Etymology
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Words related to run

*rei- 
Proto-Indo-European root meaning "to flow, run."

It forms all or part of: derive; ember-days; rennet (n.1); Rhine; rialto; rill; rio; rival; rivulet; run; runnel.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit rinati "causes to flow," ritih "stream, course;" Latin rivus "stream;" Old Church Slavonic reka "river;" Middle Irish rian "river, way;" Gothic rinnan "run, flow," rinno "brook;" Middle Low German ride "brook;" Old English riþ "stream;" Old English rinnan, Old Norse rinna "to run," Dutch ril "running stream."
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home run (n.)
1856, from home (n.) + run (n.).
long run (n.)

also long-run, "ultimate outcome," 1620s, from long (adj.) + run (n.); the notion is "when events have run their course," as in the phrase in the long run "after a long course of experience." As an adjective from 1804.

riverrun (n.)

"course a river shapes through a landscape," 1939, coined by Joyce; see river (n.) + run (n.).

runnel (n.)

"rivulet, small stream of water," 1570s (Hakluyt), an alteration (by influence of run) of Middle English ryneil, from Old English rinelle, rynel, a diminutive with -el (2) + ryne "a stream" (see run (n.)).

run-of-the-mill (adj.)

"ordinary, unspectacular," 1922, a figurative use of a commercial phrase attested by 1909 in reference to material yielded by a mill (n.1), etc., before sorting for quality (compare common run "usual, ordinary type," from 1712). From run (n.) on the notion of "a continuous stretch of grinding."

also-ran (n.)
1896, originally in reference to horse-races, from the verbal phrase, from also + past tense of run (v.). Probably from the way non-placing horses were listed in race results.
hit-and-run (adj.)
1940, in reference to military raids, etc., from hit (v.) + run (v.). As a noun phrase, Hit and run is from 1899 as a baseball play, 1924 as a driver failing to stop at an automobile accident he caused.
irritate (v.)
1530s, "stimulate to action, rouse, incite," from Latin irritatus, past participle of irritare "excite, provoke, annoy;" according to de Vaan, probably a verb from Proto-Italic *rito- "stirred," from the same PIE root that produced English run (v.). Meaning "annoy, make impatient" in English is from 1590s. The earlier verb in English was irrite (mid-15c.), from Old French irriter. Related: Irritated; irritating.
long-running (adj.)
1943, of theatrical productions, from long (adv.) + present participle of run (v.). Related: Longest-running.