Volumetric flow rates

Determination of the volumetric flow rate of a pipe flow requires only a measurement of average flow velocity. Both Doppler and cross-correlation flowmeters provide such an averaged flow rate measurement. Designs and performance of the two types of flowmeters are described here. Results from calibration tests conducted at an Argonne National Laboratory (ANL) flow facility and prototype instrument demonstration tests at coal-conversion pilot plants are presented. 

The facility is equipped with an on-line, timed, weight/volume diversion system that diverts the mainstream into the weighing and volumetric tanks while the content of a reserve tank is dumped into the upper holdup tank. In this way, the sudden loss of flow was compensated for and a constant pump head was maintained. The density of the medium can be monitored to within 1 % and was obtained by combining the flow speed and weight readout. A solid weight 

Quite a number of technologies are available for measuring volumetric flow rates. These include differential pressure transmitters, vortex meters and magnetic flow meters. Each has its advantages and disadvantages. 

The differential pressure transmitter is the most popular and has been in use the longest. Its measurement principle is quite simple. Create a restriction in the line with an orifice plate and measure the pressure drop across the restriction. The measurement takes advantage of the physical relationship between pressure drop and flow. That is, the fluid velocity is proportional to the square root of the pressure drop, and in turbulent flow, the volumetric flow rate is essentially the velocity of the fluid multiplied by the cross-sectional area of the pipe (Fig. 11). 

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For calculation of the volumetric flow rate only the cross section area of the pipe is to be known. In order to give flow under standard conditions the temperature and pressure must be measured, and for conversion to mass flow the composition or density of the gas must be determined. These process parameters are often monitored by calibrated instrumentation. 

Accuracies of the flow meters discussed herein are specified as either a percentage of the full-scale flow or as a percentage of the actual flow rate. It may be convenient in some appHcations to compare the potential inaccuracies in actual volumetric flow rates. For example, in reading two Hters per minute (LPM) on a flow meter rated for five LPM, the maximum error for a 1% of full-scale accuracy specification would be 0.01 x 5 = 0.05 LPM. If another flow meter of similar range, but having 1% of actual flow rate specification, were used, the maximum error would be 0.01 x 2 = 0.02 LPM. To minimize errors, meters having full-scale accuracy specifications are normally not used at the lower end of their range. Whenever possible, performance parameters should be assessed for the expected installation conditions, not the reference conditions that are the basis of nominal product performance specifications. 

Meters can be further divided into three subgroups depending on whether fluid velocity, the volumetric flow rate, or the mass flow rate is measured. The emphasis herein is on common flow meters. Devices of a highly specialized nature, such as biomedical flow meters, are beyond the scope of this article. 

Measurement by Electromagnetic Effects. The magnetic flow meter is a device that measures the potential developed when an electrically conductive flow moves through an imposed magnetic field. The voltage developed is proportional to the volumetric flow rate of the fluid and the magnetic field strength. The process fluid sees only an empty pipe so that the device has a very low pressure drop. The device is useful for the measurement of slurries and other fluid systems where an accumulation of another phase could interfere with flow measurement by other devices. The meter must be installed in a section of pipe that is much less conductive than the fluid. This limits its appHcabiHty in many industrial situations. 

The framework for the solution of porous media flow problems was estabUshed by the experiments of Henri Darcy in the 1800s. The relationship between fluid volumetric flow rate, hydraulic gradient, and cross-sectional area, yi, of flow is given by the Darcy formula ... 

Fig. 17. Heat-transfer coefficient comparisons for the same volumetric flow rates for (A) water, 6.29 kW, and a phase-change-material slurry (O), 10% mixture, 12.30 kW and ( ), 10% mixture, 6.21 kW. The Reynolds number was 13,225 to 17,493 for the case of water.

Computer Models, The actual residence time for waste destmction can be quite different from the superficial value calculated by dividing the chamber volume by the volumetric flow rate. The large activation energies for chemical reaction, and the sensitivity of reaction rates to oxidant concentration, mean that the presence of cold spots or oxidant deficient zones render such subvolumes ineffective. Poor flow patterns, ie, dead zones and bypassing, can also contribute to loss of effective volume. The tools of computational fluid dynamics (qv) are useful in assessing the extent to which the actual profiles of velocity, temperature, and oxidant concentration deviate from the ideal (40). 

Flow. The principal types of flow rate sensors are differential pressure, electromagnetic, vortex, and turbine. Of these, the first is the most popular. Orifice plates and Venturi-type flow tubes are the most popular differential pressure flow rate sensors. In these, the pressure differential measured across the sensor is proportional to the square of the volumetric flow rate. 

Capillary viscometers are useful for measuring precise viscosities of a large number of fluids, ranging from dilute polymer solutions to polymer melts. Shear rates vary widely and depend on the instmments and the Hquid being studied. The shear rate at the capillary wall for a Newtonian fluid may be calculated from equation 18, where Q is the volumetric flow rate and r the radius of the capillary the shear stress at the wall is = r Ap/2L. 

