B Pressure in a viscous liquid versus non-viscous fluids

[Kashmir]

Hc verma, concepts of Physics, vol 1 pg 258
"We define pressure of fluid at the point A as : $P= F/\Delta S$
For a homogeneous and non-viscous fluid, this quantity does not depend on orientation of $\Delta S$ and hence we talk of pressure at a point".

Why did the author stress that the definition holds only for non-viscous fluids?
What happens to viscous fluids? Does the pressure depend on orientation in viscous fluids ?

 

[Chestermiller]

Are you familiar with with the constitutive equation (rheological equation of state) for a Newtonian fluid in 3D in terms of the fluid viscosity, "pressure," and velocity gradient tensor? This is the more general version of Newton's law of viscosity that we learned about in freshman physics, and forms the basis of most of the fluid dynamics that we work with in practice. It includes not only shear stresses, but normal stress as well. The Newtonian fluid model reduces to an isotropic stress tensor (pressure) in the limit of static equilibrium.

 

[Kashmir]

Are you familiar with with the constitutive equation (rheological equation of state) for a Newtonian fluid in 3D in terms of the fluid viscosity, "pressure," and velocity gradient tensor? This is the more general version of Newton's law of viscosity that we learned about in freshman physics, and forms the basis of most of the fluid dynamics that we work with in practice. It includes not only shear stresses, but normal stress as well. The Newtonian fluid model reduces to an isotropic stress tensor (pressure) in the limit of static equilibrium.

Thank you.
No, I've not studied it.

 

[Chestermiller]

Thank you.
No, I've not studied it.

See Transport Phenomena by Bird et al