Volumetric flow rate measurement

The mass flow streams at tray j are shown in Figure 6.1 for a countercurrent process of a dilute system. Here the total molar flow rate of the rising gas is constant at V moles/min while the total molar flow rate of the sinking liquid is constant at L moles/min. Both L and V are molar flow rates as long as Xj and Yj are molar fractions. If, however, Xj and Yj describe concentrations, measured in mo/e/m3, then L and V are volumetric flow rates measured in m3/min. 

In axial-flow viscometers, the sample is made to flow through a duct of regular cross-section. Capillary (circular cross-section) and slit (rectangular cross-section) viscometers are controlled stress instruments a known pressure difference (which causes shear stress in the sample) is applied over the duct length, and the resulting volumetric flow rate measured. In the extrusion viscometer, a controlled shear rate instrument, the sample is extruded through a capillary tube by the action of a constant speed piston, acting on the sample in a cylindrical reservoir to which the capillary is attached. The pressure difference between the ends of the capillary is measured. 

In the 1082 LC/SFC flow control system the contribution of the pump B solvent stream to the overall solvent flow, computed from the Independent volumetric flow rate measurements, depends upon the relative compressibilities of the two fluids. Here it is assumed that pure carbon dioxide and the 10K (molar) modifier/ carbon dioxide mixtures have about the same compressibilities and so the actual modifier concentration is given simply by the product of (tB)(0.1). 

The formulas just developed allow the relation of pressure gradient, velocity profile, and volumetric flow rate os long as the shear stress-shear rate relation (flow curve) for the fluid is known. The problem in viscometry is just the reverse How is the flow curve obtained from pressure drop-volumetric flow rate measurements in a cylindrical tube If the mathematical form of the flow curve, that is, a particular constitutive equation, is assumed a priori, the integrated equations as developed above may be used to establish the parameters in the constitutive relation. For example, if it is assumed that the power law represents the flow curve of a fluid under investigation, two readings of dP/dx versus Q in a tube of known R will allow calculation of K and n from (16.13). However, in the general case, the form of the constitutive equation is not known a priori, and must be established by viscometry. This may be done, first by integrating (16.12) by parts... 

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. 

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. 

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). 

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. 

For the consecutive reactions 2A B and 2B C, concentrations were measured as functions of residence time in a CSTR. In all experiments, C o = 1 lb moPfF. Volumetric flow rate was constant. The data are tabulated in the first three columns. Check the proposed rate equations,... 

A turbine flowmeter consists of a straight flow tube containing a turbine which is free to rotate on a shaft supported by one or more bearings and located on the centerline of the tube. Means are provided for magnetic detection of the rotational speed, which is proportional to the volumetric flow rate. Its use is generally restric ted to clean, noncorrosive fluids. Additional information on construction, operation, range, and accuracy can be obtained from Holzbock (Instruments for Measurement and Control, 2d ed., Reinhold, New York, 1962, pp. 155-162). For performance characteristics of these meters with liquids, see Shafer,y. Basic Eng., 84,471-485 (December 1962) or May, Chem. Eng., 78(5), 105-108 (1971) and for the effect of density and Reynolds number when used in gas flowmetering, see Lee and Evans, y. Basic Eng., 82, 1043-1057 (December 1965). 

Velocity and Volumetric Flow Rate The U.S. EPA has published Method 2 as a reference method for determining stack-gas velocity and volumetric flow rate. At several designated sampling points, which represent equal portions of the stack volume (areas in the stack), the velocity and temperature are measured with instrumentation shown in Fig. 25-27. 

Measurements to determine volumetric flow rate usuaUy require approximately 30 min. Since sampling rates depend on stack-gas velocity, a preliminaiy velocity check is usuaUy made prior to testing for pollutants to aid in selecting the proper equipment and in determining the approximate sampling rate for the test. 

For determination of the total mass-emission rate of SO9, the moisture content and the volumetric flow rate of the exhaust gas stream must also be measured. 

The reactor in Fig. 5 operates as follows. A feed solution containing a given concentration of pollutant is pumped to the adsorbent module at a fixed volumetric flow rate. The module is kept isothermal by a temperature control unit, such as a surrounding water bath. Finally, the concentration of the outlet solution is measured as a function of time from when the feed was introduced to the adsorbent module. These measurements are often plotted as breakthrough curves. Example breakthrough curves for an aqueous acetone solution flowing... 

J The viscosity characteristics of a polymer melt are measured using both a capillary rheometer and a cone and plate viscometer at the same temperature. The capillary is 2.0 mm diameter and 32.0 mm long. For volumetric flow rates of 70 x 10 m /s and 200 x 10 m /s, the pressures measured just before the entry to the capillary are 3.9 MN/m and 5.7 MN/m, respectively. 

