v = [root](2g/[zeta]) [root](mi) = c [root](mi); (2a)
where c is a coefficient depending on the roughness and form of the
channel.
The coefficient of friction [zeta] varies greatly with the degree of
roughness of the channel sides, and somewhat also with the velocity.
It must also be made to depend on the absolute dimensions of the
section, to eliminate the error of neglecting the variations of
velocity in the cross section. A common mean value assumed for [zeta]
is 0.00757. The range of values will be discussed presently.
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 [zeta] in (2a), we get the very
simple and long-known approximate formula for the mean velocity of a
stream--
v = ¼ ½ [root](2mf). (3)