Reduced Order Model for Viscosity and Mass Density Sensing by A U-Shaped Wire

This paper focuses on the basic principle of measuring viscosity and density with U-shaped tungsten wire sensor, and develops a model for measuring liquid viscosity and density with the help of oscillating ball model. Firstly, the working mechanism of the wire resonator is deeply analyzed. Then, by reducing the order of the fluid dynamic function, a simplified model is established for measuring the viscosity and density of liquid with U-shaped tungsten resonator. The experimental results show that the maximum error of viscosity is 7.22% and the average error is 2.81% when the viscosity ranges from 4.526mPa.s to 62.01mPa.s. In the range of 0.8486g/cm³ to 0.8711g/cm³, the maximum density error is 7.00% and the average density error is 1.89%. In summary, the simplified model proposed in this paper can accurately measure the viscosity and density of liquids.