The concept of ''effective viscosity'' $\nueff$ of superfluid helium, widely used to interpret decaying turbulence, is tested in the steady-state case. We deduce $\nueff$ from measurements of vortex line density, $\LL$, in a grid flow. The scaling of $\LL$ with velocity confirms the validity of the heuristic relation defining $\nueff$, $\epsilon = \nueff \left(\kappa \LL\right)^2$, where $\epsilon$ is the energy dissipation rate and $\kappa$ the circulation quantum. Within $1.17\, - 2.16\,{\rm K}$, $\nueff$ is consistent with that from decays, allowing for uncertainties in flow parameters. Numerical simulations of the two-fluid equations yield a second estimation of $\nueff$ within an order of magnitude with all experiments. Its temperature dependence, more pronounced in numerics than experiments, shows a cross-over from a viscous-dominated to a mutual-friction-based dissipation as temperature decreases, supporting the idea that the effective viscosity of a quantum turbulent flow is an indicator of the dissipative mechanisms at play.