Fairly certain there is something here in De architectura http://www.gutenberg.org/files/20239/20239-h/29239-h.htm

Searched for you, page 244 "let the bed of the channel have a gradient of not less than a quarter of an inch for every hundred feet"

The next question is 'why,' and in this Vitruvius has always be a little light in the details. He was a pragmatist and it was because it was what worked.

Chapter 4 explains how they found the gradient.

Interesting enough, Vitruvius also advised to not use lead pipes for drinking water (ahem... Flint; 2,000 years later) "Hence, water ought by no means to be conducted in lead pipes, if we want to have it wholesome."