"current of water that drives a mill-wheel," late 15c., from mill (n.1) + race (n.1) in the "current" sense.
Entries linking to mill-race
mill n.1
Middle English mille, "building fitted to grind grain," Old English mylen "a mill" (10c.), an early Germanic borrowing from Late Latin molina, molinum "mill" (source of French moulin, Spanish molino), originally fem. and neuter of molinus "pertaining to a mill," from Latin mola "mill, millstone," related to molere "to grind," from PIE root *mele- "to crush, grind." The -n- gradually was lost in English but survives in the surname Milner. Also from Late Latin molina, directly or indirectly, are German Mühle, Old Saxon mulin, Old Norse mylna, Danish mølle, Old Church Slavonic mulinu.
The meaning "mechanical device for grinding grain for food" is from 1550s. The broader sense of "machine for grinding or pulverizing any solid substance" is attested from 1670s. Other types of manufacturing machines driven by wind or water, that transform raw material by a process other than grinding began to be called mills by early 15c. Sense of "large building fitted with machinery for manufacturing" is from c. 1500. In old slang also "a typewriter" (1913); "a boxing match or other pugilistic bout" (1819).
race n.1
[act of running] late Old English, also rase, "a narrative, an account;" c. 1300, "an act of swift running, a hurried attack," also "a course of life or conduct, a swift current;" from Old Norse rās "a running, a rush (of water)," cognate with Old English ræs "a running, a rush, a leap, jump; a storming, an attack;" or else a survival of the Old English word with spelling and pronunciation influenced by the Old Norse noun and the verb. The Norse and Old English words are from Proto-Germanic *res- (source also of Middle Dutch rasen "to rave, rage," German rasen, Old English raesettan "to rage" (of fire)), from a variant form of PIE *ers- (1) "be in motion" (see err).
Originally a northern word, it became general in English c. 1550. Formerly used more broadly than now, of any course which has to be run, passed over, or gone through, such as the course of time or events or a life (c. 1300) or the track of a heavenly body across the sky (1580s). To rue (one's) race (15c.) was to repent the course one has taken.
Meaning "contest of speed involving two or more competitors; competitive trial in running, riding, etc." is from 1510s. For the sense of "artificial stream leading water to a mill, etc.," see race (n.3). Meaning "electoral contest for public office" is by 1827.