Old English sincan (intransitive) "become submerged, go under, subside" (past tense sanc, past participle suncen), from Proto-Germanic *senkwan (source also of Old Saxon sinkan, Old Norse sökkva, Middle Dutch sinken, Dutch zinken, Old High German sinkan, German sinken, Gothic sigqan), from PIE root *sengw- "to sink."
The transitive use (mid-13c.) supplanted Middle English sench (compare drink/drench) which died out 14c. Related: Sank; sunk; sinking. Sinking fund is from 1724. Adjective phrase sink or swim is from 1660s. To sink without a trace is World War I military jargon, translating German spurlos versenkt.
early 15c., "cesspool, pit for reception of wastewater or sewage," from sink (v.). Figurative sense of "place where corruption and vice abound" is from 1520s. Meaning "drain for carrying water to a sink" is from late 15c. Sense of "shallow basin (especially in a kitchen) with a drainpipe for carrying off dirty water" first recorded 1560s. In science and technical use, "place where heat or other energy is removed from a system" (opposite of source), from 1855.