  Background: The near-equilibrium properties of a QCD plasma can be encoded
into transport coefficients such as bulk and shear viscosity. In QCD, the ratio
of these transport coefficients to entropy density, $\zeta/s$ and $\eta/s$,
depends non-trivially on the plasma's temperature.
  Purpose: We show that in a 0+1D boost-invariant fluid, a
temperature-dependent $\zeta/s(T)$ or $\eta/s(T)$ can be described by an
equivalent effective viscosity $\left\langle \zeta/s
\right\rangle_{\textrm{eff}}$ or $\left\langle \eta/s
\right\rangle_{\textrm{eff}}$. We extend the concept of effective viscosity in
systems with transverse expansion, and discuss how effective viscosities can be
used to identify families of $\zeta/s(T)$ and $\eta/s(T)$ that lead to similar
hydrodynamic evolution.
  Results: In 0+1D, the effective viscosity is expressed as a simple integral
of $\zeta/s(T)$ or $\eta/s(T)$ over temperature, with a weight determined by
the speed of sound of the fluid. The result is general for any equation of
state with a moderate temperature dependence of the speed of sound, including
the QCD equation of state. In 1+1D, a similar definition of effective viscosity
is obtained in terms of characteristic trajectories in time and transverse
direction. This leads to an infinite number of constraints on an infinite
functional space for $\zeta/s(T)$ and $\eta/s(T)$.
  Conclusions: The definition of effective viscosity in a 0+1D system clarifies
how infinite families of $\zeta/s(T)$ and $\eta/s(T)$ can result in nearly
identical hydrodynamic temperature profiles. By extending the study to a
boost-invariant cylindrical (1+1D) fluid, we identify an approximate but more
general definition of effective viscosity that highlight the potential and
limits of the concept of effective viscosity in fluids with limited symmetries.
