  Hydrodynamic flow occurs in an electron liquid when the mean free path for
electron-electron collisions is the shortest length scale in the problem. In
this regime, transport is described by the Navier-Stokes equation, which
contains two fundamental parameters, the bulk and shear viscosities. In this
Article we present extensive results for these transport coefficients in the
case of the two-dimensional massless Dirac fermion liquid in a doped graphene
sheet. Our approach relies on microscopic calculations of the viscosities up to
second order in the strength of electron-electron interactions and in the
high-frequency limit, where perturbation theory is applicable. We then use
simple interpolation formulae that allow to reach the low-frequency
hydrodynamic regime where perturbation theory is no longer directly applicable.
The key ingredient for the interpolation formulae is the "viscosity transport
time" $\tau_{\rm v}$, which we calculate in this Article. The transverse nature
of the excitations contributing to $\tau_{\rm v}$ leads to the suppression of
scattering events with small momentum transfer, which are inherently
longitudinal. Therefore, contrary to the quasiparticle lifetime, which goes as
$-1/[T^2 \ln(T/T_{\rm F})]$, in the low temperature limit we find $\tau_{\rm v}
\sim 1/T^2$.
