Flow element

Note that the second term involves a j3 value which is about 100 times larger than the j3 value of the first term. Since the proportionality between j3 and r is expected to be about the same for both classes of flow elements, this ratio also... 

La.mina.r Flow Elements. Each of the previously discussed differential-pressure meters exhibits a square root relationship between differential pressure and flow there is one type that does not. Laminar flow meters use a series of capillary tubes, roUed metal, or sintered elements to divide the flow conduit into innumerable small passages. These passages are made small enough that the Reynolds number in each is kept below 2000 for all operating conditions. Under these conditions, the pressure drop is a measure of the viscous drag and is linear with flow rate as shown by the PoiseuiHe equation for capilary flow ... 

Compressed-Air. Enough flow elements should be provided to permit accurate assessment of use by different operating departments within a plant. Compressed air is often unmetered thus there is Httle motivation to reduce use. A large fraction is often lost through leakage at fittings. 

Throughput is therefore proportional to mass flow rate. For a given mass now rate, throughput is independent of pressure. The relation between throughput and pressure drop Ap =pi—po across a flow element is written in terms of the conductance C. Resistance is the reciprocal of conduc tance. Conductance has dimensions of volume per time. 

Flow is an important measurement whose calibration presents some challenges. When a flow measurement device is used in applications such as custody transfer, provision is made to pass a known flow through the meter. However, such a provision is costly and is not available for most in-process flowmeters. Without such a provision, a true cahbration of the flow element itself is not possible. For orifice meters, calibration of the flowmeter normally involves cahbration of the differential pressure transmitter, and the orifice plate is usually only inspected for deformation, abrasion, and so on. Similarly, cahbration of a magnetic flowmeter normally involves cahbration of the voltage measurement circuitry, which is analogous to calibration of the differential pressure transmitter for an orifice meter. 

The pitot-venturi flow element is capable of developing a pressure differential 5 to 10 times that of a standard pitot tube. This is accomplished by employing a pair of concentric venturi elements in place of the pitot probe. The low-pressure tap is connected to the throat of the inner venturi, which in turn discharges into the throat of the outer venturi. For a discussion of performance and application of this flow element, see Stoll, Trans. Am. Soc. Mech. Eng., 73, 963-969 (1951). 

The correct flow to use is the compressor suction. However, a flow element such as an orifice in the compressor suction can rob inordinate horsepower. Therefore, sometimes the discharge flow is measured and the suction flow computed within the controller by using pressure measurements. Other times the compressor intake nozzle is calibrated and used as a flow element. The correct AP to use is the discharge minus the suction pressure. 

The flow transmitter (transducer block) senses the flow element differential pressure, converts this signal to a signal proportional to the process flow, and sends it to the flow controller. 

Fig ure 9-3. Models for segregated reaetors Piston flow elements in parallel. 

Figure 9-4. Single-piston flow element with side exits.

This chapter describes the room air conditioning process, including the interaction of different flow elements room air distribution, heating and cooling methods, process sources, and disturbances. Air handling equipment, including toom air heaters, is discussed in the form of black boxes as far as possible. 

The air, contaminant, and water vapor mass flow elements in outer boundaries and between the zones are created by... 

Mixing between zones due to turbulence and disturbances The heat flow elements are created by... 

The key flow elements in the zoning strategy arc the supply air jets, plumes of the buoyancy sources, buoyant airflows along the surfaces, and turbulent mixing between the controlled and the uncontrolled zones, as in Fig. 8.32. These flow elements have significant influence on the effectiveness of the system. 

The availability of local quantities and only a minimal number of physical assumptions are the two key features of CFD. As a result, CFD has the following advantages over other methods such as multizone or flow element methods, which are useful for average values ... 

Interaction of different flow elements such as jets, plumes, and boundary layers is inherently considered. 

The terms zonal model and flow element are also used for the simplified characterization of the flow field in a single enclosure. There, a zone represents a partial volume of air in the enclosure, whereas in the multizone models described here, a zone represents a specific enclosure which is connected to other enclosures by air conductances (see The Airflow Network later). 

Flow element (primary) (When no measuring inslmmenl is provided)... 

