Flow measurement

Gases are compressible and change volume when placed under pressure, are heated or are cooled. A volume of gas under one set of pressure and temperature conditions is not equivalent to the same gas under different conditions. References will be made to "actual" flow rate through a meter and "standard" or "base" flow rate through a meter with units such as acm/h (actual cubic meters per hour), sm³/sec (standard cubic meters per second), kscm/h (thousand standard cubic meters per hour), LFM (linear feet per minute), or MMSCFD (million standard cubic feet per day).

Gas mass flow rate can be directly measured, independent of pressure and temperature effects, with ultrasonic flow meters, thermal mass flowmeters, Coriolis mass flowmeters, or mass flow controllers.

For liquids, various units are used depending upon the application and industry, but might include gallons (U.S. or imperial) per minute, liters per second, liters per m² per hour, bushels per minute or, when describing river flows, cumecs (cubic meters per second) or acre-feet per day. In oceanography a common unit to measure volume transport (volume of water transported by a current for example) is a sverdrup (Sv) equivalent to 10⁶ m³/s.

Because they are used for domestic water measurement, piston meters, also known as rotary piston or semi-positive displacement meters, are the most common flow measurement devices in the UK and are used for almost all meter sizes up to and including 40 mm (1+1⁄2 in). The piston meter operates on the principle of a piston rotating within a chamber of known volume. For each rotation, an amount of water passes through the piston chamber. Through a gear mechanism and, sometimes, a magnetic drive, a needle dial and odometer type display are advanced.

A positive displacement flowmeter of the oval gear type. Fluid forces the meshed gears to rotate; each rotation corresponds to a fixed volume of fluid. Counting the revolutions totalizes volume, and the rate is proportional to flow.

An oval gear meter is a positive displacement meter that uses two or more oblong gears configured to rotate at right angles to one another, forming a T shape. Such a meter has two sides, which can be called A and B. No fluid passes through the center of the meter, where the teeth of the two gears always mesh. On one side of the meter (A), the teeth of the gears close off the fluid flow because the elongated gear on side A is protruding into the measurement chamber, while on the other side of the meter (B), a cavity holds a fixed volume of fluid in a measurement chamber. As the fluid pushes the gears, it rotates them, allowing the fluid in the measurement chamber on side B to be released into the outlet port. Meanwhile, fluid entering the inlet port will be driven into the measurement chamber of side A, which is now open. The teeth on side B will now close off the fluid from entering side B. This cycle continues as the gears rotate and fluid is metered through alternating measurement chambers. Permanent magnets in the rotating gears can transmit a signal to an electric reed switch or current transducer for flow measurement. Though claims for high performance are made, they are generally not as precise as the sliding vane design.[2]

Gear meters differ from oval gear meters in that the measurement chambers are made up of the gaps between the teeth of the gears. These openings divide up the fluid stream and as the gears rotate away from the inlet port, the meter's inner wall closes off the chamber to hold the fixed amount of fluid. The outlet port is located in the area where the gears are coming back together. The fluid is forced out of the meter as the gear teeth mesh and reduce the available pockets to nearly zero volume.

Helical gear flowmeters get their name from the shape of their gears or rotors. These rotors resemble the shape of a helix, which is a spiral-shaped structure. As the fluid flows through the meter, it enters the compartments in the rotors, causing the rotors to rotate. The length of the rotor is sufficient that the inlet and outlet are always separated from each other thus blocking a free flow of liquid. The mating helical rotors create a progressive cavity which opens to admit fluid, seals itself off and then opens up to the downstream side to release the fluid. This happens in a continuous fashion and the flowrate is calculated from the speed of rotation.

This is the most commonly used measurement system for measuring water supply in houses. The fluid, most commonly water, enters in one side of the meter and strikes the nutating disk, which is eccentrically mounted. The disk must then "wobble" or nutate about the vertical axis, since the bottom and the top of the disk remain in contact with the mounting chamber. A partition separates the inlet and outlet chambers. As the disk nutates, it gives direct indication of the volume of the liquid that has passed through the meter as volumetric flow is indicated by a gearing and register arrangement, which is connected to the disk. It is reliable for flow measurements within 1 percent.[3]

The turbine flowmeter (better described as an axial turbine) translates the mechanical action of the turbine rotating in the liquid flow around an axis into a user-readable rate of flow (gpm, lpm, etc.). The turbine tends to have all the flow traveling around it.