Piston Cylinder (Extrusion). Pressure-driven piston cylinder capillary viscometers, ie, extmsion rheometers (Fig. 25), are used primarily to measure the melt viscosity of polymers and other viscous materials (21,47,49,50). A reservoir is connected to a capillary tube, and molten polymer or another material is extmded through the capillary by means of a piston to which a constant force is appHed. Viscosity can be determined from the volumetric flow rate and the pressure drop along the capillary. The basic method and test conditions for a number of thermoplastics are described in ASTM D1238. Melt viscoelasticity can influence the results (160). 

The diameter of the air core varies with the feed volumetric flow rate. If the rate is too low, there is no air core and all of the pulp leaves the cyclone as underflow if the rate is too high, the air core expands, closing off the apex and forcing all of the pulp to leave the cyclone as overflow. Consequently there is a minimum and maximum volumetric feed rate. Because the pressure drop is proportional to the square of the volumetric feed rate, the minimum and maximum rates can be monitored by the pressure drop. The ratio of the maximum pressure drop to the minimum pressure drop should be less than 4, meaning the maximum to minimum volumetric feed rate should be less than 2. 

The Displacement Distance theory suggests that since the stmcture of the flame is only quantitatively correct, the flame height can be obtained through the use of the displacement length or "displacement distance" (35,36) (eq. 12), where h = flame height, m V = volumetric flow rate, m /s and D = diffusion coefficient. 

In any gas burner some mechanism or device (flame holder or pilot) must be provided to stabilize the flame against the flow of the unbumed mixture. This device should fix the position of the flame at the burner port. Although gas burners vary greatly in form and complexity, the distribution mechanisms in most cases are fundamentally the same. By keeping the linear velocity of a small fraction of the mixture flow equal to or less than the burning velocity, a steady flame is formed. From this pilot flame, the main flame spreads to consume the main gas flow at a much higher velocity. The area of the steady flame is related to the volumetric flow rate of the mixture by equation 18 (81,82)... 

The volumetric flow rate of the mixture is, in turn, proportional to the rate of heat input (eq. 19) ... 

The function of clear-Hquor advance can be illustrated by considering a simple operation, shown in Figure 13, in which Qcv < 0 volumetric flow rates of clear-Hquor fed to the crystallizer, in the clear-Hquor advance, and in the output slurry. In such systems the population density function is given by the expression... 

Both catalyst space velocity and bed geometry play a role. The gas hourly space velocity (GHSV) is used to relate the volumetric flow rate to the catalyst volume. GHSV has units of inverse hour and is defined as the volume flow rate per catalyst volume. 

For theJth. component, my = m iDy is the component mass flow rate in stream i is the mass fraction of component j in stream i and q is the net reaction rate (mass generation minus consumption) per unit volume V that contains mass M. If it is inconvenient to measure mass flow rates, the product of density and volumetric flow rate is used instead. 

Vacuum flow is usually described with flow variables different from those used for normal pressures, which often leads to confusion. Pumping speed S is the actual volumetric flow rate of gas through a flow cross section. Throughput Q is the product of pumping speed and absolute pressure. In the SI system, Q has units of Pa m vs. 

The volume fraction, sometimes called holdup, of each phase in two-phase flow is generally not equal to its volumetric flow rate fraction, because of velocity differences, or slip, between the phases. For each phase, denoted by subscript i, the relations among superficial velocity V, in situ velocity Vj, volume fraclion Rj, total volumetric flow rate Qj, and pipe area A are... 

Figure 6-32, taken from Govier and Aziz, schematically indicates four flow pattern regions superimposed on a plot of pressure gradient vs. mixture velocity = Vl -t- V5 = Qj + ( s)/A where and Vs are the superficial liquid and solid velocities, Qi, and ( 5 are liquid and solid volumetric flow rates, and A is the pipe cross-sectional area. is the transition velocity above which a bed exists in the bottom of the pipe, part of which is stationary and part of which moves by saltation, with the upper particles tumbling and bouncing over one another, often with Formation of dunes. With a broad particle-size distribution, the finer particles may be fully suspended. Near V 4, the pressure gra-... 

Impellers are sometimes viewed as pumping devices the total volumetric flow rate Q discharged by an impeller is made dimensionless in a pumping number ... 

A Projected area m q Average volumetric flow rate mVs... 

The participant A is identified by the subscript a. Thus, the concentration is C the number of mols is n -, the frac tional conversion is the partial pressure is p and the rate of decomposition is /. Capital letters are also used to represent concentration on occasion thus, A instead of C. The flow rate in mol is n but the prime ( ) is left off when the meaning is clear from the context. The volumetric flow rate is V reactor volume is or simply V of batch reac tors the total pressure is 7C and the temperature is T. The concentration is = n /V or n IV. ... 

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