A slit die is designed on the assumption that the material is Newtonian, using apparent viscous properties derived from capillary rheometer measurements, at a particular wall shear stress, to calculate the volumetric flow rate through the slit for the same wall shear stress. Using the correction factors already derived, obtain an expression for the error involved in this procedure due to the melt being non-Newtonian. Also obtain an expression for the error in pressure drop calculated on the same basis. What is the magnitude of the error in each case for a typical power law index n = 0.377... 

Flow Rate. The values for volumetric or mass flow rate measurement are often determined by measuring pressure difference across an orifice, nozzle, or venturi tube. Other flow measurement techniques include positive displacement meters, turbine flowmeters, and airflow-measuring hoods. 

Equation (8.4) defines the average concentration, Ugut, of material flowing from the reactor. Omit the V ir) term inside the integral and normalize by the cross-sectional area, Ac = ttR, rather than the volumetric flow rate, Q. The result is the spatial average concentration a patiai, and is what you would measure if the contents of the tube were frozen and a small disk of the material was cut out and analyzed. In-line devices for measuring concentration may measure a panai rather than Uout- Is the difference important ... 

The reactor volume is taken as the volume of the reactor physically occupied by the reacting fluids. It does not include the volume occupied by agitation devices, heat exchange equipment, or head-room above liquids. One may arbitrarily select the temperature, pressure, and even the state of aggregation (gas or liquid) at which the volumetric flow rate to the reactor will be measured. For design calculations it is usually convenient to choose the reference conditions as those that prevail at the the inlet to the reactor. However, it is easy to convert to any other basis if the pressure-volume-temperature behavior of the system is known. Since the reference volumetric flow rate is arbitrary, care must be taken to specify precisely the reference conditions in order to allow for proper interpretation of the resultant space time. Unless an explicit statement is made to the contrary, we will choose our reference state as that prevailing at the reactor inlet and emphasize this choice by the use of the subscript zero. Henceforth,... 

Like the definition of the space time, the definition of the space velocity involves the volumetric flow rate of the reactant stream measured at some reference condition. A space velocity of 10 hr-1 implies that every hour, 10 reactor volumes of feed can be processed. 

Fa o may also be written as the product of a volumetric flow rate and a reactant concentration where both are measured at some reference temperature and pressure and correspond to zero fraction conversion. Thus... 

Reactor inlet conditions are particularly useful as reference conditions for measuring the input volumetric flow rate in that they not only give physical meaning to CA0 and but also usually lead to cancellation of CA0 with a similar term appearing in the reaction rate expression. 

It is particularly convenient to choose the reference conditions at which the volumetric flow rate is measured as the temperature and pressure prevailing at the reactor inlet, because this choice leads to a convenient physical interpretation of the parameters and CA0 and, in many cases, one finds that the latter quantity cancels a similar term appearing in the reaction rate expression. Unless otherwise specified, this choice of reference conditions is used throughout the remainder of this text. For constant density systems and this choice of reference conditions, the space time t then becomes numerically equal to the average residence time of the fluid in the reactor. 

We will use the Bernoulli equation in the form of Eq. (6-67) for analyzing pipe flows, and we will use the total volumetric flow rate (Q) as the flow variable instead of the velocity, because this is the usual measure of capacity in a pipeline. For Newtonian fluids, the problem thus reduces to a relation between the three dimensionless variables ... 

In Section II.B of Chapter 3, the tube flow viscometer was described in which the viscosity of any fluid with unknown viscous properties could be determined from measurements of the total pressure gradient (— A4>/L) and the volumetric flow rate (Q) in a tube of known dimensions. The viscosity is given by... 

An orifice meter is used to measure the flow rate of CC14 in a 2 in. sch 40 pipe. The orifice diameter is 1.25 in., and a mercury manometer attached to the pipe taps across the orifice reads 1/2 in. Calculate the volumetric flow rate of CC14 in ft3/s. (SG of CC14 = 1.6.) What is the permanent energy loss in the flow above due to the presence of the orifice in ft lbf/lbm Express this also as a total overall unrecovered pressure loss in psi. 

Optical probes were used to measure the bubble size, frequency and velocity within the dense bed. The bubble velocity for an actively bubbling bed was found to closely agree with the drift flux form proposed by Davidson and Harrison (1963). In contrast, the volumetric flow rate of the bubbles was found to be far less than that predicted by the two-phase hypothesis (Fig. 40). 

Various units are employed. Usually volumetric flow rates are measured at STP, 32. F or 0 C and 1 atm. 

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