Intro4u2u

Positive displacement meters measure the volume
flow rate (QV) directly by repeatedly trapping a
sample of the fluid. The total volume of liquid
passing through the meter in a given period of time
is the product of the volume of the sample and the
number of samples. Positive displacement meters
frequently totalize flow directly on an integral
counter, but they can also generate a pulse output
which may be read on a local display counter or by
transmission to a control room. Because each pulse
represents a discrete volume of fluid, they are
ideally suited for automatic batching and
accounting. Positive displacement meters can be
less accurate than other meters because of leakage
past the internal sealing surfaces. Three common
types of displacement meters are the piston, oval
gear, and nutating disc.

Head Meters

Head meters are the most common types of meter
used to measure fluid flow rates. They measure
fluid flow indirectly by creating and measuring a
differential pressure by means of an obstruction to
the fluid flow. Using well-established conversion
coefficients which depend on the type of head meter
used and the diameter of the pipe, a measurement
of the differential pressure may be translated into a
volume rate.
From the Equation of Continuity, assuming
constant density (incompressible fluid) it can be
seen that:

This equation is one of the most important
relationships in fluid mechanics. It demonstrates
that for steady, uniform flow, a decrease in pipe
diameter results in an increase in fluid velocity. In
addition, from Bernoulli’s equation on the
conversation of energy, it is further seen that total
head pressure (H) must remain constant
everywhere along the flow or:

The first term of the equation is called “potential
head” or “potential energy”. The second term is
known as the “velocity head” or “kinetic energy”.
Because potential and kinetic energy together are
constant, it is clear that an increase in velocity as
described by the Equation of Continuity must also
be accompanied by a decrease in potential energy or
line pressure. It is this relationship between velocity
and pressure that provides the basis for the
operation of all head-type meters.
Head meters are generally simple, reliable, and
offer more flexibility than other flow measurement
methods. The head-type flowmeter almost always
consists of two components: the primary device and
the secondary device. The primary device is placed
in the pipe to restrict the flow and develop a
differential pressure. The secondary device
measures the differential pressure and provides a
readout or signal for transmission to a control
system. With head meters, calibration of a primary
measuring device is not required in the field.

The
primary device can be selected for compatibility
with the specific fluid or application and the
secondary device can be selected for the type or
readout of signal transmission desired.

Orifice Plates

A concentric orifice plate is the simplest and least
expensive of the head meters (Figure 2). Acting as a
primary device, the orifice plate constricts the flow
of a fluid to produce a differential pressure across
the plate. The result is a high pressure upstream
and a low pressure downstream that is proportional
to the square of the flow velocity. An orifice plate
usually produces a greater overall pressure loss
than other primary devices. A practical advantage
of this device is that cost does not increase
significantly with pipe size.

Venturi Tubes

Venturi tubes exhibit a very low pressure loss
compared to other differential pressure head
meters, but they are also the largest and most
costly. They operate by gradually narrowing the
diameter of the pipe (Figure 3), and measuring the
resultant drop in pressure. An expanding section of
the meter then returns the flow to very near its
original pressure. As with the orifice plate, the
differential pressure measurement is converted into
a corresponding flow rate. Venturi tube applications
are generally restricted to those requiring a low
pressure drop and a high accuracy reading. They
are widely used in large diameter pipes such as
those found in waste treatment plants because their
gradually sloping shape will allow solids to flow
through.

Flow Nozzle

Flow nozzles may be thought of as a variation on the venturi tube. The nozzle opening is an elliptical
restriction in the flow but with no outlet area for
pressure recovery (Figure 4). Pressure taps are
located approximately 1/2 pipe diameter downstream
and 1 pipe diameter upstream. The flow nozzle is a
high velocity flowmeter used where turbulence is
high (Reynolds numbers above 50,000) such as in
steam flow at high temperatures. The pressure drop
of a flow nozzle falls between that of the venturi
tube and the orifice plate (30 to 95 percent).

Pitot Tubes

In general, a pitot tube for indicating flow consists
of two hollow tubes that sense the pressure at
different places within the pipe. These tubes can be
mounted separately in the pipe or installed together
in one casing as a single device. One tube measures
the stagnation or impact pressure (velocity head
plus potential head) at a point in the flow. The other
tube measures only the static pressure (potential
head), usually at the wall of the pipe. The
differential pressure sensed through the pitot tube
is proportional to the square of the velocity. To
install a pitot tube, you must determine the location
of maximum velocity with pipe traverses. Although
a pitot tube may be calibrated to measure fluid flow
to ±1/2 percent, changing velocity profiles may cause
significant errors. Pitot tubes are primarily used to
measure gases because the change in the flow
velocity from average to center is not as substantial
as in other fluids. Pitot tubes have found limited
applications in industrial markets because they can
easily become plugged with foreign material in the
fluid. Their accuracy is dependent on the velocity
profile which is difficult to measure.

Target Meters

A target meter consists of a disc or a “target” which
is centered in a pipe (Figure 5). The target surface is
positioned at a right angle to the fluid flow. A direct
measurement of the fluid flow rate results from the
force of the fluid acting against the target. Useful
for dirty or corrosive fluids, target meters require no
external connections, seals, or purge systems. Much
data is necessary, however, to determine the
optimum size of the target and calibration is
essential for its proper operation.

Elbow Tap Meters

An elbow tap operates by using a 45 degree pipe
elbow in the fluid flow. A high pressure tap is taken
from the outside of the elbow and a low pressure tap
is taken from the inside of the elbow. This provides a
differential pressure which is proportional to the
flow rate. Measuring the differential pressure
depends on the centrifugal force of the fluid flowing
through the elbow. Hence, gas with its low density is
not a good application for elbow taps. This also
explains why a short curvature in the elbow
develops a much greater differential pressure than
a long curvature. The pressure drop of an elbow tap
is no greater than that of the elbow. Though
repeatable, accuracy of an elbow tap meter is only
within ±5 percent.

Rotameters

Rotameters (also known as variable-area
flowmeters) are typically made from a tapered glass
tube that is positioned vertically in the fluid flow
(Figure 6). A float that is the same size as the base
of the glass tube rides upward in relation to the
amount of flow. Because the tube is larger in
diameter at the top of the glass than at the bottom,
the float resides at the point where the differential
pressure between the upper and lower surfaces
balance the weight of the float. In most rotameter
applications, the flow rate is read directly from a
scale inscribed on the glass; in some cases, an
automatic sensing device is used to sense the level
of the float and transmit a flow signal. These
“transmitting rotameters” are often made from
stainless steel or other materials for various fluid
applications and higher pressures. Rotameters may
range in size from 1/4 inch to greater then 6 inches.
They measure a wider band of flow (10 to 1) than an
orifice plate with an accuracy of ±2 percent, and a
maximum operating pressure of 300 psig when
constructed of glass. Rotameters are commonly used
for purge flows and levels.

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	Flow Measurement - Rosemount
	Positive Displacement Meters
	Velocity Meters
	Mass Flowmeters

While the flow measurement technologies discussed in this chapter–magnetic, vortex, and ultrasonic–are neither exclusively nor exhaustively electronic in nature, they do represent a logical grouping of flow measurement technologies. All have no moving parts (well, maybe vibrating), are relatively non-intrusive, and are made possible by today’s sophisticated electronics technology.

Magnetic flowmeters, for example, are the most directly electrical in nature, deriving their first principles of operation from Faraday’s law. Vortex meters depend on piezoelectric sensors to detect vortices shed from a stationary shedder bar. And today’s ultrasonic flowmeters owe their successful application to sophisticated digital signal processing.

Magnetic Flowmeters

The operation of magnetic flowmeters is based on Faraday’s law of electromagnetic induction. Magmeters can detect the flow of conductive fluids only. Early magmeter designs required a minimum fluidic conductivity of 1-5 microsiemens per centimeter for their operation. The newer designs have reduced that requirement a hundredfold to between 0.05 and 0.1.

The magnetic flowmeter consists of a non-magnetic pipe lined with an insulating material. A pair of magnetic coils is situated as shown in Figure 4-1, and a pair of electrodes penetrates the pipe and its lining. If a conductive fluid flows through a pipe of diameter (D) through a magnetic field density (B) generated by the coils, the amount of voltage (E) developed across the electrodes–as predicted by Faraday’s law–will be proportional to the velocity (V) of the liquid. Because the magnetic field density and the pipe diameter are fixed values, they can be combined into a calibration factor (K) and the equation reduces to:

E = KV

The velocity differences at different points of the flow profile are compensated for by a signal-weighing factor. Compensation is also provided by shaping the magnetic coils such that the magnetic flux will be greatest where the signal weighing factor is lowest, and vice versa.

