Flow measurement
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Flow measurement is the quantification of bulk fluid or gas movement. It can be measured in a variety of ways. Dependent on the quantity measured different symbols are used. The volumetric flow rate is usually given the symbol Q and the mass flow rate the symbol 
.
[edit] Units of measurement
Volumetric flow rate is sometimes measured in "standard cubic centimeters per minute" (abbreviation sccm), a unit acceptable for use with SI except that the additional information attached to the unit symbol. The SI standard would be m3/s (with any appropriate prefix, with temperature and pressure specified). The term "standard" indicates that the given flow rate assumes a standard temperature and pressure. Many other similar abbreviations are also in use, such as standard cubic feet per minute or per second. Other units used include gallons (U.S. liquid or imperial) per minute, liters per second, bushels per minute, and acre-feet per day.
[edit] Mechanical flow meters
There are three main types of mechanical meter
- Piston Meter
- Woltmann Meter
- Jet Meter.
Piston meters, or Semi-Positive displacement meters are the most common in the UK and are used for almost all meter sizes up to and including 40mm (1 1/2"). The piston meter operates on the principle of a piston rotating within a chamber of known volume. For each rotation, an amount of water passed through the piston chamber.
Woltman meters, commonly referred to as Helix meters are popular at larger sizes. Jet meters (single or Multi-Jet) are increasing in popularity in the UK at larger sizes and are commonplace in the EU, largely due to the inferior quality of drinking water compared to the UK.
Another method of measurement, known as a venturi meter, is to constrict the flow in some fashion, and measure the differential pressure that results across the constriction. This method is widely used to measure flow rate in the transmission of gas through pipelines, and has been used since Roman Empire times.
Another simple method of measurement uses an orifice plate, which is basically a plate with a hole through it. It is placed in the flow and constricts the flow. It uses the same principle as the venturi meter in that the differential pressure relates to the velocity of the fluid flow (Bernoulli's equation).
Measurement of the pressure within a pitot tube in the flowing fluid, or the cooling of a heated element by the passing fluid are two other methods that are used. These types of sensors are advantageous in that they are rugged, so not easily damaged in an extreme environment.
A pitot tube is an L shaped tube which is also able to measure fluid flow. An advantage is that it does not disturb the flow as much as a venturi meter or an orifice plate would. It works by measuring the difference between the static pressure and the dynamic pressure.
[edit] Vortex flowmeters
Another method of flow measurement involves placing an object (called a shedder bar) in the path of the fluid. As the fluid passes this bar, disturbances in the flow called vortices are created. The vortices trail behind the cylinder in two rolls, alternatively from the top or the bottom of the cylinder. This vortex trail is called the Von Kármán vortex street after von Karman's 1912 mathematical description of the phenomenon. The speed at which these vortices are created is proportional to the flow rate of the fluid. Inside the shedder bar is a piezoelectric crystal, which produces a small, but measurable, voltage pulse every time a vortex is created. The frequency of this voltage pulse is also proportional to the fluid flow rate, and is measured by the flowmeter electronics.
[edit] Magnetic, ultrasound and coriolis flow meters
Modern innovations in the measurement of flow rate incorporate electronic devices that can correct for varying pressure and temperature (i.e. density) conditions, non-linearities, and for the characteristics of the fluid.
[edit] Magnetic flow meters
The most common flowmeter apart from the mechanical flow meters, is the magnetic flow meter, commonly referred to as a "mag meter". A magnetic field is applied to the metering tube, which results in a potential difference proportional to the flow velocity perpendicular to the flux lines. The physical principle at work is Faraday's law of electromagnetic induction. The magnetic flow meter requires a conducting fluid, e.g. water, and an electrical insulating pipe surface, e.g. a rubber lined non magnetic steel tube.
[edit] Ultrasonic flow meters
Ultrasonic flowmeters measure the difference of the propagation time (transit time) of ultrasonic pulses propagating in (normally an inclination angle around 30 to 45° is used) flow direction and against the flow direction. This time difference is a measure for the averaged velocity of the fluid along the path of the ultrasonic beam. By using the absolute transit times both the averaged fluid velocity and the speed of sound can be calculated. Using the two transit times tup and tdown and the distance between receiving and transmitting transducers L and the inclination angle α one can write the equations 
and 
, where v is the average velocity of the fluid along the sound path and c is the speed of sound.
Measurement of the doppler shift resulting in reflecting an ultrasonic beam off the flowing fluid is another recent, accurate innovation made possible by electronics.
