formulation of flow generated by the rotating cylinder

eaglemre

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