This discussion focuses on the shear stress direction and velocity gradient in laminar fluid flow, specifically within a cylindrical pipe. The shear stress is defined by the equation τ = μ(du/dy), where μ represents viscosity, du is the velocity difference, and dy is the distance between the top and bottom planes of a fluid slab. The Cauchy stress relationship is emphasized for determining stress on surfaces of arbitrary orientation, with specific attention given to the stress tensor components for a viscous Newtonian fluid. Participants are encouraged to consult resources such as "Transport Phenomena" by Bird, Stewart, and Lightfoot for deeper understanding.
PREREQUISITESFluid mechanics students, engineers working with fluid dynamics, and researchers focusing on viscous flow analysis will benefit from this discussion.
The term in #19 follows from the equations for the stress tensor components for a viscous Newtonian fluid. Are you familiar with these equations?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??
See page 29 of http://web.mit.edu/2.25/www/pdf/viscous_flow_eqn.pdfRahulx084 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 Eqns. 43 of that same reference.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