The turbine wheel is set in the path of a fluid stream. The flowing fluid impinges on the turbine blades, imparting a force to the blade surface and setting the rotor in motion. When a steady rotation speed has been reached, the speed is proportional to fluid velocity.

Turbine flowmeters are used for the measurement of natural gas and liquid flow.[4] Turbine meters are less accurate than displacement and jet meters at low flow rates, but the measuring element does not occupy or severely restrict the entire path of flow. The flow direction is generally straight through the meter, allowing for higher flow rates and less pressure loss than displacement-type meters. They are the meter of choice for large commercial users, fire protection, and as master meters for the water distribution system. Strainers are generally required to be installed in front of the meter to protect the measuring element from gravel or other debris that could enter the water distribution system. Turbine meters are generally available for 4 to 30 cm (1+1⁄2–12 in) or higher pipe sizes. Turbine meter bodies are commonly made of bronze, cast Iron, or ductile iron. Internal turbine elements can be plastic or non-corrosive metal alloys. They are accurate in normal working conditions but are greatly affected by the flow profile and fluid conditions.

Fire meters are a specialized type of turbine meter with approvals for the high flow rates required in fire protection systems. They are often approved by Underwriters Laboratories (UL) or Factory Mutual (FM) or similar authorities for use in fire protection. Portable turbine meters may be temporarily installed to measure water used from a fire hydrant. The meters are normally made of aluminum to be lightweight, and are usually 7.5 cm (3 in) capacity. Water utilities often require them for measurement of water used in construction, pool filling, or where a permanent meter is not yet installed.

The Woltman meter (invented by Reinhard Woltman in the 19th century) comprises a rotor with helical blades inserted axially in the flow, much like a ducted fan; it can be considered a type of turbine flowmeter.[5] They are commonly referred to as helix meters, and are popular at larger sizes.

A single jet meter consists of a simple impeller with radial vanes, impinged upon by a single jet. They are increasing in popularity in the UK at larger sizes and are commonplace in the EU.

The paddle wheel assembly generates a flow reading from the fluid flowing through the pipe instigating the spinning of the paddlewheel. Magnets in the paddle spin past the sensor. The electrical pulses produced are proportional to the rate of flow..

Paddle wheel flowmeters consist of three primary components: the paddle wheel sensor, the pipe fitting and the display/controller. The paddle wheel sensor consists of a freely rotating wheel/impeller with embedded magnets which are perpendicular to the flow and will rotate when inserted in the flowing medium. As the magnets in the blades spin past the sensor, the paddle wheel meter generates a frequency and voltage signal which is proportional to the flow rate. The faster the flow the higher the frequency and the voltage output.

The paddle wheel meter is designed to be inserted into a pipe fitting, either 'in-line' or insertion style. These are available with wide range of fittings styles, connection methods and materials such as PVDF, polypropylene, and stainless steel. Similar to turbine meters, the paddle wheel meter require a minimum run of straight pipe before and after the sensor.[6]

Flow displays and controllers are used to receive the signal from the paddle wheel meter and convert it into actual flow rate or total flow values. The processed signal can be used to control the process, generate an alarm, send signals to external etc.

Paddle wheel flowmeters (also known as Pelton wheel sensors) offer a relatively low cost, high accuracy option for many flow system applications, typically with water or water-like fluids.[6]

A multiple jet or multijet meter is a velocity type meter which has an impeller which rotates horizontally on a vertical shaft. The impeller element is in a housing in which multiple inlet ports direct the fluid flow at the impeller causing it to rotate in a specific direction in proportion to the flow velocity. This meter works mechanically much like a single jet meter except that the ports direct the flow at the impeller equally from several points around the circumference of the element, not just one point; this minimizes uneven wear on the impeller and its shaft. Thus these types of meters are recommended to be installed horizontally with its roller index pointing skywards.

