Say, we have bottled viscous liquid - such as a dishwashing liquid. There are two different caps for the bottle. One with a smaller hole, one with slightly bigger hole. Both holes are very small though.
Now, we invert the bottle with cap 1 on (smaller hole) then again with cap 2 (slightly bigger hole) .
Will the same liquid exhibit different (apparent viscosity) or same?
(What's apparent viscosity?)
The regular, diffusive viscosity, of dimension $m^2/s$ that appears in the Navier-Stokes equations divided by $\rho$, is mainly dependent on temperature in most newtonian fluids.
If your fluid is non-newtonian, then the viscosity is a function of stress, and it will change its value relative to how much it can relax, i.e. it is going to be a function of your hole diameter.
