Other Flow Obstruction Meters
Any obstruction inserted into a duct or pipe that creates a measurable pressure difference can be used as a flow meter. The three basic standardized flow measurement devices presented above are perhaps more suitable for laboratory work than installation as permanent ductwork instruments in ventilation applications. They are sensitive to flow disturbances, relatively expensive, require considerable space, and have a narrow measurement range and a high permanent pressure loss. For these reasons, numerous attempts have been made to develop instruments without these drawbacks. Some of them, like the
TABLE 12.6 Some Required Straight Lengths {LID) for Orifice Plates and Nozzles38

Dali tube,47 which is a modification of the venturi, have even been standard instruments. Several other solutions based on plates, rings, or wingtype obstructions are commercially available. This wide variety of devices is not covered here. For further information, the reader should contact the manufacturers of such instruments.
The principle of the traversing method is to measure the local velocity at one or several points of the flow crosssection and then calculate the flow rate based on this information. Generally speaking, an integration of the local velocity over the flow crosssection is made. Mathematically, this is expressed as
(12.35)
Where Qv is the volume flow rate, V is the local velocity, and DA is a differential area of the flow crosssection. In practice the number of measured local velocities is finite, and the integration is carried out using different graphical or numerical methods. For duct flow, a standard is available describing the traversing methods where a Pitotstatic tube for velocity measurement is used.4* This document divides the determination of the flow rate into three categories: graphical integration, numerical integration, and arithmetical methods.
The graphical integration method is based on graphical presentation of the average flow profile. For a circular duct, the crosssection is virtually divided into several concentric ring elements. The spatial mean velocity Vm of such an element is determined as an arithmetical mean of local velocities along the circumference of the corresponding radius. For a circular crosssection the flow rate can be expressed as
(12.36) 
Qv = TtR
Where R is the radius of the duct and R is the radial distance from the duct center point. For graphical integration the spatial mean velocities Vm are plotted against (r/R)2. The area under this curve is then the integral term in Eq.
(12.35) And has only to be multiplied by the duct crosssection area. For this method the measuring points may be located at any position in order to obtain satisfactory knowledge of the velocity profile.
In the numerical integration method, the graphical velocity profile is replaced by an algebraic curve, and the integration is carried out numerically. A procedure has been described48 where the velocity profile is approximated using a thirddegree curve between the successive pairs of mean velocity values. A simpler approach, though not included in standards, is the use of the general formulas for numerical integration. For example, Simpson’s rule49 for an even (2N) Number of equal subintervals between the velocity points along the radius gives
_t> 
4r 
, A ..
Where the number of velocity points is 2N — 1 (the center point and the point at the duct wrall cancel out of the sum) and the distance between successive points along the radius is 1 /(2k). For a rectangular crosssection similar methods are available.
Sn the arithmetical methods50,51 a circular flow crosssection is divided into concentric rings and a central element. The areas of the elements are equal except for the outermost ring, which has only half of that area. A hypothesis is made for the velocity profile for each element. For example the Loglinear rule assumes a velocity profile of
V = A log Y + By + C , (12.38)
Where Y is the distance from the duct wall and A, B, and C are constants. Based on the velocity profile assumption, measurement points for each element are located in places where the (measured) local velocity is equal to the mean velocity of the element. This approach allows certain measurement point locations, dependent on the number of the points and the assumed velocity profile, to be determined. Table 12.7 gives measuring points for the iog — linear rule in a round duct.
The volume flow rate is calculated as the arithmetical mean of the measured velocities multiplied by the duct crosssectional area. The number of diameters along which the traversing occurs is not defined. If a nearsymmetrical velocity profile is expected, an even traverse along one diameter may be sufficient. In case of a more disturbed profile, traversing along two or more diameters is recommended.
In the case of a rectangular crosssection, a variety of methods and corresponding measurement point locations exist.48’52 Table 12.8 shows the required measuring points for the logTchebycheff rule, where the velocity distribution in the wallconnected elements is logarithmic and in the central elements polynomial.
As an example, for the 5×6 = 30 points case, the principle for placing the measurement points is shown in Fig. 12.23.
