It is often convenient to estimate the fall of the stream in feet per mile, instead of in feet per foot. If f is the fall in feet per mile,
f = 5280 i.
Putting this and the above value of ζ in (2a), we get the very simple and long-known approximate formula for the mean velocity of a stream—
v = 1⁄4 1⁄2 √ (2mf).
(3)
The flow down the stream per second, or discharge of the stream, is
Q = Ωv = Ωc √ (mi).
(4)
§ 97. Coefficient of Friction for Open Channels.—Various expressions have been proposed for the coefficient of friction for channels as for pipes. Weisbach, giving attention chiefly to the variation of the coefficient of friction with the velocity, proposed an expression of the form
ζ = α (1 + β/v),