the channel in which the current of water driving a mill wheel flows to the mill.
the current itself.

1470–80; mill1 + race1 Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
millrace or millrun (ˈmɪlˌreɪs)
1.  the current of water that turns a millwheel
2.  the channel for this water
millrun or millrun

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Example sentences
Near the sawmill shore, near what might have been safety, the ice simply ended
  in a deep flow of river water from the millrace.
Millrace employs two in addition to the company's owners.
Next they set to work deepening the stream so that the millrace would have
  adequate power.
Years before, this shallow ditch on the shortest line between river and swamp
  had been used as a millrace.
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