6 BULLETIN 852, U. S. DEPARTMENT OF AGRICULTURE. 
In addition to the above losses, there may be others, such as those 
due to bends and valves or other obstructions; but as a general thing, 
these items do not enter the design of concrete pipes, especially for 
irrigation purposes. For this purpose the pipe is laid on such gentle 
curves, both horizontal and vertical, that such losses need not be 
considered. 
In 1775, Chezy, a French engineer, offered his now well-known 
formula for "the flow of water in both open channels and closed 
conduits : 
7= C^Rs (3) 
Here C is a coefficient, originally thought to be constant, but now 
known to vary with functions of the slope, the hydraulic radius, the 
velocity, and with some factor representing the retarding influences in 
the channel. Some of the formulas used in this country for the design 
of pipes have accepted the Chezy formula as a basis and made only 
such modifications as experience dictated. 
Since the hydraulic elements secured in the field experiments 
furnish the necessary data for the determination of the factor repre- 
senting the retarding influences in all the formulas most used in this 
country, this publication will show this factor as developed by field 
tests for several formulas as follows: 
(a) The Chezy formula (3). 
V= O^W= CR°- 5 s - 5 (4) 
(b) The Kutter modification of the Chezy formula: 1 
Mii + 41 . M + »_»»» 
(«■ 
66 + 
0.00281\ i 
VSs (5) 
S J-y/R 
in which is elaborated so that it takes into consideration the 
influence of the hydraulic grade and of the mean hydraulic radius 
and introduces a new variable, n, which is supposed to represent all 
the retarding influences. 
(c) The Weisbach formula, which has been used by textbooks as 
a general formula for flow of water in clean pipes : 
(d) The Williams-Hazen general formula 2 for many kinds of 
pipes : 
V= cV?°- 63 s°- 54 0.001 - °- 04 (7) 
* 
1 E. Ganguillet and W. R. Kutter, translated by Rudolph Hering and John C Trautwine, jr. A General 
Formula for the Uniform Flow of Water m Rivers and other Channels, New York, 1907, 2d ed. 
2 Hydraulic Tables, Williams and Hazen, 2d ed., New York, 1909, p. 1. 
