EuroCirCol is a conceptual design study of a Future Circular Collider (FCC-hh) which aims to expand the current energy and luminosity frontiers that the LHC has established. The vacuum chamber of this 50 TeV, 100 km collider, will have to cope with unprecedented levels of synchrotron radiation power for proton colliders, dealing simultaneously with a tighter magnet aperture. Since the high radiation power and photon flux will release large amounts of gas into the system, the difficulty to keep a low level of residual gas density increases considerably compared with the LHC. This article presents a study of the beam induced vacuum effects for the FCC-hh novel conditions, the different phenomena which, owing to the presence of the beam, have an impact on the vacuum level of the accelerator. To achieve this, a novel beam screen has been proposed, featuring specific mitigating measures aimed at dealing with the beam induced effects. It is concluded that thanks to the new beam screen design, the vacuum level in the FCC-hh shall be adequate, allowing to reach the molecular density requirement of better than 1×1015 H2/m3 with baseline beam parameters within the first months of conditioning