  When electrons flow as a viscous fluid in anisotropic metals, the reduced
symmetry can lead to exotic viscosity tensors with many additional, nonstandard
components. We present a viscometry technique that can, in principle, measure
the multiple dissipative viscosities allowed in isotropic and anisotropic
fluids alike. By applying representation theory to exploit the intrinsic
symmetry of the fluid, our viscometry is also exceptionally robust to both
boundary complications and ballistic effects. We present the technique via the
illustrative example of dihedral symmetry, relevant in this context as the
point symmetry of 2D crystals. Finally, we propose a present-day realizable
experiment for detecting, in a metal, a novel hydrodynamic phenomenon: the
presence of rotational dissipation in an otherwise isotropic fluid.
