This study uses HI image data from the WALLABY pilot survey with the ASKAP telescope, covering the Hydra cluster out to 2.5$r_{200}$. We present the projected phase-space distribution of HI-detected galaxies in Hydra, and identify that nearly two thirds of the galaxies within $1.25r_{200}$ may be in the early stages of ram pressure stripping. More than half of these may be only weakly stripped, with the ratio of strippable HI (i.e., where the galactic restoring force is lower than the ram pressure in the disk) mass fraction (over total HI mass) distributed uniformly below 90%. Consequently, the HI mass is expected to decrease by only a few 0.1 dex after the currently strippable portion of HI in these systems has been stripped. A more detailed look at the subset of galaxies that are spatially resolved by WALLABY observations shows that, while it typically takes less than 200 Myr for ram pressure stripping to remove the currently strippable portion of HI, it may take more than 600 Myr to significantly change the total HI mass. Our results provide new clues to understanding the different rates of HI depletion and star formation quenching in cluster galaxies.
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