Dual Estimation Approach to Falling-Ball Viscometry Using Terminal and Transient Velocity Data from Video Tracking

Mahendra Kusuma Nugraha; Ernawatil Gani; Berton Maruli Siahaan

doi:10.21009/1.12108

Authors

Mahendra Kusuma Nugraha 1 Department of Physics, Faculty of Mathematics and Natural Science, Sam Ratulangi University
Ernawatil Gani 1 Department of Physics, Faculty of Mathematics and Natural Science, Sam Ratulangi University
Berton Maruli Siahaan 1 Department of Physics, Faculty of Mathematics and Natural Science, Sam Ratulangi University

DOI:

https://doi.org/10.21009/1.12108

Keywords:

viscometry, free-fall motion, terminal velocity, transient phase

Abstract

In this study, a motion-tracking analysis method was applied to a viscometry system to measure free-fall velocity and determine the viscosity of a fluid. Experiments were conducted by dropping a marble into a tube containing the test liquid with known density, then recording its free-fall motion with a digital camera at 30 frames per second and analysing the data with Tracker software. From the calculated terminal velocity analysis across two trials ((7.46 ± 0.01) × 10^-4 m/s and (8.64 ± 0.01) × 10^-4 m/s), the viscosity values obtained were 3.0 Pa·s and 2.59 Pa·s, respectively, which are well within the acceptable range. An alternative approach using exponential curve fitting to analyse the transient phase did not yield results as accurate or comparable to the previous, because the data showed a linear relationship between position and time. In two consecutive trials, the viscosity values calculated using this method are 2.81 × 10^-2 Pa·s and 3.02 × 10^-2 Pa·s. This condition was likely caused by the camera's limited frame rate, which was insufficient to capture the continuous, subtle changes in downward velocity during the first phase of free-fall motion, which occurred over a very short period. Therefore, in a basic, simple yet standard experimental setup, viscosity can be reliably calculated only by measuring the terminal velocity in accordance with Stokes' law.

References

Abboud, K. and Elbir, B. (2024) “Calculating the Dynamic Viscosity of a Fluid using Image Processing of a Falling Ball,” Journal of Emerging Investigators [Preprint]. Available at: https://doi.org/10.59720/23-198.

Akhlis, I. et al. (2020) “The Determination of Fluid Viscosity using Tracker-Assisted Falling Ball Viscosimeter,” Journal of Physics: Conference Series. Institute of Physics Publishing. Available at: https://doi.org/10.1088/1742-6596/1567/4/042102.

Ballereau, P., Truong, D. and Matias, A. (2016) “Absolute Falling Ball Viscometer, Adapted to the Low Viscosities of Liquids,” International Journal of Metrology and Quality Engineering, 7(3). Available at: https://doi.org/10.1051/ijmqe/2016015.

Brizard, M. et al. (2005) “Design of a High Precision Falling-Ball Viscometer,” Review of Scientific Instruments, 76(2). Available at: https://doi.org/10.1063/1.1851471.

Chen, Z. et al. (2021) “Validity and Reliability of a Phone App and Stopwatch for the Measurement of 505 Change of Direction Performance: A Test-Retest Study Design,” Frontiers in Physiology, 12. Available at: https://doi.org/10.3389/fphys.2021.743800.

Chernetckiy, I. et al. (2021) The Application of Tracker Video Analysis for Distance Learning of Physics. Available at: www.stemua.science.

Ganni, S. et al. (2018) “A software-based tool for video motion tracking in the surgical skills assessment landscape,” Surgical Endoscopy, 32(6), pp. 2994–2999. Available at: https://doi.org/10.1007/s00464-018-6023-5.

Ganni, S. et al. (2020) “Validation of Motion Tracking Software for Evaluation of Surgical Performance in Laparoscopic Cholecystectomy,” Journal of Medical Systems, 44(3). Available at: https://doi.org/10.1007/s10916-020-1525-9.

Kadam, P., Fang, G. and Zou, J.J. (2024) “Object Tracking Using Computer Vision: A Review,” Computers. Multidisciplinary Digital Publishing Institute (MDPI). Available at: https://doi.org/10.3390/computers13060136.

Karl, J.M. et al. (2018) “Frame by Frame Video Analysis of Idiosyncratic Reach-to-Grasp Movements in Humans,” Journal of Visualized Experiments, 2018(131). Available at: https://doi.org/10.3791/56733.

Liu, C. and Xie, Y. (2024) “Innovative Application of Computer Vision and Motion Tracking Technology in Sports Training,” EAI Endorsed Transactions on Pervasive Health and Technology, 10. Available at: https://doi.org/10.4108/eetpht.10.5763.

Pan, Z. et al. (2025) “Precise Real-Time Measurement of Liquid Viscosity Using Digital Video Data,” Advanced Intelligent Systems [Preprint]. Available at: https://doi.org/10.1002/aisy.202500297.

Reuter, A.S. and Schindler, M. (2023) “Motion Capture Systems and Their Use in Educational Research: Insights from a Systematic Literature Review,” Education Sciences. MDPI. Available at: https://doi.org/10.3390/educsci13020167.

Scott, B. et al. (2022) “Healthcare applications of single camera markerless motion capture: a scoping review,” PeerJ. PeerJ Inc. Available at: https://doi.org/10.7717/peerj.13517.

Syifa, N.H. (2022) “Determination oF Terminal Velocity And Fluid Viscosity using Falling Ball Viscometer with Video Tracker Application,” Jurnal Pendidikan Fisika, 10(2), pp. 75–81. Available at: http://journal.uin-alauddin.ac.id/indeks.php/PendidikanFisika.

Tang, J.X. (2016) “Measurements of Fluid Viscosity using a Miniature Ball Drop Device,” Review of Scientific Instruments, 87(5). Available at: https://doi.org/10.1063/1.4948314.