Industrial Flow Measurements

Industrial Flow Measurements

Technological processes in the industry require measurements of flows for the purpose of the control of the processes. Optimum performance of some equipment and operations need specific flow rates. Hence, the accurate measurement of flow rates is very important in industrial applications.

Flow measurements consist of measuring the flow rate of solids, liquids and gases. The two basic ways of measuring the flow are (i) on volumetric basis, and (ii) on weight basis. Solid materials are measured in terms of either weight per unit time or mass per unit time. Very rarely solid quantity is measured in terms of volume. Liquids are measured either in volume rate or in weight rate. Gases are normally measured in volume rate.

The units used to describe the flow measured can be of several types depending on how the specific process needs the information. Solids are normally expressed in weight rate like tons/hour, or kg/minute etc. Liquids can be expressed either in weight rate or in volume rate like tons/hour, kg/minute, litres/hour, litres/minute, and cum/hour etc. Gases are normally expressed in volume rate either at NTP (normal temperature and pressure) or STP (standard temperature and pressure) such as Std. cum/hour or N cum/hour etc. Steam is generally expressed in weight rate like tons/hour, or kg/minutes etc., since the density of the steam at different temperatures and pressures vary. Hence the measurement is converted into weight rate of water which is used to produce steam at the point of measurement.

Fluids are classified into two types, namely incompressible and compressible. Fluids in liquid phase are incompressible whereas fluids in gaseous phase are compressible. Liquid occupies the same volume at different pressures where as gases occupy different volumes at different pressures. This point has to be taken care of while calibrating the flow meters. The measurements taken at actual conditions are to be converted either to standard temperature (0 deg C) and pressure (760 mm Hg) base (STP base) or to Normal temperature (20 deg C) and pressure (760 mm Hg) base (NTP base). The various terms used for the flow and flow rate sensing are described below.

Velocity – It is a measure of speed and direction of an object. When related to fluids, it is the rate of flow of fluid particles in a pipe. The speed of particles in a fluid flow varies across the flow, i.e., where the fluid is in contact with the constraining walls (the boundary layer) the velocity of the liquid particles is virtually zero while in the centre of the flow the liquid particles have the maximum velocity. Thus, the average rate of flow is used in flow calculations. The units of flow are normally meters per second (mps), and so on. The pressures associated with fluid flow are defined as static, impact, or dynamic.

Laminar flow – Laminar flow (Fig 1) of a liquid occurs when its average velocity is comparatively low and the fluid particles tend to move smoothly in layers. The velocity of the particles across the liquid takes a parabolic shape.

Turbulent flow – It occurs when the flow velocity is high and the particles no longer flow smoothly in layers and turbulence or a rolling effect occurs (Fig 1). The flattening of the velocity profile takes place.

ViscosityIt is a property of a gas or liquid which is a measure of its resistance to motion or flow. A viscous liquid has a much higher viscosity than water and water has a higher viscosity than air. A viscous liquid, because of its high viscosity, flows very slowly and it is very hard to move an object through it. Viscosity (dynamic) can be measured in poise or centipoise, whereas kinematic viscosity (without force) is measured in stokes or centistokes. Dynamic or absolute viscosity is used in the Reynolds and flow equations. Typically the viscosity of a liquid decreases as temperature increases.

Reynolds number (R) -The Reynolds number is a derived relationship combining the density and viscosity of a liquid with its velocity of flow and the cross-sectional dimensions of the flow and takes the form R = (V x D x d)/v where V is the average fluid velocity, D is the diameter of the pipe, d is the density of the liquid, and v is the absolute viscosity.

Flow patterns – Flow patterns (Fig 1) can be considered to be laminar, turbulent, or a combination of both. Osborne Reynolds observed in 1880 that the flow pattern could be predicted from physical properties of the liquid. If the Reynolds number for the flow in a pipe is equal to or less than 2000 the flow is laminar, from 2000 to around 5000 is the intermediate region where the flow can be laminar, turbulent, or a mixture of both, depending upon other factors, and  beyond 5000 the flow is always turbulent.

Fig 1 Flow patterns

Vortex formation – A projecting obstruction at the wall extends the length of the boundary layer and restrains the fluid even more in the vicinity of the wall so that downstream of this restriction a dead zone with a slightly negative pressure exists. The fluid flows from the region of higher velocity into this dead zone and creates vortices (Fig 1).

Karman Vortex Street – When a body is placed in the middle of a media flow, separation occurs and vortices are formed on both sides if velocity or Reynolds number R is above a certain value. It is interesting to note, that after a vortex has formed on one side a similar vortex forms on the other side which causes the first one to be shed. That periodic vortices are shed from each side alternately was discovered by Karman after whom the vortex street is named. These usually undesirable vortices are utilized as the basis for the measurement in vortex flow meters.

Bernoulli equation – The Bernoulli equation is an equation for flow based on the law of conservation of energy, which states that the total energy of a fluid or gas at any one point in a flow is equal to the total energy at all other points in the flow.

Energy factors – Most flow equations are based on the law of energy conservation and relate the average fluid or gas velocity, pressure, and the height of fluid above a given reference point. This relationship is given by the Bernoulli equation. The equation can be modified to take into account energy losses due to friction and increase in energy as supplied by pumps. Energy losses in flowing fluids are caused by friction between the fluid and the containment walls and by fluid impacting an object. In most cases, these losses are to be taken into account. Whilst these equations apply to both liquids and gases, they are more complicated in gases because of the fact that gases are compressible.

Flow rate – It is the volume of fluid passing a given point in a given amount of time.

Total flow – It is the volume of the fluid flowing over a period of time.

The variety of choices available for the flow measuring devices is very large since nearly every flow meter category can be further sub-divided into a variety of distinctly different sub-categories.