Manufacturers determine each magmeter’s K factor by water calibration of each flowtube. The K value thus obtained is valid for any other conductive liquid and is linear over the entire flowmeter range. For this reason, flowtubes are usually calibrated at only one velocity. Magmeters can measure flow in both directions, as reversing direction will change the polarity but not

T9904-09_Fig_01
Figure 4-1: Click on figure to enlarge.

the magnitude of the signal.

The K value obtained by water testing might not be valid for non-Newtonian fluids (with velocity-dependent viscosity) or magnetic slurries (those containing magnetic particles). These types of fluids can affect the density of the magnetic field in the tube. In-line calibration and special compensating designs should be considered for both of these fluids.

Magmeter Excitation

The voltage that develops at the electrodes is a millivolt signal. This signal is typically converted into a standard current (4-20 mA) or frequency output (0-10,000 Hz) at or near the flowtube. Intelligent magnetic transmitters with digital outputs allow direct connection to a distributed control system. Because the magmeter signal is a weak one, the lead wire should be shielded and twisted if the transmitter is remote.

The magmeter’s coils can be powered by either alternating or direct current (Figure 4-2). When ac excitation is used, line voltage is applied to the magnetic coils. As a result, the flow signal (at constant flow) will also look like a sine wave. The amplitude of the wave is proportional to velocity. In addition to the flow signal, noise voltages can be induced in the electrode loop. Out-of-phase noise is easily filtered, but in-phase noise requires that the flow be stopped

T9904-09_Fig_02
Figure 4-2: Click on figure to enlarge.

(with the pipe full) and the transmitter output set to zero. The main problem with ac magmeter designs is that noise can vary with process conditions and frequent re-zeroing is required to maintain accuracy.

In dc excitation designs, a low frequency (7-30 Hz) dc pulse is used to excite the magnetic coils. When the coils are pulsed on (Figure 4-2), the transmitter reads both the flow and noise signals. In between pulses, the transmitter sees only the noise signal. Therefore, the noise can be continuously eliminated after each cycle.

This provides a stable zero and eliminates zero drift. In addition to being more accurate and able to measure lower flows, dc meters are less bulky, easier to install, use less energy, and have a lower cost of ownership than ac meters. One new dc design uses significantly more power than the earlier generations and thereby creates a stronger flowtube signal.

Another new design uses a unique dual excitation scheme that pulses the coils at 7 Hz for zero stability and also at 70 Hz to obtain a stronger signal. Magmeter transmitters can be supplied with either ac or dc power. A two-wire, loop-powered dc magnetic flowmeter is also available in an intrinsically safe design, but its performance is reduced because of power limitations.

Pulsed ac meters have also been introduced recently, eliminating the zero stability problems of traditional ac designs. These devices contain circuitry that periodically disrupts the ac power, automatically zeroing out the effects of process noise on the output signal.

Today, dc excitation is used in about 85% of installations and ac magmeters claim the other 15% when justified by the following conditions:

When air is entrained in large quantities in the process stream;

When the process stream is a slurry and the solid particle sizes are not uniform and/or the solid phase is not homogeneously mixed within the liquid; or

When the flow is pulsating at a frequency under 15 Hz.

When any of the above three conditions exist, the output of a pulsed dc meter is likely to be noisy. In some cases, one can minimize the noise problem (hold the fluctuations within 1% of setpoint) by filtering and damping the output signal. If more than 1 to 3 seconds of damping is required to eliminate the noise, it is always better to use an ac meter.

Flowtubes, Liners, & Probes

The face-to-face dimensions of flanged flowtubes (lay lengths) usually meet the recommendations of the International Organization for Standardization (ISO). The dimensions of short-form magmeters usually meet these guidelines as well. Magnetic flowtubes and liners are available in many materials and are widely used in all the process industries, including food, pharmaceutical, mining, and metals.

Some liner materials (particularly PFA) can be damaged when pry bars are used while installing it or removing it from process piping. They can also be damaged by over-torquing the flange bolts. Liner protectors are available to help prevent such damage.

Any flowtube can generally be used with any transmitter offered by the same manufacturer. Depending on its construction and features, the cost of a 2-in. magnetic flowmeter can range from $1,500 to $5,000. This cost has been coming down, but is still higher than that of the least expensive flow sensors.

Magnetic flowmeters also can be packaged as probes and inserted into process pipes through taps. These probes contain both the electrodes and magnetic coils. The flowing process fluid induces a voltage at the electrodes, which reflects the velocity at the probe tip and not the average fluid velocity across the pipe. These magmeters are inexpensive and retractable. Therefore, the process does not have to be shut down to install or remove them. Metering accuracy is highly dependent on the relationship between the measured velocity and the average velocity in the pipe.

Electrodes

In conventional flowtubes, the electrodes are in contact with the process fluid. They can be removable or permanent if produced by a droplet of liquid platinum as it sinters through a ceramic liner and fuses with the aluminum oxide to form a perfect seal. This design is preferred due to its low cost, its resistance to abrasion and wear, its insensitivity to nuclear radiation, and its suitability for sanitary applications because there are no cavities in which bacteria can grow. On the other hand, the ceramic tube cannot tolerate bending, tension, or sudden cooling and cannot handle oxidizing acids or hot and concentrated caustic.

T9904-09_Fig_03
Figure 4-3: Click on figure to enlarge.

In a more recent capacitively- coupled design, non-contacting electrodes are used. These designs use areas of metal sandwiched between layers of liner material. They are available in sizes under eight inches in diameter and with ceramic liners. Magmeters using these non-contacting electrodes can “read” fluids having 100 times less conductivity than required to actuate conventional flowtubes. Because the electrode is behind the liner, these designs are also better suited for severe coating applications.

Recent Developments

When a magnetic flowmeter is provided with a capacitance level sensor embedded in the liner, it can also measure the flow in partially full pipes. In this design, the magmeter electrodes are located at the bottom of the tube (at approximately 1/10 the pipe diameter) in order to remain covered by the fluid. Compensation is provided for wave action and calibration is provided for full pipe, no flow (static level), and partially filled pipe operation.

Another recent development is a magnetic flowmeter with an unlined carbon steel flowtube. In this design, the measuring electrodes mount externally to the unlined flowtube and the magnetic coils generate a field 15 times stronger than in a conventional tube. This magnetic field penetrates deep into the process fluid (not just around the electrode as with standard magmeter probes). The main advantage is low initial and replacement costs, since only the sensors need be replaced.

Selection & Sizing

Magnetic flowmeters can detect the flow of clean, multi-phase, dirty, corrosive, erosive, or viscous liquids and slurries as long as their conductivity exceeds the minimum required for the particular design. The expected inaccuracy and rangeability of the better designs are from 0.2-1% of rate, over a range of 10:1 to 30:1, if the flow velocity exceeds 1 ft/sec. At slower flow velocities (even below 0.1 ft/s), measurement error increases, but the readings remain repeatable.

It is important that the conductivity of the process fluid be uniform. If two fluids are mixed and the conductivity of one additive is significantly different from that of the other process fluid, it is important that they be completely intermixed before the blend reaches the magmeter. If the blend is not uniform, the output signal will be noisy. To prevent that, pockets of varying conductivity can be eliminated by installing a static mixer upstream of the magmeter.

Magmeter size is determined by capacity tables or charts published by the manufacturer. Figure 4-3 provides a flow capacity nomograph for line sizes from 0.1 in. to 96 in. For most applications, flow velocities should fall between 3 ft/sec and 15 ft/sec. For corrosive fluids, the normal velocity range should be 3-6 ft/sec. If the flowtube is continuously operated below 3 ft/sec, metering accuracy will deteriorate, while continuous operation exceeding the upper limit of the normal velocity range will shorten the life of the meter.

The obstructionless nature of the magmeter lowers the likelihood of plugging and limits the unrecovered head loss to that of an equivalent length of straight pipe. The low pressure drop is desirable because it lowers pumping costs and aids gravity feed systems.

