Monday, October 27, 2008
In this study, the authors considered that there are two factors affecting the experimental results—the resolution of the camera and the curve-fitting equation in Figure 2. When the pin for fixing the falling ball is released, it represents the ball beginning to fall. In this study, the authors checked the images recorded per 1/30 sec one by one, and tried to find one that recorded the initial movement and one that recorded the ball passing the end line.
Nevertheless, it is difficult to distinguish which picture recorded the pin moving away from the falling ball when the camera’s resolution is not high enough to zoom in on the pin. Therefore, an effective camera can promote the accuracy and stability of the measurement of dynamic viscosity in the vertical falling ball viscometer. On the other hand, the study selected Cd = 30/Re instead of the Stokes’ law of Cd = 24/Re, because the curve-fitting line of Cd = 30/ Re is much better in Figure 2. If one uses the curve-fitting line of Cd= 24/Re, the relative error will increase to be over 10%.
The restriction in this measuring method is that the Reynolds number must be less than 5. Therefore, the sphere falling ball must be changed when the falling Reynolds number is larger than 5, because it violates the derivation of Eq. (7) in this study. Nevertheless, the method in this study extends the suitable range from Re<1 to Re<5, i.e., it extends the available range of the falling ball. This means that the method can decrease the chances of changing the falling ball in the experiment. In addition, according to the theory of Stokes’ law, the figure of drag coefficient versus Reynolds number depicts the properties of a perfect sphere ball moving in a liquid. In this research, although the authors measured the out-of-roundness of the sphere ball, they did not analyze the error due to the effect of the out-of-roundness. The authors hope to further investigate the effect of out-of-roundness on the measurement results in future work, and validate the accuracy of the method by measuring more reference liquids.
A new method for measuring dynamic viscosity based on the falling ball viscometer has been developed. The characteristics of the method are that Newton’s law of motion includes the acceleration term, and the dynamic viscosity must be calculated by a numerical code with an iteration scheme. Because the falling tube is vertical to the ground, which is different from the devices claimed in international standards, the study refers to it as the vertical falling ball viscometer.
The study used SAE 30 oil as the sample liquid, and the results indicated that the confidence interval of measurement is ±0.0034 with a confidence level of 99.73%, and the measuring error of viscosity is close to 6%. It is hoped that future work will increase the measurement accuracy and stability by utilizing a camera with higher resolution, and consider the effect of the out-of-roundness of the falling ball on the measurement.
- The Measurement, Instrumentation, and Sensors Handbook; Leblanc, G.E.; Secco, R.A.; Kostic, M.; Webster, J.G., Eds.; CRC Press: Boca Raton, FL, 1999; pp 30-1–30-23.
- Esposito, A. Fluid Mechanics with Applications; Prentice-Hall: Englewood Cliffs, NJ, 1998; pp 58–66 and 578–607.
- Finnemore, E.J.; Franzini, J.B. Fluid Mechanics with Engineering Applications; McGraw-Hill: Boston, MA, 2002, pp 374–82.
- Plastics—determination of viscosity using a falling ball viscometer—part 1: inclined-tube method. Standard no. ISO 12058-1, 1997.
- Measurement of viscosity using the Hoppler falling ball viscometer. Standard no. DIN 53015, 2001.
- Brizard, M.; Megharfi, M.; Mahe, E.; Verdier, C. Design of a high precision falling ball viscometer. Rev. Sci. Instr. 2005, 76(2), 025109-1–025109-6.
- Torobin, L.B.; Gauvin, W.H. Fundamental aspects of solid-gas flow, part I: introductory concepts and idealized sphere motion in viscous regime. Can. J. Chem. Eng. 1959, 37, 129–41.
- Bailey, A.B. Sphere drag coefficient for subsonic speeds in continuum and free-molecule flows. J. Fluid Mechan. 1974, 6(2), 401–10.
- Hoerner, S.F. Fluid-Dynamic Drag; Hoerner Fluid Dynamics: Midland Park, NJ, 1958; pp 3–8.
- Basic concepts in metrology—evaluating measurements of a single measurand and expression of uncertainty. Standard no. DIN 1319-3, 1996.
The authors are with the Department of Mechanical Engineering, Lee Ming Institute of Technology, 2-2, Lee Zhuan Rd., Taishan, Taipei 24305, Taiwan, ROC; tel.: +886 2 29097811, ext. 2258; fax: +886 2 29095888; e-mail: email@example.com.