In fluid dynamics, always when some textbook talks about stress tensor, there is a figure like this: 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 τxz should be equal to τzx: the overall torque of the system be zero, thus no rotation (?). But I don't understand why there have to be two σz, one acting on the upper x-y surface and one acting on the lower x-y surface and these two σz have opposite directions, thus they cancel out??? (the same question for σx and σy) 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!!!!!