Homework Help: Torque on a point on a sphere in a fluid/finding pressure?

1. Jul 7, 2013

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?

2. Relevant equations

3. The attempt at a solution

2. Jul 7, 2013

haruspex

What equations do you have for drag?

3. Jul 8, 2013

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

4. Jul 8, 2013

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.

5. Jul 17, 2013

6283186

They're the same.

6. Jul 17, 2013

haruspex

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.