# GRX-Q - Flowing bodies

With this type of flow measurement floating bodies, spring washers or flaps are exposed to the flow. After the differential pressure method, variable area flow measurement is one of the most frequently used methods. In the following, the variable area flowmeters as well as the spring washers and flaps are described in more detail.

**Variable area flowmeter**

The method is used for flow measurement of liquids and gases. After the differential pressure method, the flow meter is one of the most frequently used methods and is characterized by a good price-performance ratio. It is easy to install and has a good robustness.

The flow measurement is realized by means of a resistance body in a conical measuring tube or a conical resistance body in an orifice plate. The measuring principle is based on a fluid flowing vertically from bottom to top, which flows around the resistance body. Under constant conditions, a balance of forces is created between the fluid and the flow around the resistance body (see Fig. 2-12 - cut-out system).

The change in the flow velocity of the fluid results in a change in the height (lift height h) of the float, which is triggered by the dependence of the force exerted by the fluid. The relationship between the force and the flow velocity is based on the law of resistance.

The weight and buoyancy force of the float remain constant. The coefficient of resistance changes due to the conical tube with the height of lift of the body and the Re-number. The resulting equilibrium equation can be described as follows:

this results in a condition of equilibrium:

In a measuring arrangement, the variables *V**K*, *ρ**K*, *ρ**M*, *g* and *A**K* are constant. As a result, a change in the flow velocity *v**M* only changes the resistance coefficient *c**W*. Thus the relationship between the stroke height *h* and the flow velocity *v**M* is contained in the drag coefficient *c**W*. It follows that the resistance coefficient is a function of *h* and Re-number.

As a consequence, a calculation of the resistance coefficient is not accessible. The values must be determined empirically by calibrating the measuring arrangement. This determination can be carried out with the aid of VDI/VDE 3513. The guideline helps the user to create a flow scale in connection with the characteristic values of the fluid and the measuring device. The guideline can also be used to transfer an existing scale for the flow rate to another medium.

The variable area flow meters can be applied to almost any gaseous or liquid medium. Very common are these measuring instruments with a glass cone on which the scale is printed and can thus be read directly. For opaque gases or liquids, variable area flowmeters made entirely of metal are suitable.

This measuring method is insensitive to dirt and impurities, provided the particle size of the impurity does not exceed the annular gap width between the float and the conical measuring tube. Variable area flowmeters do not require a straight inlet section and can be used directly behind pipe bends or valves. The pressure losses of the devices are low and can be kept at a very low level with appropriate dimensioning. The accuracy of the sensors is stated as 2 %, but can be reduced to up to 1 % after extensive calibration.

**Spring washer flowmeter**

Spring disc flowmeters operate on a similar principle to variable area flowmeters. Instead of the weight of the resistor body, the counterforce creates a measuring spring, thus forming an equilibrium with the fluid flowing around it. [BON-02]

The range spring is rigidly connected on one side to the inlet of the conical measuring tube and on the other side to a freely movable spring washer (see Fig. 2-13). The spring is dimensioned so that it remains far below the elastic limit even at maximum deflection. This ensures a long service life of the spring. The measuring spring with the spring washer are guided concentrically on a rod inside the conical measuring tube on which they can be moved almost frictionless.

The spring is deflected by the change in the flow velocity of the fluid flowing around it until a state of equilibrium is restored. This means that the position of the spring washer is the measure for the respective flow rate.

The following physical principles are based on a dynamic equilibrium between the flow force and the spring force:

The volume flow *q*_{v} is calculated from the mean flow velocity v_{M} and the cross-section of the annular gap *A*_{R}*.*

With the equations (eq. 2-15) and (eq. 2-16)

the volume flow q_{v} is obtained after equilibration and dissolution.

The range of application or the possible uses of the spring washer flowmeter are the same as those of the variable area flowmeter. The device is characterized in particular by the simple exchange of the range spring with scale. The measuring range can be adapted to the respective condition by replacing the spring. The flow meter is implemented in the pipeline as in the variable area method and does not require any flow path. The relatively small moving masses are also advantageous, which favour the dynamic properties of the system. A major difference compared with variable area flowmeters is the independent installation position. Due to the range spring used, the spring disc flowmeter can also be installed in horizontally running pipes.

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