The present subject matter relates to a method and an apparatus in the form of a machine system (1200) for machining a component (100) with an internal passage (115). In an aspect, the method comprises periodically injecting 5 abrasive slurry back and forth through the internal passage (115) at a pressure ranging from about 25 bar to about 35 bar. The abrasive slurry comprises a mixture of abrasive particles having a size in the range of about 40 μm to about 60 μm, and a slurry medium. The volume fraction of the abrasive particles in the slurry medium is about 40% to about 50%. Further, the injection of the abrasive 10 slurry is performed for a predefined number of process cycles at predetermined time versus pressure changes to obtain the component having a final average surface roughness of less than about 3.0 μm.