Flow rate and total flow measurement

Fluid flow measurement can be divided into several types. Each type needs specific considerations of such factors as accuracy requirements, cost considerations, and use of the flow information to obtain the required end results. Normally the flow meter measures the flow indirectly by measuring a related property such as a differential pressure across a flow restriction or a fluid velocity in a pipe. A number of different fundamental physical principles are used in flow measurement devices. The features, characteristics, and limitations of some of the more widely used flow sensor categories are described below. 

There are different methods for measuring the flow rate and the total flow. Each method has its own specific characteristics. In the following, the most important measuring principles are described and compared to each other.

Total flow meters, normally volume totalizers, are devices filled with a defined volume which is then measured and integrated to determine the total flow volume. Direct volume totalizers have movable measuring chambers with a defined volume. Indirect volume totalizers, on the contrary, do not have closed measuring chambers, but work either mechanically by using rotary vanes and transporting partial volumes between the vanes, or electrically with pulses which are proportional to the volume.

Flow meters also use the direct method for measured value acquisition. They measure either the flow velocity or the kinetic energy of the flow.

The task of selecting the technically best and most cost effective measuring device for an application is quite difficult. The following device descriptions and selection criteria assist the process of selection.

Volume totalizers

Volume totalizers (Fig 2) with moving measuring chambers driven by the measuring medium are also known as displacement meters. They are suitable for both liquids and gases. They are direct volume totalizers since they transport the measuring medium in chambers with defined, geometrically limited volumes. Among the direct volume totalizers are those with measuring vanes (also known as turbine totalizers) and volume totalizers with forced flow changes. In this method a pulse total is generated which represents a specific (not geometrically bounded) volume.

Fig 2 Types of volume totalizers

Oval gear totalizers – The measuring element of an oval gear totalizer (Fig 2) consists of two oval gears. The driving liquid produces the required torque, which varies as a function of the gear position, to rotate the gears. For example, the torques on the lower gear in the left side of Fig 2 cancel each other while the torque on the upper gear is one sided and actually causes the rotation. Around the upper gear a bounded crescent like volume exists which is pushed towards the outlet of the meter. Each rotation of the pair of oval gears transports a defined liquid volume. The number of rotations is hence an exact measure of the quantity of liquid which has flowed through the meter. The precision teeth assure a good seal between the two gears. The clearance between the oval gears and the walls of the measuring chambers is so small that the leakage flow (gap loss) is negligible.

The rotations of the pair of oval gears are transmitted without a stuffing box to an indicator either by a permanent magnet coupling or by a feedback-free magnetic field controlled pulse transmitter. The gears and bearings are subject to mechanical wear. Through selection of materials for the housing, oval gears, and bearings as well as by design consideration of expansions due to high temperatures, oval gear totalizers are suitable for almost all operating conditions.

The error limits represent the relationship to the measuring medium, especially as a function of its viscosity. For low viscosities and a given accuracy, the span is appreciably smaller than for higher viscosities. It is comprehensible that the pressure drop increases with increasing viscosity.

Oscillating piston totalizers – In this type of totalizer (Fig 2), the oscillating piston in a cylindrical housing a hollow cylinder, oscillates eccentrically. In this manner it transports defined volumes. The stationary outer cylinder (4) is also the housing, in which a dividing wall (1) and a guide ring (3) are mounted. The dividing wall on the bottom of the housing provides the boundary between the inlet (E) and outlet (A) openings. The bearing for the oscillating piston (5) is mounted in the sleeve (2) and is guided along the dividing wall. Openings for filling and draining are located in its base. In positions (a) and (b) the oscillating piston volume V2 is filled. The liquid forces the oscillating piston away so that the housing volume V1 can be filled. At the same time the force from the piston causes the portion of the liquid volume V1 in the right side to be discharged. When position (d) is reached, the volume V1 has been completely discharged once and refilled, the volume V2 begins its discharge phase. One rotation of the oscillating piston encompasses both volumes, V1 and V2. The movement of the piston bearing (2) is transmitted to an indicator using a magnet and follower arrangement. In a direct piston totalizer the magnetic coupling is not utilized and the rotary motion of the piston is transmitted directly from the piston to the totalizer.

Since the oscillating piston wears rapidly, proper material selection is very important. Various materials are available such as gray cast iron, bronze, hard rubber, carbon and plastics. For high temperature operation an intermediate spacer is used to provide additional separation from the totalizer. Oscillating piston totalizers are especially used for water and oil measurement.

These totalizers have high accuracy attainable at high viscosity due to a decrease in leakage losses (gap losses). The oscillating piston totalizers are still operational at viscosities as high as 10,000 mPa·s (millipascal-second).

Lobed impeller gas totalizers – These consist of two rotating impellers, designed with a figure eight cross-section (Fig 2). The impellers rotate in opposite directions due to the forces exerted by the gas being measured. The shape of the impellers prevents contact while the gap between them remains constant. A gear drive external to the measuring chamber synchronizes the impellers. During each rotation four crescent shaped volumes are moved through the measuring chamber. The number of rotations is proportional to the gas flow. The rotation is coupled using an adjustable fine tooth gear train to the totalizer.

An unmeasured flow, which is a function of the pressure drop, flows through the gaps. The negative error is compensated by an adjustment. The viscosity of gases increases at high pressures and reduces the losses in the gaps which compensates for the higher losses which otherwise exists due to the higher pressure difference.

The pulsations in the gas discharge can cause the pipe system connected to the meter to vibrate. If resonance occurs, loud noises and sudden pressure drops can result. This condition is not to be allowed to occur. If necessary, noise or pulsation dampers are to be used.

The pressure drop results from the mechanical and dynamic resistances in the meter. The dynamic portion increases appreciably with increasing load. Lobed impeller meters are very susceptible to contamination. Since contamination affects the pressure drop, it is required to be monitored and the meter cleaned when required.

