Formulation of flow generated by the rotating cylinder

AI Thread Summary
The discussion centers on determining the frictional torque on a high-speed spindle where flow is generated by the rotation of a cylinder, with no external flow present. The participant references Munson's book, questioning the validity of using a free vortex model, where tangential velocity (Vtheta) is inversely proportional to radius (1/r), at high rotation speeds. Concerns are raised about the implications of a negative derivative of Vtheta for calculating shear stress on the cylinder's surface. The participant seeks alternative formulations or resources for better understanding this phenomenon. Visual aids are noted as essential for comprehending the described flow dynamics.
eaglemre
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Hi All;

I try to find the frictional torque on a high speed spindle. There is no flow past the cylinder, the flow is generated due the rotation of the cylinder.
I read book of Munson and it is written there that this kind of flow can be modeled by a free votex approach.
Is free vortex formulation where Vtheta is proportional to 1/r valid for high rotation speeds or do I need another model?
To calculate the shear stress on the surface of the cylinder the derivative of the Vteta is required and in this case it becomes negative.Does this cause any problem?
Are there any other simple formulation for these kind of problem?
I will be glad for your answers.I would be great if you can give some link or suggest a book for this very simple formulation.

Regards
 
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