Formulation of flow generated by the rotating cylinder

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SUMMARY

The discussion focuses on calculating the frictional torque on a high-speed spindle where flow is generated by the rotation of the cylinder. The user references Munson's book, questioning the validity of the free vortex model, specifically whether the formulation where Vθ is proportional to 1/r is applicable at high rotation speeds. Concerns are raised about the implications of a negative derivative of Vθ on shear stress calculations. The user seeks alternative formulations and resources for better understanding.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically vortex flow.
  • Familiarity with shear stress calculations in rotating systems.
  • Knowledge of the free vortex model and its applications.
  • Basic proficiency in interpreting fluid mechanics literature, such as Munson's textbook.
NEXT STEPS
  • Research the applicability of the free vortex model at high rotation speeds.
  • Explore alternative models for calculating shear stress in rotating cylinders.
  • Study the implications of negative derivatives in fluid dynamics.
  • Review additional resources or textbooks on vortex dynamics and torque calculations.
USEFUL FOR

Mechanical engineers, fluid dynamics researchers, and students studying rotational flow dynamics will benefit from this discussion, particularly those focusing on torque calculations in high-speed applications.

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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