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In hydrostatics it's easy to prove that normal stress is independent of orientation of surface at a particular point as there is no shear stress there. It's derivation is also simple where we take a tetrahedron and then prove it. So pressure is a scalar quantity there. My doubt is in fluid dynamics when viscosity comes in picture will this hold true? Because then there will be shear stresses. Hence can we say pressure is orientation independent for viscous flowing fluid?

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Normal stress generally depends on orientation of the surface. You can decompose any stress tensor into sum of hydrostatic and deviatoric parts. Hydrostatic part has only normal stresses which are equal in every direction (orientation independent), but the deviatoric part depends on orientation and has in general normal as well as shear stresses. Hydrostatics is a special case, where the tensor has only this hydrostatic part, so normal stress components of the tensor have the same value for any orientation.

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