# Shear Stress on Rough Surface

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 October 7, 2021, 04:45 Shear Stress on Rough Surface #1 New Member   Boqi Ren Join Date: Aug 2018 Posts: 2 Rep Power: 0 Hi everyone I'm writing here to ask some questions about the calculation of wall shear stress on the rough surface. As we know, the definition of wall shear stress is so for the rough surface, can I calculate the shear stress in the following way? Where t means the tangential direction of the local surface, and n means the normal direction. And, could you recommend some relative reference to me? THANK YOU VERY MUCH! Last edited by Sylorn; October 7, 2021 at 04:57. Reason: to correct the formulations

October 7, 2021, 11:05
#2
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
 Originally Posted by Sylorn Hi everyone I'm writing here to ask some questions about the calculation of wall shear stress on the rough surface. As we know, the definition of wall shear stress is so for the rough surface, can I calculate the shear stress in the following way? Where t means the tangential direction of the local surface, and n means the normal direction. And, could you recommend some relative reference to me? THANK YOU VERY MUCH!

Since the surface is rough you should evaluate the normal derivative at x=x(s), y=y(s), not at y=0.
The action of the stress can be better see if you write the contribution of the stress tensor on a finite surface:

Int[S] n.Td dS

Td being the deviatoric part having zero trace.

October 7, 2021, 23:45
#3
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Boqi Ren
Join Date: Aug 2018
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Quote:
 Originally Posted by FMDenaro Since the surface is rough you should evaluate the normal derivative at x=x(s), y=y(s), not at y=0. The action of the stress can be better see if you write the contribution of the stress tensor on a finite surface: Int[S] n.Td dS Td being the deviatoric part having zero trace.
FMDenaro, Thank you very much!
Yes, as you said, the wall shear stress should be on the wall, so in the second equation, y=0 is not correct.
But I still feel confused with . Could you explain this term in more detail?

October 8, 2021, 11:25
#4
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Lucky
Join Date: Apr 2011
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Quote:
 Originally Posted by Sylorn FMDenaro, Thank you very much! Yes, as you said, the wall shear stress should be on the wall, so in the second equation, y=0 is not correct. But I still feel confused with . Could you explain this term in more detail?

It's the tensor form of shear stress. du/dy the way Isaac Newton did it is for 1D.

 Tags rough wall, shear stress