  We explore the possibility of simulating the grade-two fluid model in a
geometry related to a contraction rheometer, and we provide details on several
key aspects of the computation. We show how the results can be used to
determine the viscosity $\nu$ from experimental data. We also explore the
identifiability of the grade-two parameters $\alpha_1$ and $\alpha_2$ from
experimental data. In particular, as the flow rate varies, force data appears
to be nearly the same for certain distinct pairs of values $\alpha_1$ and
$\alpha_2$; however we determine a regime for $\alpha_1$ and $\alpha_2$ for
which the parameters may be identifiable with a contraction rheometer.
