Radial and tangential velocities for Inviscid flow (fluid mechanics)

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Discussion Overview

The discussion revolves around the understanding of radial and tangential velocities in the context of inviscid flow, particularly focusing on their behavior at the surface of a cylinder. Participants explore the conditions under which these velocity components are zero.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant seeks clarification on when tangential and radial velocities are zero in relation to a stream-function.
  • Another participant questions whether the discussion pertains to flow past a cylinder or a sphere, specifying that it is about cylinders.
  • A participant explains that at the surface of the cylinder, the radial component must be zero to prevent flow through the solid surface, while the tangential component does not have to be zero.
  • The same participant notes that stagnation points at the leading and trailing edges of the cylinder result in both velocity components being zero at those points.

Areas of Agreement / Disagreement

Participants generally agree on the behavior of the radial and tangential velocities at the surface of a cylinder, but there may be nuances regarding the conditions at stagnation points that are not fully resolved.

Contextual Notes

The discussion does not delve into specific mathematical formulations or assumptions underlying the definitions of radial and tangential velocities.

wahaj
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After I have an expression for the stream-function in a problem, I can differentiate to get the tangential and radial velocities because I need those to solve the problem. But I don't understand when the tangential velocity will be 0 and when the radial is 0. Can some on explain?
 
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wahaj said:
After I have an expression for the stream-function in a problem, I can differentiate to get the tangential and radial velocities because I need those to solve the problem. But I don't understand when the tangential velocity will be 0 and when the radial is 0. Can some on explain?

Is this for flow past a cylinder or past a sphere?

Chet
 
I didn't realize there was a difference but cylinders for this question.
 
If you're referring to the radial and tangential velocity components at the surface of the cylinder, then the radial component has to be zero, since you can't have flow through the solid surface of the cylinder. For inviscid flow, the tangential component of the velocity does not have to be zero at a solid surface. The leading edge and the trailing edge of the cylinder are both stagnation points, so both components of velocity are zero at these points.

Chet
 
Thanks for clearing this up.
 

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