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

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Homework Help Overview

The discussion revolves around the behavior of a rotating sphere falling through a fluid, specifically focusing on the torque experienced at various points on the sphere's surface and its relationship to pressure exerted by the fluid. The subject area includes fluid dynamics and rotational motion.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to understand whether torque is uniform across the sphere's surface and how to relate this torque to fluid pressure. Some participants inquire about the equations for drag and the relationship between the axis of rotation and the sphere's direction of travel.

Discussion Status

Participants are exploring the implications of torque on pressure and discussing the relationship between the sphere's rotation and the fluid dynamics involved. Some guidance has been offered regarding the equations for drag, and there is an ongoing examination of how these concepts interrelate, particularly concerning the Magnus effect.

Contextual Notes

There is a noted uncertainty regarding the connection between torque and pressure, as well as the implications of the sphere's latitude on torque calculations. Participants are also considering the effects of shear forces in the fluid.

6283186
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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

 
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What equations do you have for drag?
 
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
 
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.
 
They're the same.
 
6283186 said:
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.
 

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