Publication NumberUS 4118973
Assignees
  • Canadian Patents & Development Limited
StatusIssued Patent
Application Number05/831087
AvailabilityUnknown
Filing Date1977-09-06
Publication Date1978-10-10

Abstract

An apparatus for measuring the flow rate and/or viscous characteristics of a fluid comprises a casing, having a fluid passage which is elongated in cross-section with two parallel, opposed sides and has a flared entry portion leading to a portion of constant cross-section. Formulae are given, using substantially pure water as a standard, from which a suitable geometry for the flared entry portion can be deduced. Fluid pressure detectors are provided for detecting a fluid pressure differential in the fluid passage such that the fluid characteristic to be measured may be deduced from the pressure differential when laminar flow is maintained in the passage. When laminar flow is maintained the apparatus is capable of measuring a wide range of flow rates and/or viscosities of an extensive variety of fluids in a consistent and deducible manner with minimal pressure loss.

Claims

  • 1. An apparatus for measuring the flow rate and/or viscosity of a fluid comprising: a. a casing having a fluid passage, which is elongated in cross-section normal to the mean direction for fluid flow therein with two parallel, opposed major boundary surface portions which are parallel in a plane normal to the mean direction for fluid flow therebetween, the fluid passage comprising a flared entry portion and a portion having, in the mean direction for fluid flow therein, continuous boundary surface and a substantially constant cross-section, the flared entry portion being flared to decrease in width, without increasing in breadth, in the mean direction for fluid flow therein and forming an unobstructed flow path to the portion having, in the mean direction for fluid flow therein, a continuous boundary surface and a substantially constant cross-section, a fluid inlet to the casing and forming a substantially unobstructed flow path for fluid to the whole of an inlet area to the flared entry portion of the fluid passage, said inlet area being normal to the mean direction for flow of fluid at an inlet end of the flared entry portion, and fluid outlet from the casing and forming a substantially unobstructed flow path for fluid from the whole area of an outlet end of the fluid passage said outlet area being normal to the mean direction for flow of fluid at the outlet end of the fluid passage, and wherein b. the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein has a magnitude of mean breadth which is at least as large as that given by a mean breadth to mean width ratio of 1.5 to 1, and an area in any plane normal to the mean direction for fluid flow therein which does not vary more than in the region of 2% from the mean area calculated in this manner for substantially the whole length of the said portion having continuous boundary surface and a substantially constant cross-section, and wherein c. the geometry of the flared entry portion of the fluid passage is such that, with laminar flow being maintained in the whole of the fluid passage, using substantially pure water at 70° F. as a standard, the flared entry portion has a "figure of merit", M which is calculated using consistent units from the relationship: ##EQU21## where, G.sub.2 = the mass flow rate of the substantially pure water through the fluid passage when the Reynolds number, R.sub.e, is at least 2000 in the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, and the Reynolds number, R.sub.e, in the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section is defined in consistent units by the relationship: ##EQU22## h = the width separating the parallel opposed major boundary surface portions, of the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, U = the mean velocity of the substantially pure water through the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, ρ = the density of the substantially pure water, μ = the absolute viscosity of the substantially pure water, ΔE.sub.2 = a static pressure differential between the substantially pure water at or upstream of the fluid inlet to the casing and the substantially pure water within the fluid passage at a position within the portion having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein and where the flow rate is G.sub.2 as previously defined immediately above and which is downstream of an outlet end of the flared entry portion by at least an amount L.sub.e and is determined in consistent units by the relationship: L.sub.e = 0.04 R.sub.e h when the Reynolds number, R.sub.e, is that where the flow rate is G.sub.2 as previously defined immediately above in the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, K.sub.2 is a constant and is defined in consistent units by ##EQU23## G.sub.1 = the mass flow rate of the substantially pure water through the fluid passage when the Reynolds number R.sub.e, is less than G.sub.2 and is at least 1000 in the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, and ΔE.sub.1 = a static pressure differential between the substantially pure water at or upstream of the fluid inlet to the casing and the substantially pure water within the fluid passage at a position within the portion having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein and where the flow rate is G.sub.1 as previously defined immediately above and which is downstream of the outlet end of the flared entry portion by at least an amount L.sub.e as previously defined, and where the flared entry portion "figure of merit", M, is within the limits determined by the relationship in consistent units: ##EQU24## where d.sub.h = the hydraulic diameter of the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for the flow of fluid therein, and is defined in consistent units by, ##EQU25## where A = cross-sectional area of the portion of the fluid passage having continuous boundary surface, and a substantially constant cross-section, normal to the mean direction for fluid flow therein, C = wetted perimeter of the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section, in a plane normal to the mean direction for fluid flow therein, and where h is as previously defined, and d. fluid pressure detecting means in the casing for detecting a fluid pressure differential in the fluid passage, between spaced positions in the mean direction for fluid flow therein, at least one of the positions being in the portion having continuous boundary surface and a substantially cross-section, whereby e. at least one fluid characteristic to be measured, selected from the group consisting of flow rate and viscosity, is related to the pressure differential indicated by the fluid pressure detecting means and is deducible therefrom in a consistent manner for any given fluid when laminar flow is maintained in the whole of the fluid passage.
  • 2. An apparatus according to claim 1, wherein the flared entry portion is continuously curved in the direction for fluid flow.
