  When measuring the observed pressure, density or temperature profiles of the
intracluster gas, and hence the mass of clusters of galaxies, projection
effects or departures from the spherical symmetry hypothesis may induce biases.
In order to estimate how strongly the cluster observed properties depend on the
direction of observation, we use a constrained hydrodynamical simulation of
Virgo cluster that replicates the actual cluster of galaxies. In this case
study, we analyse Virgo properties when they are projected along different
directions including along the Milky Way-Virgo axis which mimics our
observation direction. We compare the hydrostatic mass and the hydrostatic mass
bias from the projection along the different observation directions to that
derived from the 3D simulation. We show that projection effects impact the
determination of Virgo mass. We particularly demonstrate that the mass and
pressure along the line of sight correlates with the 2D and 3D-deprojected
electron density and pressure profiles intensity and thus impacts the derived
hydrostatic mass. We also show that the deviations to the hydrostatic
equilibrium induced by pressure discontinuities within the cluster are
emphasized by the deprojection process and thus makes the hydrostatic mass
estimation invalid at these radii.
