Fluid flow venturi meter

Discharge coefficients for critical flow nozzles are, in general, the same as those for subsonic nozzles. See Grace and Lapple, Trans. Am. Soc. Mech. Fug., 73, 639-647 (1951) and Szaniszlo, ]. Eug. Power, 97, 521-526 (1975). Arnberg, Britton, and Seidl [J. Fluids Eug., 96, 111-123 (1974)] present discharge-coefficient correlations for circular-arc venturi meters at critical flow. For the calciilation of the flow of natural gas through nozzles under critical-flow conditions, see Johnson,/. Ba.sic Eng., 92, 580-589 (1970). 

The venturi meter, in which the fluid is gradually accelerated to a throat and gradually retarded as the flow channel is expanded to the pipe size. A high proportion of the kinetic energy is thus recovered but the instrument is expensive and bulky. 

An important application of Bernoulli s equation is in flow measurement, discussed in Chapter 8. When an incompressible fluid flows through a constriction such as the throat of the Venturi meter shown in Figure 8.5, by continuity the fluid velocity must increase and by Bernoulli s equation the pressure must fall. By measuring this change in pressure, the change in velocity can be determined and the volumetric flow rate calculated. 

The flow of fluids is most commonly measured using head flowmeters. The operation of these flowmeters is based on the Bernoulli equation. A constriction in the flow path is used to increase the flow velocity. This is accompanied by a decrease in pressure head and since the resultant pressure drop is a function of the flow rate of fluid, the latter can be evaluated. The flowmeters for closed conduits can be used for both gases and liquids. The flowmeters for open conduits can only be used for liquids. Head flowmeters include orifice and venturi meters, flow nozzles, Pitot tubes and weirs. They consist of a primary element which causes the pressure or head loss and a secondary element which measures it. The primary element does not contain any moving parts. The most common secondary elements for closed conduit flowmeters are U-tube manometers and differential pressure transducers. 

Orifice meters, Venturi meters and flow nozzles measure volumetric flow rate Q or mean velocity u. In contrast the Pitot tube shown in a horizontal pipe in Figure 8.7 measures a point velocity v. Thus Pitot tubes can be used to obtain velocity profiles in either open or closed conduits. At point 2 in Figure 8.7 a small amount of fluid is brought to a standstill. Thus the combined head at point 2 is the pressure head P/( pg) plus the velocity head v2/(2g) if the potential head z at the centre of the horizontal pipe is arbitrarily taken to be zero. Since at point 3 fluid is not brought to a standstill, the head at point 3 is the pressure head only if points 2 and 3 are sufficiently close for them to be considered to have the same potential head... 

Differential pressure transmitters (or DP cells) are widely used in conjunction with any sensor that produces a measurement in the form of a pressure differential (e.g. orifice plate, venturi meter, flow nozzle, etc.). This pressure differential is converted by the DP cell into a signal suitable for transmission to a local controller and/or to the control room. DP cells are often required to sense small differences between large pressures and to interface with difficult process fluids. Devices are available that provide pneumatic, electrical or mechanical outputs. 

The coefficients for venturi meters, flow nozzles, and orifice meters vary with Reynolds number as shown in Figs. 10.7 to 10.10. The curve for an orifice meter shown in Fig. 10.10 covers an unusually wide range of both viscosity and Reynolds number. The fluids used were water and a series of oils up to a very viscous road oil, and for each fluid a number of different velocities were used, so that the curve represents points for many combinations of velocity and viscosity. Although the orifice plate may not be a standard beveled form, the value of C for high Reynolds numbers agrees closely with the value of C in Fig. 10.10 for a diameter ratio of 0.75. 

Basic equations for the design and operation of orifice meters, venturi meters, and rotameters can be derived from the total energy balances presented at the beginning of this chapter. The following equations apply when the flowing fluid is a liquid, and they also give accurate results for the flow of gases if the pressure drop caused by the constriction is less than 5 percent of the upstream pressure ... 

A venturi meter is a device to measure fluid flow rates, which in its operation resembles the orifice meter (Section 3.2b). It consists of a tapered constriction in a line, with pressure taps leading to a differential manometer at points upstream of the constriction and at the point of maximum constriction (the throat). The manometer reading is directly related to the flow rate in the line. 