  • 3. An apparatus according to claim 2, wherein the flared entry portion has a gradual and continuous increase in radius of curvature in the direction for fluid flow.
  • 4. An apparatus according to claim 2, wherein the flared entry portion is radiused.
  • 5. An apparatus according to claim 1, wherein the flared entry portion is chamfered.
  • 6. An 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, which are elongated in cross-section normal to the mean direction for fluid flow therein with each passage having two parallel, opposed major boundary surface portions, which are parallel in a plane normal to the mean direction for fluid flow therethrough, each fluid passage comprising a flared entry portion and a portion having, in the mean direction for fluid flow therein, continuous boundary surface and a substantially constant cross-section, the flared entry portion of each passage being flared to decrease in width, without increasing in breadth, in the mean direction for fluid flow therein and forming an unobstructed flow path to the portion, having in the mean direction for fluid flow therein, continuous boundary surface and a substantially constant cross-section, a fluid inlet to the casing forming a substantially unobstructed flow path for fluid to the whole of an inlet area to the flared entry portion of each fluid passage, for each fluid passage said inlet area being normal to the mean direction for flow of fluid at an inlet end of the flared entry portion, a fluid outlet from the casing forming a substantially unobstructed flow path for fluid from the whole area of an outlet end of each fluid passage, for each fluid passage, said outlet area being normal to the mean direction for flow of fluid at the outlet end of that fluid passage, and wherein b. the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein has a magnitude of mean breadth which is at least as large as that given by a mean breadth to mean width ratio of 1.5 to 1, and an area in any plane normal to the mean direction for fluid flow therein which does not vary more than in the region of 2% from the mean area calculated in this manner for the whole length of the said portion of that fluid passage having continuous boundary surface and a substantially constant cross-section, and wherein c. the geometry of the flared entry portion of each fluid passage is such that, with laminar flow being maintained in the whole of each fluid passage, using substantially pure water at 70° F. as a standard, the flared entry portion of each fluid passage has a "figure of merit", M which is substantially the same for each fluid passage and which is calculated using consistent units from the relationship: ##EQU26## where, G.sub.2 = the mass flow rate of the substantially pure water through each of the fluid passages when the Reynolds number R.sub.e, is at least 2000 in the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, and the Reynolds number, R.sub.e, in the portion of each of the fluid passages having continuous boundary surface and a substantially constant cross-section is defined in consistent units by the relationship: ##EQU27## h = the width separating the parallel opposed major boundary surface portions, of the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, U = the mean velocity of the substantially pure water through the portion of each of the fluid passages having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, ρ = the density of the substantially pure water, μ = the absolute viscosity of the substantially pure water, ΔE.sub.2 = a static pressure differential between the substantially pure water at or upstream of the fluid inlet to the casing and the substantially pure water within each fluid passage at a position within the portion having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein and where the flow rate is G.sub.2 as previously defined immediately above and which is downstream of an outlet end of the flared entry portion by at least an amount L.sub.e and is determined in consistent units by the relationship: L.sub.e = 0.04 R.sub.e h when the Reynolds number, R.sub.e, is that where the flow rate is G.sub.2 as previously defined immediately above in the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, K.sub.2 is a constant and is defined in consistent units, ##EQU28## where G.sub.1 = the mass flow rate of the substantially pure water through each of the fluid passages when the Reynolds number R.sub.e, is less than G.sub.2 and is at least 1000 in the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, and ΔE.sub.1 = a static pressure differential between the substantially pure water at or upstream of the fluid inlet to the casing and the substantially pure water within each fluid passage at a position within the portion having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein and where the flow rate is G.sub.1 as previously defined immediately above and which is downstream of the outlet end of the flared entry portion by at least an amount L.sub.e as previously defined, and where the flared entry portion "figure of merit", M, is within the limits determined by the relationship in consistent units: ##EQU29## where d.sub.h = the hydraulic diameter of the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for the flow of fluid therein, and is defined in consistent units by, ##EQU30## A = cross-sectional area of the portion of each fluid passage having continuous boundary surface, and a substantially constant cross-section, normal to the mean direction for fluid flow therein, C = wetted perimeter of the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section, in a plane normal to the mean direction for fluid flow therein, and where h is as previously defined, and d. fluid pressure detecting means in the casing for detecting a fluid pressure differential in at least one of the fluid passages being spaced positions in the mean direction for fluid flow therein, at least one of the positions, being in a portion of that fluid passage having continuous boundary surface and a substantially constant cross-section, whereby e. at least one fluid characteristic to be measured, selected from the group consisting of flow rate and viscosity, is related to the pressure differential indicated by the pressure detecting means and is deducible therefrom in a consistent manner for any given fluid when laminar flow is maintained in the whole of each fluid passage.
  • 7. An apparatus according to claim 6, wherein each flared entry portion is continuously curved in the direction for fluid flow.
  • 8. An apparatus according to claim 7, wherein each flared entry portion has a gradual and continuous increase in radius of curvature in the direction for fluid flow.
  • 9. An apparatus according to claim 8, wherein the flared entry portion is radiused.
  • 10. An apparatus according to claim 6, wherein the flared entry portion is chamfered.
  • 11. An apparatus according to claim 6, wherein the flared entry portion has a double chamfer.