Float actuated devices : Level

Float actuated devices measure liquid level using a float, which lies on the surface of the liquid and changes its position as the liquid level varies. Fig. 5.1 presents a schematic view of a float-actuated device.

Figure 5.1. Schematic diagram of a float-and-cable actuated device.

The level of the liquid 1 in the tank 2 is under measurement. A sensitive element 3 (a float of a cylindrical shape) is placed on the surface of this liquid. This sensor is connected through a cable 4 and two rotating wheels 5 with a balancing weight 6. A position of the balancing weight and a pointer 7, attached to it, in respect to a scale 8 determines the level of the liquid in the tank. Density of the float should be less that that of the liquid. Usually, plastic materials are used for manufacturing of floats.
Application of these devices assumes that the float is immersed in the liquid by the middle of its height. Therefore, when density of the liquid changes an error introduces into results of level measurement. Let’s calculate this error. 

The condition of balance for the float may be written in the form:

(5.1)
where
Ffl = mfl * gloc

- gravitational force acted on the float N,

   - resultant force from the balancing weight, cable and friction
in the wheels, N ;
 

 - Archimedes’ force acted on the float, N ; 


mfl      - mass of the float, kg  ;

gloc   - local gravitational acceleration, m/s2 ;    

   
  - density of the liquid under the float and gas (or vapour) above it,respectively, kg/m3 ;


 Sfl - horizontal cross-section area of the float,  m2; 

        - heights of the float parts in the liquid and in the gas (or vapour)
above it, respectively,


Equation (5.1) can be re-written as follows:

(5.2)

Let for the unchanged level the density of the liquid has increased by the value of 
Δρ liq . Then, the depth of immersion of the float into the liquid and gas (or vapour) will change by the value of  
 

 

, where the sign “+” stands for the immersion of the float into the gas (or vapour) and the sign “-“ stands for the immersion of the float into the liquid. 

Taking into account that 

 

does not change considerably.

We can re-write equation (5.2) as follows:

(5.3)

Let 

Then,

 

(5.4)

 Neglect the variation of the Archimedes’ force acting from gas on the float, or

(5.5)

Now we get :

(5.6)
 or

 (5.7)
Finally, we get an error due to change in liquid density:

(5.8)

These devices have a simple design, high accuracy, wide range of measuring levels and the possibility of level measurement for aggressive and viscous liquids. However, they are not able to measure levels in tanks under pressure.

Article Source:: Dr. Alexander Badalyan, University of South Australia