Analytical Instrumentation

Density Measurement – Vibrating Element Densitometers

Vibrating Element Densitometers Principle:

If a body containing or surrounded by a fluid is set to resonance at its natural frequency, then the frequency of oscillation of the body will vary as the fluid properties and conditions change.

The natural frequency is directly proportional to the stiffness of the body and inversely proportional to the combined mass of the body and the fluid. It is also dependent on the shape, size, and elasticity of the material, induced stress, mass, and mass distribution of the body.

Piezoelectric Drives:

A wide range of piezoelectric materials are available to meet the requirements of the vibrating driving elements. The piezoelectric actuators are mechanically fixed to the vibrating element by means of adhesives. Therefore, attention should be paid to the careful placement of the support to reduce the stress experienced by the piezoelectric element due to the thermal and pressure stresses while the instrument is in service.

There are different types of vibration based densitometers used in industries some of them are listed below:

Vibrating Tube Densitometers:

These devices are suitable for highly viscous liquids or slurry applications. The mode of operation of vibration tube meters is based on the transverse vibration of tubes:

The tube and drive mechanisms are forced to vibrate in a single plane. As the liquid moves inside the tube, the density of the entire mass of the liquid is measured. The single tube has the disadvantage of presenting an obstruction to the flow, so it experiences some pressure losses. The twin tube, on the other hand, offers a very small blockage.

The twin tube is designed to achieve a good dynamic balance, with the two tubes vibrating in antiphase. Their nodes are fixed at the ends, demonstrating maximum sensitivity to installation defects, clamping, and mass loading.

The main design problems of the vibrating tube sensors are in minimizing the influence of end padding and overcoming the effects of pressure and temperature. Bellows are used at both ends of the sensor tubes to isolate the sensors from external vibrations. Bellows also minimize the end loadings due to differential expansions and installation stresses.

Tuning Fork Densitometers:

These densitometers make use of the natural frequency of low-mass tuning forks, shown :

In some cases, the fluid is taken into a small chamber in which the electromechanically driven forks are situated. In other cases, the fork is inserted directly into the liquid. Calibration is necessary in each application.

Advantages of vibrating element Densitometers:

  • They are suitable for both liquids and gases
  • They can be designed for real-time measurements.
  • They can easily be interfaced because they operate on frequencies and are inherently digital
  • They are relatively robust and easy to install


  • They are not directly related to the primary measurements; therefore, they must be calibrated.
  • All of them have problems in the measurement of multiphase liquids.


Instrumentation Engineer

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