An orifice pack is provided for delivering pressurized air to a compressor bleed valve of a gas turbine engine. The orifice pack has a diffusion chamber in serial flow communication with a tapering passage and a first outlet passage for venting a first portion of the pressurized air from the diffusion chamber. A second outlet passage branches off from the diffusion chamber at an axial location between the inlet and the tapering passage. The second outlet passage is fluidly connected to the compressor bleed valve for directing a second portion of the pressurized air from the diffusion chamber to the compressor bleed valve.