NON-CONTACT SEAL FOR ROTATIONAL EQUIPMENT WITH RADIAL THROUGH-HOLE

An assembly (30) is provided for rotational equipment. This assembly includes a plurality of seal shoes (64), a seal base (62) and a plurality of spring elements (66). The seal shoes (64) are arranged about a centerline (32) in an annular array. The seal shoes (64) include a first seal shoe (64) configured with an aperture (88) that extends radially through the first seal shoe (64). The seal base (62) circumscribes the annular array of seal shoes (64). The spring elements (66) include a first spring element (66). The first spring element (66) includes a first mount (114), a second mount (116) and a spring beam (118). The first mount (114) is connected to the first seal shoe (64). The second mount (116) is connected to the seal base (62). The spring beam (118) extends laterally between and is connected to the first mount (114) and the second mount (116).