Turbine totalizers – Turbine totalizers are indirect volume totalizers in which the flow causes a vaned rotor to revolve. The number of rotor revolutions is proportional to the total flow and the frequency of the revolutions to the flow rate. The various designs are differentiated by the direction of the inflow and by the method utilized for measured value acquisition.

Rotary vane totalizer – In the rotary vane totalizer (Fig 2), the flow entry is tangential and causes the wheel to revolve in the totalizer. A gear train is utilized to transmit the rotations of the wheel axle to the totalizer which, in wetted designs, is located in the measuring medium. Rotary vane totalizers are available as single jet or as multi-jet designs.

Dry design units separate the indicator chamber from the measuring chamber and transmit the rotation through a magnetic coupling. Rotary vane totalizers are used as domestic water meters and also, in hot water design, as volume measuring elements for smaller heat quantity totalizers.

Woltman totalizer – In case of a Woltman totalizer (Fig 2), the axle of the totalizer rotor is in parallel with the flow direction. This means the flow is axial to the turbine wheel. A low-friction gear train connects the axle to the totalizer through a magnetic coupling. There are two distinct designs of Woltman totalizers. One is with a horizontal turbine wheel (WP) and the other is with a vertical turbine wheel (WS). The vertical design offers the advantage of minimal bearing friction and hence a higher sensitivity. The pressure drop however is appreciably higher because of the shape of the flow passage. The horizontal design allows the totalizer to be mounted in any orientation (e.g. vertical), a larger flow range and lower pressure drops. The Woltman totalizer is used primarily as a water meter, but also as a volume measuring element for heat quantity totalizers.

There is a combination water totalizer (WPV) which has been designed for wide spans. It is a combination of two totalizers, a large (main totalizer) and a small (secondary) one. An automatic pressure controlled spring loaded valve switches to the range that is best suited for the measuring ranges of both totalizers. While the cold water meters have an upper temperature limit of 40 deg C, the hot water meter can be used upto 120 deg C. With appropriate material selections the Woltman totalizer can also be used in industrial applications for de-ionized water.

Turbine flow meter – Turbine wheel totalizers (WP), normally known as turbine flow meters (Fig 3), are similar in their design to Woltman totalizers, with one essential difference i.e. the measurement of the rotation is made electrically with almost no feedback on the rotor. The turbine rotors are light in weight producing minimal friction in the bearings. As a result, the span can be expanded since the system responds with greater sensitivity. Smaller nominal diameters are possible. The turbine flow meter measures gases and liquids with increased viscosities.

A coil in the housing opposite the rotor measures the signal using various methods as given below.

  • A magnet in one vane induces a voltage pulse in the coil during every revolution.
  • The coil encloses a magnet. The vanes are made of a ferro-magnetic material. As the vanes pass the magnet, the magnetic field is distorted inducing a voltage pulse.
  • A high-frequency AC voltage (10 kHz) is applied to the coil. The ferro-magnetic vane varies the amplitude of the supply voltage resulting in a secondary frequency superimposed on the carrier frequency.

In all three cases, a frequency signal is generated which is proportional to the number of revolutions and hence to the flow rate. The signal is fed to a preamplifier in the connected converter. In this manner the totalizer, each of whose individual pulses represents a defined volume, becomes a flow meter as a result of the time based frequency which is generated. This device can measure at higher viscosities, with the restriction, however, that the start of the linear proportional range is shifted. Further, the span is reduced as the viscosity increases.

A special turbine flow meter variation is the turbine gas totalizer for measuring large gas flows. The gas flow velocity is increased by a reducer at the inlet with a ring shaped cross-section and guided over the freely turning rotor. The revolutions which are measured are mechanically transmitted to the totalizer using a gear train.

Fig 3 Types of flow meters

Vortex flow meter – There are several examples of the effects of vortex formation at bodies around which there is flow. Normally a flow obstruction causes vortices. On a free standing body vortices are formed on both sides which are alternately shed resulting in the formation of a Karman Vortex Street. If the geometric distance is ‘l’ between two consecutive vortices and the time interval is ‘t’ when viewed from a fixed reference point, then the vortex shedding frequency ‘f’ is around ‘l/t’, Strouhal discovered a relationship between geometry and velocity (v) in which ‘f’ is around ‘v/d’. In this relationship equation, ‘d’ is the diameter of the round bluff body. The Strouhal number ‘St’, a proportionality constant named after Strouhal, gives ‘f = St x (v/d)’. The requirement for the bluff body is that the geometry of vortex formation does not change with the flow rate and that the Strouhal number remains constant over a wide range of Reynolds number. The shape and the area ratio in the pipe define the manner of vortex shedding and the constancy of the Strouhal number. The pressure drop is not to be too large. The optimum shape of the bluff body has been determined empirically and through calculations. The minimum Reynolds number value Rmin defines the lower range value, i.e. the span decreases with increasing viscosity. The upper limit of ‘R’ is so high that it is negligible for the upper range value.

There are various methods of vortex determination. The vortices generate periodic pressure and velocity variations. These provide a corollary means for the measurement. The sensor is placed either behind the bluff body or in the bluff body in such a manner that it can vibrate freely (the location is determined by the nominal diameter and the type of connection). Its tongue is forced to vibrate at the shedding frequency by the pressure differences. Piezo-elements inside the sensor convert the resulting pressure forces into electrical measuring pulse signals which can be amplified. An arrangement of four Piezo-sensors is normally selected to cancel pipeline vibrations.

