Shear stress direction and the velocity gradient

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The discussion focuses on the behavior of fluid flow in laminar conditions, specifically examining stress in a cylindrical fluid element within a pipe. It highlights the relationship between shear stress, viscosity, and velocity gradients, emphasizing how shear stress acts in different directions depending on the radial position within the fluid. The Cauchy stress relationship is introduced to explain how stress can be determined on surfaces of arbitrary orientation, with a focus on applying this concept to specific problems in fluid dynamics. Participants also engage in clarifying the implications of traction vectors and the stress tensor for both cylindrical and cubical fluid elements. Overall, the conversation aims to deepen understanding of fluid mechanics principles and their mathematical representations.
  • #31
sir but how to get the term in #19 ? and sir one more doubt If we have a cubical element how we are going to write the term #19 ? Is it going to remain the same??
 
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  • #32
Rahulx084 said:
sir but how to get the term in #19 ? and sir one more doubt If we have a cubical element how we are going to write the term #19 ? Is it going to remain the same??
The term in #19 follows from the equations for the stress tensor components for a viscous Newtonian fluid. Are you familiar with these equations?

When you have a cubical element (or rectangular parallelepiped), you use the stress tensor in component form for Cartesian coordinates.
 
  • #33
I think I'm not familiar with that. Actually sir this isn't in my course but I'm learning it because it seems so interesting plus your great explanations . Can you provide me with only the results of cubical element or if there is any source where I can find it so that I can look after , or maybe you tell me sir.
 
  • #34
Rahulx084 said:
I think I'm not familiar with that. Actually sir this isn't in my course but I'm learning it because it seems so interesting plus your great explanations . Can you provide me with only the results of cubical element or if there is any source where I can find it so that I can look after , or maybe you tell me sir.
See page 29 of http://web.mit.edu/2.25/www/pdf/viscous_flow_eqn.pdf
 
  • #35
can you just give me the result for stress tensor of cubical and parallelopiped one ? It would be so nice of you . Thanks
 
  • #36
Rahulx084 said:
can you just give me the result for stress tensor of cubical and parallelopiped one ? It would be so nice of you . Thanks
See Eqns. 43 of that same reference.
 

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