Problem Applications

The magmeter cannot distinguish entrained air from the process fluid; therefore, air bubbles will cause the magmeter to read high. If the trapped air is not homogeneously dispersed, but takes the form of air slugs or large air bubbles (the size of the electrode), this will make the output signal noisy or even disrupt it. Therefore, in applications where air entrainment is likely, the meter should be sized so that the flow velocity under normal flow conditions is 6-12 ft/sec.

Coating of the electrodes is another common magmeter problem. Material build-up on the inner surfaces of the meter can electrically isolate the electrodes from the process

T9904-09_Fig_04
Figure 4-4: Click on figure to enlarge.

fluid. This can cause a loss of signal or a measurement error, either by changing the diameter of the flowtube or by causing span and zero shifts. Naturally, the best solution is prevention. One preventive step is to size the meter such that, under normal flow conditions, the flowing velocity will be relatively high: at least 6-12 ft/sec, or as high as practical considering the possibility of erosion and corrosion.

Another method of prevention is to use electrodes that protrude into the flow stream to take advantage of the turbulence and washing effect. In more severe service, a mechanical cleaning system can be installed and used intermittently or continuously to eliminate coating and build-ups.

Installation

The magnetic flowmeter must always be full of liquid. Therefore, the preferred location for magmeters is in vertical upward flow lines. Installation in horizontal lines is acceptable if the pipe section is at a low point and if the electrodes are not at the top of the pipe. This prevents air from coming into contact with the electrodes. When the process fluid is a slurry and the magmeter is installed at a low point, it should be removed during long periods of shutdown, so that solids will not settle and coat the internals.

If it is essential to drain the magmeter periodically, it should be provided with an empty tube zero option. When this option is activated, the output of the transmitter will be clamped to zero. Detection of empty tube conditions is by circuitry connected to extra sets of electrodes in the flowtube. The empty tube zero feature can also be activated by an external contact, such as a pump status contact.

Magmeters require five diameters of straight pipe upstream and two diameters downstream in order to maintain their accuracy and minimize liner wear. Liner protectors are available to protect the leading edge of the liners from the abrasive effects of process fluids. If the magmeter is installed in a horizontal pipe exceeding 30 ft in length, the pipe should be supported on both sides of the meter.

The magnetic flowmeter must be electrically grounded to the process liquid. This is because the magmeter is part of the path for any stray current traveling down the pipeline or through the process liquid. Bonding, by grounding the meter at both ends to the process fluid, provides a short circuit for stray currents, routing them around the flowtube instead of through it. If the system is not properly grounded, these currents can create a zero shift in the magnetic flowmeter output.

Electrical bonding to the process fluid can be achieved by metal ground straps. These straps connect each end of the flowtube to the adjacent pipeline flanges, which, in turn, are in contact with the process liquid. Straps are used when the piping is electrically conductive. When the pipe is non-conductive or lined, grounding rings are used. The grounding ring is like an orifice plate with a bore equal to the nominal size (inside diameter) of the flowtube. It is installed between the flanges of the flowtube and adjacent process piping on the upstream and downstream sides. The flowtube is bonded to the process fluid by being connected to the metallic grounding rings, and is grounded by being wired to a good conductor, such as a cold water pipe.

In larger sizes and in exotic materials, grounding rings can become expensive; grounding electrodes (a

T9904-09_Fig_05
Figure 4-5: Click on figure to enlarge.

third electrode placed in the flowtube for bonding with the process fluid) can be used instead. Another cost-saving option is to use a plastic grounding ring with a metal electrode insert.

Vortex Flowmeters

As a young person fishing in the mountain streams of the Transylvanian Alps, Theodor von Karman discovered that, when a non-streamlined object (also called a bluff body) is placed in the path of a fast-flowing stream, the fluid will alternately separate from the object on its two downstream sides, and, as the boundary layer becomes detached and curls back on itself, the fluid forms vortices (also called whirlpools or eddies). He also noted that the distance between the vortices was constant and depended solely on the size of the rock that formed it.

On the side of the bluff body where the vortex is being formed, the fluid velocity is higher and the pressure is lower. As the vortex moves downstream, it grows in strength and size, and eventually detaches or sheds itself. This is followed by a vortex’s being formed on the other side of the bluff body (Figure 4-4). The alternating vortices are spaced at equal distances.

The vortex-shedding phenomenon can be observed as wind is shed from a flagpole (which acts as a bluff body); this is what causes the regular rippling one sees in a flag. Vortices are also shed from bridge piers, pilings, offshore drilling platform supports, and tall buildings. The forces caused by the vortex-shedding phenomenon must be taken into account when designing these structures. In a closed piping system, the vortex effect is dissipated within a few pipe diameters downstream of the bluff body and causes no harm.

Vortex Meter Design

A vortex flowmeter is typically made of 316 stainless steel or Hastelloy and includes a bluff body, a vortex sensor assembly and the transmitter electronics, although the latter can also be mounted remotely (Figure 4-5). They are typically available in flange sizes from 1/2 in. to 12 in. The installed cost of vortex meters is competitive with that of orifice meters in sizes under six inches. Wafer body meters (flangeless) have the lowest cost, while flanged meters are preferred if the process fluid is hazardous or is at a high temperature.

Bluff body shapes (square, rectangular, t-shaped, trapezoidal) and dimensions have been experimented with to achieve the desired characteristics. Testing has shown that linearity, low Reynolds number limitation, and sensitivity to velocity profile distortion vary only slightly with bluff body shape. In size, the bluff body must have a width that is a large enough fraction of the pipe diameter that the entire flow participates in the shedding. Second, the bluff body must have protruding edges on the upstream face to fix the lines of flow separation, regardless of the flow rate. Third, the bluff body length in the direction of the flow must be a certain multiple of the bluff body width.

Today, the majority of vortex meters use piezoelectric or capacitance-type sensors to detect the pressure oscillation around the bluff body. These detectors

T9904-09_Fig_06
Figure 4-6: Click on figure to enlarge.

respond to the pressure oscillation with a low voltage output signal which has the same frequency as the oscillation. Such sensors are modular, inexpensive, easily replaced, and can operate over a wide range of temperature ranges–from cryogenic liquids to superheated steam. Sensors can be located inside the meter body or outside. Wetted sensors are stressed directly by the vortex pressure fluctuations and are enclosed in hardened cases to withstand corrosion and erosion effects.

External sensors, typically piezoelectric strain gages, sense the vortex shedding indirectly through the force exerted on the shedder bar. External sensors are preferred on highly erosive/corrosive applications to reduce maintenance costs, while internal sensors provide better rangeability (better low flow sensitivity). They are also less sensitive to pipe vibrations. The electronics housing usually is rated explosion- and weatherproof, and contains the electronic transmitter module, termination connections, and optionally a flow-rate indicator and/or totalizer.

Sizing & Rangeability

Vortex shedding frequency is directly proportional to the velocity of the fluid in the pipe, and therefore to volumetric flow rate. The shedding frequency is independent of fluid properties such as density, viscosity, conductivity, etc., except that the flow must be turbulent for vortex shedding to occur. The relationship between vortex frequency and fluid velocity is:

St = f(d/V)

Where St is the Strouhal number, f is the vortex shedding frequency, d is the width of the bluff body, and V is the average fluid velocity. The value of the Strouhal number is determined experimentally, and is generally found to be constant over a wide range of Reynolds numbers. The Strouhal number represents the ratio of the interval between vortex shedding (l) and bluff body width (d), which is about six (Figure 4-4). The Strouhal number is a dimensionless calibration factor used to characterize various bluff bodies. If their Strouhal number is the same, then two different bluff bodies will perform and behave similarly.

Because the volumetric flowrate Q is the product of the average fluid velocity and of the cross-sectional area available for flow (A):

Q = AV = (A f d B)/St

where B is the blockage factor, defined as the open area left by the bluff body divided by the full bore area of the pipe. This equation, in turn, can be rewritten as:

Q = fK

where K is the meter coefficient, equal to the product (A f d B). As with turbine and other frequency-producing flowmeters, the K factor can be defined as pulses per unit volume (pulses per gallon, pulses per cubic foot, etc.). Therefore, one can determine flowrate by counting the pulses per unit time. Vortex frequencies range from one to thousands of pulses per second, depending upon the flow velocity, the character of the process fluid, and the size of the meter. In gas service, frequencies are about 10 times higher than in liquid applications.

