Shear stress direction and the velocity gradient

yes, understood , this is for steady flow right?
 
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yes, understood , this is for steady flow right?
Yes. So now what do you get if you divide the equation by ##2\pi r \delta r \delta z## and then take the limit as ##\delta r## and ##\delta z## approach zero?
 
Sir , I think there should not be ##\delta_{z}## in the third term of force balance in which we have pressure
 
##\frac 1 r## ##\frac {dr\tau_{rz}} {dr}## + ##\frac {dp} {dz}## , this is what I'm getting sir .
 
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##\frac 1 r## ##\frac {dr\tau_{rz}} {dr}## + ##\frac {dp} {dz}## , this is what I'm getting sir .
Excellent. So now you have some actual experience at applying the Cauchy Stress Relationship to a problem. Does that help answering your questions?
 
sir but how to get the term in #19 ? and sir one more doubt If we have a cubical element how we are gonna write the term #19 ? Is it going to remain the same??
 
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sir but how to get the term in #19 ? and sir one more doubt If we have a cubical element how we are gonna 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.
 
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.
 
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can you just give me the result for stress tensor of cubical and parallelopiped one ? It would be so nice of you . Thanks
 

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