Measurement of flow rate

Flow Measurement Measurement of flow rates of clean gases presents no problem. Flow measurement of dirty gases is usually... 

An example of cascade control could be based on the simulation example DEACT and this is shown in Fig. 2.35. The problem involves a loop reactor with a deactivating catalyst, and a control strategy is needed to keep the product concentration Cp constant. This could be done by manipulating the feed rate into the system to control the product concentration at a desired level, Cjet- In this cascade control, the first controller establishes the setpoint for flow rate. The second controller uses a measurement of flow rate to establish the valve position. This control procedure would then counteract the influence of decreasing catalyst activity. 

In this chapter we will illustrate and analyze some of the more common methods for measuring flow rate in conduits, including the pitot tube, venturi, nozzle, and orifice meters. This is by no means intended to be a comprehensive or exhaustive treatment, however, as there are a great many other devices in use for measuring flow rate, such as turbine, vane, Coriolis, ultrasonic, and magnetic flow meters, just to name a few. The examples considered here demonstrate the application of the fundamental conservation principles to the analysis of several of the most common devices. We also consider control valves in this chapter, because they are frequently employed in conjunction with the measurement of flow rate to provide a means of controlling flow. 

Dodge and Metzner (1959) deduced the velocity profile from their measurements of flow rate and pressure gradient for turbulent flow of power law fluids in pipes. For the turbulent core, the appropriate equation is... 

Flow Measurements Measurement of flow rates of clean gases presents no problem. Flow measurement of gas streams containing solids is almost always avoided. The flow of solids is usually controlled but not measured except solids flows added to or taken from the system. Solids flows in the system are usually adjusted on an inferential basis (temperature, pressure level, catalyst activity, gas analysis, heat balance, etc.). In many roasting operations, the color of the calcine discharge material indicates whether the solids feed rate is too high or too low. 

This contrasts with physical measurement of flow rate, in which the measured response is often proportional to the square root of flow rate, e.g. pressure drop across an orifice plate. Thus some flow measurement devices are only suitable for measuring a narrow band of flow rates. 

Figure 4 to that In Figure 5. Our computer software has been modified to allow for these changes by using the elution time of cyclic trlmer as a measure of flow rate for a given run. The system Is calibrated by using polystyrene spiked with cyclic trlmer. For each run, elution volumes are normalized on the basis of cyclic trlmer elution. This technique assumes constant flow rate during each run and compensates for run-to-run variations. ...

K.M. Hoard, Measurement of Flow Rates Using Surface Coil Nuclear Magnetic Resonance Vol. MSc. University of Arlington, Arlington, 1989. 

Air rate through the cake—and thus, vacuum-pump capacity—can be determined from measurements of flow rate as a function of time. Integration of these data over the times involved in the first and second stages of drying in continuous filters yields vacuum-pump-capacity data. 

Let the total number of measurements of flow rate be and Qi be the flow rate at time t . The mean flow rate, Qmean. is then... 

In addition to a proper choice of collecting material (filter paper), a reliable measurement of flow rate is required. Flow meters are classified into rotameters and integrating flow meters. The latter are further classified into wet-gas meters and dry-gas meters. A rotameter has a specially graduated vertical tube, whose diameter increases in the ascending direction, containing a spinning top-shaped or spherical float. A gas-stream is admitted into the bottom of the tube and the float is held at a vertical position which varies in proportion to the flow rate of gas. 

The Bernoulli theorem can also be applied to the measurement of flow rate. The passage of an incompressible fluid through a constriction results in an increase in velocity from Ui to uj, which is associated with a decrease in pressure from Pi to P2, which can be measured directly. The volumetric flow rate Q = Mifli = M2fl2 by algebraic rearrangement (which is not shown). The final linear velocity M2 can be described by Eq. (5). 

The great majority of automatic process control systems involve one or more of only five process variables, namely, pressure, temperature, flow rate, composition, and liquid level. Many of these variables are measured by the same kind of instrument, and indeed, all of them under certain circumstances can be evaluated in terms of pressures. Thus temperature can be measured by the pressure exerted by a confined gas in the gas thermometer the differential pressure across a restriction in a flow line is a measure of flow rate the pressure exerted by a boiling liquid mixture... 

Incorporation of a 10 or 12 liter surge flask permits the filling of up to a 2 liter vessel without creating a negative pressure (VERBOTEN ) or having to greatly increase the flow rate of gas through the purifier. The optional Nujol bubbler assembly provides a qualitative measure of flow rate. 