[edit] Coriolis flow meters
Using the Coriolis effect that causes a laterally vibrating tube to distort, a direct measurement of mass flow can be obtained in a Coriolis flow meter. Furthermore a direct measure of the density of the fluid is obtained. Coriolis measurement can be very accurate and is very insensitive to variations in the medium that is measured, the same measurement tube can be used for measuring anything between Hydrogen gas and for instance Peanut butter without recalibration.
[edit] Biomedical Transit-time Ultrasound Technology
Transit-time ultrasound technology for biomedical flow measurement was pioneered by Cornelis J. Drost who, working as a senior researcher at the N.Y.S. School of Veterinary Medicine at Cornell University, Ithaca, NY during the late 1970s, sought a measurement modality that did not have the problems inherent with electromagnetic flowmetry.
A transit-time ultrasound perivascular flowprobe (Fig. 1) consists of a probe body which houses ultrasonic transducers and a fixed acoustic reflector. The transducers are positioned on one side of the vessel or tube under study and the reflector is positioned at a fixed position between the two transducers on the opposite side. Electronic ultrasonic circuitry directs a flowprobe through the following cycles:
[edit] Upstream Transit-Time Measurement Cycle
An electrical excitation causes the downstream transducer to emit a plane wave of ultrasound. This ultrasonic wave intersects the vessel or tubing under study in the upstream direction, then bounces off the fixed "acoustic reflector." It again intersects the vessel and is received by the upstream transducer where it is converted into electrical signals. From these signals, the flowmeter derives an accurate measure of the "transit time" it takes for the wave of ultrasound to travel from one transducer to the other.
[edit] Downstream Transit-Time Measurement Cycle
The same transmit-receive sequence is repeated, but with the transmitting and receiving functions of the transducers reversed so that the flow under study is bisected by an ultrasonic wave in the downstream direction. The flowmeter again derives and records from this transmit-receive sequence an accurate measure of transit time it takes for the wave of ultrasound to travel from one transducer to the other.
Just as the speed of a swimmer depends, in part, on water currents, the transit time of ultrasound passing through a conduit is affected by the motion of liquid flowing through that vessel. During the upstream cycle, the sound wave travels against flow and total transit time is increased by a flow-dependent amount. During the downstream cycle, the sound wave travels with the flow and total transit time is decreased by the same flow-dependent amount. Using wide beam ultrasonic illumination, the Transonic flowmeter subtracts the downstream transit times from the upstream transit times. This difference in the integrated transit times is a measure of true volume flow.
[edit] Wide Beam Illumination
One ray of the ultrasonic beam undergoes a phase shift in transit time proportional to the average velocity of the liquid times the path length over which this velocity is encountered. With wide-beam ultrasonic illumination (Fig. 2), the receiving transducer sums (integrates) these velocity - chord products over the vessel's full width and yields volume flow: average velocity times the vessel's cross sectional area. Since the transit time is sampled at all points across the vessel diameter, volume flow measurement is independent of the flow velocity profile. Ultrasonic beams which cross the acoustic window without intersecting the vessel do not contribute to the volume flow integral. Volume flow is therefore sensed by perivascular probes even when the vessel is smaller than the acoustic window (Fig. 2).
[edit] Laser Doppler Theory
A low intensity beam of monochromatic light, emitted from a laser diode inside a BLF21-Series flowmeter travels via the probe’s fiber optic light guide through the probe head to illuminate the tissue under study.
There, the laser beam is scattered by reflective components within the tissue. A portion of the light is reflected back, via the probe’s receiving fiber optic light guide, onto a photo detector inside the flowmeter. Generally, this received light has been reflected many times by stationary structures within the tissue as well as by one or more moving particles (mainly red blood cells) within the tissue. It is the moving Doppler effect.
The received signal spectrum is processed in the BLF21 monitor in accordance with algorithms derived by Dr. R.F. Bonner for this type of reflective environment1 to calculate volume flow (ml x min-1 x 100-1 g) of tissue. While the actual volume of tissue sampled by the BLF21A varies with the optical properties of the tissue, it is approximately 1mm3.
FLOW ˜ ml x min-1 x 100-1 g tissue
While theory puts output for a laser Doppler flowmeter in units of milliliters per minute per hundred grams sampled (ml x min-1 x 100-1g of tissue), in practice this is somewhat problematic for several reasons. The most significant reason is that the actual volume of tissue sampled is unknown. This volume is assumed in the calculations to be 1 mm3, but it may vary widely with differing optical properties of the tissue. The output of the flow monitor is proportional to absolute flow in the tissue sampled, but since this quantity of tissue sample is different from one spot to another and one patient to another, the “constant” of proportionality differs for each placement of a probe.
