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Figure 1-1: Click on figure to enlarge.
the Sumerian cities of Ur, Kish, and Mari near the Tigris and Euphrates Rivers around 5,000 B.C. Even today, the distribution of water among the rice patties of Bali is the sacred duty of authorities designated the "Water Priests."
Our understanding of the behavior of liquids and gases (including hydrodynamics, pneumatics, aerodynamics) is based on the works of the ancient Greek scientists Aristotle and Archimedes. In the Aristotelian view, motion involves a medium that rushes in behind a body to prevent a vacuum. In the sixth century A.D., John Philoponos suggested that a body in motion acquired a property called impetus, and that the body came to rest when its impetus died out.
In 1687, the English mathematician Sir Isaac Newton discovered the law of universal gravitation. The operation of angular momentum-type mass flowmeters is based directly on Newton's second law of angular motion. In 1742, the French mathematician Rond d'Alembert proved that Newton's third law of motion applies not only to stationary bodies, but also to objects in motion.
The Flow Pioneers
A major milestone in the understanding of flow was reached in 1783 when the Swiss physicist Daniel Bernoulli published his Hydrodynamica. In it, he introduced the concept of the conservation of energy for fluid flows. Bernoulli determined that an increase in the velocity of a flowing fluid increases its kinetic energy while decreasing its static energy. It is for this reason that a flow restriction causes an increase in the flowing velocity and also causes a drop in the static pressure of the flowing fluid.The permanent pressure loss through a flowmeter is expressed either as a percentage of the total pressure drop or in units of velocity heads, calculated as V2/2g, where V is the flowing velocity and g is the gravitational acceleration (32.2 feet/second2 or 9.8 meters/second2 at 60° latitude). For example, if the velocity of a flowing fluid is 10 ft/s, the velocity head is 100/64.4 = 1.55 ft. If the fluid is water, the velocity head corresponds to 1.55 ft of water (or 0.67 psi). If the fluid is air, then the velocity head corresponds to the weight of a 1.55-ft column of air.
The permanent pressure loss through various flow elements can be expressed as a percentage of the total pressure drop (Figure 1-1), or it can be expressed in terms of velocity heads. The permanent pressure loss through an orifice is four velocity heads; through a vortex shedding sensor, it is two; through positive displacement and turbine meters, about one; and, through flow venturis, less than 0.5 heads. Therefore, if an orifice plate (Figure 1-2) with a beta ratio
Figure 1-2: Click on figure to enlarge.
of 0.3 (diameter of the orifice to that of the pipe) has an unrecovered pressure loss of 100 in H2O, a venturi flow tube could reduce that pressure loss to about 12 in H2O for the same measurement.
In 1831, the English scientist Michael Faraday discovered the dynamo when he noted that, if a copper disk is rotated between the poles of a permanent magnet, electric current is generated. Faraday's law of electromagnetic induction is the basis for the operation of the magnetic flowmeter. As shown in Figure 1-3, when a liquid conductor moves in a pipe having a diameter (D) and travels with an average velocity (V) through a magnetic field of B intensity, it will induce a voltage (E) according to the relationship:
where C is the constant for units conversion.
Over the past several years, the performance of magnetic flowmeters has improved significantly. Among the advances are probe and ceramic insert designs and the use of pulsed magnetic fields (Figure 1-4), but the basic operating principle of Faraday's law of electric induction has not changed.
In 1883, the British mechanical engineer Osborne Reynolds proposed a single, dimensionless ratio to describe the velocity profile of flowing fluids:
Figure 1-3: Click on figure to enlarge.
Where D is the pipe diameter, V is the fluid velocity, ρ is the fluid density, and µ is the fluid viscosity.
He noted that, at low Reynolds numbers (below 2,000) (Figure 1-5), flow is dominated by viscous forces and the velocity profile is (elongated) parabolic. At high Reynolds numbers (above 20,000), the flow is dominated by inertial forces, resulting in a more uniform axial velocity across the flowing stream and a flat velocity profile.
Until 1970 or so, it was believed that the transition between laminar and turbulent flows is gradual, but increased understanding of turbulence through supercomputer modeling has shown that the onset of turbulence is abrupt.
When flow is turbulent, the pressure drop through a restriction is proportional to the square of the flowrate. Therefore, flow can be measured by taking the square root of a differential pressure cell output. When the flow is laminar, a linear relationship exists between flow and pressure drop. Laminar flowmeters are used at very low flowrates (capillary flowmeters) or when the viscosity of the process fluid is high.
In the case of some flowmeter technologies, more than a century elapsed between the discovery of a
Figure 1-4: Click on figure to enlarge.
scientific principle and its use in building a flowmeter. This is the case with both the Doppler ultrasonic and the Coriolis meter.
In 1842, the Austrian physicist Christian Doppler discovered that, if a sound source is approaching a receiver (such as a train moving toward a stationary listener), the frequency of the sound will appear higher. If the source and the recipient are moving away from each other, the pitch will drop (the wavelength of the sound will appear to decrease). Yet it was more than a century later that the first ultrasonic Doppler flowmeter came on the market. It projected a 0.5-MHz beam into a flowing stream containing reflectors such as bubbles or particles. The shift in the reflected frequency was a function of the average traveling velocity of the reflectors. This speed, in turn, could be used to calculate a flowrate.