If the flow profile of the measuring medium is distorted (vortices, swirl) as it flows into the measuring section, the vortices cannot form properly. For this reason, straight steadying sections are to be provided upstream of the device, the length of which depends on the type of the distortion.  Vortex flow meters (Fig 3) can be used for measuring the flow of steam, gases and liquids. The model of flow meter with integral mount design integrates the sensor and transmitter in a single unit with a local indicator for the flow rate and totalized flow value. The transmitter is based on a digital signal processor and generates the 4-20 mA analog output signals. As a two-wire device, it requires a supply voltage of 14 V DC- 46 V DC which is fed through the analog output two-wire line. A binary output is available in addition to the analog output. This output can be configured as a pulse output or limit contact (contact output). The measurement display for gases and liquids is made in direct reading engineering units. Utilizing an integrated Pt 100 in the flow sensor, a saturated steam measurement or temperature monitoring option can be incorporated. The transmitter can also be mounted remotely at a distance from the sensor if a special cable is used.

Swirl flow meters – In the swirl flow meters (Fig 3), a guide body whose shape is similar to a stationary turbine rotor is located in the inlet of the measuring device. The measuring medium is forced to rotate and flows through the meter tube of the swirl flow meter in a thread like rotation. The swirl stabilizes in the cylindrical section of the meter tube. A consideration of the cross sections in this region shows that the rotational velocity at the wall is relatively small and increases toward the tube centre until a stable vortex core is formed at the centre. During the transition of the flow into the expanding section of the tube the vortex core is displaced because a back flow occurs in the expander section.

The vortex core forms a spiral like secondary rotation whose frequency is linearly proportional to the flow rate over a wide range. This secondary rotation is measured with a Piezo-sensor. The Piezo-sensor utilizes the resultant pressure differences for its pulse measurements. The same sensors are used in both the swirl and vortex flow meters. The vortex shedding frequency is between 1 Hz and 2000 Hz. The higher frequencies indicating higher flow rates. In the transmitter the sensor signals are converted into further processable outputs. The transmitter used for the swirl flow meter is the same as the one used for the vortex flow meter.

The special advantage of a swirl flow meter over other systems is the fact that it needs only short inlet and outlet sections. It is important to avoid cavitation when measuring liquids. Sufficient static pressure is required to exist in the measuring section for this reason.

 Flow meters for differential pressure measurement

The relationship between the pressure drop due to a restricted pipe section and the volume flow rate is a physical phenomenon which is the basis for the differential pressure measurements, where a differential pressure flow primary in the piping (which is required to be running full) causes a pressure difference or differential pressure. Fig 4 shows the pressure curve in a primary flow differential pressure product (orifice plate). It shows the conversion of the energy forms. In the restricted section, the kinetic energy (dynamic pressure Pdyn) increases due to the increase in velocity and the pressure energy (static pressure Pstat) decreases. The pressure differential is due to the difference between the static pressures upstream and the pressure at or directly downstream of the restriction. A partial recovery of the energy occurs downstream of the restriction due to the reduction in the velocity, but there remains some permanent, unrecovered pressure drop Pbl.

Beta ratio in an orifice plate is the ratio between the line inner diameter to bore size of the orifice. The flow coefficient is found to be stable between beta ratio is between 0.2 to 0.7 below which the uncertainty in flow measurement increases. The differential pressure measurement method is a universally utilized measuring principle for flow measurement. Differential pressure flow meters can be used for measuring gases and liquids even at extremely high pressures and temperatures. The meters have been optimized by extensive developmental activities over decades and the results are published as standards.

Various designs are available which can provide the optimal meter for the operating conditions and requirements of the user. An important consideration is, for example, the pressure drop, which as a rule is to be small, or the length of the straight inlet and outlet sections, which can be relatively short for venturi tubes.

The most cost effective design is the orifice plate. Fig 4 shows corner tap arrangements in (B, D) as individual taps and in (A) using angular chambers. The D and D/2 tap arrangement is shown in (C). The pressure connections for the flange tap arrangement (E) with standard 25.4 mm spacing are made by drilling through the flanges. They are often combined with an annular chamber arrangement (A).

Fig 4 Orifice plate and orifice designs

Nozzles have lower pressure drops, but need especially precise manufacture. Venturi tubes and Venturi nozzles are characterized by small pressure drops. Both are also available in shortened versions. The pressure drop is an important factor in evaluating the various designs. Pressure drop means energy loss and increased pumping/compression.

While comparing the range of possible installations between orifices, nozzles and venturi tubes and nozzles, it is quite apparent that orifices are universal, but have the basic disadvantage of high pressure drop. It is important that the edges of the orifice remain sharp. This causes the orifice to be sensitive to contamination and abrasion.

It is easily understandable that meters as thoroughly studied as differential pressure meters can satisfy many special requirements. Hence, for measuring media containing solids, segmental orifices are utilized in which the measuring zone is restricted only at the top. Also wedge meters are a good solution for such kind of applications. For measuring media with high viscosities, the quarter circle nozzle can be used to Reynolds numbers as low as 50. Nozzles with a throat diameter of 0.6 mm can be used to meter liquid flow rates as low as 2 litres per hour. These nozzles are together with or without the differential pressure transmitter in a single assembly available.

Compact orifice flow meters

To overcome the technical and economic issues involved in correctly creating an orifice- based flow metering installation, the concept of compact orifice flow meters has been created. These comprise all of the traditional components such as (i) orifice carrier, (ii) pressure taps, (iii) 3-valve manifold, (iv) differential pressure transmitter (optionally a multivariable transmitter), and (v) optional integral temperature assembly for gas/steam flow calculations, fabricated into a single flow meter assembly.

As a one-piece, factory-assembled flow meter, compact orifice flow meter has a greatly-reduced number of potential leakage points and takes minimal efforts to install them correctly. Accuracy is enhanced by the compact orifice flow meter being easily and precisely centered in the piping using the supplied tool. Due to its integral mount design and the reduced number of potential leakage points, this measuring device offers improved long-term stability.

