1. Viscous Flow Around Metal Spheres
Terminal Velocity and Acceleration Profile as a Function of Radius

2. Introduction Characterize viscous flow around a sphere
Find dependence of terminal velocity on radius
Find dependence of acceleration profile on radius

3. Introduction Classical problem in fluid dynamics
Special flow regime called Stoke’s Flow
Viscous forces dominate the flow
Often used to determine fluid viscosity

4. Our Experimental Setup
Graduated cylinder filled with glycerin
Different sizes of metal balls
Digital Camcorder

5. Experimental Setup
6 different sized steel balls

6. Experimental Setup

7. Experimental Setup
A video data file of the 6.35mm balls

8. Theoretical Models
Terminal Velocity

10. Anticipated terminal velocity v. radius.

11. Theoretical Models
Acceleration Profile

12. Theoretical Models

13. Theoretical Models

14. Theoretical Models

15. Theoretical Models

18. Theoretical Models Navier Stokes Analysis Non-dimensionalizing the Eqns

19. Theoretical Models For Stokes Flow Re<<1 So the Equations simplify to

20. Theoretical Models Navier Stokes Analysis

21. Theoretical Models Analytical Soln for the Sphere

22. Theoretical Models The Analytical Expression for Drag Force F matches Dimensional Analysis
Stoke’s Law

23. Results & Analysis
Used video from camcorder to find experimental speeds
Calculated theoretical speeds using model
Compared:
Experimental
Theoretical
Predicted Scaling Rate from Dimensional Analysis (V ~ r^2)

24. Results & Analysis

25. Results & Analysis Error sources
Viscosity is a function of temperature!

26. Results & Analysis Error Sources (cont.)
Bubbles effectively reduce viscosity when they’re in a ball’s path
Bubbles effectively increase buoyancy when they’re piggybacking on a ball
Sidewall effects (disruption of flow lines)
Instrument resolution (time and distance)

27. Results & Analysis Velocity Profile Analysis
Terminal velocity reached for smallest ball in seconds, faster than camera.
Reached for largest ball in second, but times and distances involved were still too fast:

28. Results & Analysis

29. Results & Analysis

30. Conclusion
Experimental terminal velocity matches with dimensional analysis and theoretical model
significant errors due to temperature and other effects
Acceleration profile cannot be measured with current equipment
resolution is too low relative to phenomena to be observed