A pressurized water reactor vessel having a flow skirt formed from a perforated cylinder structure supported in the lower reactor vessel head at the outlet of the downcomer annulus, that channels the coolant flow through flow holes in the wall of the cylinder structure. The flow skirt is supported at a plurality of circumferentially spaced locations on the lower reactor vessel head that are not equally spaced or vertically aligned with the core barrel attachment points, and the flow skirt employs a unique arrangement of hole patterns that assure a substantially balanced pressure and flow of the coolant over the entire underside of the lower core support plate.