Displacer level instruments exploit Archimedes’ Principle to detect liquid levels by continuously measuring the weight of an object (called the displacer) immersed in the process liquid. As the liquid level increases, the displacer experiences a greater buoyant force, making it appear lighter to the sensing instrument, which interprets the loss of weight as an increase in level and transmits a proportional output signal.
Displacement interface level measurement
Displacer level instruments may be used to measure liquid-liquid interfaces just the same as hydrostatic pressure instruments. One important requirement is that the displacer always is fully submerged (“flooded”). If this rule is violated, the instrument will not be able to discriminate between a low (total) liquid level and a low interface level.
If the displacer instrument has its own “cage,” it is important that both pipes connecting the cage to the process vessel (sometimes called “nozzles”) be submerged. This ensures the liquid interface inside the cage matches the interface inside the vessel. If the upper nozzle ever goes dry, the same problem can happen with a caged displacer instrument as with a “sight glass” level gauge.
Calculating buoyant force on a displacer element due to a combination of two liquids is not as difficult as it may sound. Archimedes’ Principle still holds that buoyant force is equal to the weight of the fluid(s) displaced. All we need to do is calculate the combined weights and volumes of the displaced liquids to calculate buoyant force. For a single liquid, the buoyant force is equal to the weight density of that liquid (γ) multiplied by the volume displaced (V):
Fbuoyant = γV
For a two-liquid interface, the buoyant force is equal to the sum of the two liquid weights displaced, each liquid weight term being equal to the weight density of that liquid multiplied by the displaced volume of that liquid:
Fbuoyant = γ1V1 + γ2V2
Assuming a displacer of the constant cross-sectional area throughout its length, the volume for each liquid’s displacement is simply equal to the same area (πr²) multiplied by the length of the displacer submerged in that liquid:
Fbuoyant = γ1πr²l1 + γ2πr²l2
Since the area (πr²) is common to both buoyancy terms in this equation, we may factor it out for simplicity’s sake:
Fbuoyant = πr² (γ1l1 + γ2l2)
Determining the calibration points of a displacer-type level instrument for interface applications is relatively easy if the LRV and URV conditions are examined as a pair of “thought experiments” just as we did with hydrostatic interface level measurement. First, we imagine what the displacer’s condition would “look like” with the interface at the lower range value, then we imagine a different scenario with the interface at the upper range value.
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