Shear stress direction and the velocity gradient

[Rahulx084]

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??

 

[Chestermiller]

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.

 

[Rahulx084]

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.

 

[Chestermiller]

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

 

[Rahulx084]

can you just give me the result for stress tensor of cubical and parallelopiped one ? It would be so nice of you . Thanks

 

[Chestermiller]

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.