Finding the constant in the velocity function?

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Homework Help Overview

The discussion revolves around determining the constant 'a' in a velocity function, with references to wall equations and the concept of "no slip" conditions in fluid dynamics.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants express confusion about the relationship between wall equations and the velocity function, questioning how the velocity function could be arbitrary. There is also inquiry into the meaning of "no slip at the walls" and its implications for the velocity at those boundaries.

Discussion Status

Participants are actively engaging with the concepts, seeking clarification on the definitions and relationships involved. Some guidance has been offered regarding the "no slip" condition, but there is no explicit consensus on the connection to the constant 'a' or the velocity function.

Contextual Notes

There is a focus on understanding the implications of boundary conditions in fluid dynamics, particularly how they relate to the velocity function and the constant 'a'.

theBEAST
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Homework Statement


I am confused about how to get the constant a in this equation.
A9UENXX.png


The Attempt at a Solution


Apparently you can get the constant a from the wall equations. However I don't see how the wall equations are related to the velocity function. The velocity function could have been ANY arbitrary function right? So how can it be related to something else?
 
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theBEAST said:

Homework Statement


I am confused about how to get the constant a in this equation.
A9UENXX.png


The Attempt at a Solution


Apparently you can get the constant a from the wall equations. However I don't see how the wall equations are related to the velocity function. The velocity function could have been ANY arbitrary function right? So how can it be related to something else?
What does "no slip at the walls" mean?

Does it mean that the water flow right along each wall is zero?
 
theBEAST said:

Homework Statement


I am confused about how to get the constant a in this equation.
A9UENXX.png


The Attempt at a Solution


Apparently you can get the constant a from the wall equations. However I don't see how the wall equations are related to the velocity function. The velocity function could have been ANY arbitrary function right? So how can it be related to something else?

No slip at the walls means that u = 0 when (y,z) lies on either wall. We also have u = 0 when y = a + |z|.
 
Ray Vickson said:
No slip at the walls means that u = 0 when (y,z) lies on either wall. We also have u = 0 when y = a + |z|.

Wow cool, thank you :)
 

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