Flow Measurement: Volume Flow Rate

Volume flow rate is an appropriate way of quantifying the flow of all materials that are in a gaseous, liquid, or semiliquid slurry form (where solid particles are suspended in a liquid host), although measurement accuracy is inferior to mass flow measurement as noted earlier.

Materials in these forms are usually carried in pipes, and various instruments can be used to measure the volume flow rate as described later. As noted in the introduction, these all assume laminar flow. In addition, flowing liquids are sometimes carried in an open channel, in which case the volume flow rate can be measured by an open channel flowmeter.

Differential Pressure (Obstruction-Type) Meters

Differential pressure meters involve the insertion of some device into a fluid-carrying pipe that causes an obstruction and creates a pressure difference on either side of the device. Such meters are sometimes known as obstruction-type meters or flow restriction meters. Devices used to obstruct the flow include the orifice plate, Venturi tube, flow nozzle, and Dall flow tube,.When such a restriction is placed in a pipe, the velocity of the fluid through the restriction increases and the pressure decreases. The volume flow rate is then proportional to the square root of the pressure difference across the obstruction. The manner in which this pressure difference is measured is important. Measuring the two pressures with different instruments and calculating the difference between the two measurements is not satisfactory because of the large measurement error that can arise when the pressure difference is small. Therefore, the normal procedure is to use a differential pressure transducer, which is commonly a diaphragm-type device.

The pitot static tube is another device that measures flow by creating a pressure difference within a fluid-carrying pipe. However, in this case, there is negligible obstruction of flow in the pipe. The pitot tube is a very thin tube that obstructs only a small part of the flowing fluid and thus measures flow at a single point across the cross section of the pipe. This measurement only equates to average flow velocity in the pipe for the case of uniform flow. The annubar is a type of multiport pitot tube that measures the average flow across the cross section of the pipe by forming the mean value of several local flow measurements across the cross section of the pipe.

All applications of this method of flow measurement assume laminar flow by ensuring that the flow conditions upstream of the obstruction device are in steady state; a certain minimum length of straight run of pipe ahead of the flow measurement point is specified to achieve this.

The minimum lengths required for various pipe diameters are specified in standards tables.

However, a useful rule of thumb widely used in process industries is to specify a length of 10 times the pipe diameter. If physical restrictions make this impossible to achieve, special flow-smoothing vanes can be inserted immediately ahead of the measurement point.

Flow restriction-type instruments are popular because they have no moving parts and are therefore robust, reliable, and easy to maintain. However, one significant disadvantage of this method is that the obstruction causes a permanent loss of pressure in the flowing fluid. The magnitude and hence importance of this loss depend on the type of obstruction element used, but where the pressure loss is large, it’s sometimes necessary to recover the lost pressure by an auxiliary pump further down the flow line. This class of device is not normally suitable for measuring the flow of slurries, as the tappings into the pipe to measure the differential pressure are prone to blockage, although the Venturi tube can be used to measure the flow of dilute slurries.

--- approximately the way in which the flow pattern is interrupted when an orifice plate is inserted into a pipe. Other obstruction devices also have a similar effect to this, although the magnitude of pressure loss is smaller. Of particular interest is the fact that the minimum cross-sectional area of flow occurs not within the obstruction but at a point downstream of there. Knowledge of the pattern of pressure variation along the pipe is also of importance in using this technique of volume-flow-rate measurement. This shows that the point of minimum pressure coincides with the point of minimum cross-section flow a little way downstream of the obstruction. --- there is a small rise in pressure immediately before the obstruction. It’s therefore important not only to position the instrument measuring P2 exactly at the point of minimum pressure, but also to measure the pressure P1 at a point upstream of the point where the pressure starts to rise before the obstruction.

In the absence of any heat transfer mechanisms, and assuming frictionless flow of an incompressible fluid through the pipe, the theoretical volume flow rate of the fluid, Q, is given by …

[...]

where A1 and P1 are the cross-sectional area and pressure of the fluid flow before the obstruction, A2 and P2 are the cross-sectional area and pressure of the fluid flow at the narrowest point of the flow beyond the obstruction, and r is the fluid density.