There is also a standardized method based on the estimation of the flow rate on one measurement point only.53 In this method the velocity probe is placed in the duct so that the measured local velocity is equal to the mean axial velocity. In fully developed turbulent duct flow, this distance from the wall
TABLE 12.7 Measuring Point Distances for the Loglinear Rule Circular CrossSection50
Number of measurement points per Diameter Distance from wall in duct diameters

TABLE 12.8 Measuring Point Distances for the LogTchebycheff Rule, Rectangular CrossSection48’52
Number of measurement points per Traversing line Distance from wall (l/L or H/H)

Is Y = 0.242R. This approach has severe restrictions, as the velocity profile in the measurement crosssection has to be very close to the fully developed profile, requiring minimum upstream straight lengths of about 30 to 80 duct diameters depending on the type of the nearest flow disturbance.
Apart from ducts, the traversing principle can be utilized in any crosssection where the flow rate has to be determined, such as supply or exhaust grills, the
L

Surface of a large heating/cooling coil, or the intake opening of a fan. If the velocity is high enough, the Pitotstatic tube may be used. On the other hand, the vane anemometer is a convenient instrument for traversing larger surfaces, as it Has an Integrating character due to its larger dimensions.
12.3.9.5 Tracer Method
The use of tracers for airflow measurement in ventilation ducts is not very common. There are several reasons for this. Compared to other flow measurement methods, tracers require more complicated equipment, skilled personnel, and are more expensive. There are, however, situations when conventional measurement methods are not applicable. For instance, if the space available Is Small, and hence the flow meter cannot be installed, or if no space is free to carry out traversing measurements, the use of a tracer might be an alternative.
Tracer methods are not as well standardized as some of the conventional methods. One standard54 is available, but it comprises radioactive tracers only, which are perhaps not the best alternative for measurements in buildings. In principle, at least three different measurement methods are available:5j the constant injection method, the pulse injection method, and the concentration decay method. Of these three, the first is the best approach for normal ventilation measurements. The other methods require special instrumentation and do not produce as reliable results.
Constant Injection Method
The tracer is injected into the duct at a constant rate and mixed with the flowing air. The concentration of the airtracer mixture is measured further downstream. Assuming perfect mixing and that the air entering the test section has a zero concentration, the air volume flow rate Qm can be calculated based on the mass balance of the tracer
QVa = p1rfpL, (12.39)
Pa 1 t‘‘!/(
Where Pt and Tt are the pressure and (Kelvin) temperature of the injected tracer, Pa and Ta are the corresponding quantities for the air, Qvt is the volume flow rate of the injected tracer and Cvt is the downstream measured tracer (volume) concentration. Good mixing of the tracer and air between the injection point and the measurement crosssection is essential. Failure to achieve this will result in errors. The injection and the sampling should be carried out by a multipoint approach. A ring, cross, or rectangle formed tube with many small holes is a good injection device that will spread the tracer effectively. Similar solutions can be used for sampling. A fan is an ideal mixing device between the injection and the sampling sections. The error due to incomplete mixing using a fan has been shown to be only few percentage points,56 In the case of a straight empty duct between the injection and sampling sections and a onepoint injection/sampling, a distance of at least 80 duct diameters is required to keep the incomplete mixing error less than 5%. Adding a multipoint injection/sampling and some mixing elements can reduce the corresponding distance to 1020 duct diameters;57 see Table 12.9.
As a tracer, either a gas or particles can be used. In ventilation ductwork measurement, gas is recommended. Particles tend to adhere to the duct surface,
TABLE 12.9 Required Mixing Lengths (L/D) to Keep the Error due to Incomplete Mixing Smaller Than 5% or 10%57
L/D
Maximum Maximum
Type of injection, sampling, and duct section error 5 % error 10 %
Straight duct without disturbance 80 60
Injection at center, sampling at center Straight duct without disturbance
Injection through a ring whose diameter is 63% of the duct’s (four holes in ring)
TOC o "15" h z (a) Sampling at center 25 20
(bj Sampling at four points in duct (situated as in injection) 15 10
Duct with two 90" bends
Injection through a ring whose diameter is 63% of the duct’s (four holes in ring)
(a) Sampling at center 20 15
(b) Sampling at four points in the duct (situated as in injection) 10 5
Injection before a fan and sampling after the fan 10 5
Injection through a ring whose diameter is 63 % of the duct’s
(four holes in ring)
Which will adversely influence the measurement and also hygiene. Widely used tracer gases are nitrous oxide (N20) and sulfur hexafluoride (SF6), which are readily detectable using infrared analyzers or gas chromatographs. It is advisable to use a diluted tracer with a density close to air density. Otherwise mixing with air in the duct is difficult, and can lead to large measurement errors. Tracers having strong ozonedepleting features are not recommended.
