Why Does Ball-to-Viscometer Diameter Ratio Matter in Viscosity Measurements?

[cuddlesome]

We had a experiment on a metal ball dropped on a Falling sphere viscometer containing a certain liquid(I forgot what was it). I just don't know why our professor asked us to get the ratio of the spherical metal ball's diameter and the diameter of the Falling sphere viscometer and plot the velocity of the spherical metal ball vs. this ratio. I hope someone can help me...

 

[FredGarvin]

The key to think about is the area of the annulus created by the ball being in the tube. That annulus is the flow area that the fluid has to get around the sphere. Just using your intuition, what do you think should happen if that area were to decrease, i.e. use a larger diameter sphere?

The test correlates a fluid's viscosity to the rate at which the sphere drops. If you were to use an improper sized sphere, the fluid would seem either more or less viscous than it really is.