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

In summary, the conversation discusses the torque and pressure exerted by a rotating sphere falling through a fluid. The equations for drag are mentioned, which include parameters such as fluid density, velocity, and drag coefficient. The relationship between the axis of rotation and the direction of travel is then questioned, with the conclusion that they are the same. The discussion then moves on to the torque at different points on the surface and its connection to pressure, with the possibility of the Magnus effect being involved.
  • #1
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?



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  • #2
What equations do you have for drag?
 
  • #3
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
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
They're the same.
 
  • #6
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.
 

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

1. What is torque on a point on a sphere in a fluid?

Torque on a point on a sphere in a fluid refers to the rotational force applied on a specific point on a sphere when it is submerged in a fluid. It is caused by the difference in pressure acting on opposite sides of the point, which creates a net torque.

2. How is torque on a point on a sphere in a fluid calculated?

Torque on a point on a sphere in a fluid can be calculated using the formula T = r x F, where T is the torque, r is the radius of the sphere, and F is the force acting on the point. The force, in this case, is the difference in pressure multiplied by the area of the point.

3. What factors affect the torque on a point on a sphere in a fluid?

The torque on a point on a sphere in a fluid is affected by the radius of the sphere, the density of the fluid, the viscosity of the fluid, and the velocity of the fluid. All of these factors play a role in determining the pressure difference and thus, the torque.

4. How does torque on a point on a sphere in a fluid relate to pressure?

Torque on a point on a sphere in a fluid is directly related to pressure as it is caused by the difference in pressure acting on opposite sides of the point. The greater the pressure difference, the greater the torque on the point will be.

5. What is the significance of calculating torque on a point on a sphere in a fluid?

Calculating torque on a point on a sphere in a fluid is important in understanding the stability and balance of objects submerged in fluids. It is also crucial in determining the forces acting on different points of the sphere and can be used in various engineering and scientific applications.

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