Why do we say that the viscous force between the flow of two different fluids is the same, in the boundary conditions? Shouldn't it be symmetric, once there must be an action reaction from the 3rd law?Boundary condition
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1$\begingroup$ The fluid above exerts a shear force in one direction, and the fluid below exerts a shear force in the opposite direction. This follows from applying the Cauchy stress relation to the stress tensor on both sides of the surface. The normal and tangential components of the stress tensor are continuous across the interface, but, with this condition being satisfied, the Cauchy stress relation tells us that the upper fluid exerts a shear force in one direction on the interface and the lower fluid exerts a shear force in the opposite direction. Look up "Cauchy stress relationship." $\endgroup$– Chet MillerCommented Oct 27, 2017 at 18:50
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$\begingroup$ @ChesterMiller That looks like an answer, not a comment. $\endgroup$– sammy gerbilCommented Oct 27, 2017 at 21:00
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$\begingroup$ @GeorgeSailor Who is the "we" you are referring to? If you are questioning a textbook, please can you provide a reference and ideally also upload an image of the relevant text? $\endgroup$– sammy gerbilCommented Oct 27, 2017 at 21:02
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The fluid above exerts a shear force on the interface in one direction, and the fluid below exerts a shear force in the opposite direction. This follows from applying the Cauchy stress relation to the stress tensor on both sides of the surface. The normal and tangential components of the stress tensor are continuous across the interface, but, with this condition being satisfied, the Cauchy stress relation tells us that the upper fluid exerts a shear force in one direction on the interface and the lower fluid exerts a shear force in the opposite direction. Look up "Cauchy stress relationship." Use of the Cauchy stress relationship guarantees (among other things) that Newton's 3rd law is automatically satisfied at a surface.
answered Oct 27, 2017 at 21:11