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Measurement of Flow of Fluids

In modern industrial technology, pipelines are largely used for conveying a wide variety of gases liquids and even solids. Surely, it is important to be able to measure the rate of flow of materials conveyed through pipelines i.e., the quantity that passes in the unit of time (ft.3/sec., m3/min., etc) Flow measuring devices are of various kinds. The present article is concerned only with so-called volumetric meters. Such meters are used more particularly for the measurement of the gas and water, respectively.

Both gas and liquid flow can be measured in volumetric or mass flow rates such as litres per second or kg/s. These measurements can be converted between one another if the materials density is known. The density for a liquid is almost independent of the liquids conditions, however this is not the case for a gas, whose density highly depends upon pressure and temperature.

Flow-measuring devices of the direct type for liquids function on either of two principles: (1) a measuring chamber of known capacity is repeatedly filled and emptied (Fig.1) (2) the rotating measuring element displaces a known quantity of liquid in performing each revolution (Figs 2 to 5). These displacement-type meters, though differing in design and technical features, all operate on the same principle, which will here be described more particularly with reference to the oval-runner meter (Fig.5).

It consists of two rotating elements of oval cross-sectional shape which mesh with each other. They are enclosed within a cylindrical casing which forms the measuring chamber and is provided with an inlet and an outlet. Fig.6 shows the oval rotating elements in four successive positions in the course of one revolution, during which each crescent-shaped space at the top and bottom of the measuring chamber is twice filled.

The total volume of liquid that is passed through the measuring chamber from the inlet to the outlet during each revolution of the oval elements is equal to 4 Fs h, where Fs is the cross-sectional area of each crescent-shaped space and h is the transverse dimension of the measuring chamber (perpendicularly to the plane of the drawing in Fig.6). The power for driving the oval elements is supplied by the liquid flow itself (Fig.7a).

The pressure difference Dp across the meter acts upon the major and minor projected areas f and F of the lower oval element in (Fig.7a), which areas are thus subjected to the resultant forces PF and Pf respectively (Fig.7b). Since PF is larger than Pf and moreover has a larger lever arm with respect to the center of rotation of the oval element, the latter is thus subjected to a torque (turning moment) which causes it to rotate. The upper oval element, when in the position shown in Fig.7b is subjected to a torque of zero magnitude, since the resultant forces acting on each side of the center balance each other.

When the two elements have each rotated through 90 degrees, the situation is reversed, in that now the upper element is subjected to its maximum torque and on the lower element (as shown in Fig.7a) diminishes to zero, while that on the upper element increases to its maximum value. The meter is self-starting in the sense that the oval elements will begin to rotate from any position as soon as the liquid flow commences, provided that the liquid to be measured has a pressure sufficient to overcome the inertia and friction of the elements.

To minimize friction, the latter are not in contact with the wall of the measuring chamber. There is thus a slight gap between each element and the wall, so that a certain small amount of leakage occurs. If this leakage is neglected, the speed of rotation is proportional to the rate of flow of the liquid, since the quantity that passes through the measuring chamber in each revolution of the oval elements is constant (and equal to Fig.4 Fs h).

Fig.1 shows the construction of an oval-runner meter. The two oval elements can rotate freely on their spindles. The upper element is connected to a gear wheel which drives another gear wheel, mounted at the center of the casing, and this in turn drives a magnetic coupling.

The latter transmits the rotation of the oval elements and prevents the penetration of liquid in to the indicating mechanism. Fig.2 shows a single-pointer dial mechanism with a pointer which rotates continuously while measuring is in progress. The pointers of the two pointer dial mechanism illustrated in Fig.3 can be reset to zero on completion of the measuring operation.

As already stated, a certain amount of leakage occurs in consequence of the clearances between the rotating elements and the wall of the chamber. The amount of leakage, besides obviously being dependent on the precision of manufacture of the meter and the rate of flow, is dependent on the viscosity of the fluid passing through the meter.

Fig.4 shows an installation for testing the performance of an oval-runner meter, more particularly with liquids of different viscosity. The object of the gas separator is to remove any gas dissolved in the liquid, as its presence produces errors in the measurements. With this equipment the accuracy of the meter can be checked for different flow rates and different liquids.