Page 26 - Instrumentation and Measurement

2.4.2 Displacer Gauge

When an object is partially or wholly immersed in a fluid it experiences an upthrust force equal to
the weight of fluid displaced by the object. This is known as Archimedes’ principle. Thus, a change
in the amount of an object below the surface of a liquid will result in a change in the upthrust. The
resultant force acting on such an object is then its weight minus the upthrust and thus depends on the
depth to which the object is immersed. For a vertical cylinder of cross-sectional area A in a liquid of
density ρ, if a height h of the cylinder is below the surface then the upthrust is hAρg, where g is the
acceleration due to gravity, and so the apparent weight of the cylinder is (mg - hAπg), where m is the
mass of the cylinder. Such displacer gauges need calibrating for liquid level determinations for
particular liquids since the upthrust depends on the liquid density. Figure 2.19 shows a simple version
of a displacer gauge. A problem with displacers is that there is the problem of fluids coating the floats
and apparently changing the buoyancy.

FIGURE 2.19 Displacer gauge.

2.4.3 Electrical Conductivity Level Indicator

Conductivity methods can be used to indicate when the level of a high electrical conductivity liquid
reaches a critical level. One form has two probes, one probe mounted in the liquid and the other either
horizontally at the required level or vertically with its lower end at the critical level (Figure 2.20).
When the liquid is short of the required level, the resistance between the two probes is high since part
of the electrical path between the two probes is air. However, when the liquid level reaches the critical
level, there is a path entirely through the liquid and so the conductivity drops. Foaming, splashing,
and turbulence can affect the results.

FIGURE 2.20 Conductivity level indicator.

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