The K factor is determined by the manufacturer, usually by water calibration in a flow lab. Because the K factor is the same for liquid, gas and vapor applications, the value determined from a water calibration is valid

T9904-09_Fig_07
Figure 4-7: Click on figure to enlarge.

for any other fluid. The calibration factor (K) at moderate Reynolds numbers is not sensitive to edge sharpness or other dimensional changes that affect square-edged orifice meters.

Although vortex meter equations are relatively simple compared to those for orifice plates, there are many rules and considerations to keep in mind. Manufacturers offer free computer software for sizing, wherewith the user enters the fluid’s properties (density, viscosity, and desired flow range) and the program automatically sizes the meter.

The force generated by the vortex pressure pulse is a function of fluid density multiplied by the square of fluid velocity. The requirement that there be turbulent flow and force sufficient to actuate the sensor determines the meter’s rangeability. This force has to be high enough to be distinguishable from noise. For example, a typical 2-in. vortex meter has a water flow range of 12 to 230 gpm. If the density or viscosity of the fluid differs from that of water, the meter range will change.

In order to minimize measurement noise, it is important to select a meter that will adequately handle both the minimum and maximum process flows that will be measured. It is recommended that the minimum flow rate to be measured be at least twice the minimum flow rate detectable by the meter. The maximum capacity of the meter should be at least five times the anticipated maximum flowrate.

Accuracy & Rangeability

Because the Reynolds number drops as viscosity rises, vortex flowmeter rangeability suffers as the viscosity rises. The maximum viscosity limit, as a function of allowable accuracy and rangeability, is between 8 and 30 centipoises. One can expect a better than 20:1 rangeability for gas and steam service and over 10:1 for low-viscosity liquid applications if the vortex meter has been sized properly for the application.

The inaccuracy of most vortex meters is 0.5-1% of rate for Reynolds numbers over 30,000. As the Reynolds number drops, metering error increases. At Reynolds numbers less than 10,000, error can reach 10% of actual flow.

While most flowmeters continue to give some indication at near zero flows, the vortex meter is provided with a cut-off point. Below this level, the meter output is automatically clamped at zero (4 mA for analog transmitters). This cut-off point corresponds to a Reynolds number at or below 10,000. If the minimum flow that one needs to measure is at least twice the cut-off flow, this does not pose a problem. On the other hand, it can still be a drawback if low flowrate information is desired during start-up, shutdown, or other upset conditions.

Recent Developments

Smart vortex meters provide a digital output signal containing more information than just flow rate. The microprocessor in the flowmeter can automatically correct for insufficient straight pipe conditions, for differences between the bore diameter and that of the mating pipe, for thermal expansion of the bluff body, and for K-factor changes when the Reynolds number drops below 10,000.

Intelligent transmitters are also provided with diagnostic subroutines to signal component or other failures. Smart transmitters can initiate testing routines to identify problems with both the meter and with the application. These on-demand tests can also assist in ISO 9000 verification.

Some recently introduced vortex flowmeters can detect mass flow. One such design measures both the vortex frequency and the vortex pulse strength simultaneously. From these readings, the density of the process fluid can be determined and the mass flow calculated to within 2% of span.

Another newer design is provided with multiple sensors to detect not only the vortex frequency, but also the temperature and pressure of the process fluid. Based on that data, it determines both the density and the mass flow rate. This meter offers a 1.25% of rate accuracy when measuring the mass flow of liquids and a 2% of rate accuracy for gases and steam. If knowledge of process pressure and temperature is of value for other reasons, this meter provides a convenient, less costly alternative to installing separate transmitters.

Applications & Limitations

Vortex meters are not usually recommended for batching or other intermittent flow applications. This is because the dribble flow-rate setting of the batching station can fall below the meter’s minimum Reynolds number limit. The smaller the total batch, the more significant the resulting error is likely to be.

Low pressure (low density) gases do not produce a strong enough pressure pulse, especially if fluid velocities are low. Therefore, it is likely that in such services the rangeability of the meter will be poor and low flows will not be measurable. On the other hand, if reduced rangeability is acceptable and the meter is correctly sized for normal flow, the vortex flowmeter can still be considered.

If the process fluid tends to coat or build-up on the bluff body, as in sludge and slurry service, this will eventually change the meter’s K factor. Vortex-shedding flowmeters are not recommended for such applications. If, however, a dirty fluid has only moderate amounts of non-coating solids, the application is likely to be acceptable. This was demonstrated by a 2-year test on a limestone slurry. At the end of the test, the K factor was found to have changed only 0.3% from the original factory calibration, although the bluff body and flowtube were badly scarred and pitted.

When measuring multi-phase flow (solid particles in gas or liquid; gas bubbles in liquid; liquid droplets in gas), vortex meter accuracy will drop

T9904-09_Fig_08
Figure 4-8: Click on figure to enlarge.

because of the meter’s inability to differentiate between the phases. Wet, low-quality steam is one such application: the liquid phase should be homogeneously dispersed within the steam, and vertical flow lines should be avoided to prevent slugging. When the pipe is horizontal, the liquid phase is likely to travel on the bottom of the pipe, and therefore the inner area of the pipe should be kept open at the bottom. This can be achieved by installing the bluff body horizontally. Measurement inaccuracy in such applications is about 5% of actual flow, but with good repeatability.

The permanent pressure loss through a vortex meter is about half that of an orifice plate, roughly two velocity heads. (A velocity head is defined as V2/g, where V is the flow velocity and g is the gravitational constant in consistent units.) If the pipe and meter are properly sized and of the same size, the pressure drop is likely to be only a few psi. However, downsizing (installing a smaller-than-line-size meter) in order to increase the Reynolds can increase the head loss to more than 10 psi. One should also make sure that the vena contracta pressure does not drop below the vapor pressure of the process fluid, because that would cause cavitation. Naturally, if the back-pressure on the meter is below the vapor pressure, the process fluid will flash and the meter reading will not be meaningful.

The main advantages of vortex meters are their low sensitivity to variations in process conditions and low wear relative to orifices or turbine meters. Also, initial and maintenance costs are low. For these reasons, they have been gaining wider acceptance among users.

Installation Recommendations

When installing a vortex flowmeter in an existing process where the flow range is not known, it is recommended

T9904-09_Fig_09
Figure 4-9: Click on figure to enlarge.

to first make some approximate measurements (using portable pitot or clamp-on ultrasonic devices). Otherwise, there is no guarantee that a line-size vortex meter will work at all.

The vortex meter requires a well-developed and symmetrical flow velocity profile, free from any distortions or swirls. This necessitates the use of straight up- and downstream piping to condition the flow. The straight length of pipe must be the same size as the meter (Figure 4-6) and its length should be about the same as required for an orifice installation with a beta ratio of 0.7 (see Chapter 2). Most vortex flowmeter manufacturers recommend a minimum of 30 pipe diameters downstream of control valves, and 3 to 4 pipe diameters between the meter and downstream pressure taps. Temperature elements should be small and located 5 to 6 diameters downstream.

About half of all vortex meter installations require the “necking down” of oversized process piping by concentric reducers and expanders. Even if flow straighteners are installed, some straight (relaxation) piping will still be required.

Vortex meters can be installed vertically, horizontally, or at any angle, as long as they are kept flooded. The meter can be kept flooded by installing it in a vertical upward flow line (Figure 4-6B). When installing the flowmeter in a downward (Figure 4-6C) or horizontal (Figure 4-6D) flow, the downstream piping should be kept elevated. Check valves can be used to keep the piping full of liquid when there is no flow. Block and bypass valves are required if the replacement of the sensor in the particular design requires the stopping of the flow and the opening up of the process.

Mating flanges (on the schedule 40 or schedule 80 mating piping) must have the same diameter and smooth bore as the flowmeter. Weld neck flanges are preferred, and reducing flanges should not be used. The inner surface of the mating pipe should be free from mill scale, pits, holes, reaming scores and bumps for a distance of 4 diameters upstream and 2 diameters downstream of the meter. The bores of the meter, the gaskets and the adjacent piping must be carefully aligned to eliminate any obstructions or steps.

