# GRX-Q - Differential pressure method

Flow measurement using the differential pressure method is frequently used in chemical engineering and comparable industries. This method allows liquids, gases and vapours to be used even at extreme temperatures, fast flows, high pressure or with corrosive media for which direct volume meters cannot always be used.

Extensive standardisation has been developed for these processes at national and international level. With the help of the standard, it is possible for every user to create and calculate a flow measurement tailored to his specific application.

In the standard

- Aperture with different pressure taps,
- nozzles and Venturi nozzles, as well as
- classical venturi tubes

were recorded. These will be discussed in more detail in the course of this chapter.

The differential pressure method is based on a throttle within closed, full-flow pipelines. The cross-sectional constriction at one point in the pipe increases the flow velocity of the medium flowing through it at the same volume flow rate. An ideal flow, in which the fluid is assumed to be frictionless, describes the continuity of the flow GL 2-1.

Figure 2-7 shows a graphic representation of the differential pressure method. Assuming an incompressible medium, the volumes V1= A1∙s1 and V2= A2∙s2 at points 1 (inlet) and

2 (constriction) of equal size.

Using the Bernoulli equation, which is based on the assumption of a stationary process with an incompressible fluid, the flow velocities before or in the constriction can be calculated via the differential pressure *∆p = **p*_{2 }*- **p*_{1.}

Since the location energies *g∙**h*_{1} and *g∙**h*_{2} take up a very small share, they can be neglected.

With (equation 2-3) and *∆p=**p*_{2}*-**p*_{1} follows after changeover:

Inserting into the continuity equation (eq. 2-2) gives

The equations do not take into account the losses caused by pipe friction and the resulting separation of the jet. The jet can therefore no longer fill the entire cross-section of the throttle device. At the narrowest point there is a smaller cross-section than given by the shape. In the standard this is described by the flow coefficient α, which is determined empirically. The flow coefficient α depends only on the Reynolds (Re) Number for standardized throttle devices with incompressible fluids.

**Orifices**

The different types of orifice plates all have the same shape. According to DIN EN ISO 5167-2 they are distinguished by the position of the pressure tapping. The inner diameter of the orifice plate must always be greater than or equal to 12.5 mm. In addition, a diameter ratio of β = d/D ≥ 0.10 and ≤ 0.75 is specified. [DIN EN ISO 5167-2]

The pressure withdrawals are realized either via individual bores or ring withdrawals. The tapping points are divided into positive and negative pressure tapping, which are located in front of and behind the orifice plate. The boreholes of the tapping points must all have the same diameter. They should also be burr-free and sharp. The diameters of the pressure tapping holes should be as small as possible and should not exceed a maximum of 12 mm.

In general, the installation sizes, including the measuring set-up of orifices, are relatively large. This is due to the arrangement of the sampling bores and the resulting long socket pipes. An exception is the corner orifice plate. Due to the short socket pipes, the entire measurement arrangement can be implemented as a single component. The measuring set-up therefore only needs to be placed between the flanges of the connecting pipe.

The flow pattern in the orifice plate is characterized by the sharp leading edge. The flow breaks away from the wall and forms freely. Behind the edge the jet narrows.

**Nozzles**

The standard deals with two types of standard nozzles and the Venturi nozzle. The standard nozzles can be further divided into the long radius nozzle and the ISA 1932 nozzle. (see Figure 2-9) [DIN EN ISO 5167-3]

In contrast to the orifice plate, the flow inside the nozzle is forced through a rounded inlet and is guided into a cylindrical pipe with the same cross-section of the inlet. As a result, the jet exits without contraction.

The ISA 1932 nozzles (also known as Deutsch Normdüsen) have almost constant flow rates for *Re _{D}*

_{}> 10

^{5}due to the sharp rounding, while the flow rates of the long radius nozzle increase continuously with the Re-number. However, the ISA 1932 nozzle is unusable below

*Re*

_{D}_{}> 10

^{5}, as the jet breaks away from the nozzle wall in this area and thus leads to a jumpy behavior of the flow rate number α.

The Venturi nozzle is very similar in design to the standard orifice plate (see Fig. 2-12). The front side is identical to that of an ISA nozzle, but the cross-sectional constriction is returned to the original cross-section via a diffuser. The angle of the diffuser must be less than or equal to 30°. The diffuser has a significant share in the pressure loss of the nozzle.

**Venturi tube**

Venturi tubes consist of conical and straight pipe sections, which have a pressure loss that is four to six times lower than that of orifices and nozzles. The standard DIN EN ISO 5167-4 freely distinguishes different types of classic venturi tubes with

- cast-rough inlet cone
- machined inlet cone
- rough inlet cone welded from sheet steel.

The shape and location of the pressure tapping points is defined for each of the three versions. An opening angle of 21° ± 1° is specified for the inlet cone. The diffuser may have a total opening angle of between 7° and 15° (see Fig. 2-11), but it is recommended to select a diffuser total opening angle of between 7° and 8°, otherwise flow separation will occur [DIN EN ISO 5167-4]. The classic Venturi tube may be shortened. Please note that the diffuser section may be shortened by up to 35% of its length at the end. Within this range there is no significant change in pressure loss.

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