CA1241580A - Volumetric flow rate determination in conduits not directly accessible - Google Patents

Volumetric flow rate determination in conduits not directly accessible

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Publication number
CA1241580A
CA1241580A CA000492565A CA492565A CA1241580A CA 1241580 A CA1241580 A CA 1241580A CA 000492565 A CA000492565 A CA 000492565A CA 492565 A CA492565 A CA 492565A CA 1241580 A CA1241580 A CA 1241580A
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Prior art keywords
catheter
tube
sectional area
flow restriction
balloon
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CA000492565A
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French (fr)
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G. Gilbert Johnston
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    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B8/00Diagnosis using ultrasonic, sonic or infrasonic waves
    • A61B8/06Measuring blood flow
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B8/00Diagnosis using ultrasonic, sonic or infrasonic waves
    • A61B8/12Diagnosis using ultrasonic, sonic or infrasonic waves in body cavities or body tracts, e.g. by using catheters
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B8/00Diagnosis using ultrasonic, sonic or infrasonic waves
    • A61B8/44Constructional features of the ultrasonic, sonic or infrasonic diagnostic device
    • A61B8/4444Constructional features of the ultrasonic, sonic or infrasonic diagnostic device related to the probe
    • A61B8/445Details of catheter construction
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01FMEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
    • G01F1/66Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow by measuring frequency, phase shift or propagation time of electromagnetic or other waves, e.g. using ultrasonic flowmeters
    • G01F1/663Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow by measuring frequency, phase shift or propagation time of electromagnetic or other waves, e.g. using ultrasonic flowmeters by measuring Doppler frequency shift

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  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Physics & Mathematics (AREA)
  • Heart & Thoracic Surgery (AREA)
  • Molecular Biology (AREA)
  • Nuclear Medicine, Radiotherapy & Molecular Imaging (AREA)
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  • Radiology & Medical Imaging (AREA)
  • Engineering & Computer Science (AREA)
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  • General Health & Medical Sciences (AREA)
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  • Ultra Sonic Daignosis Equipment (AREA)

Abstract

VOLUMETRIC FLOW RATE DETERMINATION
IN CONDUITS NOT DIRECTLY ACCESSIBLE
Abstract A catheter, particularly adapted for cardiac output determination, comprises an elongated tube of flexible material, the tube having a substantially rigid distal portion on which is disposed an ultrasonic transducer and a proxi-mate; inflatable balloon. The ultrasonic transducer is arranged so as to direct a beam of ultrasound toward a transverse plane that bisects the balloon, and is connected by appropriate leads to a conventional Doppler circuit. With the balloon deflated, the signal from the Doppler circuit is sensed to measure bloodvelocity. Thereafter, the balloon is inflated so that it has a predetermined cross-sectional area in the transverse plane. The signal from the Doppler circuit is again sensed to measure blood velocity. Using a simple mathematical relationship, the effective internal cross-sectional area of the blood vessel isdetermined from the two measured velocities and from the predetermined cross-sectional area of the balloon when inflated. The volumetric flow rate is then determined by multiplying the first measured velocity by the effective internal cross-sectional area.

Description

~L~,4~580 VOLUMETRIC l~LOW RATE D~1~13RMINATION
IN CONDUlTS NOT DIRECTLY ACCESSIBLE
Field of the Invention This invention generally relates to methods and apparatus for fluid 5 flow determinations and, more particularly, to such methods and apparatus thatdetermine the volumetric flow rate of blood within, and the effective internal cross-sectional area of, portions of a biological circulatory system.
Background of the Invention Determination of the volumetric flow rate of fluid within a conduit 10 that is not directly accessible is typified by the determination of cardiac output, i.e., the volumetric flow rate of blood in the pulmonary artery. Various methodshave been commonly implemented in cardiac output determination and various other methods and apparatus have been proposed. The hallmark method is that expounded by Adolf Fick in 1870, and subsequently developed coincident with 15 modern cardiac catheterization techniques. 8100d samples;~re obtained from the pulmonary artery and from a systemic artery, and their oxygen content is measured. The consumption of oxygen per unit time, under steady state conditions, is either assumed or measured. Cardiac output is then calculated by dividing the oxygen consumption by the difference between the measured 20 arterial and mixed-venous oxygen content. Unfortunately, the method is complicated, cumbersome to use, and yields poorly reproducible results.
Dye-dilution methods also have been used widely but are not considered to be significantly more accurate or precise. Such methods employ an indicator dye which is injected as a bolus into a blood vessel. Thereafter, the 25 changing concentration of indicator dye is measured at a downstream site and plotted versus time. Cardiac output is then computed by integrating a portion under the resultant curve. Dye-dilution methods are hampered by problems of cumbersome apparatus, loss of indicator dye, recirculation of indicator dye, andanatomic circulatory shunts.

