viscosity, and the fluid detection means comprises static pressure taps.
  • 25. Apparatus according to claim 15, wherein the fluid pressure detecting means comprises at least three static pressure taps each in a fluid passage and at spaced locations from each other between the said spaced positions, and the fluid pressure indicating means comprises a plurality of pressure measuring instruments each connected to one of the static pressure taps so that the static pressure distribution between the said spaced positions can be deduced.
  • 26. Apparatus according to claim 15, wherein the said spaced positions are in one fluid passage, and the fluid pressure detecting means comprises two total pressure probes in the casing located the said spaced positions.
  • 27. Apparatus according to claim 15, wherein the said spaced positions are in different fluid passages, and the fluid pressure detecting means comprises two total pressure probes in the casing and located at the said spaced positions.
  • 28. Apparatus according to claim 15, wherein the fluid pressure detecting means comprises two total pressure probes in the casing and in communication with each of the said positions.
  • 29. Apparatus according to claim 15, wherein one of the said spaced positions is located between the inlet and the outlet of one of the fluid passage at a position such that the detected pressure differential is measurably sensitive to variations of fluid viscosity and the fluid detection means comprises total pressure probes.
  • 30. Apparatus according to claim 15, wherein the fluid pressure detecting means comprises at least three total pressure probes each in one of the fluid passages and at spaced locations from each other between the said spaced positions, and the fluid pressure indicating means comprises a plurality of pressure measuring instruments each connected to one of the total pressure probes so that the total pressure distribution between the said spaced positions can be deduced.
  • 31. Apparatus according to claim 15, wherein the casing is a cylindrical casing containing an outer, annular shaped fluid inlet cavity, a plurality of similar, coaxial, annular intermediate, fluid passages, each for substantially radial inward flow of fluid therethrough, and an inner, fluid outlet cavity, and wherein the outer annular shaped fluid inlet cavity forms a substantially unobstructed flow path to the whole outer periphery of each intermediate annular shaped fluid passage, and the inner fluid outlet cavity forms a substantially unobstructed flow path from the whole inner, periphery of each intermediate, annular shaped fluid passage for the escape of fluid from the casing, and the fluid pressure detecting means is for detecting a fluid pressure differential at two radially spaced positions each in one of the fluid passages.
  • 32. Apparatus according to claim 31, which includes a conical center body attached to one side of the cylindrical casing, and a conical outer shell surrounding and spaced from the conical center body, the conical outer shell being attached to the casing so that the space between the conical center body and the conical outer shell is a conical inlet passage extending around the whole of the fluid inlet cavity, for delivering pressurized fluid thereto from the pressurized fluid source.
  • 33. Apparatus according to claim 15, wherein the casing is a cylindrical casing containing an outer, annular shaped fluid inlet cavity, an annular, intermediate cavity, and an inner, fluid outlet cavity, and a plurality of shims extending radially inwards within the annular, intermediate cavity partition the said annular, intermediate cavity into a plurality of radially extending fluid passages, with the outer annular shaped inlet cavity forming the substantially unobstructed flow path to the whole area of the inlet end of each radial fluid passage, and the inner annular shaped outlet cavity forming a substantially unobstructed flow path from the whole area of the outlet end of each radial fluid passage, and the fluid pressure detecting means is for detecting a fluid pressure differential at two radially spaced positions in at least one of the said fluid passages.
  • 34. Apparatus according to claim 33, which includes at least one disc spacer in the annular cavity, whereby the annular, intermediate cavity is separated into one of a plurality of similar, coaxial, annular, intermediate cavities, each annular, intermediate cavity contains radially extending shims to partition the annular, intermediate cavities into similar, radially extending fluid passages, with all of the fluid passages having a substantially unobstructed flow path thereto from the outer, annular shaped fluid inlet cavity and a substantially unobstructed flow path therefrom to the inner, fluid outlet cavity.
  • 35. Apparatus according to claim 33, wherein each of the shims are similarily contoured in cross-section and are deflected between the walls of the casing to be held in position.
  • 36. Apparatus according to claim 34, wherein each of the shims are similarily contoured in cross-section and are deflected in position in each fluid passage to be thereby held in position by the casing and at least one disc spacer.
  • 37. Apparatus according to claim 33, wherein each shim has an extension which extends radially outwardly into the fluid inlet cavity, and the said shim extensions are joined by a circumferential ring attached to the extension and coaxially positioned in the fluid inlet cavity.
  • 38. Apparatus according to claim 34, wherein each shim has an extension which extends radially outwardly into the fluid inlet cavity, and the said shim extensions extending from each coaxial, annular, intermediate cavity are joined by a circumferential ring attached to the extensions and coaxially positioned in the fluid inlet cavity.