Middle English dreinen, from Old English dreahnian "to draw off gradually, as a liquid; remove by degrees; strain out," from Proto-Germanic *dreug-, source of drought, dry, giving the English word originally a sense of "to make dry." Figurative meaning of "exhaust" is attested from 1650s. Intransitive sense of "to flow off gradually" is from 1580s. Related: Drained; draining.
early 14c., dreine, "passage, pipe, or open channel for the removal of water or other liquid," from drain (v.). From 1721 as "act of draining, gradual or continuous outflow," usually figurative, of money, resources, etc. Colloquial expression down the drain "lost, vanished, gone to waste" is by 1930.