Wedge meters for critical applications

The operating principle of a wedge meter (Fig 5) is simple and easy to understand. The wedge meter is equipped with a V-shaped flow restrictor which reduces the area available to flow. Fluid velocity increases as flow is contracted at the flow restrictor. The increase in velocity results in an increase in the kinetic energy of the measuring medium. By the principle of conservation of energy, any increase in kinetic energy is to be accompanied by a corresponding decrease in potential energy (static pressure). Thus, the measuring medium directly upstream of the flow restrictor has a greater potential energy (and higher static pressure) than the medium immediately downstream of the flow restrictor. Pressure taps placed on either side of the wedge meter allows the differential pressure which develops as a result of this imbalance in potential energy to be measured. The volume flow rate can then be directly calculated from the measured differential pressure. Some of the pressure loss created by the flow restriction is recovered downstream of the wedge meter as kinetic energy is converted back to the potential energy.

A wedge meter is a refinement of a segmental orifice. Whereas the segmental orifice offers a sudden restriction to flow, the wedge meter provides for a gradual restriction. The latter has various advantages over the segmental orifice design, including immunity to erosion and immunity to build-up by any secondary phase. The immunity to erosion is the result of the slanted upstream face of the flow restrictor, which prevents damage due to impingement with any undissolved solids in the measuring medium. The opening beneath the restriction is large and allows for easy passage of any secondary phase. Eddies and back currents created provide a ‘self-scouring’ action which keeps the internals clean and free from build-up.

Wedge meters are designed to measure flow accurately in all flow regimes namely (i) laminar, (ii) transition, and (iii) turbulent. Laminar and transition flow regimes, often encountered with viscous measuring media or low flow rates, can cause other measuring elements to show considerable deviation from the square root relationship between flow rate and measured differential pressure. The discharge coefficient of a wedge meter remains highly linear from Reynolds numbers as low as 500 (laminar) to Reynolds numbers in the millions (turbulent).

The area restriction in a wedge meter is characterized by the H/D ratio, analogous to the beta ratio of a concentric orifice plate. The H/D ratio is defined as the height of the opening below the restriction divided by the internal diameter of the wedge meter. The H/D ratio can be varied to create a desired differential pressure for any specific flow rate. This gives a good degree of flexibility in selecting a suited wedge meter for a given application.

Pitot flow meters

Averaging pitot tube – An averaging pitot tube is an insertion or fixed probe which spans the process pipe diameter. The outer pitot tube of the probe has a number of pressure sensing ports facing upstream which are positioned at equal annular points in accordance with a log-linear distribution. 

The total pressures developed at each upstream port are the sum of two pressures, the static pressure and the pressure caused by the impact of the flowing medium. These pressures are averaged within the probe and the resultant pressure is the high pressure output component of the probe. The spacing of the ports ensures that the resultant average represents the medium velocity of the measuring medium across the pipe diameter. The low pressure component is generated from a single sensing port located on the downstream side of the probe, measuring the static pressure. The difference between the two pressures is proportional to the flow rate.

TORBAR averaging pitot tube – The TORBAR is an improvement on round sensor designs due to the unique profiled flats which are positioned around the downstream hole, in order to define the separation point at which the flow lines separate as the measuring medium passes around the outer pitot tube. This feature creates a stable pressure area at the downstream pressure sensing hole thereby maintaining a more constant flow coefficient at high flow velocities enabling a very wide range of flow measurement (turn down ratio).

TORBAR flow meters have been successfully used on a large variety of flow applications. These flow meters are suitable for gases, liquids and steam. Some of the many typical applications include water, natural gas, flue gas, nitrogen, combustion gases, ventilation air, sea water, cooling water, crude oil, and saturated and superheated steam. The versatility of TORBAR flow meters makes them ideal for flue stack flow rate measurement. Possible pipe diameters range from 15 mm upto 8 m. TORBAR averaging pitot tubes are available in a variety of designs to suit the application.

Fig 5 Flow meters and floats

Variable area flow meters

The flow rate of gases and liquids can be determined simply, yet relatively accurately with variable area flow meters (Fig 5). The measuring medium flows upward through a vertical conical tube whose diameter increases in the upward direction. The upward flowing fluid lifts a float located in the tube to a height so that the annulus has an area which results in an equilibrium of the forces acting on the float. Three forces act on the float, one is downward force which is the gravitational force and there are two forces acting in an upward direction which are the buoyancy force and the flow resistance force.

The annulus available for the flow changes as a result of the conical form of the meter tube with the elevation of the float. Thus, the float height provides information regarding the flow rate. When a glass meter tube is used, the measured value can be read directly from a scale.

In comparison to the differential pressure flow measuring method there is a physical analogy. The essential difference is mechanical, because the flow area remains constant in a differential pressure flow meter and the pressure difference varies with flow rate while in the variable area flow meter the flow area varies to suit the flow rate and the pressure difference remains constant.

A typical range of variable area flow meter devices includes a metal tube and a glass tube line which are used for the most different applications. The characteristics of metal tube flow meter (Fig 5) are (i) high pressure and temperature conditions, (ii) opaque measuring media, (iii) steam applications, (iv) high flow rate, (v) current and contact outputs, (vi) HART communication, and digital display. The characteristics of a glass tube line flow meter (Fig 5) are (i) low-cost solution, (ii) visual check of measuring medium, (iii) extremely low pressure conditions, and (iv) clear, transparent measuring medium.

Float – An important requirement for metering is the exact centering of the float in the meter tube. Three methods as given below have proved themselves.

  • Through slots on the float head the flowing measuring medium forces the float to rotate and centre itself. This principle, however, cannot be used with all float shapes. Additionally, there is a considerable dependence on the viscosity of the measuring medium.
  • The float is guided by three ribs or three flats (ball floats) which differ from the meter tube cone in that they are parallel to the tube axis. A variety of float shapes are possible. Even for cloudy opaque measuring media the measuring edge remains visible.
  • A guide rod in the middle of the meter tube is used to guide the float. This method is primarily used for metal tube variable area flow meters.

