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                                     TABLE 19.3  Main Categories of Closed Conduit Flowmeter
                                     Type 1—differential pressure flowmeters
                                       Sharp edged orifice plate, chord orifice plate, eccentric orifice plate, Venturi,
                                       nozzle, Pitot tube, elbow, wedge, V-cone, Dall tube, Elliot-Nathan flow tube,
                                       Epiflo
                                     Type 2—variable area flowmeters
                                       Rotameter, orifice and tapered plug, cylinder and piston, target, variable
                                       aperture
                                     Type 3—positive displacement flowmeters
                                       Sliding vane, tri-rotor, bi-rotor, piston, oval gear, nutating-disc, roots, CVM,
                                       diaphragm, wet gas
                                     Type 4—turbine flowmeters
                                       Axial turbine, dual-rotor axial turbine, cylindrical rotor, impeller, Pelton
                                       wheel, Hoverflo, propeller
                                     Type 5—oscillatory flowmeters
                                       Vortex shedding, swirlmeter, fluidic
                                     Type 6—electromagnetic flowmeters
                                       AC magnetic, pulsed DC magnetic, insertion
                                     Type 7—ultrasonic flowmeters
                                       Doppler, single path transit-time, multi-path transit-time, cross-correlation,
                                       drift
                                     Type 8—mass flowmeters
                                       Coriolis, thermal
                                     Type 9—miscellaneous flowmeters
                                       Laser anemometer, hot-wire anemometers, tracer dilution, nuclear magnetic
                                       resonance



                         The following sections will consider the most popular types of flowmeter from each of the eight main
                       categories in Table 19.3. For information on other flowmeters and those in the miscellaneous group see
                       one of the many textbooks on flow measurement such as [3–6].
                       Differential Pressure Flowmeter

                       The basic principle of nearly all differential pressure flowmeters is that if a restriction is placed in a pipeline,
                       then the pressure drop across this restriction is related to the volumetric flowrate of fluid flowing through
                       the pipe.
                         The orifice plate is the simplest and cheapest type of differential pressure flowmeter. It is simply a
                       plate with a hole of specified size and position cut in it, which can then be clamped between flanges in
                       a pipeline (Fig. 19.53). The volumetric flowrate of fluid Q in the pipeline is given by Eq. (19.66):

                                                              p
                                                        C
                                                 Q =  ------------------- e --- d 2 2 p 1 –(  p 2 )  (19.66)
                                                                   -----------------------
                                                       1 b  4 4       r
                                                         –
                       where p 1  and p 2  are the pressures on each side of the orifice plate, ρ is the density of the fluid upstream
                       of the orifice plate, d is the diameter of the hole in the orifice plate, and β is the diameter ratio d/D
                       where D is the upstream internal pipe diameter. The two empirically determined correction factors are
                       C the discharge coefficient, and ε the expansibility factor. C is affected by changes in the diameter ratio,
                       Reynolds number, pipe roughness, the sharpness of the leading edge of the orifice, and the points at
                       which the differential pressure across the plate are measured. However, for a fixed geometry it has been
                       shown that C is only dependent on the Reynolds number and so this coefficient can be determined for
                       a particular application. ε is used to account for the compressibility of the fluid being monitored. Both
                       C and  ε can be determined from equations and tables in a number of internationally recognized


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