Equation (1) is never entirely applicable in practice for two main reasons. First, the flow is always impeded by a friction force, which varies according to the type of fluid and its velocity and is quantified by a constant known as the Reynold's number. Second, the cross-sectional area of the fluid flow ahead of the obstruction device is less than the diameter of the pipe carrying it, and the minimum cross-sectional area of the fluid after the obstruction is less than the diameter of the obstruction. This latter problem means that neither A1 nor A2 can be measured accurately. Fortunately, provided the pipe is smooth and therefore the friction force is small, these two problems can be accounted for adequately by applying a constant called the discharge coefficient. This modifies Equation (16.1) to the following: where A'1 and A'2 are the actual pipe diameters before and at the obstruction and CD is the discharge coefficient that corrects for the friction force and the difference between the pipe and flow cross-section diameters.

Before the equation can be evaluated, the discharge coefficient must be calculated. As this varies between each measurement situation, it would appear at first sight that the discharge coefficient must be determined by practical experimentation in every case. However, provided that certain conditions are met, standard tables can be used to obtain the value of the discharge coefficient appropriate to the pipe diameter and fluid involved.

One particular problem with all flow restriction devices is that the pressure drop, (P1_P2), varies as the square of the flow rate Q according to Equation (2). The difficulty of measuring small pressure differences accurately has already been noted earlier. In consequence, the technique is only suitable for measuring flow rates that are between 30 and 100%of the maximum flow rate that a given device can handle. This means that alternative flow measurement techniques have to be used in applications where the flow rate can vary over a large range that can drop to below 30% of the maximum rate.

Orifice plate:

The orifice plate is a metal disc with a concentric hole in it, which is inserted into the pipe carrying the flowing fluid. Orifice plates are simple, inexpensive, and available in a wide range of sizes. In consequence, they account for almost 50% of the instruments used in industry for measuring volume flow rate. One limitation of the orifice plate is that its inaccuracy is typically at least _2% and may approach _5%. Also, the permanent pressure loss caused in the measured fluid flow is between 50 and 90% of the magnitude of the pressure difference, (P1_P2). Other problems with the orifice plate are a gradual change in the discharge coefficient over a period of time as the sharp edges of the hole wear away and a tendency for any particles in the flowing fluid to stick behind the hole, thereby reducing its diameter gradually as the particles build up. The latter problem can be minimized by using an orifice plate with an eccentric hole. If this hole is close to the bottom of the pipe, solids in the flowing fluid tend to be swept through, and buildup of particles behind the plate is minimized.

A very similar problem arises if there are any bubbles of vapor or gas in the flowing fluid when liquid flow is involved. These also tend to build up behind an orifice plate and distort the pattern of flow. This difficulty can be avoided by mounting the orifice plate in a vertical run of pipe.

Venturis and similar devices:

A number of obstruction devices are available that are specially designed to minimize pressure loss in the measured fluid. These have various names such as Venturi, flow nozzle, and Dall flow tube. They are all much more expensive than an orifice plate but have better performance. The smooth internal shape means that they are not prone to solid particles or bubbles of gas sticking in the obstruction, as is likely to happen in an orifice plate. The smooth shape also means that they suffer much less wear and, consequently, have a longer life than orifice plates. They also require less maintenance and give greater measurement accuracy.

Venturi: The Venturi has a precision-engineered tube of a special shape. This offers measurement uncertainty of only _1%. However, the complex machining required to manufacture it means that it’s the most expensive of all the obstruction devices discussed.

Permanent pressure loss in the measured system is 10_15% of the pressure difference (P1_P2) across it.

Dall flow tube: The Dall flow tube consists of two conical reducers inserted into a fluid carrying pipe. It has a very similar internal shape to the Venturi, except that it lacks a throat.