A wide variety of float shapes (Fig 5) are available such as (i) ball float, (ii) viscosity-immune float, (iii) viscosity-dependent float, and (iv) float for low pressure drop. The weight, shape and materials are adapted to the individual installations. The ball float is the measuring element preferably used for purge meters. Its weight can be determined by selecting from a variety of materials. Shape changes are not possible. Hence, the flow coefficient is defined. The ball shape is responsible for the viscosity effect. The float with the cone directed downward is used rather in larger sized variable area flow meters than in small ones. Also, there are the very light floats with relatively low pressure drops. This design requires minimum upstream pressures and is usually preferred for gas flow measurement.

Pressure drop – The pressure drop occurs primarily at the float because the energy required to produce the measuring effect is derived from the pressure drop of the flowing measuring medium. On the other hand, the constructional restrictions in the device fitting cause a pressure drop. The pressure drop at the float is dependent on its largest outside diameter and its weight and hence is independent of its elevation in the meter tube, i.e. it is constant. The pressure drop through the restrictions in the fittings, however, increases as the square of the increasing flow velocity. The resultant pressure drop is the reason for the requirement of a minimum upstream pressure.

 Electro-magnetic flow meters

If an electrical conductor is moved in a magnetic field which is perpendicular to the direction of motion and to the conductor, an electrical voltage is induced in the conductor whose magnitude is proportional to the magnetic field strength and the velocity of the movement. This characterization of the laws of induction also applies to the movement of a conductive liquid in a pipe through a magnetic field.

To utilize the principle shown in Fig 6 needs that a magnetic field exists within the pipe and that the induced voltages can be measured without any interference. Two coils generate the magnetic field which extends through the pipe only if it is not shunted by permeable pipe materials. Austenitic steel does not hinder the magnetic field and hence it is the most commonly used material for the meter pipe in the electro-magnetic flow meter. To prevent shorting out of the measuring signal, the meter tube is to be provided with an insulating internal lining. The measuring voltage is measured by means of two metallic electrodes which are in electrical contact with the measuring medium. An additional requirement for the operation is that the measuring medium is to be an electrical conductor.

Fig 6 Electro-magnetic flow meter

The measuring voltage measured at the electrodes is the sum of all the elemental voltages induced in the entire area of the magnetic field within the meter tube. The magnitude of the elemental voltages at the electrodes, i.e. the ratio of the partial voltage due to each element to the total measuring voltage UE at the electrodes is a function of the geometric location of that element.

The measuring voltage is smaller than 0.5 mV per 1 m/s of flow velocity. The magnitude of the noise voltages superimposed on the signal voltage can sometimes be appreciably larger. The connected transmitter has the function to reject the influences of the noise signals and to convert and amplify the measurement signal so that other connected evaluation units such as indicators, recorders, or controllers can be operated.

The electro-magnetic flow meter consists of a sensor and a transmitter. Determining factors for the selection of the appropriate sensor are its material and the type of process connection. Inside the meter tube, the tube liner and the electrodes are in contact with the measuring medium. As a result, they are to be made of materials which are chemically resistant to the measuring medium which, in some cases, can be extremely aggressive.

Ultrasonic Flow meters

The sound velocity ‘c’ which is a material property value is the propagation velocity of a sound wave in a medium. It changes with the density of the measuring medium. Hence, it is temperature dependent in liquids and pressure and temperature dependent in gases. When a sound impulse is transmitted from location A, it arrives at a second location B with the velocity of sound at time ‘t’, where ‘t = l/c’. The time changes when the sound carrier is also in motion, in fact, it is the sum of the sound velocity in the measuring medium and the measuring medium velocity ‘v’. This effect is utilized in an ultrasonic flow meter.

Fig 7 Ultrasonic flow meter

There are two basic methods for ultrasonic flow measurements (Fig 7) namely (i) transit time method, and (ii) Doppler method.

In case of transit time method, the measurement value is independent of the sound velocity, the pressure, the temperature and the density of the measuring medium. An essential requirement for the transit time measurement is the acoustic transparency of the measuring medium. There should be few solid particles or gas bubbles in the measuring medium.

For ultrasonic flow rate measurements using the Doppler effect, there has to be in-homogeneities or impurities (dispersers) in the measuring medium so that a portion of the sound energy can be reflected. Ultrasonic flow meters are available in two variants. There are inline systems and clamp-on systems.

Coriolis mass flow meters

For cost and material balance calculations mass flow information is preferred in technical processes since it is independent of physical influences when compared to volume flow information. Pressure, density, temperature and viscosity do not change the mass. Hence, the mass flow rate is the favoured measuring variable. Mass can only be measured indirectly, e.g. with the help of Newtons second law which states that force times acceleration equals mass. When weighing the acceleration is due to gravity and this law is applicable. For the mass of a liquid be determined using this relationship, one is to accelerate the liquid in a rotating system and measure the inertia effects. A physical effect named after the French mathematician Coriolis is utilized.

When a mass flows through a vibrating pipe Coriolis forces exist which bend or twist the pipe. These very small meter tube distortions are measured by optimally located sensors and evaluated electronically. Since the measured phase shift between the sensor signals is proportional to the mass flow rate, the mass flow rate through the Coriolis mass flow meter can be determined directly.

This measuring principle is independent of density, temperature, viscosity, pressure and conductivity. The meter tubes always vibrate at resonance. The resonant frequency which exists is a function of the meter tube geometry, the material properties and the mass of the measuring medium vibrating in the meter tube. It provides exact information about the density of the medium to be measured. In summary, it can be stated that the Coriolis mass flow meter can be used to simultaneously measure the mass flow rate, density and temperature of a measuring medium.