The history of the Coriolis flowmeter is similar. The French civil engineer Gaspard Coriolis discovered in 1843 that the wind, the ocean currents, and even airborne artillery shells will all drift sideways because of the earth's rotation. In the northern hemisphere, the deflection is to the right of the motion; in the southern hemisphere, it is to the left. Similarly, a body traveling toward either pole will veer eastward, because it retains the greater eastward rotational speed of the lower altitudes as it passes over the more slowly rotating earth surface near the poles. Again, it was the slow evolution of sensors and electronics that delayed creation of the first commercial Coriolis mass flowmeter until the 1970's.
It was the Hungarian-American aeronautical engineer Theodore von Karman who, as a child growing up in Transylvania (now Romania), noticed that stationary rocks caused vortices in flowing water, and that the distances between these traveling vortices are constant, no matter how fast or slow the water runs. Later in life, he also observed that, when a flag flutters in the wind, the wavelength of the flutter is independent of wind velocity and depends
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solely on the diameter of the flag pole. This is the theory behind the vortex flowmeter, which determines flow velocity by counting the number of vortices passing a sensor. Von Karman published his findings in 1954, and because by that time the sensors and electronics required to count vortices were already in existence, the first edition of the Instrument Engineers' Handbook in 1968 was able to report the availability of the first swirlmeter.
The computer has opened new frontiers in all fields of engineering, and flow measurement is no exception. It was only as long ago as 1954 that another Hungarian-American mathematician, John Von Neumann, built Uniac--and even more recently that yet another Hungarian-American, Andy Grove of Intel, developed the integrated circuit. Yet these events are already changing the field of flowmetering. Intelligent differential pressure cells, for example, can automatically switch their range between two calibrated spans (one for 1-10%, the other for 10-100% of D/P), extending orifice accuracy to within 1% over a 10:1 flow range. Furthermore, it is possible to include in this accuracy statement not only hysteresis, rangeability, and linearity effects, but also drift, temperature, humidity, vibration, over-range, and power supply variation effects.
With the development of superchips, the design of the universal flowmeter also has become feasible. It is now possible to replace dye-tagging or chemical-tracing meters (which measured flow velocity by dividing the distance between two points by the transit time of the trace), with traceless cross-correlation flowmeters (Figure 1-6). This is an elegant flowmeter because it requires no physical change in the process--not even penetration of the pipe. The measurement is based on memorizing the noise pattern in any externally detectable process variable, and, as the fluid travels from point A to point B, noting its transit time.
Flow Sensor Selection
The purpose of this section is to provide information to assist the reader in making an informed selection of flowmeter for a particular application. Selection and orientation tables are used to quickly focus on the most likely candidates for measurement. Tables 1-I and 1-II have been prepared to make available a large amount of information for this selection process.At this point, one should consider such intangible factors as familiarity of plant personnel, their experience with calibration and maintenance, spare parts availability, mean time between failure history, etc., at the particular plant site. It is also recommended that the cost of the installation be computed only after taking these steps. One of the most common flow measurement mistakes is the reversal of this sequence: instead of selecting a sensor which will perform properly, an attempt is made to justify the use of a device because it is less expensive. Those "inexpensive" purchases can be the most costly installations.
The basis of good flowmeter selection is a clear understanding of the requirements of the particular application. Therefore, time should be invested in fully evaluating the nature of the process fluid and of the overall installation. The development of specifications that state the appl
Figure 1-5: Click on figure to enlarge.
ication requirements should be a systematic, step-by-step process.
The first step in the flow sensor selection process is to determine if the flowrate information should be continuous or totalized, and whether this information is needed locally or remotely. If remotely, should the transmission be analog, digital, or shared? And, if shared, what is the required (minimum) data-update frequency? Once these questions are answered, an evaluation of the properties and flow characteristics of the process fluid, and of the piping that will accommodate the flowmeter, should take place (Table 1-I). In order to approach this task in a systematic manner, forms have been developed, requiring that the following types of data be filled in for each application:
Fluid and flow characteristics: In this section of the table, the name of the fluid is given and its pressure, temperature, allowable pressure drop, density (or specific gravity), conductivity, viscosity (Newtonian or not?) and vapor pressure at maximum operating temperature are listed, together with an indication of how these properties might vary or interact. In addition, all safety or toxicity information should be provided, together with detailed data on the fluid's composition, presence of bubbles, solids (abrasive or soft, size of particles, fibers), tendency to coat, and light transmission qualities (opaque, translucent or transparent?).
Expected minimum and maximum pressure and temperature values should be given in addition to the normal operating values. Whether flow can reverse, whether it does not always fill the pipe, whether slug flow can develop (air-solids-liquid), whether aeration or pulsation is likely, whether sudden temperature changes can occur, or whether special precautions are needed during cleaning and maintenance, these facts, too, should be stated.
