Buoyancy : Indirect level measurement
Uses the theory of Archimedes Principle which states that “the force produced when a body is submerged into liquid with a constant density is equal to the fluid displaced”; which means that, when a body is fully or partially immersed in any liquid, it is reduced in weight by an amount equal to the weight of the volume of the liquid displaced.
In diagram A, the displacer is suspended by a spring scale that shows the weight of the displacer in the air. This would represent ‘0%’ in the level measurement application. The full weight of the displacer is entirely supported by the spring (3 lbs).
In diagram B, the water is at level that represents ‘50%’ of the full measurement span. Note that the scale indicates a weight of 2 lbs. The loss in weight of the displacer (1 lbs) is equal to the weight of the volume of water displaced.
When the water level is increased to a full level scale (diagram C), the net weight of the displacer is 1 lbs, which represent ‘100%’ of the measurement. It lost 2 lbs when the water level arises along the longitudinal axis of the displacer.
We can see that the weight of the displacer is inversely proportional to the liquid level in the chamber where the displacer is immersed.
CALCULATING THE WEIGHT FORCES
The following applies in general to the buoyancy force acting on the displacer:
FA = Vx ⋅ ρ1 ⋅ g + ( V - Vx ) ⋅ ρ2 ⋅ g
where, FA = Buoyancy force
V = Volume of displacer
Vx = Volume of medium displaced by measuring body with density ρ1
ρ1 = Mean density of heavier medium
ρ2 = Mean density of lighter medium
g = Local acceleration due to gravity (e.g. 9.81 ms−2)
FG = Displacer body weight force
The force acting on the transmitter is inversely proportional to liquid level changes.
Determining the displacer diameters:
To make optimum use of the transmitter, the displacer should be dimensioned so that the greatest possible buoyancy force is generated over the measuring range. On the other hand, the maximum possible diameter of the displacer must be taken into consideration.
The following equation can be used to exactly dimension the displacer:
where, D = Outside diameter of displacer in mm
FA = Buoyancy force of displacer in N
g = Acceleration due to gravity (9,807 m/s² )
ρ1 = Density of heavier liquid in kg/ m³
ρ2 = Density of gas or lighter liquid in kg/m³
L = Measuring range in mm
(note : ρ2 is negligible if ρ2 = gas at atmospheric pressure or with ratio ρ2 : ρ1 less than 0.5 %.)
Displacer Actuated Level Instruments:
A simple working concept of this instrument can be illustrate in the figure below;
According to Archimedes Principle, the displacer, when submerged in liquid, will ‘lose’ its weight, and this weight loss is proportional to the level of the liquid. Thus, a level, density, or interface level change in the measured fluid causes a change in the displacer position. This change is transferred to the torque tube assembly. As the measured fluid changes, the torque tube assembly rotates and the indicating needle attached to the torque tube will have indication.
This rotary motion can then be extent for remote signal and indication. It is transferred to the transmitter level assembly. The rotary motion moves a magnet attached to the lever assembly, changing the magnetic field that is sensed by the Half-effect position sensor. The sensor then converts the magnetic field signal to an electronic signal. The current drier circuit in the transmitter develops a 4~20mA signal proportional to the dc amplifier voltage output.