In order to measure flow rates, it is necessary to choose flowmeters allowing for measurements of flow rates... 

Rate constants measured in discharge-flow systems depend upon measurements of (a) the velocity of flow u, and (b) the partial pressures of reactants. For a reaction first-order in atom concentration [A], the rate constant is given by = iJ d In [A]/dx = — (RTZFlAp)d In [A]/ dx, where SF is the total flow rate, A is the cross-section area of the flow tube, p is the total pressure, and x is the displacement along the tube axis. For simple reactions of higher overall orders, the dependences of rate constants upon the parameters SF, A, p and reagent flow rate F< are summarized in Table 4.2. The importance of accurate measurements of flow rates and of total pressure, particularly for reactions of overall second and third orders, is clear. For example, realistic random errors of 1 % in/ , and of 3% in SFand F<, lead to an error of 12% in Atj. 

The importance of accurate measurements of flow rates and total pressure in minimizing random errors in rate constants has been demonstrated. The most satisfactory method of reducing systematic errors arising from the physical behaviour of the flow system is to ensure conditions under which deviations from simple flow occur to a negligible extent. 

Pressure measurement is a critical factor not only in the oil and gas industry but also for the operation of process equipment including reactors, distillation columns, pipelines, and for the measurement of flow rate. It is a scalar quantity and equals the perpendicular force exerted on a surface with the units of force per surface area ... 

Whereas the transport of water to major centers allowed civilizations to flourish, the measurement and control of fluid flow has been a critical aspect of the development of industrial processes. Not only is metering flow important to maintaining stable and safe operating conditions, it is the prime means to account for the raw materials consumed and the finished products manufactured. While pressure and temperature are critical operating parameters for plant safety, the measurement of flow rate has a direct impact on process economics. For basic chemicals (as opposed to specialty chemicals or pharmaceuticals) like ethylene, propylene, methanol, sulfuric acid, etc. profit margins are relatively low and volumes are large, so high precision instruments are required to ensure the economic viability of the process. 

Choi et al. [1] examined the apparent slip effects of water in hydrophobic and hydrophilic microchannels experimentally using precision measurements of flow rate versus pressure drop. They correlated their experimental results to that from analytical solution of flow through a channel with slip velocity at the wall. There was clear difference between the flows of water on a hydrophilic and hydrophobic surface indicating the effect of slip flow (Fig. 2). Neto et al. [3] have reported clear evidence of boundary slip for a sphere-flat geometry from force measurements using atomic force microscopy. The degree of slip is observed to be the function of both liquid viscosity and shear rate (Fig. 4). 

The measurement of flow rate is one of main subjects in experimental fluid mechanics. However, the thermocapacitive flow sensor may have electronic and semiconductor components, such as a capacitor, an n-channel MOS transistor, an oscillation circuit, and a microfabrication. Therefore, the thermocapacitive flow sensor is a multidisciplinary tool and some of its electronic and semiconductor components need to be explained. 

The capacity factor k is essentially a corrected retention time (Equation [3.18]) that takes into account variations in mobile phase flow rate and thus provides a more robust indicator of analyte retention for a given combination of stationary and mobile phases. As is a unique property of a given solute A for a given stationary-mobile phase combination, the adjusted (corrected) retention volume V,a (Equation [3.15] (or the corresponding retention time) can be used as a tag for analyte identification. Thus the precision and accuracy of measurement of Vja become important and depend on those of the measurement of flow rate U since in practice retention times rather than volumes are the measured quantities. In response to this limitation of the V,a parameter, the capacity ratio of a solute (k) ) was defined as the ratio of its distribution (partition) coefficient to the phase ratio (Vm/V s) of the column with respect to analyte A ... 

In chemical reaction engineering numerical simulation and identification of reaction systems is of an outstanding importance. Evaluating reaction rate parameters is a common problem for the chemical engineer. Based on proposed chemical mechanisms and carefully done measurements of flow rates, pressures, temperatures and compositions the rate constants have to be determined. Details of numerical methods to tackle this problem is given by Bock [26] or Deuflhard and Nowak [27, 28]. In general a system of chemical reactions is described by a set of differential equations which corresponds to a proposed chemical reaction mechanism. The set of differential equations evaluates the nc concentrations C of the involved species. They may be described... 

For measurement of flow rates (volumetric/mass) of gases and liquids... 

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