run off at the mouth

Old English muþ "mouth, opening, door, gate," from Proto-Germanic *munthaz (cf. Old Saxon, Old Frisian muth, Old Norse munnr, Danish mund, Middle Dutch mont, Dutch mond, Old High German mund, German Mund, Gothic munþs "mouth"), with characteristic loss of nasal consonant in Old English (cf. tooth, goose, etc.), from PIE *mnto-s (cf. Latin mentum "chin"). In the sense of "outfall of a river" it is attested from late Old English; as the opening of anything with capacity (a bottle, cave, etc.) it is recorded from c.1200. Mouth-organ attested from 1660s.