Excessive pipe vibration can be eliminated by supporting the piping on both sides of the meter, or by rotating the meter so that the sensor is moved out of the plane of the vibration. Process noise due to valve chattering, steam traps, or pumps can result in high readings or non-zero readings under zero-flow conditions. Most meter electronics allow for increasing the noise filter settings, but increased noise reduction usually also decreases the low-flow sensitivity of the meter. One option is to relocate the meter to a less noisy part of the process.

Ultrasonic Flowmeters

The speed at which sound propagates in a fluid is dependent on the fluid’s density. If the density is constant, however, one can use the time of ultrasonic passage (or reflection) to determine the velocity of a flowing fluid.

Some manufacturers produce transducer systems that operate in the shear-mode, sending a single pulse and receiving a single pulse in return. Narrow-beam systems are commonly subject to walk-away (the signal completely missing the downstream transducer). Wide-beam systems overcome beam refraction and work better in changing liquid density and temperature. With the advent of digital signal processing, it has become possible to apply digital signal coding to the transmitted signal. This can eliminate many of the problems associated with noise and variations in liquid chemistry.

The Doppler Shift

In 1842, Christian Doppler discovered that the wavelength of sound perceived by a stationary observer appears shorter when the source is approaching and longer when the source is moving away. This shift in frequency is the basis upon which all Doppler-shift ultrasonic flowmeters work.

Doppler flowmeter transducers operate at 0.640 MHz (in clamp-on designs) and at 1.2 MHz in wetted sensor designs. The transducer sends an ultrasonic pulse or beam into the flowing stream. The sound waves are reflected back by such acoustical discontinuities as particles, entrained gas bubbles, or even by turbulence vortices (Figure 4-7A). For clamp-on designs, measurement inaccuracy ranges from ±1% to ±5% full scale (FS).

The meter detects the velocity of the discontinuities, rather than the velocity of the fluid, in calculating the flow rate. The flow velocity (V) can be determined by:

V = (f0 - f1)Ct/2f0 cos(a)

Where Ct is the velocity of sound inside the transducer, f0 is the transmission frequency, f1 is the reflected frequency, and a is the angle of the transmitter and receiver crystals with respect to the pipe axis. Because Ct /2f0cos(a) is a constant (K), the relationship can be simplified to:

V = (f0 - f1)K

Thus, flow velocity V (ft/sec) is directly proportional to the change in frequency. The flow (Q in gpm) in a pipe having a certain inside diameter (ID in inches) can be obtained by:

Q = 2.45V(ID)2 = 2.45[(f0 - f1)K](ID)2

The presence of acoustical discontinuities is essential for the proper operation of the Doppler flowmeter. The generally accepted rule of thumb is that for proper signal reflection there be a minimum of 80-100 mg/l of solids with a particle size of +200 mesh (+75 micron). In the case of bubbles, 100-200 mg/l with diameters between +75 and +150 microns is desirable. If either the size or the concentration of the discontinuities changes, the amplitude of the reflected signal will shift, introducing errors.

Doppler flowmeters are often used to measure the flow of such fluids as

T9904-09_Fig.10
Figure 4-10: Click on figure to enlarge.

slurries. If the solids concentration is too high (in excess of 45% by weight), or if too much air or gas is entrained (especially if the bubbles are very fine), these discontinuities will attenuate the reflected Doppler signal to the point where it cannot be distinguished from the background noise in the pipe.

The reflected Doppler signal is shifted from the transmitted frequency by approximately 6 Hz for every foot per second of velocity. Therefore, if the flow velocity is less than 1 ft/sec, ultrasonic flowmetering is not practical. There seems to be no upper limit to detectable flow velocity, as successful installations at velocities in the 40-50 ft/sec range are well documented.

Transit Time Measurement

In this design, the time of flight of the ultrasonic signal is measured between two transducers–one upstream and one downstream (Figure 4-7B). The difference in elapsed time going with or against the flow determines the fluid velocity.

When the flow is zero, the time for the signal T1 to get to T2 is the same as that required to get from T2 to T1. When there is flow, the effect is to boost the speed of the signal in the downstream direction, while decreasing it in the upstream direction. The flowing velocity (Vf) can be determined by the following equation:

Vf = Kdt/TL

where K is a calibration factor for the volume and time units used, dt is the time differential between upstream and downstream transit times, and TL is the zero-flow transit time.

Theoretically, transit-time ultrasonic meters can be very accurate

T9904-09_Fig.11
Figure 4-11: Click on figure to enlarge.

(inaccuracy of ±0.1% of reading is sometimes claimed). Yet the error in these measurements is limited by both the ability of the signal processing electronics to determine the transit time and by the degree to which the sonic velocity (C) is constant. The speed of sound in the fluid is a function of both density and temperature. Therefore, both have to be compensated for. In addition, the change in sonic velocity can change the refraction angle (”a” in Figure 4-7B), which in turn will affect the distance the signal has to travel. In extreme cases, the signal might completely miss the downstream receiver. Again, this type of failure is known as walk-away.

Design Variations

Clamp-on ultrasonic meters come in either single or dual-sensor versions. In the single-sensor version, the transmit and receive crystals are potted into the same sensor body, which is clamped onto a single point of the pipe surface (Figure 4-8). In the dual-sensor version, the transmit crystal is in one sensor body, while the receive crystal is in another.

Clamp-on transit time meters have been available since the early 1970s. Their aim is to rival the performance of wetted spool-piece designs, but without the need to break the pipe or stop the process to install the meter. This goal has not yet been reached.

Clamp-on Doppler flowmeters are subject to interference from the pipe wall itself, as well as from any air space between the sensor and the wall. If the pipe wall is made of stainless steel, it might conduct the transmit signal far enough so that the returning echo will be shifted enough to interfere with the reading. There are also built-in acoustic discontinuities in concrete-lined, plastic-lined, and fiberglass-reinforced pipes. These are significant enough to either completely scatter the transmitted signal or attenuate the return signal. This dramatically decreases flowmeter accuracy (to within only ±20%), and, in most cases, clamp-on meters will not work at all if the pipe is lined.

Wetted transducer designs–both Doppler and transit time are available–overcome many of these signal attenuation limitations. The full-pipe transit-time meter originally consisted of a flanged spool section with wetted transducers mounted in the pipe wall in transducer wells opposite to one another but at 45-degree angles to the flow (Figure 4-9A). Transit-time flowmeters can be either single-path or multiple-path designs (Figure 4-9B).

Single-path flowmeters are provided with a single pair of transducers that make a single-line velocity measurement. They use a meter factor that is pre-determined by calibration to compensate for variations in velocity profile and for flow section construction irregularities.

In the design of multi-path flowmeters, several sets of transducers are placed in different paths across the flow section, thereby attempting to measure the velocity profile across the entire cross-section of the pipe. Multi-path instruments are used in large-diameter conduits, such as utility stacks, and in other applications where non-uniform flow velocity profiles exist.

Transit-time meters can also be used to measure both very hot (e.g., liquid sulfur) and very cold (liquid nitrogen) fluids, and also to detect very low flows. Wetted-transducer designs for small pipes (down to 1/2 in.) are called axial or co-axial designs (Figure 4-10). These devices permit transit-time measurement along a path length significantly greater than the diameter of the pipe, increasing low-flow sensitivity.

Originally, ultrasonic flowmeters were divided into those using the Doppler-shift principle and those using the transit-time principle. More recently, flowmeters are capable of measuring the flow of both clean fluids and of slurries with entrained solids or other acoustical discontinuities. Microprocessors have made it possible to switch automatically from clean fluid mode to particulate mode based on the “correlation factor”. This figure of merit dramatically improves the accuracy of overall performance. In some carefully engineered applications, installed accuracy to within 0.5% of reading has been reported.

Applications & Performance

Doppler flowmeters are not recommended for clean fluid applications. Transit-time flowmeters, on the other hand, are often used to measure the flow of crude oils and simple fractions in the petroleum industry. They also work well with viscous liquids, provided that the Reynolds number at minimum flow is either less than 4,000 (laminar flow) or above 10,000 (turbulent flow). Serious non-linearities are present in the transition region (Figure 4-11).

Transit-time flowmeters are the standard for measuring cryogenic liquids down to -300°C and are also used in molten metal flowmetering. Measurement of liquid argon, liquid nitrogen, liquid helium and molten sulfur have often been reported. Spool-section type flowmeters are most often used for these applications, especially the axial and co-axial designs.

