  The MeerKAT Fornax Survey maps the distribution and kinematics of atomic
neutral hydrogen gas (HI) in the nearby Fornax galaxy cluster using the MeerKAT
telescope. The 12 deg^2 survey footprint covers the central region of the
cluster out to ~ Rvir and stretches out to ~ 2 Rvir towards south west to
include the NGC 1316 galaxy group. The HI column density sensitivity (3 sigma
over 25 km/s) ranges from 5e+19/cm^2 at a resolution of ~ 10" (~ 1 kpc at the
20 Mpc distance of Fornax) down to ~ 1e+18/cm^2 at ~ 1' (~ 6 kpc), and slightly
below this level at the lowest resolution of ~ 100" (~ 10 kpc). The HI mass
sensitivity (3 sigma over 50 km/s) is 6e+5 Msun. The HI velocity resolution is
1.4 km/s. In this paper we describe the survey design and HI data processing,
and we present a sample of six galaxies with long, one-sided, star-less HI
tails (of which only one was previously known) radially oriented within the
cluster and with measurable internal velocity gradients. We argue that the
joint properties of the HI tails represent the first unambiguous evidence of
ram pressure shaping the distribution of HI in the Fornax cluster. The
disturbed optical morphology of all host galaxies supports the idea that the
tails consist of HI initially pulled out of the galaxies' stellar body by tidal
forces. Ram pressure was then able to further displace the weakly bound HI and
give the tails their present direction, length and velocity gradient.