Besides being unknown, the volume of tissue sampled is very small; this is both a strength and a weakness. Since the volume sampled is so small, laser Doppler flowmetry can look at very localized perfusion without being influenced by underlying tissues. But it can be misunderstood as, for example, a gauge of a whole organ perfusion rather than very local perfusion. This can be exaggerated by the unit (ml x min-1 x 100-1g of tissue. Assuming the nominal 1 mm3 is sampled, this sample weighs about 0.001 g; therefore, the more correct but unprecedented unit to quote would be hundreths of microliters per minute per milligram of tissue (0.01µ1 x mg-1 of tissue.) Of course, these units have the same ratio of volume to weight but it is important to remember that only about 1/100,000 of that one hundred grams of tissue is being sampled.
While typical range for certain tissues (notably free flap donor sites used in microvascular reconstructions) are very desirable and potentially useful, they must be used with upmost care. These ranges are subject to very large tolerances because meter to meter, probe to probe, tissue site to tissue site and patient to patient, variations are all additive.
From this discussion, we can conclude that the best and highest usage for laser Doppler flowmetry is for relative measurements. If the probe can be placed at one location, to continually monitor a given site for the duration of the critical period, the changes notes are directly proportional to absolute volume flow changes in the sampled tissue when proper monitoring technique is maintained. _____________________________________________________________
1Bonner, R.F., Clem, T.R., Bowen, P.D., Bowman, R.L., “Laser-Doppler Continuous Real-Time Monitor of Pulsatile and Mean Blood Flow in Tissue Microcirculation”, in Scattering Techniques, Applied to Supra-Molecular and Nonequilibrium Systems. Chen, S.H., Chu, B., Nossal, R., eds. New York: Plenum, pp 685-702.
[edit] Flow/dilution Technology; The Gold Standard for Hemodynamic Measurements during Hemodialysis
Flow/dilution technology for hemodynamic measurements during hemodialysis was pioneered by Nikolai Krivitski PhD, DSc during the early 1990s. Krivitski sought an easy-to-use method to measure recirculation, access blood flow and cardiac output to assess the quality of hemodialysis during the session. The technology married two well-established technologies: ultrasonic transit time and indicator dilution. Transit-time ultrasound had already been used to measure volume flow through sterile tubing with a clip-on tubing sensor. Krivitski developed the patented “Krivitski Method®” where, by temporarily reversing the blood lines at the needle connections, the proper mixing conditions are created to measure assess flow with classical indicator dilution equations. The two principles behind the measurements are outlined below.
[edit] Principle I:
Differential Transit-Time Ultrasound - Delivered Blood Flow
The clip-on sensor transmits a beam of ultrasound through the blood line. Two transducers pass ultrasonic signals back and forth, alternately intersecting the flowing blood in upstream and downstream directions. The Hemodialysis Monitor derives an accurate measure of the changes in "transit time" (time it takes for the wave of ultrasound to travel from one transducer to the other) resulting from the motion of the blood in the vessel. The difference between the upstream and downstream transit times is a measure of volume flow.
During hemodialysis two matched flow/dilution sensors are clipped onto the arterial and venous dialysis lines (Fig 1). The monitor continuously displays delivered blood flow. Comparison of this reading with the pump flow setting (i.e., the flow the pump tries to deliver) provides an opportunity to identify and correct dialysis delivery
[edit] Principle II:
Ultrasound Indicator Dilution - Patient Blood Flows & Recirculation The velocity of ultrasound in blood (1560-1590 m/sec) is determined primarily by its blood protein concentration. The Transonic® Hemodialysis Monitor and clip-on Flow/dilution Sensors measure ultrasound velocity. A bolus of isotonic saline (ultrasound velocity: 1533 m/sec) introduced into the blood stream dilutes the blood and reduces the ultrasound velocity. The sensor records this saline bolus as a conventional indicator dilution curve.
A bolus of saline indicator is introduced into the blood line. As the saline passes through the blood lines, the arterial and venous sensors each register an indicator dilution curve. The following measurements can be selected:
| - Access Recirculation: the Hemodialysis Monitor identifies the direct reflux of the venous saline indicator bolus into the arterial line (Fig. 3). The ratio of indicator concentrations equals access recirculation. High timing resolution enables identification of zero access recirculation (Fig. 3). |
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| - Cardiac Output: with blood lines in the normal configuration and no direct recirculation present, cardiopulmonary recirculation provides a measure of cardiac output (Fig. 6). The full saline indicator bolus travels into the heart where it is mixed (diluted) into the full cardiac output. Part of this diluted indicator then reappears at the Transonic® arterial sensor. Cardiac output and Cardiac Index are calculated via conventional Stewart-Hamilton analysis. |
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[edit] Flow/Dilution Hemodialysis Monitoring System
The Flow-QC® Hemodialysis Monitoring System consists of an ultrasonic blood property monitor, clamp-on flow/dilution sensors, and a data analysis software package. This self-contained, compact system is moved from patient to patient during routine dialysis treatments.
