Dynamic Viscosity Measurement Method Based on the Stokes Drag of Prolate Ellipsoidal Mass

Abstract

Viscometer plays an important role in the field of tribology. One way to measure viscosity is to use the Stokes drag principle in the underdamped harmonic oscillation phenomenon. This paper proposes a dynamic viscosity measurement method based on the related physical laws. Our experimental model involves a prolate ellipsoidal mass that experiences underdamped harmonic oscillation within viscous liquid samples. We observed the oscillations of the prolate ellipsoid to obtain the viscous damping coefficient of each sample and substituted it to the theoretical formula of dynamic viscosity. Experimental data suggest that the mathematical model has failed to predict the viscosity values of the samples. In addition, the regression curve of the reference viscosity and the measured viscous damping coefficient shows that the two quantities have an exponential relation instead of linear relation as explained in the theoretical model. We considered the regression formula as the empirical measurement transfer function and used it to measure the viscosity of an ISO VG 150 industrial oil sample. This measurement resulted in a 2.40 % of relative error percentage. Lastly, this measurement method is only valid for measuring samples with viscosities ranging from 0.0400 Pa s to 0.256 Pa s.