  We describe recent attempts to extract the shear viscosity of the dilute
Fermi gas at unitarity from experiments involving scaling flows. A scaling flow
is a solution of the hydrodynamic equations that preserves the shape of the
density distribution. The scaling flows that have been explored in the
laboratory are the transverse expansion from a deformed trap ("elliptic flow"),
the expansion from a rotating trap, and collective oscillations. We discuss
advantages and disadvantages of the different experiments, and point to
improvements of the theoretical analysis that are needed in order to achieve
definitive results. A conservative bound based on the current data is that the
minimum of the shear viscosity to entropy density ration is that eta/s is less
or equal to 0.5 hbar/k_B.

Quantum Gases;High Energy Physics - Phenomenology;Nuclear Theory