~415~30 The problems of indicator dye loss and recirculation essentially were solved by the thermal dilution modification introduced by Fegler in 1953.
In this method, a bolus of cold solution or "dye" is injected into the blood vessel through a proximal port of a multiple lumen catheter, and the subsequent 5 "dilution" or changing blood temperature with time is measured downstream through the use of a thermistor located on the distal end of the catheter. The resultant concentration- time variation is electronically integrated and cardiacoutput computed therefrom. A representative catheter for use in thermal dilution methods can be seen in U.S.P. 3,726,269, Webster, Jr. In its most widely 10 used form, this type of catheter also has an inflatable segment or balloon which is used as a flotation device to facilitate positioning of the catheter in the pulmonary artery. Reference, for example, U.S.P. 3,995,623, Blake et al., 4,024,873, Antoshkiw et al., 4,105,022, Antoshkiw et al., and 4,329,993, Lieber et al. Thermal dilution methods have proven, however, to be no more 15 accurate than the Fick method, require cumbersome apparatus, and yield information intermittently.
A plethora of additional methods and apparatus, all employing intravascular catheters or probes, have been proposed for cardiac output measurements. These include apparatus that determine cardiac output by 20 measurement of the differential temperature that results from localized heating of the blood (U.S.P. 3,359,974, Khalil; 3,798,967, Gieles et al.); that use electro-magnetic energy (U.S.P. 3,347,224, Adams); or that measure the conductivity of the blood (U.S.P. 3,896,373, Zelby). Yet another alterna~ve technique deter-mines cardiac output from balloon and arterial pressure signals obtained from a 25 balloon catheter (U.S.P. 3,985,123, Herzlinger et al.).
Perhaps the most promising methods for cardiac output determina-tions are those utilizing a catheter bearing an ultrasonic transducer. Reference, for example, U.S.P. 3,430,625, McLeod, Jr., which discloses an intravascular catheter bearing a pair of ultrasonic transducers at its tip. The transducers are 30 coupled with a Doppler circuit which applies a high-frequency electrical signal (typically in the mHz range) to one of the transducers so as to cause the transmission of ultrasonic energy therefrom. An electrical output signal from the other transducer resulting from returns of the transmitted ultrasonic energyfrom the blood cells, is compared with the high-requency electrical signal 35 applied to the transmitting transducer to develop a Doppler signal that is representative of any frequency shift caused by relative movement between the blood cells and the catheter The Doppler signal is therefore directly related to ~LZ4~0 blood velocity. Improved apparatus of this type, using a single transducer for transmission and reception, can be seen in United States Patent 3,443,433, Liston et al.
slood velocity by itself is not sufficient to determine cardiac output because the concurrent effective internal cross-sectional area of the blood vessel must also be known. In the past, such determination of effective internal cross-sectional area has been accomplished by the use of transducer arrays and range-gating or signal-power ratio processing methods, all of which require intricate and meticulously constructed transducers as well as complex electronic processing units. Reference, in this regard, United States Patent 3,542,014, Peronneau, 4,142,412, McLeod et al., 4,237,729, McLeod et al., 4,259,870, McLeod et al., and 4,232,373, Jackson et al. Although these methods are capable of providing superior accuracy and precision in the determination of cardiac output, the complexity and expense of the catheter and oE the related signal processing apparatus has significantly limited their widespread commercial application.
It is therefore the principal object of the invention to provide a method and apparatus for volumetric flow rate determin-ation, such as cardiac output determination, which employ a simply and inexpensively constructed catheter bearing an ultrasonic trans-ducer that can be discarded after a single use and which requires minimal signal processing in the necessary concurrent determination of conduit effective internal cross-sectional area.
Summary of the Invention ; Briefly, the invention resides in a method for determin-ing the effective internal cross-sectional area of a conduit, com-~.2~ Q