Monitor: The Flow-QC® Monitor processes information collected from the flow/dilution sensors before sending it to the computer for analysis and display. The monitor and computer communicate with each other through a serial cable. The monitor also displays ultrasound signal strength and delivered blood flow.
Computerized Data Analysis: The software records, stores and displays dilution curves, measurement values, historical graphs and detailed reports. It also has the capability of documenting interventions and identifying patients at risk for thrombosis, and produces clinic and patient statistics.
Sensors: Precision ultrasound flow/dilution sensors detect patient blood property data. One sensor is clipped to the venous blood line and the other to the arterial blood line with a small amount of petroleum jelly serving as ultrasound couplant.
[edit] True Delivered Blood Flow (Qb)
Transonic “gold standard” transit-time ultrasound flow technology is used to verify the actual blood flow delivered by the dialysis machine. Each sensor emits an ultrasound beam which travels through the tubing and blood both in upstream and downstream directions (Fig. 1). When the ultrasound beam travels in the direction of flow, the time it takes for the beam to traverse the distance through the tubing and blood (the transit-time) is decreased by a flow-dependent amount. When the beam travels in the opposite direction, against the flow in the tube, the beam’s transit time is increased by a flow-dependent amount. By subtracting upstream and downstream transit times, volume flow is calculated.
[edit] Access Recirculation (AR)
Clip-on flow/dilution sensors monitor the ultrasound velocity in blood. Ultrasound travels at 1560 to 1590 m/sec in blood. This velocity is determined primarily by the blood protein concentration. The greater the protein concentration, the faster ultrasound will travel. By introducing a bolus of isotonic saline (1533 m/sec) into the blood, the protein concentration is diluted and the ultrasound velocity is decreased. The reduced ultrasound velocity is recorded by the flow/dilution sensors and the monitor. When Access Recirculation exists, saline will immediately flow back into the arterial line (Fig. 2). Flow-QC® software converts the data into conventional dilution curves, the first representing the saline dilution as flow passes through the venous sensor and the second representing the saline dilution as flow passes through the arterial sensor. Recirculation is calculated as a ratio of the area under the arterial curve to the area under the venous curve (Fig. 3).
Recirculation is a late indicator of a failing access and generally occurs when access flow (AF) is less than dialysis pump flow (Qb). Because Transonic ultrasound dilution technology is able to separate actual vascular access recirculation from cardio-pulmonary recirculation (Fig. 4), measurement of zero percent access recirculation (0% AR) (Fig. 5) has become a reality.4,5 Technologies which cannot separate cardio-pulmonary recirculation from vascular access recirculation always indicate a false positive recirculation due to the presence of the former recirculation.
Figure 6 shows the typical flow of blood in a patienht with recirculation due to a venous stenosis. Access flow is not adequate for the demands of the pump setting. Lack of flow at the arterial needle is compensated for by reclaiming some part of the freshly dialyzed blood from the venous line.
A stenosis exists between the needles creates an important exception to the rule that recirculation (AR) usually occurs when access flow (AF) is less than dialysis pump flow (Qb) (Fig. 7). Because a stenosis limits flow through the access, the pump simply bypasses the stenosis (area of greatest hydrodynamic resistance). In this case zero recirculation (0% AR) can be reported although access flow (AF) is less than delivered blood flow (Qb). When Flow-QC® monitoring first indicates vascular access recirculation but the recirculation disappears after the blood lines are reversed, the hemodialysis lines have been inadvertently reversed. Published data report that dialysis occurs with the needles inadvertently reversed in 4-20% of cases.
[edit] Access Flow (AF)
Access Flow measurements are performed using the Krivitski Method® by reversing the blood lines at the needle connections. The dialyzer removes blood from the venous side of the access and returns it to the arterial side (Fig. 8). This creates mixing conditions used by the Krivitski Method® to generate an indicator dilution measurement of access flow.
