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.
word-forming element in nouns of act, process, function, condition, from Old French and French -age, from Late Latin -aticum "belonging to, related to," originally neuter adjectival suffix, from PIE *-at- (source of Latin -atus, past participle suffix of verbs of the first conjugation) + *-(i)ko-, secondary suffix forming adjectives (see -ic).
<a href="https://www.etymonline.com/word/drainage">Etymology of drainage by etymonline</a>
Harper, D. (n.d.). Etymology of drainage. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/drainage