Torque on a point on a sphere in a fluid/finding pressure?

[6283186]

If there is a rotating sphere (falling through a fluid) a) is the torque the same at every point on the sphere's surface, and b) how would I use said torque to work out the pressure exerted by opposite 'sides' of the sphere on the fluid?

Homework Equations

The Attempt at a Solution

 

[haruspex]

What equations do you have for drag?

 

[6283186]

drag = 1/2 ρf v^2 Cd A

where pf is the fluid density, v is the velocity of the sphere, Cd is the drag coefficient for the sphere (0.1 for smooth, 0.6 for rough) and A is the reference (cross-sectional) area

 

[haruspex]

I forgot to ask what the relationship is between the axis of rotation and the vertical (the direction of travel). Are they the same or orthogonal? If orthogonal, think about the v term of the drag for different points on the surface.
I assume what this is leading to is an explanation of the Magnus effect. Intuitively, I think I see how the difference in shear forces leads to the required pressure difference, but I'm not an expert in this area.

 

[6283186]

They're the same.

 

[haruspex]

They're the same.

In that case, the torque at a point on the surface will clearly depend on its latitude, and you could write the equation down fairly easily. But I've no idea how this connects with pressure.