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 tiling, 

 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: 



V= C-yjWs (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). 



F= O^Ri= CR°- 5 s - 5 (4) 



(b) The Kutter modification of the Chezy formula: 1 



1.811 , .. rc , 0.00281 

 + 41.66H 



n 



l+i41 . m + m>2Sl\_r : 







t/Rs (5) 



HR 



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: 



F= CV2 - 63 s°- 54 0.001 - 004 (7) 



1 E. Ganguillet and W. B. Kutter, translated by Rudolph Ilering and John C Trautwine, jr. A General 

 Formula for the Uniform Flow of Water m Rivers and other Channels, New York, 1907, 2d ed. 

 J Hydraulic Tables, Williams and Hazen, 2d ed., New York, 1909, p. 1. 