The advantages of this measurement method are (i) universal measuring system for flow rate, density and temperature, independent of conductivity, inlet and outlet sections, flow profile, density and, thus, pressure and temperature of the measuring medium, (ii) direct mass flow measurement, (iii) very high measuring accuracy (typically +/- 0.15 % of rate), (iv) multi-variable measuring principle, simultaneous measurement of mass flow rate, volume flow rate, density, and temperature and (v) no moving parts, hence wear free. The disadvantages this measurement method are (i) relatively high initial cost (for an accuracy of 0.15 % of rate), (ii) installation limitations for multi-phase measuring media or high gas content, (iii) deposits or abrasion can lead to errors, especially in the density measurement, and (iv) limited material selections for process wetted parts, corrosion resistance is required to be checked.

The overwhelming majority of Coriolis instruments today are based on the twin tube principle with a flow splitter and two bent meter tubes. The advantage of this design is temperature stability and in particular, the decoupling of the meter pipe vibrations from external vibrations. The amplitudes of the vibrations, which are required for determining the phase shift, are measured between the two meter tubes and not relative to the housing. Possible vibrations of the housing hence have no effect on the measurements. Based on the appreciably more stable and defined signals this system provides the most accurate measurements coupled with insensitivity to outside influences. A well designed twin tube meter requires minimum energy to start and keep the system resonating and generates measurement signals even for the smallest flow rates. The twin tube design is used in around 80 % to 90 % of present applications.

Besides the twin tube design there is also the single tube design. In order to maintain the insensitivity to external vibrations, the meter tubes in this design are bent into loops. The amplitudes of the vibrations, and thereby the phase shift, are measured between the tube loops and not relative to the housing. This principle offers distinct advantages for the smaller size meters because a flow splitter in not required. The straight single pipe design has advantages in that it can be more easily cleaned, has a reduced pressure drop and is less harsh on the measuring medium. However, these advantages come with a lower accuracy and a higher sensitivity to external vibrations.

Because of the straight meter tube, the amplitude differences are to be measured relative to the housing. If the housing is also vibrating, the effects are difficult to compensate. Moreover, the measured signals are appreciable smaller which also contributes to the reduced accuracy, especially for the density measurement. It is difficult to start and keep a single straight tube resonating. The elasticity of a pipe is directly related to its wall thickness. Hence, vibrating straight tubes are to be constructed thin and are available only for limited nominal diameters. For abrasive or corrosive measuring media, however, the thin wall sections of the meter tube can add additional safety concerns.

Thermal mass flow meters for gases

The most commonly used flow meters for gases measure the operating volume flow. This requires additional measurements of pressure and temperature to calculate the mass flow rate. These corrective measures add cost and increase the complexity of the measurements. In addition they decrease the measuring system accuracy. The thermal mass flow measurement for gases, on the contrary, provides mass flow rate in kg/hour directly without any additional measurements or calculations. Using the normal density of the gas, the normal volume flow rate can be calculated, e.g. in N cum/hour. There are two industrial methods used for thermal gas mass flow rate measurement, hot film anemometers and calorimetric or capillary meters.

Hot film anemometer – This method uses the flow rate dependent heat transfer from a heated body to the measuring medium. In the fields which are relevant for process engineering, this flow rate dependent cooling is not a function of the pressure and temperature, but of the type and number of particles which get into contact with the hot surface. This means the method determines the mass flow rate of the measuring medium directly.

The sensor unit consists of two measurement resistors that are part of an electrical bridge circuit. One of these resistors assumes the temperature of the flowing gas, whereas the other resistor is electrically heated and, at the same time, cooled by the gas mass flow. A control circuit applies heat to the resistor so that a constant temperature difference exists between the resistors. The power is, thus, a measure of the gas mass flow rate. This provides the measured value directly in the units namely kg/hour or standard cum/hour. The density correction of the measured value otherwise required is no longer necessary. The compact design of the sensor unit assures a minimum pressure drop of typically 1 milli bar. For thin film sensors the response time is in the milliseconds range. Vibration insensitivity and an extremely wide span at accuracies up to 1 % of rate are the rule for all thermal mass flow meters.

For digital devices the measuring principle has been further developed to include a gas temperature measurement and appreciably extended diagnostic functions. The measuring range can be expanded to 1:150 due to the improved signal quality. The separate measurement of the gas temperature can be used to compensate for the temperature dependence of the gas constants. The diagnostic functions can be used as a preventative maintenance tool to evaluate the operating time, temperature spikes and system loads.

Different device concepts have been developed for pneumatic, test bench, machine construction, hygienic and chemical process applications. Their primary difference is the design of the sensor units, dependent on whether quick response, flexibility or chemical resistance is needed.

Flow measurement in open channels and free surface pipelines

Open channels are found extensively in the water and waste water plants. They are characterized by one surface bounded by the atmosphere. The same is valid for free surface pipelines which are additionally found in the process industry. The measurement methods are described below.

Measuring weirs – For large water flows and small slopes, where the water can be dammed and the flow stream is completely ventilated measuring overflows are the appropriate measuring equipment. Ventilation means that air has free access under the overflow so that the stream will separate and fall freely. Measuring weirs consist of thin wall plates with sharp metering edges placed perpendicular to the flow direction. Various shapes are used as a function of the application conditions. For smaller flow rates a V-notch weir is used. V-notch weirs are suitable for flow rates between 2 l/s and 100 l/s. By paralleling a number of V-notch weirs a reasonable arrangement can be designed for higher flow rates.For good edge conditions the span is 1:100. For very large flow rates rectangular weirs are used, with the disadvantage of a limited measuring accuracy in the lower part of the measuring range.

