  We evaluate the viscous damping of anisotropic flow in heavy-ion collisions
for arbitrary temperature-dependent shear and bulk viscosities. We show that
the damping is solely determined by effective shear and bulk viscosities, which
are weighted averages over the temperature. We determine the relevant weights
for nucleus-nucleus collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and 200 GeV,
corresponding to the maximum LHC and RHIC energies, by running ideal and
viscous hydrodynamic simulations. The effective shear viscosity is driven by
temperatures below $210$ MeV at RHIC, and below $280$ MeV at the LHC, with the
largest contributions coming from the lowest temperatures, just above
freeze-out. The effective bulk viscosity is driven by somewhat higher
temperatures, corresponding to earlier stages of the collision. We show that at
a fixed collision energy, the effective viscosity is independent of centrality
and system size, to the same extent as the mean transverse momentum of outgoing
hadrons. The variation of viscous damping is determined by Reynolds number
scaling.