Suppose the flow rate of an incompressible fluid is to be measured in a venturi meter in which the cross-sectional area at point 1 is four times that at point 2. 

The value of Cd depends on conditions of flow and shape of the constriction. For a well-shaped constriction (notably circular cross section), it would vary between 0.95 and 0.99 for turbulent flow. The value is much lower in laminar flow because the kinetic energy correction is larger. The return of the fluid to the original velocity by means of a diverging section forms a flow-measuring device known as a Venturi meter. 

FIGURE 5.23 Expansion factor for square-edged orifice and nozzle or venturi meter (a) k= 1.3, (b) k= 1.4. (From Crane Co., Flow of Fluids through Valves, Fittings, and Pipe, Technical Manual 410, Crane Co., New York (1978).)... 

Pressure recovery. If the flow through the venturi meter were frictionless, the pressure of the fluid leaving the meter would be exactly equal to that of the fluid entering the meter and the presence of the meter in the line would not cause a permanent loss in pressure. The pressure drop in the upstream cone — pj would be completely recovered in the downstream cone. Friction cannot be completely eliminated, of course, and a permanent loss in pressure and a corresponding loss in power do occur. Because of the small angle of divergence in the recovery cone, the permanent pressure loss from a venturi meter is relatively small. In a properly designed meter, the permanent loss is about 10 percent of the venturi differential Pa Pb and approximately 90 percent of the differential is recovered. 

The preceding discussion of fluid meters was concerned only with the flow of fluids of constant density. When fluids are compressible, similar equations and discharge coefficients for the various meters may be used. Equation (8.35) for venturi meters is modified to the form... 

AREA METERS ROTAMETERS. In the orifice, nozzle, or venturi, the variation of flow rate through a constant area generates a variable pressure drop, which is related to the flow rate. Another class of meters, called area meters, consists of devices in which the pressure drop is constant, or nearly so, and the area through which the fluid flows varies with flow rate. The area is related, through proper calibration, to the flow rate. 

The differential producing flow meter is a device used to create varying static pressure, within a flow stream that can be used to determine the flow rate of the fluid. These devises have been used for over 1000 years [10]. Today, differenfial flow meters are the most common and reliable flow meters used in industry. This section will discuss three common types of differential producing flow meters Orifice meter, Venturi meter, and Nozzle meter. 

There are many other types of flow meters that can be used such as venturi meters, vortex shedder flow meters, and Coriolis flow meters. Any of these may be preferred depending on the application. Fluid flow can also be measured indirectly using chemical analysis and mass and energy balance calculations. Air flow measurements are commonly made this way since an oxygen analyzer is generally more accurate than a thermal mass flow meter. 

So far we have considered only flows which were in one direction, as in a pipe or down a straight riverbed. In the few cases in which the fluid flow was not one-dimensional, as around a sphere or in a pipe elbow or venturi meter, we have introduced experimental data to allow us to treat the problem as if it were one-dimensional. Although this one-dimensional approach adequately covers many of the practical problems in fluid mechanics, it is not satisfactory for the complicated ones, particularly for the aerodynamics problems. To solve these more complicated problems, two additional ideas are needed potential flow and the boundary layer. 

Evaporation. The pounds of water evaporated in evaporators per pound of steam is appro-ximately O.Son, where n i.s the number of effects. Flow of Fluids. Venturi meter VCwa)" ( 0 = 0.98 2gAff ... 

The value of the term T—the expansion factor—can be derived for a Venturi meter by assuming that the fluid is an ideal gas and the flow is isentropic ... 

Kolupada, S. (1960). John W. Ledoux. Journal of the Hydraulics Division ASCE 86(HY1 42. P Ledoux, J.W. (1913).A mechanism for metering and recording the flow of fluids through Venturi tubes, orifices, or conduits, by integrating velocity head. Trans. ASCE 76 1148-1171. Ledoux, J.W. (1914). The Pitot tube theory. Journal AWWA 1(3) 536-537. 

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