  We investigate the expansion dynamics of a dilute Fermi gas at unitarity in
the context of dissipative fluid dynamics. Our aim is to quantify the effects
of shear viscosity on the time evolution of the system. We compare exact
numerical solutions of the equations of viscous hydrodynamics to various
approximations that have been proposed in the literature. Our main findings
are: i) Shear viscosity leads to characteristic features in the expansion
dynamics; ii) a quantitative description of these effects has to include
reheating; iii) dissipative effects are not sensitive to the equation of state
P(n,T) as long as the universal relation P=(2/3)E is satisfied; iv) the
expansion dynamics mainly constrains the cloud average of the shear viscosity.