Raw wastewater applications usually have too few acoustic discontinuities for Doppler flowmeters. On the other hand, raw wastewater is not clean enough all the time for transit-time measurement. Other wastewater-related applications are equally problematic, as the solids concentration can be too high for either transit-time or Doppler flowmeters to work properly. In still other wastewater applications, the problem is that the acoustical absorbency of the mostly organic solids in wastewater attenuates the ultrasonic signals.

The use of multi-path flowmeters in raw wastewater and storm water applications is common, while Doppler or cross-correlation hybrid designs are most often used to measure activated sludge and digested sludge flows.

For mining slurries, Doppler flowmeters typically work well. Among the few problem applications are those in HDPE pipe, because the pipe wall flexes enough to change the diameter of the measurement area. This affects the accuracy of the meter. In addition, the flexure of the pipe wall can often break the acoustic coupling of the transducer to the outside of the pipe, causing failure. Another problem area is the measurement of slurries that are acoustically absorbent, such as lime or kaolin slurries. These applications fail because the highly absorbent solids attenuate the signal below usable strength. Lower frequency (0.45 MHz) sensors have been tried for these applications, but success has been limited.

Multi-path, transit-time flowmeters also measure stack gas flows in power-plant scrubbers, even in very large diameter stacks

There is a need for accurate flow measurement of numerous liquids, gases and vapors in many industries. For instance, food processing plants need to have an accurate measure of types of materials that go into the products on a large, automated scale. In the semiconductor industry, small amounts of gases have to be applied to the production process. Accurate delivery of these gases is essential to ensure the quality of the finished product.

As already mentioned, the mass flow or the volume flow are the measurements that are needed in these processes. In the case of mass flow, the Coriolis flow meter (also known as the inertial flow meter) is commonly used.

The Coriolis flow meter gets it’s name from the Coriolis effect that was first described by Gaspard-Gustave Coriolis in 1835. Coriolis worked in understanding the behaviors of objects in motion due to the various forces that applied to them. To this extent, the Coriolis mass flow meter works in this manner.

If a liquid or gas is passing through a tube it applies a force to the tube. When the tube is already moving, then the substance passing through it will change the movement or vibration of that tube. The change in the amplitude of the vibration of the tube can be used to determine the mass of a flow of the substance passing through the tube.

This is possible provided various other factors are known about the tube, such as the width, the type of material that it is made from, the vibrating frequency of the tube and it’s inertia. The flow density of the material passing through the tube is also needed.

Coriolis flowmeters are popular because they need little maintenance. By comparison to other devices that perform flow measurement they are well designed to the extent that little can go wrong with them. They do not need to be re-calibrated like other types of flow meters.

With this said, the flow meter does need to be checked from time to time, especially if the substances that pass through the tubing are hot or corrosive.

If you are using these types of substances the chances are you will have noted this when initially specifying the type of flow meter you need. Many flow meters will not be able to handle hot liquids or corrosive gases. A specially made flow meter would be required for these purposes.

When it comes to selecting a coriolis meter, you want to make sure it meets all your needs. You should also look for the best you can afford as this is a fair measure of the quality of the meter. Coriolis flow meters, and gas mass flow meters, are designed to be accurate and they’re designed to save you time and money so you will make this initial expense back on increased efficiency in the workplace

Coriolis flowmeters are relatively new compared to other flowmeters. They were not seen in industrial applications until 1980’s. Coriolis meters are available in a number of different designs. A popular configuration consists of one or two U-shaped, horseshoe-shaped, or tennis-racket-shaped (generalized U-shaped) flow tube with inlet on one side and outlet on the other enclosed in a sensor housing connected to an electronics unit.

The flow is guided into the U-shaped tube. When an osillating excitation force is applied to the tube causing it to vibrate, the fluid flowing through the tube will induce a rotation or twist to the tube because of the Coriolis acceleration acting in opposite directions on either side of the applied force. For example, when the tube is moving upward during the first half of a cycle, the fluid flowing into the meter resists being forced up by pushing down on the tube. On the opposite side, the liquid flowing out of the meter resists having its vertical motion decreased by pushing up on the tube. This action causes the tube to twist. When the tube is moving downward during the second half of the vibration cycle, it twists in the opposite direction. This twist results in a phase difference (time lag) between the inlet side and the outlet side and this phase difference is directly affected by the mass passing through the tube.

A more rescent single straight tube design is available to measure some dirty and/or abrasive liquids that may clog the older U-shaped design.

An advantage of Coriolis flowmeters is that it measures the mass flow rate directly which eliminates the need to compensate for changing temperature, viscosity, and pressure conditions. Please also note that the vibration of Coriolis flowmeters has very samll amplitude, usually less than 2.5 mm (0.1 in), and the frequency is near the natural frequency of the device, usually around 80 Hz. Finally, the vibration is commonly introduced by electric coils and measured by megnetic sensors.

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Further Information

Suppose that the fluid is flowing into the U-shaped tube at velocity V and the tube is vibrating at angular velocity . Consider a small section of the fluid that is on the inlet side away from the point of flexture at distance r.

Please note that the amplitudes of the vibration and twist are extremely small compared to the size of the U-shaped tube. The above graphics are highly exaggerated for illustration purposes.

The Coriolis force on the small fluid section m is

During the down cycle, the tube applys an upward resisting force to the fluid or the fluid pushes the tube down. On the outlet side, the Coriolis force has the opposite direction.

To simply the problem, we assume that the tube has a perfect U shape with a cross section area of A. The length and width are l, d, respectively. The opposite directions of Coriolis forces on inlet and outlet sides result in a twisting moment Tc

A K factor can be introduced to compensate for the more generalized U-shape.

where Qm = AV is the mass flow rate.

The governing equation of twisting is

where Iu is the inertia of the U-shaped tube, Cu is the damping coefficient, Ku is the stiffness, is the twist angle, and t is time.

Recall that the Coriolis flowmeters are vibrating the U-shaped tube to generate the rotation, the real angular velocity is function of vibrating frequency :

Assuming that the damping term Cu is negligible, the equation of twisting becomes

The particular solution (steady-state solution) of the twist angle is

Furthermore, the velocity of the turning corners of the U-shaped tube are  and the displacement difference between these two corners is d/2. Therefore, the time lag between these two corners is

By measuring the time lag , the mass flow rate can be obtained

In vibration analysis, it is custom to use the natural frequency as a basis and normalize frequency terms against it. The natural frequency of the U-shaped tube system is (note that Iu includes the mass of the fluid in the tube)

The mass flow rate then becomes

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Common Specifications

Common specifications for commercially available Coriolis flowmeters are listed below:

Fluid Phase:

Score     Phase     Condition
Liquid      Clean
Direct Mass
Dirty
Non-Newtonian
Viscous
Slurry      Abrasive
Gas      Clean
Dirty
Liquid      Corrosive
Slurry      Fibrous
: Recommended
: Limited applicability
Line Size:     6 ~ 200 mm (0.25 ~ 8 inch)
Turndown Ratio:     100 : 1

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Pros and Cons

•     Pros:
-     Higher accuracy than most flowmeters
-     Can be used in a wide range of liquid flow conditions
-     Capable of measuring hot (e.g., molten sulphur, liquid toffee) and cold (e.g., cryogenic helium, liquid nitrogen) fluid flow
-     Low pressure drop
-     Suitable for bi-directional flow
•     Cons:
-     High initial set up cost
-     Clogging may occur and difficult to clean
-     Larger in over-all size compared to other flowmeters
-     Limited line size availability

So you want to measure flow? The answer would seem to be to purchase a flowmeter. With fluid flow defined as the amount of fluid that travels past a given location, this would seem to be straightforward — any flowmeter would suffice. However, consider the following equation describing the flow of a fluid in a pipe.

Q = A x v

Q is flow rate, A is the crosssectional area of the pipe, and v is the average fluid velocity in the pipe. Putting this equation into action, the flow of a fluid traveling at an average velocity of a 1 meter per second through a pipe with a 1 square meter cross-sectional area is 1 cubic meter per second. Note that Q is a volume per unit time, so Q is commonly denoted as the “volumetric” flow rate. Now consider the following equation:

W = rho x Q

Where W is flow rate (again - read on), and rho is the fluid density. Putting this equation into action, the flow rate will be 1 kilogram per second when 1 cubic meter per second of a fluid with a density of 1 kilogram per cubic meter is flowing. (The same can be done for the commonly-used “pounds”. Without getting into details — a pound is assumed to be a mass unit.) Note that W is a mass per unit time, so W is commonly denoted as the “mass” flow rate. Now — which flow do you want to measure? Not sure? In some applications, measuring the volumetric flow is the thing to do.

