Significance of independence of viscosity and viscosity

Question

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.

Answer 1

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).