Venturi flume flow meter – For flow measurement using measuring weirs the water is to be dammed which can cause changes in the inflow area under certain conditions. These restrictions do not apply to a Venturi flume. Hence, it can react to the smallest flow rates. As with the Venturi nozzle the constriction of the flow cross sectional area results in an energy conversion, which accelerates the measuring medium in the region of the constriction. The constrictions are normally at the sides. However, there are some however with elevated floor sections.

The water level upstream of the flume inlet (head water) is quiet and the water is in the sub-critical regime. This occurs automatically because the water is dammed causing the flow velocity to decrease resulting in sub-critical flow conditions. The acceleration of the water in the constricted region is to bring the water to a supercritical state, so that the tail water conditions do not have an effect on the flow level ahead of the constriction. Only when this condition is assured then a unique relationship exists between the level of the head water and the flow rate. Subsequently, a sub-critical flow state can be reached again after the channel expansion characterized by a hydraulic jump and a standing wave. A back flow must be avoided, because it influences the operation of the measuring system.

Channel flow meter sensor – Once the measuring weirs or venturi flumes have been installed, which provide defined relations between the measurable values and the flow rate, a device is still needed with which the liquid level can be measured and converted to flow rate proportional values. The head-water level can be measured directly or indirectly. Direct measurement method is by float measurement while the indirect measurement method is by (i) hydrostatic pressure measurement, (ii) non-contact water level measurement using an echo-sounder, and (iii) hydrostatic pressure measurement using a bubbler.

Float measurement – The water level is sampled by a float whose elevation is mechanically transmitted to a non-linear scale or is electrically linearized and converted to a standardized output signal. Contamination, fouling, mechanical abrasion, and frost can affect the float and transmitting element, and since these affect the flow profile they are responsible for errors. Possibly the float has to be installed in a separate float chamber. Additionally, increased maintenance expenditures are to be expected. These are the reasons that a float measurement is seldom used in these applications.

Hydrostatic pressure measurement – The hydrostatic pressure is the force exerted by a column of water above a reference point. The measured pressure is proportional to the height. The measuring cell operates as a differential pressure meter in the sense that the minus side is open to the atmospheric pressure. This pre-pressure is applied to both sides of the diaphragm and is, thus, self-cancelling. As the transmitter is mounted to the side wall, the zero of the transmitter can be adjusted such that the lower range value is based on the channel floor. Naturally, communication between the device and modern process control systems is possible through an interface or a fieldbus coupler. The measuring ranges lie between 0.01 kg/sq cm and 102 kg/sq cm. The diaphragm flush-mounted to the inner wall of the flume is unaffected by deposits and contamination.

Bubbler method – In bubbler method, a probe is inserted into the measuring medium either from the side or from the bottom and air or an inert gas is injected into the flume and the air bubbles to the top, thus the name bubbler method. For injecting the gas a purge meter with needle valve and differential pressure regulator is used. After the regulator, which acts as a restriction, a pressure exists in the probe which is the same as the hydrostatic pressure at the end of the tube. The needle valve is used to set the bubble flow rate and the differential pressure regulator to maintain a constant flow rate. A pressure transmitter processes the level proportional pressure. The advantage of the bubbler method lies in the fact that the sensitive measuring elements are not in contact with the measuring medium and are hence not subjected to chemical or mechanical attack. Additionally, the cost for providing sufficient protection for use in hazardous areas is minimal.

Echo-sounder method – The most successful water level measurement method is the non contacting echo-sounder method. A sound signal is transmitted from a sound generator located above the water level which, after it is reflected from the water surface, is received. The distance between the transmitter/receiver and the water level (i.e. the head water level) is calculated from the transit time of the sound wave. The sound velocity however is a function of the composition of the elements in the sound path, including temperature and humidity which can vary. A reference path, which is precisely defined mechanically, can be used to compensate for these disturbance factors.

A cone is installed at the sensor to protect against external influences, e.g. rain fall and to shield against undesirable wall reflections. The connected transmitter includes a microprocessor which uses stored curves for different flume meters to calculate the flow rate proportional 0/4-20 mA output signal. Naturally such transmitters provide self-monitoring functions, alarm contacts and volume totalizers.

Flow measurement in free surface pipelines

There are closed pipeline systems which are not continuously filled with liquid but run partially full because their size had to be selected to accommodate sporadic high flows. The most important example is in the waste water lines, in which the flow at night is small, somewhat more during the day, but is extremely high after a rain storm. This application needs a flow meter which provides accurate measuring values under all these conditions.

The waste water containing solids prevents the installation of devices projecting into the pipeline. Therefore, the ideal measuring device is an electro-magnetic flow meter. With one minor disadvantage, the actually measured variable is the flow velocity. The desired flow rate is available only after multiplying by the filled cross sectional area. Since the area, as noted above, is constantly changing there are two possible solutions for the measurement. Either to arrange the pipeline so that it always runs full or to install the electro-magnetic flow meter specifically designed for these applications.

Electro-magnetic flow meter in a Culvert

A culvert can be used to assure that the pipe always runs full and a correct measurement can be made. An argument against the culverts is the danger that solids getting deposited, especially in waste water applications. The drag force of flowing water, which increases with increasing flow rate, is often underestimated. Deposits are flushed from the culvert when the flow is high. This condition can also be induced by damming the water ahead of the culvert for short periods of time. Another possibility is to install a separate line for flushing.

Higher flow velocities in the culvert prevent deposits. The pipeline is designed with a cross sectional area that during periods of high water (rain storm) is actually undersized. A solution to this problem is to install a bypass culvert and install a weir in the main pipeline which has the disadvantage, that during high water flows, some of the water is not be metered. In contrast to the electromagnetic flow meter the culvert method has the advantage that more accurate meters can be used for partially full conditions. The cost advantage of smaller meters is usually offset by the higher construction costs.

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