prising the steps of: measuring, by the use of ultrasonic energy, the unrestrlcted velocity of fluid at points where it passes through an imaginary plane transverse to the conduit; introducing a flow restriction into the conduit, said flow restriction having a predetermined cross-sectional area in said imaginary plane;
measuring, by the use of ultrasonic energy, the restricted velocity of the fluid at points where it passes through said imaginary plane; and, determining said effective internal cross-sectional area from said unrestricted veloeity, said restricted velocity, and said predetermined eross-seetional area.
The invention also provides a eatheter for use within an intravaseular eonduit, said eatheter eomprising: an elongated tube having a proximal portion of substantially flexible material and having a distal portion; flow restrietion means earried by said distal portion of said tube, said flow restrietion means being seleetively eontrollable between a first state in which said flow restrietion means does not substantially restrict flow through a referenee plane transverse to the longitudinal axis of such distal portion when said eatheter is in use in a location substantially fixed with respect to said reference plane and a second state in whieh said flow restrietion means does substantially restriet flow through said referenee plane when said eatheter is in said loeation;
and ultrasonie transducer means earried by said distal portion proximate said flow restrietion means, said ultrasonic transdueer means being eonstrueted and arranged so as to transmit and reeeive ultrasonie energy along a beam axis that interseets said reference plane at points always external to said flow restrietion means.

~158~
-4a- 2839-874 srief Description of the Drawings The invention can best be understood by reference to the following portion of the specification, taken in conjunction with the accompanying drawings in which:
FIGURE 1 is a pictorial view of a first embodiment of a catheter constructed according to the invention, particularly illustrating the distal portion thereof;
FIGURE 2 is a cross-sectional view taken along the line
2-2 in FIGURE l;
FIGURE 3 is a cross-sectional view taken along the line
3-3 in FIGURE l;
FIGURE 4 is a pictorial view illustrating use of the catheter;
FIGURES 5 and 6 are elevational views of the catheter distal portion, as situated within a blood vessel during use;
FIGURE 7 is a pictorial view of another embodiment of the catheter, in combination with a conventional balloon catheter; and, FIGURE 8 is a cross-sectional view taken along the line 8-8 in FIGURE 7.

o Description of the Preferred Embodiment With reference now to FIGURES 1-3, the distal portion of one embodiment of the catheter is formed by a hollow, substantially cylindrical member 10 that is preferably fabricated from a rigid plastic material such as an5 acrylic and that is fitted over and secured in an appropriate manner to an elongated flexiMe tubing 20 having defined therein a plurality of lumens 12, 14,16 and 18. The proximal portion of the catheter is provided with a plurality of smaller-diameter, elongated flexible tubings 22, 24 and 26. A preferred materialfor tubings 20, 22, 24 and 26 is a standard medical grade of a flexible poly-10 urethane or polypropylene. Tubings 22, 24 and 26 are fitted into or otherwisebrought into sealed fluid communication with lumens 12, 14 and 18, respectively,and an insulated electrical cable 28 passes into and along lumen 16. Lumen 12 terminates in a port 30 disposed in the exterior surface of tubing 20 that is located approximately 30-35 cm. from the distal end of the catheter, lumen 14 15 terminates in a port 32 in the substantially cylindrical exterior surface of member 10 intermediate the proximal and distal ends thereof, and lumen 18 terminates in a port 34 disposed in the distal end of the catheter.
A balloon 36 is carried by member 10 so as to cover port 32, and the respective ends of balloon 36 are secured in any appropriate manner to the ,~ 20 exterior surface of member 10 so as to provide a fluid-tight seal. Preferably, balloon is composed of a flexible, expandable material such as a standard medicsl grade of Silastic silicon rubber. At least one and preferably a pair of ultrasonic transducers 38 are disposed at the distal end of member 10 and secured thereto by appropriate adhesive material 40. Preferably, each ultrasonic25 transducer 38 includes a piezoelectric crystal, although various ceramic poly-mers can also be used. Suitable electrical connections (not illustrated) are made between the ultrasonic transducers 38 and the leads and shield of cable 28 resident within lumen 16. The transducers (and their connections) are covered with a layer of appropriate sealing material (not illustrated) such as an epoxy 30 resin to provide an electrical and fluid seal. Finally, each of the lumens 12, 14 and 16 is filled with an appropriate sealing material, from a point along its length beyond which the lumen is no longer required~o the distal end of the catheter, as has been illustrated by sealing~material~ in lumen~(PlGURE 3).
As best illustrated in FIGURES 5 and 6, transducers 38 are 35 mounted in diametrically opposing positions on member 10, and each trans-ducer 38 is disposed so that its beam is directed toward the proximal end of member 10 and thus toward balloon 36. More specifically, the beam axis of each ultrasonic transducer is arranged at an angle with respect to the longitudinal 3L58(~

