I have calculated the shear stress at the wall of a circular pipe to be independent of the viscosity, and I am just curious as to the significance of this result. I have assumed constant pressure gradient.
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anyone can help out? – MathematicianP May 31 '19 at 10:44
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Independent under what assumptions? Fixed pressure gradient, volumetric flux? – Radost May 31 '19 at 11:01
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Sorry I have edited the question – MathematicianP May 31 '19 at 11:58
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For a constant pressure gradient in steady state case there is no acceleration of the fluid. This means that the forces have to be in balance for the fluid encased by a section of the pipe of specified length. This allows to compute the force just knowing the pressure gradient, pipe cross section, and pipe length. (As pressure at the ends and viscous interaction with the walls are the only forces in the system).
Radost
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This is just momentum conservation. In steady state fluid is not accelerating therefore forces acting on the fluid are in balance. If we had no interaction with walls then fluid would accelerate due to pressure gradient. This is counteracted by the walls. As you can see value of viscosity doesn't come into this logic, just the fact that this is how walls slow down the fluid. – Radost May 31 '19 at 22:43