TYPICAL APPLICATIONS Number of Application Type of Flow Elements ... 

The concepts of interface rheology are derived from the rheology of three-dimensional phases. Characteristic for the interface rheology is the coupling of the motions of an interface with the flow processes in the bulk close to the interface. Thus, in interface rheology the shear and dilatational stresses of the interface are in equilibrium with the corresponding shear stress in the bulk. An important feature is the compressibility of the adsorption layer of an interface in contrast, the flow elements of the bulk are incompressible. As a result, compression or dilatation of the adsorption layer of a soluble surfactant is associated with desorption and adsorption processes by which the interface tends to reinstate the adsorption equilibrium with the bulk phase. 

These simple situations can be embellished. For example, the axial dispersion model can be applied to the piston flow elements. However, uncertainties in reaction rates and mass transfer coefficients are likely to mask secondary effects such as axial dispersion. 

Real reactors can have 0 < cr < 1, and a model that reflects this possibility consists of a stirred tank in series with a piston flow reactor as indicated in Figure 15.1(a). Other than the mean residence time itself, the model contains only one adjustable parameter. This parameter is called the fractional tubularity, Xp, and is the fraction of the system volume that is occupied by the piston flow element. Figure 15.1(b) shows the washout function for the fractional tubularity model. Its equation is... 

The completely segregated stirred tank can be modeled as a set of piston flow reactors in parallel, with the lengths of the individual piston flow elements being distributed exponentially. Any residence time distribution can be modeled as piston flow elements in parallel. Simply divide the flow evenly between the elements and then cut the tubes so that they match the shape of the washout function. See Figure 15.12. A reactor modeled in this way is said to be completely segregated. Its outlet concentration is found by averaging the concentrations of the individual PFRs ... 

The importance of the linear arrangement of mixer/funnel/tubular reactor is shown when processing in a set-up with a curved flow element (0.3 m long bent Teflon tube of 0.3 mm inner diameter) in between the funnel and tubular reactor [78]. If a straight tube of equal dimensions as given above is used, plugging occius after 30 s. Hence even short curved flow passages are detrimental for micro-chan-nel-based amidation studies. 

Reaction takes place only within the plug flow element of the recycle reactor, and the gross product stream from this element is divided into two portions one becomes the net product and the second is mixed with fresh feed. The mixture of the fresh feed and recycle stream is then fed to the plug flow element. By varying the relative quantities of the net product and recycle streams, one is able to obtain widely varying performance characteristics. At... 

The basic design equation for a plug flow reactor (equation 8.2.7) may be used to describe the steady-state conversion achieved in the plug flow element of the recycle reactor ... 

Early studies of the transition to turbulence relied on flow visualization techniques for liquid flow through arrays of spheres. Jolls and Hanratty (1966) found a transition from steady to unsteady flow in the range 110<7 e< 150 for flow in a dumped bed of spheres at N — 12, and they observed a vigorous eddying motion that they took to indicate turbulence at Re — 300. In regular beds of spheres, Wegner et al. (1971) found completely steady flow with nine regions of reverse flow on the surface of the sphere for Re — 82, and similar flow elements but with different sizes in an unsteady flow at Re — 200. Dybbs and Edwards (1984) used laser anemometry and flow visualization to study flow... 

Laminar flow elements, 11 782 Laminar flowmeters, 11 662-663 Laminaria, common and scientific names, 3 188t... 

Consider the case of incompressible, horizontal flow. Equation 1.11 shows that if a flowing element of fluid is brought to rest (v2 — 0), the pressure P2 is given by... 

The continuous circulation of flow elements inside the electrolyzer is due to the donor-acceptor nature of each zone. If, however, at least one of the zones is an absorbing Markov state,... 

Differential Pressure Meters Differential pressure meters or head meters measure the change in pressure across a special flow element. The differential pressure increases with increasing flow rate. The pitot tubes described previously work on this principle. Other examples include orifices [see also Eqs. (6-111) and (8-102), and Fig. 10-14], nozzles (Fig. 10-19), targets, venturis (see also Sec. 8 and Fig. 10-17), and elbow meters. Averaging pitot tubes produce a pressure differential that is based on multiple measuring points across the flow path. 

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