Consider filling a tank. Volumetric flow may be of interest to avoid overflowing a tank where liquids of differing densities can be added. (Then again, a level transmitter and high level switch/shutoff may obviate the need for a flowmeter.) Consider controlling fluid flow into a process that can only accept a limited volume per unit time. Volumetric flow measurement would seem applicable.

In other processes, mass flow is important. Consider chemical reactions where it is desirable to react substances A, B and C. Of interest is the number of molecules present (its mass), not its volume. Similarly, when buying and selling products (custody transfer) the mass is important, not its volume.

Having discovered that there are two types of flow rates (volumetric and mass), it should not be a surprise that some flowmeters measure mass (W) while other flowmeters measure volume (Q). However, it is not quite that simple. Repeating the equations from Part 1 (for convenience), it can be seen that, assuming A is constant, Q can be determined by measuring the average fluid velocity v. Further, assuming that rho is constant, W can be determined from Q.

Q = A x v  W = rho x Q

Summarizing, some flowmeters measure volumetric flow, some flowmeters measure velocity from which the volumetric flow is determined, and some flowmeters measure mass flow. In addition, when the density is known or assumed, mass flow can be determined from the volumetric flow, and the volumetric flow can be determined from the mass flow. So you just wanted to measure flow — did you now? It all seemed so logical and simple at the time. Stick around — it gets worse. Some flowmeters use other principles to infer flow. The most common of these measurements measure the velocity head (1/2 rho v x v) to infer the volumetric flow. Notice that these flowmeters do NOT measure volume, do NOT measure mass, and do NOT measure velocity — but rather measure a combination of density and the square of velocity! Would it surprise you to discover that this is a description of (commonly-applied) head flowmeters, such as orifice plates, venturis, nozzles…? Further, in many applications, the inferred volumetric flow is used to determine the mass flow. Errors can enter the measurement process during each measurement and with each assumption. Is it any surprise that plant engineers often have difficulty closing material balances in their plants?

Summarizing (again), some flowmeters measure volume, some flowmeters measure mass, some flowmeters measure velocity, and some flowmeters measure inferentially. Understand the difference, but also understand that careful attention to detail can result in an inferential measurement that is better than the others.

Volumetric flow is expressed in units that reflect a volume per unit time. The example in Part 1 determines cubic meters and cubic feet per unit time to be volumetric flow units. Gallons and liters per unit time are also volumetric flow units. Mass flow is expressed in units that reflect a mass per unit time. The other example in Part 1 determines kilograms and pounds per unit time to be mass flow units. (Without getting into details — a pound is assumed to be a mass unit.) Note that the units of time are independent of whether volumetric or mass flow is measured.

Let’s have a quiz.
Are the following volumetric or mass liquid flow units?
gallons per minute
cubic feet per second
liters per minute
kilograms per hour
pounds per hour
grams per minute

Can one have a cubic foot of feathers?
yes/no

Can one have a gallon of feathers?
yes/no

Can one have a kilogram of feathers?
yes/no

If you answered volumetric to the first three questions, mass to the next three questions, and yes to the last three questions, you are on track.

Consider purchasing fuel for your car. How does a US gallon of gasoline purchased on a hot summer day in Las Vegas, Arizona compare with a US gallon of gasoline purchased on a cold winter night in Anchorage, Alaska? It was determined that a gallon is a volumetric unit, so logic would indicate that the same volume of gasoline was purchased. Yet the temperature difference would cause their densities, and hence their masses, to be different. Using this logic, more mass would be obtained by purchasing gasoline in colder weather. Thinking locally, one might conclude that it is more economical to purchase gasoline during the wee hours of the morning when the temperature is coldest.

As you might suspect, such is not the case. Gasoline pumps compensate for density variation that occurs due to temperature, and in doing so, they measure the amount (mass) of gasoline dispensed. Yet, a gallon of cold gasoline will occupy less volume than when hot. In essence, the measurement of a gallon of gasoline actually refers to its volume at a given temperature (such as 60 degF). As such, this is really a mass measurement unit because it refers to the flow of a specific substance at a given temperature, Returning to the quiz, let’s not be so hasty with the first three questions. They could be incomplete!
Part 3 discussed the use of volumetric units (such as gallons) to infer mass when the composition and temperature is known. The example given was that of purchasing a gallon of gasoline in a hot and cold climate. The assertion was that a gallon of gasoline purchased in hot and cold climates might have different sizes due to their differing temperatures, but their masses should be the same because the retail flowmeter is temperature compensated.

A number of e-mails questioning this assertion and further investigation resulted in the interesting discovery that retail gasoline flowmeters are not temperature-compensated in the United States, but are temperaturecompensated in Canada. In other words, either the measured volume (in the US) or the measured temperature-corrected volume (in Canada) is used to infer mass.

Consider the following general analysis:

1. Air temperature differences between hot and cold climates are large. In addition, air temperature fluctuations between day and night in a given location can be large.

2. There is a significant difference between ground temperatures in hot and cold climates. However, ground temperature fluctuations between day and night in a given location is very small. Ground temperature fluctuation between summer and winter in a given location is relatively small.

3. Gasoline will be warm when it leaves the refinery, but will cool in transport to the retailer’s underground tank. Given time in the tank, the temperature of the gasoline will approach the ground temperature.

4. Flowmeter calibration is performed using standard weights, implying a calibration to mass.

These statements imply that despite wide air temperature fluctuations, the temperature of the gasoline pumped through the flowmeter should be nearly the same as the ground temperature. Because the ground temperature does not fluctuate very much, the temperature variation of the gasoline will be small throughout the year, so the mass of a gallon of gasoline should not vary much throughout the year from a given tank. Following this logic, the mass of a gallon of gasoline sold in Alaska should be the same as one sold in Nevada.

Fluctuations in gasoline temperature cause gasoline density changes. The magnitude with which these changes affect measurement accuracy can be quantified by performing an uncertainty analysis to determine if temperature compensation is appropriate. An uncertainty analysis for this measurement would likely reveal a number of sources of measurement uncertainty, such as (but not limited to) the effects of ambient air temperature, gasoline temperature leaving the refinery, transport time from the refinery to the tank, ground temperature, tank level prior to filling, the volume of gasoline in the flowmeter piping, flowmeter piping temperature, frequency of use, and composition changes. As a minimum, such analysis would likely reveal that the consumer would not be advised to purchase gasoline from a tank that was just filled with warm gasoline. A detailed analysis may reveal other significant issues.

While this is perhaps more information than one would like to know about the subject, this discussion clearly illustrates the need to understand the process — and that the same process may be different in different locations. Sometimes … it’s just not so easy.

A brief review — Part 3 addressed mass flow measurement, volumetric flow measurement, and inferred mass flow measurement. The measurement of gasoline was given as an example of the inferred mass flow measurement (using volumetric units). Comments resulted in Part 3.1 that addressed some issues associated with retail gasoline measurements. This sparked a flurry of comments regarding how gasoline is measured at the pump. This issue attempts to tie the comments together, so reading this issue without having read previous issues may prove difficult.

Gasoline pumps in the USA measure volume and are calibrated using volumetric means. In other words, they are true volumetric devices — they measure volume and indicate gallons. Even the New York Times offered advice to the consumer on this one with “… buy gasoline during the coolest time of the day — early morning or late evening — while the gasoline is most dense…” (New York Times, September 24, 2001, Empowered II Smart Energy Management, A clean car is an efficient car, page 7).

Gasoline pumps in Canada measure volume. This volume is then compensated for the actual temperature to indicate the volume of the gasoline as if it were a certain temperature. The compensated volume is an implied mass measurement. I suspect (but do not know) that these pumps are calibrated using volumetric means that are temperature compensated. In other words, they are inferred mass measurement devices and are calibrated as such — they measure volume and indicate in (temperature-compensated) liters. In Canada, the inferred mass of the gasoline received should be the same (within the limitations of the equipment) regardless of gasoline temperature. Note however that composition differences (and additives) may cause the density at a given temperature to be different than its nominal value. As an example, a 1% increase in gasoline density from its nominal value does not affect the actual volume measured, but will cause the inferred mass measurement to be 1% lower than the actual mass flow.