This construction is much easier to manufacture, which gives the Dall flow tube an advantage in cost over the Venturi, although the typical measurement inaccuracy is a little higher (_1.5%). Another advantage of the Dall flow tube is its shorter length, which makes the engineering task of inserting it into the flow line easier. The Dall tube has one further operational advantage in that the permanent pressure loss imposed on the measured system is only about 5% of the measured pressure difference (P1_P2).

Flow nozzle: This nozzle is of simpler construction still and is therefore less expensive than either a Venturi or a Dall flow tube, but the pressure loss imposed on the flowing fluid is 30-50% of the measured pressure difference (P1_P2) across the nozzle.

Pitot static tube:

The pitot static tube is used mainly for making temporary measurements of flow, although it’s also used in some instances for permanent flow monitoring. It measures the local velocity of flow at a particular point within a pipe rather than the average flow velocity as measured by other types of flowmeters. This may be very useful where there is a requirement to measure local flow rates across the cross section of a pipe in the case of non-uniform flow. Multiple pitot tubes are normally used to do this.

The instrument depends on the principle that a tube placed with its open end in a stream of fluid, will bring to rest that part of the fluid that impinges on it, and the loss of kinetic energy will be converted to a measurable increase in pressure inside the tube. This pressure (P1), as well as the static pressure of the undisturbed free stream of flow (P2), is measured. The flow velocity can then be calculated from the formula:

The constant C, known as the pitot tube coefficient, is a factor that corrects for the fact that not all fluid incident on the end of the tube will be brought to rest: a proportion will slip around it according to the design of the tube. Having calculated v, the volume flow rate can then be calculated by multiplying v by the cross-sectional area of the flow pipe, A.

Pitot tubes have the advantage that they cause negligible pressure loss in the flow. They are also inexpensive, and the installation procedure consists of the very simple process of pushing them down a small hole drilled in the flow-carrying pipe. Their main failing is that measurement inaccuracy is typically about _5%, although more expensive versions can reduce inaccuracy down to _1%. The annubar is a development of the pitot tube that has multiple sensing ports distributed across the cross section of the pipe and thus provides an approximate measurement of the mean flow rate across the pipe.

Variable Area Flowmeters (Rotameters)

In the variable area flowmeter (which is also sometimes known as a rotameter), the differential pressure across a variable aperture is used to adjust the area of the aperture. The aperture area is then a measure of the flow rate. The instrument is reliable, inexpensive, and used extensively throughout industry, accounting for about 20% of all flowmeters sold.

Normally, because this type of instrument only gives a visual indication of flow rate, it’s of no use in automatic control schemes. However, special versions of variable area flowmeters are now available that incorporate fiber optics. In these, a row of fibers detects the position of the float by sensing the reflection of light from it, and an electrical signal output can be derived from this.

In its simplest form the instrument consists of a tapered glass tube containing a float that takes up a stable position where its submerged weight is balanced by the up thrust due to the differential pressure across it. The position of the float is a measure of the effective annular area of the flow passage and hence of the flow rate. The inaccuracy of the least expensive instruments is typically _5%, but more expensive versions offer measurement inaccuracies as low as _0.5%.

Positive Displacement Flowmeters

Positive displacement flowmeters account for nearly 10% of the total number of flowmeters used in industry and are used in large numbers for metering domestic gas and water consumption.

The least expensive instruments have a typical inaccuracy of about _2%, but the inaccuracy in more expensive ones can be as low as _0.5%. These higher quality instruments are used extensively within the oil industry, as such applications can justify the high cost of such instruments.

All positive displacement meters operate using mechanical divisions to displace discrete volumes of fluid successively. While this principle of operation is common, many different mechanical arrangements exist for putting the principle into practice. However, all versions of positive displacement meters are low friction, low maintenance, and long life devices, although they do impose a small permanent pressure loss on the flowing fluid. Low friction is especially important when measuring gas flows, and meters with special mechanical arrangements to satisfy this requirement have been developed.

