Abstract: A slurry polishing apparatus (100) comprises an assembly of an upper slurry input/output section (108), a polishing section (110), and a lower slurry input/output section (112). Each of the apparatus sections are individually detachable from the assembly to facilitate insertion and removal of a hydrodynamic or aerodynamic machine part having a complex surface shape such as a turbine fan (102). A plurality of upper slurry deflector blades (124) and lower slurry deflector blades (126) are removably attached to the polishing section (110), and positioned in the slurry flow path so as to direct the slurry mixture evenly over the entire surface of each respective fan blade (104), and corresponding exposed intermediary rotor surface (106). Because the high pressure slurry mixture flows evenly over the exposed fan surfaces, a consistent removal of metal stock is achieved across the entire polished surface.