Calculate Tangential Rotational Force of Sphere in Flow

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SUMMARY

The discussion focuses on calculating the tangential rotational force acting on a sphere in an unsteady, incompressible flow. The participant utilizes Stokes' friction law for rotational motion, specifically the equation F = -8πη₀a³Ω, where η₀ represents viscosity, a is the sphere's radius, and Ω is the sphere's velocity. The participant seeks clarification on whether the total force calculated can be used directly to determine the tangential rotational force, emphasizing the need to isolate the tangential component of the friction force.

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Homework Statement


Considering a unsteady, incompressible flow past a sphere placed in a channel. The sphere is offset somewhat from the center of the flow to destabilize what otherwise would be steady-state symmetrical flow. Calculate the tangencial rotational force at the sphere.

Homework Equations


The Attempt at a Solution


My attempt is to make use of the Stoke's friction law for rotational motion of a sphere:
F=-8 \pi \eta_0 a^3 \Omega
with \eta_0 the viscosity, a sphere radius, \Omega sphere velocity.
But this is the total force and I have to calculate only the tangencial.
 
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The friction force is a tangential force, then if I have to calculate the tangential rotational force, then I have only to calculate the friction force written above?
 

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