The rotary piston meter is a common type of positive displacement meter used particularly for the measurement of domestic water supplies. It consists of a slotted cylindrical piston moving inside a cylindrical working chamber that has an inlet port and an outlet port. The piston moves round the chamber such that its outer surface maintains contact with the inner surface of the chamber, and, as this happens, the piston slot slides up and down a fixed division plate in the chamber. At the start of each piston motion cycle, liquid is admitted to volume B from the inlet port. The fluid pressure causes the piston to start to rotate around the chamber, and, as this happens, liquid in volume C starts to flow out of the outlet port, and also liquid starts to flow from the inlet port into volume A. As the piston rotates further, volume B becomes shut off from the inlet port, while liquid continues to be admitted into A and pushed out of C. When the piston reaches the end point of its motion cycle, the outlet port is opened to volume B, and the liquid that has been transported round inside the piston is expelled. After this, the piston pivots about the contact point between the top of its slot and the division plate, and volume A effectively becomes volume C ready for the start of the next motion cycle. A peg on top of the piston causes a reciprocating motion of a lever attached to it. This is made to operate a counter, and the flow rate is therefore determined from the count in unit time multiplied by the quantity (fixed) of liquid transferred between inlet and outlet ports for each motion cycle.

The nutating disk meter is another form of positive displacement meter in which the active element is a disc inside a precision-machined chamber. Liquid flowing into the chamber causes the disc to nutate (wobble), and these nutations are translated into a rotary motion by a roller cam. Rotations are counted by a pulse transmitter that provides a measurement of the flow rate. This form of meter is noted for its ruggedness and long life. It has a typical measurement accuracy of _1.0%. It’s used commonly for water supply measurement.

The oval gear meter is yet another form of positive displacement meter that has two oval shaped gear wheels. It’s used particularly for measuring the flow rate of high viscosity fluids. It can also cope with measuring fluids that have variable viscosity.

Turbine Meters

A turbine flowmeter consists of a multi-bladed wheel mounted in a pipe along an axis parallel to the direction of fluid flow in the pipe. The flow of fluid past the wheel causes it to rotate at a rate proportional to the volume flow rate of the fluid. This rate of rotation has traditionally been measured by constructing the flowmeter such that it behaves as a variable reluctance tachogenerator. This is achieved by fabricating the turbine blades from a ferromagnetic material and placing a permanent magnet and coil inside the meter housing. A voltage pulse is induced in the coil as each blade on the turbine wheel moves past it, and if these pulses are measured by a pulse counter, the pulse frequency and hence flow rate can be deduced. In recent instruments, fiber optics are also now sometimes used to count the rotations by detecting reflections off the tip of the turbine blades.

Provided that the turbine wheel is mounted in low-friction bearings, measurement inaccuracy can be as low as _0.2%. However, turbine flowmeters are less rugged and reliable than flow restriction-type instruments and are affected badly by any particulate matter in the flowing fluid. Bearing wear is a particular problem, which also imposes a permanent pressure loss on the measured system. Turbine meters are particularly prone to large errors when there is any significant second phase in the fluid measured. For instance, using a turbine meter calibrated on pure liquid to measure a liquid containing 5% air produces a 50% measurement error. As an important application of the turbine meter is in the petrochemical industries, where gas/oil mixtures are common, special procedures are being developed to avoid such large measurement errors.

Readers may find reference in manufacturers' catalogs to a Woltmann meter. This is a type of turbine meter that has helical blades and is used particularly for measuring high flow rates. It’s also sometimes known as a helix meter.

Turbine meters have a similar cost and market share to positive displacement meters and compete for many applications, particularly in the oil industry. Turbine meters are smaller and lighter than the latter and are preferred for low-viscosity, high-flow measurements. However, positive displacement meters are superior in conditions of high viscosity and low flow rate.

