  We present a detailed analysis of the velocity structure of the Virgo cluster
using {\it XMM-Newton} observations. Using a novel technique which uses uses
the Cu K$\alpha$ instrumental line to calibrate the EPIC-pn energy scale, we
are able to obtain velocity measurements with uncertainties down to $\Delta v
\sim 100$ km/s. We created 2D projected maps for the velocity, temperature,
metallicity, density, pressure and entropy with an spatial resolution of
0.25$'$. We have found that in the innermost gas there is a high velocity
structure, most likely indicating the presence of an outflow from the AGN while
our analysis of the cluster cool core using RGS data indicates that the
velocity of the gas agrees with the M87 optical redshift. An overall gradient
in the velocity is seen, with larger values as we move away from the cluster
core. The hot gas located within the western radio flow is redshifted, moving
with a velocity $\sim 331$ km/s while the hot gas located within the eastern
radio flow is blueshifted, with a velocity $\sim 258$ km/s, suggesting the
presence of backflows. Our results reveal the effects of both AGN outflows and
gas sloshing, in the complex velocity field of the Virgo cluster.