a2ds of the catheter so as to intersect a plane PL transversely bisecting balloon 36 at the approximate midpoint thereof. Each beam axis must be unobstructed by balloon 36 not only when the balloon is unexpanded (FIGURE 5) but also when the balloon is expanded (FIGURE 6).
s With additional reference now to FIGURE 4, the distal end of the catheter is inserted into an appropriate vein and then advanced until it passes through the superior vena cava SVC, the right atrium RA, the tricuspid valve TV,the right ventricle RV, and into the main pulmonary artery PA. Tubing 22 going to the "proximal" port 30 is coupled to an appropriate pressure measuring 10 apparatus by a connector 42, and tubing 26 going to the "distal" port 34 is connected to an appropriate pressure measuring apparatus by a connector 44.
During the advancement of the catheter, pressure at either or both of these ports may be measured to assist in positioning of the catheter within the pulmonary artery PA. Cable 28 going to ultrasonic transducers 38 is coupled to a15 Doppler circuit and processor by an electrical connector 46. When the catheter has been appropriately positioned, the Doppler circuit applies a pulsed high-frequency electrical signal to the transducers which causes them to transmit ultrasonic energy. Reflected returns of the transmitted ultrasonic energy from objects within the beam of each transducer (e.g., blood cel1s moving within the 20 main pulmonary artery PA) are detected by the ultrasonic transducers and result in a corresponding return signal that is used by the Doppler circuit to develop a Doppler signal representative of the velocity of the objects within the beams ofthe ultrasonic transducers. By appropriate signal proces~ng techniques as are well known, the Doppler signal can be enhanced by the processor to eliminate 25 artifact and noise so that the Doppler signal represents solely blood velocity within the main pulmonary artery PA.
referring again to FIGURES 5 and 6, the blood velocity thus determined by the Doppler circuit is measured for the two conditions of balloon 36 illustrated. In FIGURE 5, the balloon is substantially unexpanded and30 the cross-sectional area of the catheter within transverse plane PL is such so as to have no appreciable effect upon the blood velocity within the main pulmonary artery PA in the vicinity of plane PL. In FIGURE 6, the balloon is substantiallyexpanded so that the balloon has a predetërmined and known cross-sectional area within transverse plane PL. One way to achieve such expansion is illustrated in 35 FIGURE 4, in which a syringe 50 containing a predetermined volume of fluid has been inserted into a connector 48 coupled to tubing 24, whereupon the fluid within syringe 50 may be injected into balloon 36 via tubing 24, lumen 14, and port 32 (FIGURES 1-3). Whatever the mechanism used to expand the balloon, the ~4~S13Q