Electromagnetic Flowmeters

Electromagnetic flowmeters, sometimes known just as magnetic flowmeters, are limited to measuring the volume flow rate of electrically conductive fluids. A typical measurement inaccuracy of around _1% is acceptable in many applications, but the instrument is expensive both in terms of the initial purchase cost and in running costs, mainly due to its electricity consumption. A further reason for its high cost is the need for careful calibration of each instrument individually during manufacture, as there is considerable variation in the properties of the magnetic materials used.

The instrument consists of a stainless-steel cylindrical tube fitted with an insulating liner, which carries the measured fluid. Typical lining materials used are neoprene, poly-tetrafluoroethylene, and polyurethane. A magnetic field is created in the tube by placing mains-energized field coils either side of it, and the voltage induced in the fluid is measured by two electrodes inserted into opposite sides of the tube. The ends of these electrodes are usually flush with the inner surface of the cylinder. The electrodes are constructed from a material that is unaffected by most types of flowing fluids, such as stainless steel, platinum-iridium alloys, Hastelloy, titanium, and tantalum. In the case of rarer metals in this list, the electrodes account for a significant part of the total instrument cost.

By Faraday's law of electromagnetic induction, the voltage, E, induced across a length, L, of the flowing fluid moving at velocity, v, in a magnetic field of flux density, B, is given by:

E = BLv,

where L is the distance between the electrodes, which is the diameter of the tube, and B is a known constant. Hence, measurement of voltage E induced across the electrodes allows flow velocity v to be calculated from Equation. Having thus calculated v, it’s a simple matter to multiply v by the cross-sectional area of the tube to obtain a value for the volume flow rate. The typical voltage signal measured across the electrodes is 1 mV when the fluid flow rate is 1 m/s.

The internal diameter of electromagnetic flowmeters is normally the same as that of the rest of the flow-carrying pipe work in the system. Therefore, there is no obstruction to fluid flow and consequently no pressure loss is associated with measurement. Like other forms of flowmeters, the electromagnetic type requires a minimum length of straight pipe work immediately prior to the point of flow measurement in order to guarantee the accuracy of measurement, although a length equal to five pipe diameters is usually sufficient.

While the flowing fluid must be electrically conductive, the method is of use in many applications and is particularly useful for measuring the flow of slurries in which the liquid phase is electrically conductive. Corrosive fluids can be handled, providing a suitable lining material is used. At the present time, electromagnetic flowmeters account for about 15% of the new flowmeters sold and this total is slowly growing. One operational problem is that the insulating lining is subject to damage when abrasive fluids are being handled, which can give the instrument a limited life.

New developments in electromagnetic flowmeters are producing instruments that are physically smaller than before. Also, by employing better coil designs, electricity consumption is reduced.

This means that battery-powered versions are now available commercially. Also, whereas conventional electromagnetic flowmeters require a minimum fluid conductivity of 10 mmho/cm^3 , new versions can cope with fluid conductivities as low as 1 mmho/cm^3

Vortex-Shedding Flowmeters:

The vortex-shedding flowmeter is used as an alternative to traditional differential pressure meters in many applications. The operating principle of the instrument is based on the natural phenomenon of vortex shedding, created by placing an non-streamlined obstacle (known as a bluff body) in a fluid-carrying pipe. When fluid flows past the obstacle, boundary layers of viscous, slow-moving fluid are formed along the outer surface. Because the obstacle is not streamlined, the flow cannot follow the contours of the body on the downstream side, and the separate layers become detached and roll into eddies or vortices in the low-pressure region behind the obstacle. The shedding frequency of these alternately shed vortices is proportional to the fluid velocity past the body. Various thermal, magnetic, ultrasonic, and capacitive vortex detection techniques are employed in different instruments.

Such instruments have no moving parts, operate over a wide flow range, have low power consumption, require little maintenance, and have a similar cost to measurement using an orifice plate. They can measure both liquid and gas flows, and a common inaccuracy value quoted is _1% of full-scale reading, although this can be seriously downgraded in the presence of flow disturbances upstream of the measurement point and a straight run of pipe before the measurement point of 50 pipe diameters is recommended. Another problem with the instrument is its susceptibility to pipe vibrations, although new designs are becoming available that have a better immunity to such vibrations.

