In fluid dynamics, always when some textbook talks about stress tensor, there is a figure like this:(adsbygoogle = window.adsbygoogle || []).push({});

http://www.fea-optimization.com/ETBX/hooke_help_files/stress.gif [Broken]

it shows how stress tensor is defined based on a small cubic volume.

I kind of understand why the shear stress τ_{xz}should be equal to τ_{zx}: the overall torque of the system be zero, thus no rotation (?).

But I don't understand why there have to be two σ_{z}, one acting on the upper x-y surface and one acting on the lower x-y surface and these two σ_{z}have opposite directions, thus they cancel out??? (the same question for σ_{x}and σ_{y})

If the system has these forces acting on it (all shear stress cancel out-->no torque, no rotation; all normal stress cancel out-->no translational acceleration), the velocity of the system will not change at all... but in a moving fluid, there has to be acceleration right? OR what kind of systems is the stress tensor defined for? OR mathematically when you take the limit of volume->0, since fluid is continous, the force on two sides should be balanced???

Really confusing! Thanks a lot!!!!!

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# The way textbooks talk about stress tensor confused me

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