How Do Viscous Interactions Differ in Vertical and Horizontal Geometries?

[HighPhy]

Do you know what to do next?

I have to show the following, right?

Let $h_0$ represent the small minimum clearance between the sphere (in our problem) and the cylinder. Let z = 0 represent the axial coordinate of the center of the sphere. Show that, for axial locations on either side of the sphere close to this center location, the clearance can be approximated by the parabolic shape $$h(z)=h_0+\frac{z^2}{2R}$$

 

[Chestermiller]

I have to show the following, right?

yes.