Ultrasonic Flowmeters

The ultrasonic technique of volume flow rate measurement is, like the magnetic flowmeter, a non-invasive method. It’s not restricted to conductive fluids, however, and is particularly useful for measuring the flow of corrosive fluids and slurries. In addition to its high reliability and low maintenance requirements, a further advantage of an ultrasonic flowmeter over an electromagnetic flowmeter is that the instrument can be clamped externally onto existing pipework instead of being inserted as an integral part of the flow line. As the procedure of breaking into a pipeline to insert a flowmeter can be as expensive as the cost of the flowmeter itself, the ultrasonic flowmeter has enormous cost advantages. Its clamp-on mode of operation also has significant safety advantages in avoiding the possibility of personnel installing flowmeters coming into contact with hazardous fluids, such as poisonous, radioactive, flammable, or explosive ones. Also, any contamination of the fluid being measured (e.g., food substances and drugs) is avoided. Ultrasonic meters are still less common than differential pressure or electromagnetic flowmeters, although usage continues to expand year by year.

Two different types of ultrasonic flowmeter exist that employ distinct technologies-one based on Doppler shift and the other on transit time. In the past, the existence of these alternative technologies has not always been readily understood and has resulted in ultrasonic technology being rejected entirely when one of these two forms has been found to be unsatisfactory in a particular application.

This is unfortunate because the two technologies have distinct characteristics and areas of application, and many situations exist where one form is very suitable and the other is not. To reject both, having only tried out one, is therefore a serious mistake. Ultrasonic flowmeters have become available that combine both Doppler shift and transit time technologies.

Particular care has to be taken to ensure a stable flow profile in ultrasonic flowmeter applications.

It’s usual to increase the normal specification of the minimum length of straight pipe run prior to the point of measurement, expressed as a number of pipe diameters, from a value of 10 up to 20 or, in some cases, even 50 diameters. Analysis of the reasons for poor performance in many instances of ultrasonic flowmeter application h as shown failure to meet this stable flow profile requirement to be a significant factor.

Doppler shift ultrasonic flowmeter:

The principle of operation of the Doppler shift flowmeter is shown. A fundamental requirement of these instruments is the presence of scattering elements within the flowing fluid, which deflect the ultrasonic energy output from the transmitter such that it enters the receiver. These can be provided by solid particles, gas bubbles, or eddies in the flowing fluid. The scattering elements cause a frequency shift between transmitted and reflected ultrasonic energy, and measurement of this shift enables fluid velocity to be inferred.

The instrument consists essentially of an ultrasonic transmitter-receiver pair clamped onto the outside wall of a fluid-carrying vessel. Ultrasonic energy consists of a train of short bursts of sinusoidal waveforms at a frequency between 0.5 and 20 MHz. This frequency range is described as ultrasonic because it’s outside the range of human hearing. The flow velocity, v, is given by…

[…]

…where f_t and f_r are the frequencies of the transmitted and received ultrasonic waves, respectively, c is the velocity of sound in the fluid being measured, and y is the angle that the incident and reflected energy waves make with the axis of flow in the pipe. Volume flowrate is then calculated readily by multiplying the measured flow velocity by the cross-sectional area of the fluid carrying pipe.

The electronics involved in Doppler shift flowmeters is relatively simple and therefore inexpensive. Ultrasonic transmitters and receivers are also relatively inexpensive, being based on piezoelectric oscillator technology. Therefore, as all of its components are inexpensive, the Doppler shift flowmeter itself is inexpensive. The measurement accuracy obtained depends on many factors, such as the flow profile; the constancy of pipe wall thickness; the number, size, and spatial distribution of scatterers; and the accuracy with which the speed of sound in the fluid is known. Consequently, accurate measurement can only be achieved by the tedious procedure of carefully calibrating the instrument in each particular flow measurement application. Otherwise, measurement errors can approach _10%of the reading; for this reason, Doppler shift flowmeters are often used merely as flow indicators rather than for accurate quantification of the volume flow rate.

