THE FLOW OF WATER IN IRRIGATION CHANNELS. 6 
flow and from that time the velocity remains quite 4 constant so long 
as the surrounding conditions are not changed. The tendency for 
the velocity to increase is just counteracted by the various retarding 
influences. 
The coefficient C was supposed to care for all of the various factors 
affecting the velocity, such as friction between the moving fdaments 
of water and the containing channel, but did not involve the slope 
and the mean hydraulic radius. 
At the present time the Chezy formula is, for the most part, used 
as a basis for the design of pipes and other closed conduits, while in 
the formula used for the design of open channels the value of C is 
elaborated as follows: 
i .mi. 4i.ee +0^028! 
° ijLi gg , 0-00281 1 n (2) 
Substituting this value hi formula (1) we have Kutter's formula, 
expressed in English measures: 
ri - 811 ^i aa , 0-00281 
+ 41 .66 + 
V 
n 
l+[41.66 + 5: 
s 
JVR 
VR s (3) 
In this form the formula takes into consideration the influence of 
hydraulic grade and of the mean hydraulic radius upon the coefficient 
C and introduces a new variable, n, which is supposed to represent all 
the retarding influences. 
In its elaborated form the above formula represents a vast amount 
of mathematical plotting and deduction by Wilhelm R. Kutter 
(1818-1888), aided by E. GanguiUet, both engineers in Berne, Switz- 
erland. 1 It was developed in 1869 from the data covering 81 different 
gaugings of rivers and canals, ranging from channels a few inches in 
width to the Mississippi River. 
In the use of this formula for the design of channels in which to 
convey water all of the variables are determined by the materials 
encountered, the location of the channel, and the form chosen with 
the exception of n, the factor representing the retarding influences. 
There is a wide range of values which may be assigned to this factor, 
the friction becoming greater in passing from smooth, planed boards 
through a list of such materials as concrete, mesonry, and earth in 
good condition to channels choked with grass, moss, and detritus. 
1 E. GanguiUet and W. R. Kutter, translated by Rudolph Hering and John C. Trautwine, jr. A General 
Formula for the Uniform Flow of Water in Rivers and other Channels. New York, 1907, 2d ed. 
