  We investigate a variety of different polymer solutions in shear and
elongational flow. The shear flow is created in the cone-plate-geometry of a
commercial rheometer. We use capillary thinning of a filament that is formed by
a polymer solution in the Capillary Breakup Extensional Rheometer (CaBER) as an
elongational flow. We compare the relaxation time and the elongational
viscosity measured in the CaBER with the first normal stress difference and the
relaxation time that we measured in our rheometer. All of these four quantities
depend on different fluid parameters - the viscosity of the polymer solution,
the polymer concentration within the solution, and the molecular weight of the
polymers - and on the shear rate (in the shear flow measurements).
Nevertheless, we find that the first normal stress coefficient depends
quadratically on the CaBER relaxation time. A simple model is presented that
explains this relation.
