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The measurement of pressure (and differential pressure between two points in a system) is of vital importance in studies of heat and mass transfer. A very wide range of techniques exists but the main ones, covered in this article, are the use of manometers, Bourdon gauges and pressure transducers. A good general source on pressure measurement is the book by Jones (1985). Specialized techniques relating to very high pressures are discussed by Beggs (1983).

### Manometers

Using manometers, good accuracy is possible and, by the use of inclined manometers and micromanometers, it is possible to cover a wide range of pressure (through the upper pressure limit for absolute pressure measurement is necessarily rather low). However, manometers are rather messy to use and have a poor response time (typically about 0.5 seconds).

Great care needs to be taken in ensuring that the lines connecting the manometer to the points at which measurements are to be made are filled with fluids of known density. Care also needs to be taken in the interpretation of manometer level differences in terms of the differences in pressure being measured. This is illustrated by the example shown in Figure 1 where a manometer is used to measure pressure drop in a two-phase flow system; the diagram is somewhat simplified since, in such a system, purging of lines with liquid would be used to avoid ambiguity of line content [see Hewitt (1978)]. A pressure balance can be carried out at level A:

(1)

and rearranging we have

(2)

If p1 = p2, then the manometric difference is given by

(3)

thus, there is an "offset" on the manometer which depends on the distance between the tappings and the density (pc) in the lines. In the absence of flow through the tube it follows that

(4)

and the manometric difference is

(5)

the manometer will have zero differential if the fluid in the line has the same density as the fluid in the tube.

A special form of the manometer is the barometer in which the atmospheric pressure is compared to vacuum using an inverted tube in a mercury bath as shown in Figure 2.

Table 1. Classification of transducer type: with advantages and disadvantages

Note. "Potentiometric"—diaphragm moves slidewire. "Magnetostrictive"—magnetic properties varying with force.

### Bourdon gauges

Bourdon gauges indicate pressure by the amount of deflection under internal pressure of an oval tube bent in the arc of a circle and closed at one end. Such gauges cover a wide range of conditions (vacuum up to 700 MPa), have good potential accuracy and are versatile. However, they have a rather poor response time (typically about 0.2 s). An alternative form of mechanical pressure indicator is the diaphragm gauge, which depends on the deflection of a diaphragm when subjected to a difference of pressure between the two faces. The pressure range of such gauges is more restricted than that of more conventional Bourdon gauges; the aneroid barometer is a type of diaphragm gauge.

### Pressure transducers

Pressure transducers depend on the (often very small) deflection of a diaphragm by the imposed pressure. The deflection is detected by various means and extremely fast response is possible. Table 1 gives the classification of pressure transducer types, with their advantages and disadvantages.

Obviously, by mounting pressure transducers at two points in a system, their signals can be subtracted to give the differential pressure. Alternatively, a differential pressure transducer can be used in which two pressure tapping lines are attached to the respective points in the system and to two chambers separated by a diaphragm. The movement of the diaphragm indicates the differential pressure. Of the types of transducer itemized in Table 1, the strain-gauge and reluctance transducers are ideally suitable for differential pressure measurements but the capacitance and piezoelectric types are specifically unsuitable. There are problems in using differential transducers which are similar to those mentioned for manometers above. Care has to be taken that the lines are full of a fluid of known density and the problem of the "offset" may restrict the range of the instrument (this can be counteracted by using an intermediate manometer system—see Hewitt (1978).

#### REFERENCES

Hewitt, G. F. (1978) Measurement of Two Phase Flow Parameters, Academic Press, London. ISBN: 0-12-346260-6.

Jones, E. B. (1985) Instrument Technology, Vol. 1, Mechanical Measurements, Butterworth & Co. (Publishers) Ltd, London. ISBN: 0-408-01232-1.

Peggs, G. N. (1983) High Pressure Measurement Techniques, Applied Science Publishers. London. ISBN: 0-85334-189-3.

#### References

1. Hewitt, G. F. (1978) Measurement of Two Phase Flow Parameters, Academic Press, London. ISBN: 0-12-346260-6.
2. Jones, E. B. (1985) Instrument Technology, Vol. 1, Mechanical Measurements, Butterworth & Co. (Publishers) Ltd, London. ISBN: 0-408-01232-1.
3. Peggs, G. N. (1983) High Pressure Measurement Techniques, Applied Science Publishers. London. ISBN: 0-85334-189-3.