Rotameters

This type of device (see Figure 6.3) consists of a vertical tapered tube 1 (usually made of a glass or other transparent material) and a rotor 2 (or a float), usually made of a metal (aluminium, brass, stainless steel, etc.) with higher density than that of a fluid 3 being measured. 

The rotor is produced with slots to give it rotation, so the rotor can be placed co-axial inside the tube. When the flowrate of the fluid through the tube increases the rotor is elevated upwards until the balance between forces acting on the rotor is achieved. Since the tube is tapered, then the restriction area (the area between the wall of the tube and side surface of the float) will change to accommodate flow rate being measured. Therefore, for each value of the flowrate will correspond certain position of the rotor in the tube in respect to a scale 4 and a certain value of the restriction area. 

Figure 6.3. Variable area flowmeter (rotameter).

Let's consider forces acting on the rotor during balance:

 (6.40)

or

(6.41)

(6.42)

(6.43)

where,

Equation (6.43) shows that the difference of pressures is constant and is not a function of a flowrate. Therefore, this type of device sometimes is called the flowmeter with constant differential pressure.

An equation for the evaluation of the volumetric flowrate (m3/s) has final form as follows:

(6.44)

where,

φ         -- discharge coefficient taking into account friction of the fluid with the rotor and the tube, pressure losses due to vortex of fluid under and above the rotor, and changes of the stream form when it passes through the restriction area between the rotor and the tube;

S_gap    --the area of an annular gap (restriction) between the rotor and the wall of the tube, m2.

S_gap  is defined by the geometry of the float and pipe as follows:

(6.45)

where,

The accuracy of rotameters varies from±0.25 to ±2% (for individual calibration). Their repeatability is excellent. They can measure flowrates from 0.5 cm³/min to 1135 l/min of water.

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