38 The: Colorado Experiment Station. 
ratio between the cross-section of the channel, and the length of the 
line of contact between the water and the surface. This ratio is 
termed the “hydraulic mean depth” or the “hydraulic mean radius” 
and is represented in formulas by “r.” 
The velocity also increases with the slope or inclination which 
is represented by “S” or “i,” and is the fall per 100 feet expressed 
decimally. 
The relation between the velocity and the hydraulic radius and 
slope is not a direct one, that is, doubling the fall does not double 
the velocity. But to double the velocity, the fall must be four 
times as great, or the hydraulic radius four times as great as before. 
The condition of the surface of the channel in contact with the 
water also affects the velocity, for where the surface is rough it is 
visibly reduced. While such a relation was perceived, the old 
formulae attempted to include the first two relations only, and 
became 
V = C ]/ ri 
The coefficient “c” was given values based on what experience 
had shown as applicable. There were commonly three values of 
“c” used, for small, for moderate and for large canals, and the 
results were very unsatisfactory. 
Some fifty years ago two French engineers with the aid of the 
government made an elaborate series of tests on a small canal 
where the conditions could be changed, and especially the surface 
of the channel. Darcy and Bazin were the names of these engineers, 
and from the tests, all on small channels, none over three feer wide, 
obtained the effect from varying the surface. They made a num¬ 
ber of classes depending on the surface and produced a formula 
which is still extensively used by French and Italian engineers, 
The formula did not give sufficient guide to engineers to apply 
the formula to the numerous conditions arising in practice. 
Kutter’s formula is another step to determine the value of “c” 
to be used. It is based on the work of Darcy and Bazin, but 
attempts to express the complicated relations between this coef¬ 
ficient and the size of the channel, the grade, and the roughness (by 
introducing a coefficient of roughness), all of which have an influ¬ 
ence. The relation is complex, but it is not necessary to give here 
as the value is always found by the use of tables. 
The coefficient of roughness is represented by “n.” It varies 
from .009 from smoothest boards to .035 for a rough canal in poor 
order. For most open channels with which we have to do in irri¬ 
gation it is comprised between .018 and .030, or commonly between 
.020 and .025. The results obtained depend entirely on the selec¬ 
tion of “n,” and the choice of this requires knowledge of the value 
