When the shear rate stays fixed, doubling the viscosity doubles the stress in direct proportion. Both cases keep speed difference 8 m/s over gap 4 m for rate 2 reciprocal seconds, so changing viscosity from 4 to 8 Pa*s raises the stress from 8 to 16 Pa exactly for the stated toy Newtonian model; real viscoelastic flow can have non-Newtonian viscosity, nonuniform shear, wall slip, temperature dependence, and measurement uncertainty.
Holding shear rate fixed makes the viscosity contrast honest. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Hold the shear rate fixed
Both cases use speed difference 8 m/s over gap 4 m, so the rate stays 2 reciprocal seconds.
8/4=2
Double viscosity, double stress
Changing viscosity from 4 to 8 Pa*s changes stress from 8 to 16 Pa.