Versions are now available that are being fitted inside the flow pipe, flush with its inner surface.

This overcomes the problem of variable pipe thickness, and an inaccuracy level as small as _0.5% is claimed for such devices. Other recent developments are the use of multiple path ultrasonic flowmeters that use an array of ultrasonic elements to obtain an average velocity measurement. This reduces error due to non-uniform flow profiles substantially but there is a substantial cost penalty involved in such devices.

Transit time ultrasonic flowmeter:

A transit time ultrasonic flowmeter is an instrument designed for measuring the volume flow rate in clean liquids or gases. It consists of a pair of ultrasonic transducers mounted along an axis aligned at angle y with respect to the fluid flow axis.

Each transducer consists of a transmitter-receiver pair, with the transmitter emitting ultrasonic energy that travels across to the receiver on the opposite side of the pipe. These ultrasonic elements are normally piezoelectric oscillators of the same type used in Doppler shift flowmeters.

Fluid flowing in the pipe causes a time difference between the transit times of beams traveling upstream and downstream, and measurement of this difference allows the flow velocity to be calculated. The typical magnitude of this time difference is 100 ns in a total transit time of 100 ms, and high-precision electronics are therefore needed to measure the difference. There are three distinct ways of measuring the time shift. These are direct measurement, conversion to a phase change, and conversion to a frequency change. The third of these options is particularly attractive, as it obviates the need to measure the speed of sound in the measured fluid as required by the first two methods. A scheme applying this third option. This also multiplexes the transmitting and receiving functions so that only one ultrasonic element is needed in each transducer. The forward and backward transit times across the pipe, T_f and T_b, are given by

[...]

Transit time flowmeters are of more general use than Doppler shift flowmeters, particularly where the pipe diameter involved is large and hence the transit time is consequently sufficiently large to be measured with reasonable accuracy. It’s possible then to reduce the inaccuracy value down to _0.5%. However, the instrument costs more than a Doppler shift flowmeter because of the greater complexity of the electronics needed to make accurate transit time measurements.

Combined Doppler shift/transit time flowmeters:

Recently, some manufacturers have developed ultrasonic flowmeters that use a combination of Doppler shift and transit time. The exact mechanism by which these work is rarely, if ever, disclosed, as manufacturers wish to protect details from competitors. However, details of various forms of combined Doppler shift/transit time measurement techniques are filed in patent offices.

Other Types of Flowmeters for Measuring Volume Flow Rate

Gate-type meter:

A gate meter consists of a spring-loaded, hinged flap mounted at right angles to the direction of fluid flow in the fluid-carrying pipe. The flap is connected to a pointer outside the pipe. The fluid flow deflects the flap and pointer, and the flow rate is indicated by a graduated scale behind the pointer. The major difficulty with such devices is in preventing leaks at the hinge point.

A variation on this principle is the air vane meter, which measures deflection of the flap by a potentiometer inside the pipe. This is used to measure airflow within automotive fuel-injection systems. Another similar device is the target meter. This consists of a circular, disc-shaped flap in the pipe. Fluid flow rate is inferred from the force exerted on the disc measured by strain gauges bonded to it. This meter is very useful for measuring the flow of dilute slurries but does not find wide application elsewhere as it has a relatively high cost. Measurement uncertainty in all of these types of meters varies between 1 and 5% according to the cost and design of each instrument.

Jet meter:

These come in two forms-a single jet meter and a multiple jet meter. In the first, flow is diverted into a single jet, which impinges on the radial vanes of an impeller. The multiple jet form diverts the flow into multiple jets arranged at equal angles around an impeller mounted on a horizontal axis.

A paddle wheel meter is a variation of the single jet meter in which the impeller only projects partially into the flowing fluid.

