2 BULLETIN 194, TJ. S. DEPARTMENT OE AGEICULTUEE. 
In all English-speaking and in many other countries open channels 
are quite generally designed by the use of Kutter's formula. This 
formula was derived from such tests, but for the most part under 
other than irrigation conditions and before some of the now more 
commonly used materials of construction were generally available. 
For the purpose of enlarging the number of tests under irrigation 
conditions, made by comparable methods, the experiments described 
in the body of this publication were carried out. For the sake of 
comparison, and where sufficient cases covering certain conditions 
were not found, recent tests from other sources are included in the 
summary table (see p. 19) of the results, and brief descriptions are 
given in the Appendix. 
NOMENCLATURE. 
Throughout this publication the following symbols will be used to 
designate the same element : 
A. — The mean area of the water cross section throughout the length of reach tested, 
in square feet. 
a. — The area of any particular water cross section, in square feet. 
L. — The length of reach tested, in feet. 
h. — The fall of the water surface in the reach tested, in feet. 
P. — The mean length of the wetted perimeter throughout the reach tested, in feet, 
p. — The length of the wetted perimeter at any particular cross section, in feet. 
Q. — The mean discharge of the channel during the test, in cubic feet per second. 
Pv. — The mean value of the hydraulic radius throughout the reach tested, equal to 
£, in feet. 
r. — The value of the hydraulic radius at any particular cross section, equal to 
- , in feet. 
P 
s. — The hydraulic grade or slope of the water surface, equal to =p corrected for any 
change in the mean velocity head, in feet per foot of length in the reach. 
V. — The mean velocity of the water throughout the reach tested, in feet per second. 
v. — The mean velocity at any particular cross section, in feet per second. 
n. — The coefficient of retardation, in Kutter's formula. 
C. — The coefficient of retardation, in Chezy's formula. 
HISTORICAL. 
In 1775, Chezy, a French engineer, advanced the following formula 
for the flow of water in channels: 
V = CVR"s (1) 
This formula takes account of the fact that the velocity of water 
flowing in a uniform channel does not increase for each succeeding 
second of its passage as would be the case if it followed, unhindered, 
the law of gravity, but that it acquires a certain velocity early in its 
