15.7 Resonant-wire devices
A typical resonant-wire device is
shown schematically in Figure 15.7. Wire is stretched across a chamber
containing fluid at unknown pressure subjected to a magnetic field.
The wire resonates at its natural
frequency according to its tension, which varies with pressure. Thus pressure
is calculated by measuring the frequency of vibration of the wire. Such
frequency measurement is normally carried out by electronics integrated into
the cell. These devices are highly accurate, with a typical inaccuracy figure
being ±0.2% full-scale reading. They are also particularly insensitive to
ambient condition changes and can measure pressures between 5 mbar and 2 bar.
15.8 Dead-weight gauge
The dead-weight gauge, as shown in
Figure 2.3, is a null-reading type of measuring instrument in which weights are
added to the piston platform until the piston is adjacent to a fixed reference
mark, at which time the downward force of the weights on top of the piston is
balanced by the pressure exerted by the fluid beneath the piston. The fluid
pressure is therefore calculated in terms of the weight added to the platform
and the known area of the piston. The instrument offers the ability to measure
pressures to a high degree of accuracy but is inconvenient to use. Its major
application is as a reference instrument against which other pressure-measuring
devices are calibrated. Various versions are available that allow measurement
of gauge pressures up to 7000 bar.
15.9 Special measurement devices for
low pressures
A number of special devices have been
developed for measurement of pressures in the vacuum range below atmospheric
pressure (<1.013 bar).>< 1.013 bar). These special devices include the
thermocouple gauge, the Pirani gauge, the thermistor gauge, the McLeod gauge
and the ionization gauge, and they are covered in more detail below.
Unfortunately, all of these specialized instruments are quite expensive.
The thermocouple gauge is one of a
group of gauges working on the thermal conductivity principal. The paranoia and
thermistor gauges also belong to this group. At low pressure, the kinematic
theory of gases predicts a linear relationship between pressure and thermal
conductivity. Thus measurement of thermal conductivity gives an indication of
pressure. Figure 15.8 shows a sketch of a thermocouple gauge. Operation of the
gauge depends on the thermal conduction of heat between a thin hot metal strip
in the centre and the cold outer surface of a glass tube (that is normally at
room temperature). The metal strip is heated by passing a current through it
and its temperature is measured by a thermocouple. The temperature measured
depends on the thermal conductivity of the gas in the tube and hence on its
pressure. A source of error in this instrument is the fact that heat is also
transferred by radiation as well as conduction. This error is of a constant
magnitude, independent of pressure. Hence, it can be measured, and thus
correction can be made for it. However, it is usually more convenient to design
for low radiation loss by choosing a heated element with low emissivity.
Thermocouple gauges are typically used to measure pressures in the range 10-4
mbar up to 1 mbar.
A typical form of Pirani gauge is
shown in Figure 15.9(a). This is similar to a thermocouple gauge but has a
heated element that consists of four coiled tungsten wires connected in
parallel. Two identical tubes are normally used, connected in a bridge circuit
as shown in Figure 15.9(b), with one containing the gas at unknown pressure and
the other evacuated to a very low pressure. Current is passed through the
tungsten element, which attains a certain temperature according to the thermal
conductivity of the gas. The resistance of the element changes with temperature
and causes an imbalance of the measurement bridge. Thus, the Pirani gauge
avoids the use
of a thermocouple to measure
temperature (as in the thermocouple gauge) by effectively using a resistance
thermometer as the heated element. Such gauges cover the pressure range 10-5
mbar to 1 mbar.
The thermistor gauge operates on
identical principles to the Pirani gauge but uses semiconductor materials for
the heated elements instead of metals. The normal pressure range covered is 10-4
mbar to 1 mbar.
Figure 15.10(a) shows the general
form of a McLeod gauge, in which low-pressure fluid is compressed to a higher
pressure that is then read by manometer techniques. In
essence, the gauge can be visualized
as a U-tube manometer that is sealed at one end, and where the bottom of the U
can be blocked at will. To operate the gauge, the piston is first withdrawn.
This causes the level of mercury in the lower part of the gauge to fall below
the level of the junction J between the two tubes marked Y and Z in the gauge.
Fluid at unknown pressure Pu is then introduced via the tube marked
Z, from where it also flows into the tube of cross-sectional area A marked Y.
Next, the piston is pushed in, moving the mercury level up to block the
junction J. At the stage where J is just blocked, the fluid in tube Y is at
pressure Pu and is contained in a known volume Vu. Further movement
of the piston compresses the fluid in tube Y and this process continues until
the mercury level in tube Z reaches a zero mark. Measurement of the height (h)
above the mercury column in tube Y then allows calculation of the compressed
volume of the fluid Vc as Vc = hA.
Then, by Boyle’s law:
PuVu
= PcVc
Also, applying the normal manometer
equation:
Pc = Pu + hpg
where p is the mass density of
mercury, the pressure Pu can be calculated as:
Although the smallest inaccuracy
achievable with McLeod gauges is ±1%, this is still better than that which is
achievable with most other gauges that are available for measuring pressures in
this range. Therefore, the McLeod gauge is often used as a standard against
which other gauges are calibrated. The minimum pressure normally measurable is
10-4 bar, although lower pressures can be measured if
pressure-dividing techniques are applied.
The ionization gauge is a special
type of instrument used for measuring very low pressures in the range 10-13
to 10-3 bar. Gas of unknown pressure is introduced into a glass
vessel containing free electrons discharged from a heated filament, as shown in
Figure 15.10(b). Gas pressure is determined by measuring the current flowing
between an anode and cathode within the vessel. This current is proportional to
the number of ions per unit volume, which in turn is proportional to the gas
pressure. Ionization gauges are normally only used in laboratory conditions.
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