resultant cross-sectional area within plane PL must be known and must be such so as to significantly increase the blood velocity through the remaining, unrestricted portions of the pulmonary artery in the vicinity of plane PL.
Given that the blood velocity V for the une~cpanded balloon condi-5 tion illustrated in FIGURE 5 and the blood velocity v for the expanded ballooncondition illustrated in FIGURE 6 have both been determined and recorded, and considering that the cross-sectional area a of the balloon when expanded is known, the effective internal cross-sectional area A of the main pulmonary artery PA can be easily determined by considering that the proportional relation:
V = A-a (1) can be rearranged as A = a ( v - V) (2) Having thus determined the effective internal cross-sectional area A, the volumetric flow rate (or cardiac output) is easily determined by multiplication of the effective internal cross-sectional area A by the blood velocity V.
As can be readily appreciated, the catheter described can be 20 simply and inexpensively constructed so as to permit one-time sterilization, use and disposal. If desired, automated apparatus can be provided for filling and emptying the balloon when measurements are to be made. In any event, the Doppler signal measurements and related determinations an be accomplished by a conventional Doppler circuit and a very simply programmed microprocessor.
Preferably, balloon 36 is hydrodynamically shaped so as to maintain the distal portion of the catheter centered within the blood stream and away from the walls of the pulmonary artery. To this end, the ends of balloon 36 are not rolled over on themselves during construction of the catheter, as is conventionally the case in the manufacture of other types of balloon catheters.
30 There is still a distinct possibility, however, that the distal portion of the catheter may lodge against one of the pulmonary artery wa11s, thereby sub-stantially blocldng blood flow on that side of the catheter. To avoid the resultant loss of velocity information that would result in such an event if a single ultrasbnic transducer were used, the preferred embodiment contemplates 35 as described the use of a pair of diametrically opposed transducers so that the beam of at least one of the transducers remains unobstructed at all times. Othertransducer constructions are contemplated to avoid this problem, such as a ring--8- ~Z4~5~30 type transducer emitting a conical beam at the angle relative to the catheter longitudinal axis.
The proximal and distal ports 30, 34 may be used for purposes other than pressure measurements, such as the infusion and withdrawal of appropriate 5 fluids. In fact, the principles of the invention can be applied to numerous catheter constructions such as the alternative embodiment illustrated in FIGURES 7 and 8, which is substantially identical to that previously described with the exception that tubing 20' includes an additional, central lumen 60 extending frorn its proximal end to its distal end. Lumen 60, which is larger in10 diameter than the remaining lumens in tubing 20', is used for the passage of a conventional balloon catheter 61 consisting of an elongated flexible tubing 62 that carries an inflatable balloon 64 on its distal portion. As best seen in FIGURE 8, tubing includes a pair of lumens 66 and 68, with lumen 66 terminating in a port 70 that is surrounded by balloon 64 and with lumen 68 15 terminating in the distal end of tubing 62.
In use, the catheter assembly in FIGURE 7 is inserted into the venous system until the distal portion thereofl is resident within the main pulmonary artery PA as illustrated in FIGIIRE~. Thereafter, the conventionQl balloon catheter 61 is further advanced an appropriate distance. When 20 catheter 61 has been properly positioned, balloon 64 thereon is inflated (by injection of fluid into the balloon via lumen 66 and port 70) so as to create a wedge within the peripheral artery branch. As will be appreciated by those skilled in the art, measurements can be made concurrently;,~f not only pulmonaryartery pressure and cardiac output (as previously described) but also of 25 pulmonary artery wedge pressure (by the use of an appropriate pressure measuring apparatus coupled to lumen 68 within catheter 61).
While the invention has been described with reference to a preferred embodiment, it is to be clearly understood by those skilled in the artthat the invention is not limited thereto. For example, the rigidification of the 30 catheter's distal portion afforded by member 10 is desirable to insure that the beam of each transducer 38 remains at a substantially constant angle relative tothe catheter's longitudinal QXiS (and thus relative to balloon 36) during measure-ments. An alternate embodiment of the catheter would elimlnate member 10 (wherein the transducers 38 and balloon 36 would be directly affixed to 35 tubing 20) and would maintain the desired transducer/balloon relationship by appropriate design of those elements and choice of their materials or by the insertion of a relatively stiff yet flexible wire into one of the tubing lumens after the catheter's distal portion had been appropriately positioned in-situ.

~L~,4158~

Accordingly, the scope of the invention is to be interpreted only in conjunctionwith the appended claims.

