The venturi meter

The rate of flow of water in a 150 mm diameter pipe is measured with a venturi meter with a 50 mm diameter throat. When the pressure drop over the converging section is 121 mm of water, the flowrate is 2.91 kg/s. What is the coefficient for the converging cone of the meter at this flowrate  

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The use of a small angle enlarging section is a feature of the venturi meter, as discussed in Chapter 6. 

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. 

The flow nozzle, illustrated in Fig. 10-3, is similar to the venturi meter except that it does not include the diffuser (gradually expanding) section. In fact, one standard design for the venturi meter is basically a flow nozzle with an attached diffuser (see Fig. 10-6). The equations that relate the flow rate and measured pressure drop in the nozzle are the same as for the venturi... 

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. 

This equation has the additional advantage that C varies little for diameter ratios up to 0.85, as shown in Fig. 10.10. As it is not satisfactory to use higher ratios, the marked variation beyond that point is of no importance. It will be observed that this equation is the same as that for the venturi meter and differs from it only in the numerical value of C. As given here, the equation differs from the form that h replaces pi/w, but Eqs. (10.62), (10.66), and (10.70) are really identical. 

See Derivation of head loss in a sudden expansion later in this section and the Venturi Meter in Section 3.7 for examples of the use of the Continuity Equation.]... 

The Continuity and Bernoulli Equations may be used to derive equations relating flow rate to measured pressure difference for the Venturi meter (and the orifice plate meter discussed below). 

Adding Cd, a discharge coefficient, to account for frictional losses (assumed zero in Bernoulli s Equation) and other non-idealities, we get Equation (36), the operating equation for the Venturi meter. 

The rate of flow of a liquid mixture is to be measured continuously. The flow rate will be approximately 40 gpm, and rates as low as 30 gpm or as high as 50 gpm can be expected. An orifice meter, a rotameter, and a venturi meter are available. On the basis of the following additional information, would you recommend installation of the orifice meter, the venturi meter, or the rotameter Give reasons for your choice. 

Equation (3.20) may be used if the venturi meter is not oriented horizontally. This is done by calculating the pressures at the points directly and substituting them into the equation. 

Water at 20°C flows through a venturi meter that has a throat of 25 cm. The venturi meter is measuring the flow in a 65-cm pipe. Calculate the deflection in a mercury manometer if the rate of discharge is 0.70 m /s. 

Other devices can be used to determine the flow rate from a single measurement. These are sometimes referred to as obstruction meters, since the basic principle involves introducing an obstruction (e.g., a constriction) into the flow channel and then measuring the pressure drop across this obstruction, which depends on the flow rate. Two such devices, the venturi meter and the nozzle, are illustrated in Eigures 5.14 and 5.15, respectively. In both cases, the pressure drop from a point upstream of the meter to a point in a plane with the minimum flow area (A ) is related to the velocity V2 by the Bernoulli equation ... 

The basic equation for the venturi meter is obtained by writing the Bernoulli equation for incompressible fluids between the two pressure stations at F and /. Frjction is neglected, the meter is assumed to be horizontal, and there is no pump. If Va and Vf are the average upstream and downstream velocities, respectively, and p is the density of the fluid, Eq, (4.32) becomes... 

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. 

ORIFICE METER. The venturi meter has certain practical disadvantages for ordinary plant practice. It is expensive, it occupies considerable space, and its ratio of throat diameter to pipe diameter cannot be changed. For a given meter and... 

The orifice meter is a simple and accurate device for measuring flow rates however, the pressure drop for an orifice meter can be quite large [4]. A meter that operates on the same principle as the orifice meter, but with a much smaller pressure drop, is the Venturi meter. 

The pitot-static tube is the standard device for measuring the airspeed of airplanes and is often used for measuring the local velocity in pipes or ducts, particularly in air pollution sampling procedures. One can easily identify the pitot-static probes projecting from the front of modern commercial airplanes look next time you are at an airport. For measuring flow in enclosed ducts or channels the venturi meter and orifice meters discussed below are more convenient and more frequently used. 

Example 5.7. The venturi meter in Fig. 5.8 has water flowing through it. The pressure difference P — P2 is X Ibf/in The diameter at point 1 is 1 ft, and that at point 2 is 0.5 ft. What is the volumetric flow rate through the meter ... 

The foregoinjg is ail based on a horizontal venturi meter. If we use the setup shown in Fig. 5.8 and take the manometer reading as a pressure difference to get <3ur value of — P2 in Eq. 5.31, then the result is quite independent of the angle to the vertical of the venturi meter. The reason is that the elevation change in the meter is compensated by the elevation change in the manometer legs. Consider the venturi meter in Fig. 5.10. 

The venturi meter described above is a reliable flow-measuring device. Furthermore, it causes little pressure loss (i.e., the actual value of is small). For these reasons it is widely used, particularly for large-volume liquid and gas flows. However, the meter is relatively complex to construct and hence expensive. Especially for small pipelines, its cost seems prohibitive, so simpler devices have been invented, such as the orifice meter. 

As shown in Fig. 5.11, the orifice meter consists of a flat orifice plate with a circular hole drilled in it. There is a pressure tap upstream from the orifice plate and another just downstream. If the flow direction is horizontal and we apply Bernoulli s equation, ignoring friction from point 1 to point 2, we find Eq. 5.30, exactly the same equation we found for a venturi meter. However, in this case we cannot assume frictionless flow and uniform flow across any cross section of the pipe as easily as we can in the case of the venturi meter. 

As in the case of the venturi meter, experiments indicate that if we introduce a discharge coefficient and thus form Eq. 5.31, then that coefficient is a fairly simple function of the ratio of the diameter of the orifice hole to the diameter of the pipe, j, / Dp, and the Reynolds number. The relation is... 

If the venturi meter in Example 5.7 is to be used on a day-to-day basis, then it will be useful to have a plot of flow rate versus pressure drop, so that we can read the pressure drop and simply look up the flow rate. Sketch such a plot for flow rates... 

The venturi meter in Fig. 5,30 has air flowing through it. The manometer, as shown, contains both mercury and water. The cross-sectional areas at the upstream location and at the throat-are 10 and Ift respectively. What is the volumetric flow rate of the air The discharge coefficient C equals 1.0. 

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