  We present 3D hydrodynamical simulations of ram pressure stripping of a disc
galaxy orbiting in a galaxy cluster. In this paper, we focus on the properties
of the galaxies' tails of stripped gas. The galactic wakes show a flaring
width, where the flaring angle depends on the gas disc's cross-section with
respect to the galaxy's direction of motion. The velocity in the wakes shows a
significant turbulent component of a few 100 km/s. The stripped gas is
deposited in the cluster rather locally, i.e. within ~150 kpc from where it was
stripped. We demonstrate that the most important quantity governing the tail
density, length and gas mass distribution along the orbit is the galaxy's mass
loss per orbital length. This in turn depends on the ram pressure as well as
the galaxy's orbital velocity. For a sensitivity limit of ~10^19 cm^-2 in
projected gas density, we find typical tail lengths of 40 kpc. Such long tails
are seen even at large distances (0.5 to 1 Mpc) from the cluster centre. At
this sensitivity limit, the tails show little flaring, but a width similar to
the gas disc's size. Morphologically, we find good agreement with the HI tails
observed in the Virgo cluster by Chung et al. (2007). However, the observed
tails show a much smaller velocity width than predicted from the simulation.
The few known X-ray and H$\alpha$ tails are generally much narrower and much
straighter than the tails in our simulations. Thus, additional physics like a
viscous ICM, the influence of cooling and tidal effects may be needed to
explain the details of the observations. We discuss the hydrodynamical drag as
a heat source for the ICM but conclude that it is not likely to play an
important role, especially not in stopping cooling flows.