The Pelton wheel turbine (better described as a radial turbine) translates the mechanical action of the Pelton wheel rotating in the liquid flow around an axis into a user-readable rate of flow (gpm, lpm, etc.). The Pelton wheel tends to have all the flow traveling around it with the inlet flow focused on the blades by a jet. The original Pelton wheels were used for the generation of power and consisted of a radial flow turbine with "reaction cups" which not only move with the force of the water on the face but return the flow in opposite direction using this change of fluid direction to further increase the efficiency of the turbine.

A propeller-type current meter as used for hydroelectric turbine testing.

Flow through a large penstock such as used at a hydroelectric power plant can be measured by averaging the flow velocity over the entire area. Propeller-type current meters (similar to the purely mechanical Ekman current meter, but now with electronic data acquisition) can be traversed over the area of the penstock and velocities averaged to calculate total flow. This may be on the order of hundreds of cubic meters per second. The flow must be kept steady during the traverse of the current meters. Methods for testing hydroelectric turbines are given in IEC standard 41. Such flow measurements are often commercially important when testing the efficiency of large turbines.

A Venturi meter constricts the flow in some fashion, and pressure sensors measure the differential pressure before and within 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. The coefficient of discharge of Venturi meter ranges from 0.93 to 0.97. The first large-scale Venturi meters to measure liquid flows were developed by Clemens Herschel, who used them to measure small and large flows of water and wastewater beginning at the very end of the 19th century.[8]

An orifice plate is a plate with a hole through it, placed perpendicular to the flow; it constricts the flow, and measuring the pressure differential across the constriction gives the flow rate. It is basically a crude form of Venturi meter, but with higher energy losses. There are three type of orifice: concentric, eccentric, and segmental.[9][10]

The Dall tube is a shortened version of a Venturi meter, with a lower pressure drop than an orifice plate. As with these flowmeters the flow rate in a Dall tube is determined by measuring the pressure drop caused by restriction in the conduit. The pressure differential is typically measured using diaphragm pressure transducers with digital readout. Since these meters have significantly lower permanent pressure losses than orifice meters, Dall tubes are widely used for measuring the flow rate of large pipeworks. Differential pressure produced by a Dall tube is higher than Venturi tube and nozzle, all of them having same throat diameters.

A pitot tube is used to measure fluid flow velocity. The tube is pointed into the flow and the difference between the stagnation pressure at the tip of the probe and the static pressure at its side is measured, yielding the dynamic pressure from which the fluid velocity is calculated using Bernoulli's equation. A volumetric rate of flow may be determined by measuring the velocity at different points in the flow and generating the velocity profile.[11]

Averaging pitot tubes (also called impact probes) extend the theory of pitot tube to more than one dimension. A typical averaging pitot tube consists of three or more holes (depending on the type of probe) on the measuring tip arranged in a specific pattern. More holes allow the instrument to measure the direction of the flow velocity in addition to its magnitude (after appropriate calibration). Three holes arranged in a line allow the pressure probes to measure the velocity vector in two dimensions. Introduction of more holes, e.g. five holes arranged in a "plus" formation, allow measurement of the three-dimensional velocity vector.

8-inch (203 mm) V-cone flowmeter shown with ANSI 300# (21 bar; 2.1 MPa) raised face weld neck flanges

Cone meters are a newer differential pressure metering device first launched in 1985 by McCrometer in Hemet, CA. The cone meter is a generic yet robust differential pressure (DP) meter that has shown to be resistant to effects of asymmetric and swirling flow. While working with the same basic principles as Venturi and orifice type DP meters, cone meters don't require the same upstream and downstream piping.[12] The cone acts as a conditioning device as well as a differential pressure producer. Upstream requirements are between 0–5 diameters compared to up to 44 diameters for an orifice plate or 22 diameters for a Venturi. Because cone meters are generally of welded construction, it is recommended they are always calibrated prior to service. Inevitably heat effects of welding cause distortions and other effects that prevent tabular data on discharge coefficients with respect to line size, beta ratio and operating Reynolds numbers from being collected and published. Calibrated cone meters have an uncertainty up to ±0.5%. Un-calibrated cone meters have an uncertainty of ±5.0%

