Radial and tangential velocities for Inviscid flow (fluid mechanics)

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SUMMARY

The discussion focuses on the differentiation of the stream-function to obtain tangential and radial velocities in inviscid flow around a cylinder. It is established that the radial velocity component must be zero at the surface of the cylinder due to the no-penetration condition, while the tangential velocity can be non-zero. Additionally, both velocity components are zero at the stagnation points, which are located at the leading and trailing edges of the cylinder.

PREREQUISITES
  • Understanding of stream-functions in fluid mechanics
  • Knowledge of inviscid flow principles
  • Familiarity with velocity components in fluid dynamics
  • Concept of stagnation points in flow around solid bodies
NEXT STEPS
  • Study the derivation of stream-functions in fluid mechanics
  • Learn about the no-penetration condition in fluid flow
  • Explore the concept of stagnation points in greater detail
  • Investigate flow characteristics around different geometries, such as spheres
USEFUL FOR

Fluid mechanics students, engineers working with inviscid flow, and anyone studying the behavior of fluid flow around solid objects like cylinders.

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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