12.3.9.6 Measurement of Supply or Exhaust Flows
The previous methods are mainly used to measure duct flow. When measuring flows on supply or exhaust terminals, different methods are used. The measurement on exhaust terminals is simple to carry out, as the velocity field near the terminal is relatively constant, with no steep gradients or swirls. In the case of a grill, traversing across the terminal surface using a suitable velocity instrument is a good alternative. A suitable instrument for most cases is the vane anemometer.
Different nozzleshaped tubes are available, which are pressed onto the exhaust terminal. The air passes through the tube and a onepoint velocity measurement is carried out in the throat of the device. The flow rate is determined from the calibration curve.
One of the best and most convenient methods of measuring the flow in the terminal is to use the terminal characteristic pressure difference. This requires that the manufacturer of the terminal provide calibration curves, where the flow rate is expressed as the function of the characteristic pressure difference. Some devices have integrated pressure measurement tappings, and the user has only to attach a manometer to measure the pressure difference.
Flow measurement on supply terminals is difficult, as each terminal creates its own velocity pattern, and a reliable correlation between a local velocity and
The flow rate is difficult to achieve. The balometer is a hoodshaped device that is pressed onto the terminal, and the airflow is passed through the instrument’s throat. The local velocity is measured at several points in the throat using, fixed thermal sensors. In modern balometers the flow rate is computed in an electronic module into which the calibration information has been fed,
The old, tedious, but quite reliable method is to measure the suppl) flow by the bag method. A tightly rolled plastic bag empty of air at the commencement of the test is pressed on the terminal with all the supply air passing into the bag. The filling time of the bag is measured and the flow rate calculated based on this information. The bag volume has to be determined in advance by a special measurement. Finally, the characteristic pressure difference method, mentioned above, can also be applied to supply terminals.
The measurement errors encountered in determining flow rate depend on the methods and instruments used. In conventional duct flow measurements, the greatest errorgenerating phenomenon is the irregularity and swirl of the duct flow itself. The duct flow velocity profile strongly influences the result of the measurement. The shape of the profile changes along the ductwork. At the end of a long straight duct (30 to 50 duct diameters) the profile is fully developed. Any other components such as tees, bends, or dampers reshape the velocity profile, after which it begins to move again toward the fully developed profile until it hits the next disturbance.
Because all measurement methods and instruments are sensitive to the velocity profile, the choice of the measurement crosssection is of vital importance. In most ventilation systems there is seldom enough straight duct to allow a fully developed velocity profile to develop, which is the most favorable for flow measurement. Thus, the principle in selecting the measurement crosssection is to find the place where the velocity profile is as near to the fully developed profile as possible. In practice the distance from the nearest source of disturbance upstream is maximized, ensuring that the distance to the nearest downstream disturbance is at least 3 to 5 duct diameters.
Constriction measurement devices constructed to standards42 do not necessarily require calibration. One idea of strict standardization is to define the manufacturing, tolerances, and other features in such a way that the instruments made according to these rules require no calibration. The properties are so well known that a certain accuracy can be guaranteed. If the accuracy specified in the standard is inadequate, additional calibration procedures are required. The same applies to Pitotstatic tubes made according to standard specifications.48
The simplest calibration procedure for a gas flowmeasuring device is to connect it in series with a reference meter and allow the same flow to pass through both instruments. This requires a reference instrument of better metrological quality than the calibrated instrument. One fact to consider when applying this method is that the mass flow rate in the system containing both instruments is constant (assuming no leakage), but the volume flow rate is not. The volume flow rate depends on the fluid density and the density depends on the pressure and the temperature. The correct way to calibrate is to compare either the measured mass
Flow rares or the volume flow rates which have been converted to correspond to the identical state (pressure and temperature) of the fluid.
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