Linear resistance meters, also called laminar flowmeters, measure very low flows at which the measured differential pressure is linearly proportional to the flow and to the fluid viscosity. Such flow is called viscous drag flow or laminar flow, as opposed to the turbulent flow measured by orifice plates, Venturis and other meters mentioned in this section, and is characterized by Reynolds numbers below 2000. The primary flow element may consist of a single long capillary tube, a bundle of such tubes, or a long porous plug; such low flows create small pressure differentials but longer flow elements create higher, more easily measured differentials. These flowmeters are particularly sensitive to temperature changes affecting the fluid viscosity and the diameter of the flow element, as can be seen in the governing Hagen–Poiseuille equation.[13][14]

The level of the water is measured at a designated point behind weir or in flume using various secondary devices (bubblers, ultrasonic, float, and differential pressure are common methods). This depth is converted to a flow rate according to a theoretical formula of the form ${\displaystyle Q=KH^{X}}$ where ${\displaystyle Q}$ is the flow rate, ${\displaystyle K}$ is a constant, ${\displaystyle H}$ is the water level, and ${\displaystyle X}$ is an exponent which varies with the device used; or it is converted according to empirically derived level/flow data points (a "flow curve"). The flow rate can then be integrated over time into volumetric flow. Level to flow devices are commonly used to measure the flow of surface waters (springs, streams, and rivers), industrial discharges, and sewage. Of these, weirs are used on flow streams with low solids (typically surface waters), while flumes are used on flows containing low or high solids contents.[17]

The cross-sectional area of the flow is calculated from a depth measurement and the average velocity of the flow is measured directly (Doppler and propeller methods are common). Velocity times the cross-sectional area yields a flow rate which can be integrated into volumetric flow. There are two types of area velocity flowmeter: (1) wetted; and (2) non-contact. Wetted area velocity sensors have to be typically mounted on the bottom of a channel or river and use Doppler to measure the velocity of the entrained particles. With depth and a programmed cross-section this can then provide discharge flow measurement. Non-contact devices that use laser or radar are mounted above the channel and measure the velocity from above and then use ultrasound to measure the depth of the water from above. Radar devices can only measure surface velocities, whereas laser-based devices can measure velocities sub-surface.[18]

A known amount of dye (or salt) per unit time is added to a flow stream. After complete mixing, the concentration is measured. The dilution rate equals the flow rate.

Acoustic Doppler velocimetry (ADV) is designed to record instantaneous velocity components at a single point with a relatively high frequency. Measurements are performed by measuring the velocity of particles in a remote sampling volume based upon the Doppler shift effect.[19]

In many late model automobiles, a Mass Airflow (MAF) sensor is used to accurately determine the mass flow rate of intake air used in the internal combustion engine. Many such mass flow sensors use a heated element and a downstream temperature sensor to indicate the air flowrate. Other sensors use a spring-loaded vane. In either case, the vehicle's electronic control unit interprets the sensor signals as a real-time indication of an engine's fuel requirement.

Magnetic flowmeters, often called "mag meter"s or "electromag"s, use a magnetic field applied to the metering tube, which results in a potential difference proportional to the flow velocity perpendicular to the flux lines. The potential difference is sensed by electrodes aligned perpendicular to the flow and the applied magnetic field. The physical principle at work is Faraday's law of electromagnetic induction. The magnetic flowmeter requires a conducting fluid and a nonconducting pipe liner. The electrodes must not corrode in contact with the process fluid; some magnetic flowmeters have auxiliary transducers installed to clean the electrodes in place. The applied magnetic field is pulsed, which allows the flowmeter to cancel out the effect of stray voltage in the piping system.

A Lorentz force velocimetry system is called Lorentz force flowmeter (LFF). An LFF measures the integrated or bulk Lorentz force resulting from the interaction between a liquid metal in motion and an applied magnetic field. In this case, the characteristic length of the magnetic field is of the same order of magnitude as the dimensions of the channel. It must be addressed that in the case where localized magnetic fields are used, it is possible to perform local velocity measurements and thus the term Lorentz force velocimeter is used.