;,

Claims (13)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. A catheter for use within an intravascular conduit, said catheter comprising:
an elongated tube having a proximal portion of substan-tially flexible material and having a distal portion;
flow restriction means carried by said distal portion of said tube, said flow restriction means being selectively controll-able between a first state in which said flow restriction means does not substantially restrict flow through a reference plane transverse to the longitudinal axis of such distal portion when said catheter is in use in a location substantially fixed with respect to said reference plane and a second state in which said flow restriction means does substantially restrict flow through said reference plane when said catheter is in said location; and ultrasonic transducer means carried by said distal por-tion proximate said flow restriction means, said ultrasonic trans-ducer means being constructed and arranged so as to transmit and receive ultrasonic energy along a beam axis that intersects said reference plane at points always external to said flow restriction means.
2. The catheter of claim 1, wherein said ultrasonic trans-ducer means is distal relative to said flow restriction means.
3. The catheter of claim 2, wherein said ultrasonic trans-ducer means is positioned adjacent the distal end of said tube.
4. The catheter of claim 1, wherein said ultrasonic trans-ducer means includes a pair of ultrasonic transducers that are dis-posed in diametrically opposing positions on said distal portion of said tube.
5. The catheter of claim 1, further comprising control means carried by said tube, said flow restriction means including an expandable member carried by said distal portion of said tube, said control means being for selectively contracting and expanding said expandable member to achieve said first and said second states of said flow restriction means.
6. The catheter of claim 5, wherein said expandable member is hydrodynamically shaped when expanded so as to substantially center said distal portion of said tube in the conduit when said catheter is in use.
7, The catheter of claim 6, wherein said expandable member is a balloon and said control means includes a lumen defined within said tube that extends from the proximal end of said tube to the vicinity of said balloon and a port coupling said lumen to the interior of said balloon.
8. The catheter of claim 1, wherein said distal portion of said tube is substantially rigid.
9. The catheter of claim 8, further comprising a hollow, substantially cylindrical member of substantially rigid material that is fitted over and secured to said distal portion of said tube, and wherein said flow restriction means and said ultrasonic transducer means are secured to said hollow member.
10. The catheter of claim 1, wherein said tube has defined therein first and second lumens extending from the vicinity of the proximal end of said tube to said distal portion thereof, said first lumen terminating substantially at a first port in said tube that is proximal relative to said flow restriction means and said ultrasonic transducer means and said second lumen terminating sub-stantially at a second port in said tube that is distal relative to said flow restriction means and said ultrasonic transducer means.
11. The catheter of claim 1, wherein said tube has defined therein a lumen extending from the vicinity of the proximal end of said tube to said distal portion thereof, said lumen terminating in a port in the distal end of said tube and being constructed so as to permit the passage therethrough of a balloon catheter.
12. A method for determining the volumetric flow rate of a fluid in a conduit whose effective internal cross-sectional area is unknown, comprising the steps of:
measuring, by the use of ultrasonic energy, the unre-stricted velocity of the fluid at points where it passes through an imaginary plane transverse to the conduit;
introducing a flow restriction into the conduit, said flow restriction having a predetermined cross-sectional area in said imaginary plane;
measuring, by use of ultrasonic energy, the restricted velocity of the fluid at points where it passes through said imaginary plane;
determining said effective internal cross-sectional area from said unrestricted velocity, said restricted velocity, and said predetermined cross-sectional area; and, determining said volumetric flow rate from said unre-stricted velocity and said determined effective internal cross-sectional area.
13. A method for determining the effective internal cross-sectional area of a conduit, comprising the steps of:
measuring, by the use of ultrasonic energy, the unre-stricted velocity of fluid at points where it passes through an imaginary plane transverse to the conduit;
introducing a flow restriction into the conduit, said flow restriction having a predetermined cross-sectional area in said imaginary plane;
measuring, by the use of ultrasonic energy, the restricted velocity of the fluid at points where it passes through said imaginary plane; and, determining said effective internal cross-sectional area from said unrestricted velocity, said restricted velocity, and said predetermined cross-sectional area.
CA000492565A 1984-11-01 1985-10-09 Volumetric flow rate determination in conduits not directly accessible Expired CA1241580A (en)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US667,333 1984-11-01
US06/667,333 US4637401A (en) 1984-11-01 1984-11-01 Volumetric flow rate determination in conduits not directly accessible

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CA1241580A true CA1241580A (en) 1988-09-06

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US (1) US4637401A (en)
EP (1) EP0200758B1 (en)
JP (1) JPS62500703A (en)
CA (1) CA1241580A (en)
DE (1) DE3571919D1 (en)
WO (1) WO1986002540A1 (en)

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EP0200758A1 (en) 1986-11-12
JPS62500703A (en) 1987-03-26
US4637401A (en) 1987-01-20
EP0200758B1 (en) 1989-08-02
WO1986002540A1 (en) 1986-05-09
DE3571919D1 (en) 1989-09-07

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