By introducing saline into the venous line in the same manner as for access recirculation measurements, the blood protein concentration is diluted and ultrasound velocity is reduced. This change in blood protein concentration is detected by the venous line sensor, producing the blue dilution curve (Fig. 9). The diluted blood from the venous line then enters the access and mixes with the incoming access flow. Upon reaching the arterial needle, a portion of mixed blood is removed from the access by the dialyzer, via the venous needle. The diluted blood is detected by the arterial sensor producing a red dilution curve (Fig. 8). Access flow is calculated from the ratio of the area under the venous curve to the area under the arterial curve.
[edit] Cardiac Output (CO)
Indicator dilution in systemic flow provides a measure of cardiac output when blood lines are connected in the normal configuration and there is no direct vascular access recirculation (Fig. 4). In this instance, the complete saline indicator bolus travels into the heart where it mixes with (is diluted into) the full volume of blood leaving the heart. Part of this diluted indicator then reappears at the arterial sensor. Cardiac output is calculated via conventional Stewart-Hamilton analysis. Flow-QC software permits entry of additional patient data to calculate:
• Cardiac Index (CI): cardiac output divided by the estimated Body Surface Area (BSA).
• Peripheral Resistance (PR): the average resistance to systemic blood flow and is approximated as mean arterial pressure divided by cardiac output.
• Central Blood Volume (CBV) and Central Blood Volume Index (CBVI): the volume of blood in the heart, lungs, and the great vessels. CBVI is CBV divided by weight.
[edit] Thermal Dilution for Vascular Access Intra-graft Blood Flow Measurement
The HVT100 Endovascular Flowmeter and ReoCath™ Flow Catheter system uses classical dilution-based equations for flow measurements adapted to the unique hemodynamic conditions that exist within an AV access.
Intra-access blood flow measurements obtained using the HVT100 Endovascular Flowmeter are based upon the following equation:
Where: Q = intra-access blood flow;
k = a coefficient related to the thermal properties of blood, saline = 1.08
Tb = temperature of the blood prior to injection;
Ti = temperature of injected saline;
V = volume of injected saline (10ml);
S = the area under the temperature-time dilution curve resulting from the mixing of blood and injected saline;
t = width of the dilution curve at 50% height
The expression (0.5V/t) is an average expected increase in blood flow due to the saline injection.
[edit] How the Catheters Work
ReoCath™ 6 French Antegrade and Retrograde Flow Catheters each have an external injection port connected to its respective central lumen through which room temperature saline is released into the access during angioplasty.
Each catheter has two temperature sensors (thermistors). When the room temperature saline is injected into the access, a thermister located close to the proximal end of the catheter (Fig. 3,4) records the temperature of the injected saline solution. The second thermister located close to the distal tip of the catheter (Fig. 3,4) records the thermodilution within the access.
The catheter is connected to the HVT100 Endovascular Flowmeter via a two meter extension cable. The flowmeter calculates and displays intra-graft blood flow in milliliters per minute.
International & USA Patents Pending: 6,623,436, & 6,746,408
[edit] See also
- Mass flow rate
- Volumetric flow rate
- Gas meter
- Water Meter
- Orifice plate
- Automatic Meter Reading
- Airspeed indicator
- Air flow meter
- mass flow meter
- Laser Doppler velocimetry
[edit] External links
- American Waterworks Association - North American water meter standards organization
- Aalborg Instruments
- Actaris Group a World Leader in the design and manufacturing of meters and systems for water, heat, gas and electricity markets
- Clamp On Flow Meter
- DLJ Meter - Low Cost Water Metering Solutions
- Elster Group - The World's No1 Water Meter Company
- Flow meter types, terms, and associations
- KROHNE KROHNE - Supplier of Electromagnetic, Variable Area, and Coriolis Mass flowmeter
- Cole Parmer Flowmeters - Supplier of variable area flowmeters & flow meter controllers.
- Technologies explained
- Master Meter, Inc. - North American water meter manufacturer
- Malema Flow Sensors - Supplier of ultrasonic flow meters for the semiconductor industries.
- Micro Motion - Worldwide supplier of Coriolis flow meters, services, and solutions.
- Transonic Systems, Inc. From the Laboratory to the Operating Room, we provide accurate, intuitive, and reliable tools for flow verification.
- Flowmeter Directory - The internets most popular source of flowmeter information.
- EESiFlo - Concurrent Transit Time Flow Meters.
- Overview of Vortex Flowmeters - Efunda engineering fundamentals
- VPInstruments - Manufacturer of compressed air flow meters and thermal mass flow meters.
- Applied University Research, Inc. - Advanced laser-Doppler flow instruments and aero/hydrodynamic measurements contracting.