There are two main types of ultrasonic flowmeters: Doppler and transit time. While they both utilize ultrasound to make measurements and can be non-invasive (measure flow from outside the tube, pipe or vessel, also called clamp-on device), they measure flow by very different methods.

Schematic view of a flow sensor.

Ultrasonic transit time flowmeters measure the difference of the transit time of ultrasonic pulses propagating in and against the direction of flow. This time difference is a measure for the average 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 ${\displaystyle t_{\text{up}}}$ and ${\displaystyle t_{\text{down}}}$ and the distance between receiving and transmitting transducers ${\displaystyle L}$ and the inclination angle ${\displaystyle \alpha }$ one can write the equations:

$${\displaystyle v={\frac {L}{2\;\cos \left(\alpha \right)}}\;{\frac {t_{\text{up}}-t_{\text{down}}}{t_{\text{up}}\;t_{\text{down}}}}}$$

and

$${\displaystyle c={\frac {L}{2}}\;{\frac {t_{\text{up}}+t_{\text{down}}}{t_{\text{up}}\;t_{\text{down}}}}}$$

where ${\displaystyle v}$ is the average velocity of the fluid along the sound path and ${\displaystyle c}$ is the speed of sound.

With wide-beam illumination transit time ultrasound can also be used to measure volume flow independent of the cross-sectional area of the vessel or tube.[22]

Ultrasonic Doppler flowmeters measure the Doppler shift resulting from reflecting an ultrasonic beam off the particulates in flowing fluid. The frequency of the transmitted beam is affected by the movement of the particles; this frequency shift can be used to calculate the fluid velocity. For the Doppler principle to work, there must be a high enough density of sonically reflective materials such as solid particles or air bubbles suspended in the fluid. This is in direct contrast to an ultrasonic transit time flowmeter, where bubbles and solid particles reduce the accuracy of the measurement. Due to the dependency on these particles, there are limited applications for Doppler flowmeters. This technology is also known as acoustic Doppler velocimetry.

One advantage of ultrasonic flowmeters is that they can effectively measure the flow rates for a wide variety of fluids, as long as the speed of sound through that fluid is known. For example, ultrasonic flowmeters are used for the measurement of such diverse fluids as liquid natural gas (LNG) and blood.[23] One can also calculate the expected speed of sound for a given fluid; this can be compared to the speed of sound empirically measured by an ultrasonic flowmeter for the purposes of monitoring the quality of the flowmeter's measurements. A drop in quality (change in the measured speed of sound) is an indication that the meter needs servicing.

Using the Coriolis effect that causes a laterally vibrating tube to distort, a direct measurement of mass flow can be obtained in a coriolis flowmeter.[24] Furthermore, a direct measure of the density of the fluid is obtained. Coriolis measurement can be very accurate irrespective of the type of gas or liquid that is measured; the same measurement tube can be used for hydrogen gas and bitumen without recalibration.

Coriolis flowmeters can be used for the measurement of natural gas flow.[25]

For pipe flows a so-called transit time method is applied where a radiotracer is injected as a pulse into the measured flow. The transit time is defined with the help of radiation detectors placed on the outside of the pipe. The volume flow is obtained by multiplying the measured average fluid flow velocity by the inner pipe cross-section. This reference flow value is compared with the simultaneous flow value given by the flow measurement to be calibrated.

The procedure is standardised (ISO 2975/VII for liquids and BS 5857-2.4 for gases). The best accredited measurement uncertainty for liquids and gases is 0.5%.[30]

The radiotracer dilution method is used to calibrate open channel flow measurements. A solution with a known tracer concentration is injected at a constant known velocity into the channel flow. Downstream the tracer solution is thoroughly mixed over the flow cross-section, a continuous sample is taken and its tracer concentration in relation to that of the injected solution is determined. The flow reference value is determined by using the tracer balance condition between the injected tracer flow and the diluting flow. The procedure is standardised (ISO 9555-1 and ISO 9555-2 for liquid flow in open channels). The best accredited measurement uncertainty is 1%.[30]