1650s, "act or process of draining," from drain (v.) + -age. Sense of "the water carried off by a system of rivers" is by 1860. Meaning "system by means of which something is drained" is by 1878.
Entries linking to drainage
drain v.
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.
-age
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).