We report the apparent viscosity of aqueous solutions of a well-charac
terized synthetic polyelectrolyte, the sodium salt of polystyrene sulf
onate. Using two rheometers we measure the apparent viscosity over mor
e than five decades of shear rate to determine the Newtonian viscosity
and the onset of shear thinning, which is inversely proportional to t
he relaxation time. We study five decades of polyelectrolyte concentra
tion, from the dilute to the entangled regimes, and three decades of a
dded salt (NaCl) concentration, on a single polyelectrolyte sample. Mu
ch of the viscosity data in the literature are shown to be in the shea
r thinning regime and are not indicative of the Newtonian viscosity. O
ur data for viscosity and longest relaxation time are qualitatively co
nsistent with a recent scaling theory. There are systematic deviations
from this simple theory, including the failure of the well-establishe
d Fuoss law, which is shown to be obeyed by the apparent viscosity onl
y at higher shear rates.