Pelton wheel flowmeter:

This uses a similar mechanical arrangement to the old-fashioned water wheels used for power generation at the time of the industrial revolution. Flowing fluid is directed onto the blades of the flowmeter wheel by a jet, and the flow rate is determined from the rate of rotation of the wheel. This type of flowmeter is used to measure the flow rate of a diverse range of materials, including acids, aggressive chemicals, and hot fats at both low and high flow rates.

Special versions can measure very small flow rates down to 3 ml/min.

Laser Doppler flowmeter:

This instrument gives direct measurements of flow velocity for liquids containing suspended particles flowing in a pipe. Light from a laser is focused by an optical system to a point in the flow, with fiber-optic cables being used commonly to transmit the light. The movement of particles causes a Doppler shift of the scattered light and produces a signal in a photodetector that is related to the fluid velocity. A very wide range of flow velocities between 10 mm/s and 105 m/s can be measured by this technique.

Because sufficient particles for satisfactory operation are normally present naturally in most liquid and gaseous fluids, the introduction of artificial particles is rarely needed. The technique is advantageous in measuring flow velocity directly rather than inferring it from a pressure difference. It also causes no interruption in the flow and, as the instrument can be made very small, it can measure velocity in confined areas. One limitation is that it measures local flow velocity in the vicinity of the focal point of the light beam, which can lead to large errors in the estimation of mean volume flow rate if the flow profile is not uniform. However, this limitation can be used constructively in applications of the instrument where the flow profile across the cross section of a pipe is determined by measuring the velocity at a succession of points.

The final comment on this instrument has to be that although it could potentially be used in many applications, it has competition from many other types of instruments that offer similar performance at lower cost. Its main application at the present time is in measuring blood flow in medical applications.

Thermal anemometers:

Thermal anemometry was first used in a hot-wire anemometer to measure the volume flow rate of gases flowing in pipes. A hot-wire anemometer consists of a piece of thin (typical diameter 5 mm), electrically heated wire (usually tungsten, platinum of a platinum-iridium alloy) inserted into the gas flow. The flowing gas has a cooling effect on the wire, which reduces its resistance. Measurement of the resistance change (usually by a bridge circuit) allows the volume flow rate of the gas to be calculated. Unfortunately, the device is not robust because of the very small diameter of the wire used in its construction.

However, it has a very fast speed of response, which makes it an ideal measurement device in conditions where the flow velocity is changing. It’s also insensitive to the direction of gas flow, making it a very useful measuring device in conditions of turbulent flow.

Recently, more robust devices have been made by using a thin metal film instead of a wire.

In this form, the device is known as a hot-film anemometer. Typically, the film is platinum and is deposited on a quartz probe of a typical diameter of 0.05 mm. The increased robustness means that the hot-film anemometer is also used to measure the flow rate of liquids such as water.

Coriolis meter:

While the Coriolis meter is intended primarily to be a mass flow-measuring instrument, it can also be used to measure volume flow rate when high measurement accuracy is required.

However, its high cost means that alternative instruments are normally used for measuring volume flow rate.

Open Channel Flowmeters

Open channel flowmeters measure the flow of liquids in open channels and are particularly relevant to measuring the flow of water in rivers as part of environmental management schemes. The normal procedure is to build a weir or flume of constant width across the flow and measure the velocity of flow and the height of liquid immediately before the weir or flume with an ultrasonic or radar level sensor. The volume flow rate can then be calculated from this measured height.

As an alternative to building a weir or flume, electromagnetic flowmeters up to 180 mm wide are available that can be placed across the channel to measure the flow velocity, providing the flowing liquid is conductive. If the channel is wider than 180 mm, two or more electromagnetic meters can be placed side by side. Apart from measuring the flow velocity in this way, the height of the flowing liquid must also be measured, and the width of the channel must also be known in order to calculate the volume flow rate.

As a third alternative, ultrasonic flowmeters are also used to measure flow velocity in conjunction with a device to measure the liquid depth.

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