My comments on some readers’ responses follow:

One reader questioned whether the “wee hours of the am” would be the time when the gasoline would be at its lowest temperature in an underground tank. Thermal lag for underground gasoline storage tanks is an issue, but may not be significant. For science class, my daughter measured the temperatures 1 meter above and 1 meter below grade in the fall/winter (in the New York area). I seem to remember the ground temperature changing by only 1-2 degC over a period of months. The above ground temperature changed by 20 degC (or more?) during the same period. This issue is likely to be significant for above ground storage tanks (as suggested by other readers). Note however that filling the tank may cause larger (transient) effects caused by such issues as the quantity and temperature of the gasoline prior to fill, and the quantity and temperature of gasoline added. Not being able to sell compressed natural gas measured with a Coriolis mass flowmeter in kg or lbm (pounds mass) because it was not considered ‘marketable’ to the the public illustrates resistance to change. By the way, when will gasoline be sold by the kg or lbm — or better yet, by the BTU or Joule (as suggested by another reader)? I suspect that it will not be soon.

The comments and observations about beating the measurement were amusing. Society allows people to (reasonably) operate in their own self-interest. Parting with less money for a product is clearly in the purchaser’s self-interest. (Engineers sometimes call this an “optimization problem”, but that is an issue for another day.) Comments on how to beat the system were inevitable.

The safety point regarding gasoline expansion causing explosions and fires (after topping off a gas tank in a cold climate and then parking in a warm garage) is important. Virtually everything is potentially dangerous — even a small puddle of water that turns to ice…

Both gas and liquid flow can be measured in volumetric or mass flow rates (such as litres per second or kg/s). These measurements can be converted between one another if the materials density is known. The density for a liquid is almost independent of the liquids conditions, however this is not the case for a gas, whose density highly depends upon pressure and temperature.

In engineering contexts, the volumetric flow rate is usually given the symbol Q and the mass flow rate the symbol \dot m.

[edit] Gas

Due to the nature of an Ideal gas or a Real gas, the volumetric gas flow rate will differ for the same mass flow rate when at differing temperatures and pressures. As such gas volumetric flow rate is sometimes measured in “standard cubic centimeters per minute” (abbreviation sccm). This unit, although not an SI unit is sometimes used due to the additional information attached to the unit symbol, which indicates the temperature and pressure of the gas. Many other similar abbreviations are also in use, for two reasons, firstly mass flow and volumetric flow can be equated at known conditions, and secondly due to the imperial system older units such as standard cubic feet per minute or per second may still be used in some countries. It is often necessary to employ standard gas relationships (such as the ideal gas law) to convert between units of mass flow and volumetric flow.

[edit] Liquid

For liquids other units used depend on the application and industry but might include gallons (U.S. liquid or imperial) per minute, liters per second, bushels per minute and, when describing river flows, cumecs (cubic metres per second) or acre-feet per day.

[edit] Mechanical flow meters

There are several types of mechanical flow meter

[edit] Piston Meter

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

[edit] Woltmann Meter

Woltman meters, commonly referred to as Helix meters are popular at larger sizes. Jet meters (single or Multi-Jet) are increasing in popularity in the UK at larger sizes and are commonplace in the EU.

[edit] Multi-jet Meter

A multi-jet meter is a velocity type meter which has an impeller which rotates horizontally on a vertical shaft. The impeller element is in a housing in which multiple inlet ports direct the fluid flow at the impeller causing it to rotate in a specific direction in proportion to the flow velocity. This meter works mechanically much like a paddle wheel meter except that the ports direct the flow at the impeller equally from several points around the circumference of the element, where a paddle wheel normally only receives flow from one offset flow stream.

[edit] Venturi Meter

Another method of measurement, known as a venturi meter, is to constrict the flow in some fashion, and measure the differential pressure (using a pressure sensor) that results across the constriction. This method is widely used to measure flow rate in the transmission of gas through pipelines, and has been used since Roman Empire times.

[edit] Dall Tube

The Dall tube is a shortened version of a Venturi meter with a lower pressure drop than an orifice plate. Both flow meters the flow rate of Dall tube is determined by measuring the pressure drop caused by restriction in the conduit. The pressure differential is measured using diaphragm pressure transducers with digital read out. Since these meters have significantly lower permanent pressure losses than the orifice meters, the Dall tubes have widely been used for measuring the flow rate of large pipeworks.

[edit] Orifice Plate

Another simple method of measurement uses an orifice plate, which is basically a plate with a hole through it. It is placed in the flow and constricts the flow. It uses the same principle as the venturi meter in that the differential pressure relates to the velocity of the fluid flow (Bernoulli’s principle).

[edit] Pitot tube

A Pitot tube is a pressure measuring instrument used to measure fluid flow velocity by determining the stagnation pressure. Bernoulli’s equation is used to calculate the dynamic pressure and thence fluid velocity.

[edit] Multi-hole Pressure Probe

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

[edit] Paddle wheel

The paddle wheel translates the mechanical action of paddles rotating in the liquid flow around an axle into a user-readable rate of flow (gpm, lpm, etc.). The paddle tends to be inserted into the flow.

[edit] Pelton wheel

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

[edit] Optical Flow Meters

Optical flow meters use light to determine flow rate. Small particles which accompany natural and industrial gases pass through two laser beams focused in a pipe by illuminating optics. Laser light is scattered when a particle crosses the first beam. The detecting optics collects scattered light on a photodetector, which then generates a pulse signal. If the same particle crosses the second beam, the detecting optics collect scattered light on a second photodetector, which converts the incoming light into a second electrical pulse. By measuring the time interval between these pulses, the gas velocity is calculated as V=D/T where D is the distance between the laser beams and T is the time interval.

Laser-based optical flow meters measure the actual speed of particles, a property which is not dependent on thermal conductivity of gases, variations in gas flow or composition of gases. The different operating principle enables optical laser technology to deliver highly accurate flow data, even in challenging environments which may include high temperature, low flow rates, high pressure, high humidity, pipe vibration and acoustic noise.

Optical flow meters are very stable with no moving parts and deliver a highly repeatable measurement over the life of the product. Because distance between the two laser sheets does not change, optical flow meters do not require periodic calibration after its initial commissioning. Optical flow meters require only one installation point, instead of the two installation points typically required by other types of meters. A single installation point is simpler, requires less maintenance and is less prone to errors.

Optical flow meters are capable of measuring flow from 0.1m/s to faster than 100m/s (1000:1 turn down ratio) and have been demonstrated to be effective for the measurement of flare gases, a major global contributor to the emissions associated with climate change.[1]

[edit] Turbine flow meter

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

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

[edit] Open Channel Flow Measurement

[edit] Level to Flow

The level of the water is measured at a designated point behind a hydraulic structure (a weir or flume) using various means (bubblers, ultrasonic, float, and differential pressure are common methods). This depth is converted to a flow rate according to a theoretical formula of the form Q=KHX where Q is the flow rate, K is a constant, H is the water level and X is an exponent which varies with the device used, or it is converted according to empirically derived level/flow data points (a ‘flow curve’). The flow rate can then integrated over time into volumetric flow.

[edit] Area/Velocity

The cross-sectional area of the flow is calculated from a depth measurement and the average velocity of the flow is measured directly (doppler and propeller methods are common). Velocity times the cross-sectional area yields a flow rate which can be integrated into volumetric flow.

[edit] Dye Testing

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

[edit] Thermal mass flow meters

Thermal mass flow meters generally use combinations of heated elements and temperature sensors to measure the difference between static and flowing heat transfer to a fluid and infer its flow with a knowledge of the fluid’s specific heat and density. The fluid temperature is also measured and compensated for. If the density and specific heat characteristics of the fluid are constant, the meter can provide a direct mass flow readout, and does not need any additional pressure temperature compensation over their specified range.

Technological progress allows today to manufacture thermal mass flow meters on a microscopic scale as MEMS sensors, these flow devices can be used to measure flow rates in the range of nano litres or micro litres per minute.

Thermal mass flow meters are used for compressed air, nitrogen, helium, argon, oxygen, natural gas. In fact, most gases can be measured as long as they are fairly clean and