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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?

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  • $\begingroup$ Fill in the blank: The equation relating the stress tensor to the velocity gradient tensor of a viscous Newtonian fluid is given by ....................................................... $\endgroup$
    – Chet Miller
    May 18 at 9:22

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Pressure is the only surface force acting in an inviscid fluid. In a viscous fluid, you would also have viscous stress (which can be imagined as a friction force between the fluid and the surface). And while pressure is isotropic and doesn't depend on the surface orientation, viscous stress is in general non-isotropic, and it depends on the surface orientation.

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