Concerning the piping and the area where the flowmeter is to be located, the following information
Figure 1-6: Click on figure to enlarge.
should be specified: For the piping, its direction (avoid downward flow in liquid applications), size, material, schedule, flange-pressure rating, accessibility, up or downstream turns, valves, regulators, and available straight-pipe run lengths.
In connection with the area, the specifying engineer must know if vibration or magnetic fields are present or possible, if electric or pneumatic power is available, if the area is classified for explosion hazards, or if there are other special requirements such as compliance with sanitary or clean-in-place (CIP) regulations.
The next step is to determine the required meter range by identifying minimum and maximum flows (mass or volumetric) that will be measured. After that, the required flow measurement accuracy is determined. Typically accuracy is specified in percentage of actual reading (AR), in percentage of calibrated span (CS), or in percentage of full scale (FS) units. The accuracy requirements should be separately stated at minimum, normal, and maximum flowrates. Unless you know these requirements, your meter's performance may not be acceptable over its full range.
Accuracy vs. Repeatability
In applications where products are sold or purchased on the basis of a meter reading, absolute accuracy is critical. In other applications, repeatability may be more important than absolute accuracy. Therefore, it is advisable to establish separately the accuracy and repeatability requirements of each application and to state both in the specifications.When a flowmeter's accuracy is stated in % CS or % FS units, its absolute error will rise as the measured flow rate drops. If meter error is stated in % AR, the error in absolute terms stays the same at high or low flows. Because full scale (FS) is always a larger quantity than the calibrated span (CS), a sensor with a % FS performance will always have a larger error than one with the same % CS specification. Therefore, in order to compare all bids fairly, it is advisable to convert all quoted error statements into the same % AR units.
It is also recommended that the user compare installations on the basis of the total error of the loop. For example, the inaccuracy of an orifice plate is stated in % AR, while the error of the associated d/p cell is in % CS or % FS. Similarly, the inaccuracy of a Coriolis meter is the sum of two errors, one given in % AR, the other as a % FS value. Total inaccuracy is calculated by taking the root of the sum of the squares of the component inaccuracies at the desired flow rates.
In well-prepared flowmeter specifications, all accuracy statements are converted into uniform % AR units and these % AR requirements are specified separately for minimum, normal, and maximum flows. All flowmeter specifications and bids should clearly state both the accuracy and the repeatability of the meter at minimum, normal, and maximum flows.
Table 1 provides data on the range of Reynolds numbers (Re or RD) within which the various flowmeter designs can operate. In selecting the right flowmeter, one of the first steps is to determine both the minimum and the maximum Reynolds numbers for the application. Maximum RD is obtained by making the calculation
Table 1: Click on table to enlarge.
when flow and density are at their maximum and viscosity at its minimum. Conversely, the minimum RD is obtained by using minimum flow and density and maximum viscosity.
If acceptable metering performance can be obtained from two different flowmeter categories and one has no moving parts, select the one without moving parts. Moving parts are a potential source of problems, not only for the obvious reasons of wear, lubrication, and sensitivity to coating, but also because moving parts require clearance spaces that sometimes introduce "slippage" into the flow being measured. Even with well maintained and calibrated meters, this unmeasured flow varies with changes in fluid viscosity and temperature. Changes in temperature
Table II: Click on Table to enlarge.
also change the internal dimensions of the meter and require compensation.
Furthermore, if one can obtain the same performance from both a full flowmeter and a point sensor, it is generally advisable to use the flowmeter. Because point sensors do not look at the full flow, they read accurately only if they are inserted to a depth where the flow velocity is the average of the velocity profile across the pipe. Even if this point is carefully determined at the time of calibration, it is not likely to remain unaltered, since velocity profiles change with flowrate, viscosity, temperature, and other factors.
If all other considerations are the same, but one design offers less pressure loss, it is advisable to select that design. Part of the reason is that the pressure loss will have to be paid for in higher pump or compressor operating costs over the life of the plant. Another reason is that a pressure drop is caused by any restriction in the flow path, and wherever a pipe is restricted becomes a potential site for material build-up, plugging, or cavitation.
Before specifying a flowmeter, it is also advisable to determine whether the flow information will be more useful if presented in mass or volumetric units. When measuring the flow of compressible materials, volumetric flow is not very meaningful unless density (and sometimes also viscosity) is constant. When the velocity (volumetric flow) of incompressible liquids is measured, the presence of suspended bubbles will cause error; therefore, air and gas must be removed before the fluid reaches the meter. In other velocity sensors, pipe liners can cause problems (ultrasonic), or the meter may stop functioning if the Reynolds number is too low (in vortex shedding meters, RD > 20,000 is required).
In view of these considerations, mass flowmeters, which are insensitive to density, pressure and viscosity variations and are not affected by changes in the Reynolds number, should be kept in mind. Also underutilized in the chemical industry are the various flumes that can measure flow in partially full pipes and can pass large floating or settleable solids.