Stream function along solid boundary

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SUMMARY

The discussion centers on the behavior of the stream function at slip and no-slip boundaries in fluid mechanics. It establishes that slip boundaries occur when the fluid is inviscid, resulting in no viscous stress, while no-slip boundaries require zero tangential velocity at the boundary. The key conclusion is that the stream function remains constant at both slip and no-slip boundaries when there is no normal flow, contradicting the lecturer's assertion that it is only constant at slip boundaries. This is supported by the relationship between stream function and velocity, specifically the equation unormal = -∂ψ/∂x.

PREREQUISITES
  • Understanding of fluid mechanics principles, specifically boundary conditions.
  • Familiarity with the concepts of slip and no-slip boundaries.
  • Knowledge of stream functions and their relationship to fluid velocity.
  • Basic mathematical skills to interpret equations related to fluid flow.
NEXT STEPS
  • Research the mathematical derivation of the relationship between stream function and velocity in fluid mechanics.
  • Study the solutions for inviscid and viscous flow past a sphere to observe practical applications of these concepts.
  • Explore advanced fluid dynamics literature on boundary layer theory and its implications for slip and no-slip conditions.
  • Examine case studies involving potential flow around non-symmetric obstacles to deepen understanding of stream function behavior.
USEFUL FOR

Students and professionals in fluid mechanics, particularly those studying boundary conditions and stream functions, as well as researchers focusing on fluid dynamics applications.

TomBolton10
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Hi, I am studying fluid mechanics and I am trying to get to grips with slip and no-slip boundaries.

I know that:

Slip ---> Occurs when fluid is inviscid so no viscous stress at boundary.
No-slip ---> Viscous effects mean the the tangential velocity must be zero, relative to the boundary.

Also, for both slip and no-slip boundary conditions you have no normal flow if the boundary is solid and impermeable.

However, the problem I have is that some say that if you have the no normal flow condition, then the stream function is constant regardless of whether it is a slip/no-slip boundary (http://scicomp.stackexchange.com/qu...non-symmetric-obstacle-using-stream-functions). My lecturer however said that the stream function is constant only when it is a slip boundary. Any thoughts? Who is correct?
 
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TomBolton10 said:
Hi, I am studying fluid mechanics and I am trying to get to grips with slip and no-slip boundaries.

I know that:

Slip ---> Occurs when fluid is inviscid so no viscous stress at boundary.
No-slip ---> Viscous effects mean the the tangential velocity must be zero, relative to the boundary.

Also, for both slip and no-slip boundary conditions you have no normal flow if the boundary is solid and impermeable.

However, the problem I have is that some say that if you have the no normal flow condition, then the stream function is constant regardless of whether it is a slip/no-slip boundary (http://scicomp.stackexchange.com/qu...non-symmetric-obstacle-using-stream-functions). My lecturer however said that the stream function is constant only when it is a slip boundary. Any thoughts? Who is correct?

Your lecturer is wrong, and what "some say" is correct. Just look at the relationship between stream function and velocity to see this. unormal=-∂ψ/∂x, where x is the coordinate along the wall.

Look up in the literature the solutions for inviscid- and viscous flow past a sphere. In both cases, the stream function is constant on the sphere.

Chet
 

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