THE FLOW OF WATER IIST lEEIGATIOISr CHANNELS. 3 



flow and from that time the velocity remains quite constant so long 

 as the smroimding 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 ils friction between the moving filaments 

 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: 



1-811+41.66+2:°°^ 



^ f r> rvAooi 1 /v, V'^/ 



i^Li .. , 0.00281 1 n 



Substituting this value in formula (1) we have Kutter's formula, 

 expressed in Enghsh measures: 



^1-811+41.66 + ^^^^ 



V= 



n 



1 + 



n, ^^ , 0.00281 1 n 

 [_41.66 + — ^J^^ 



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 mtroduces 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.' 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 exc<,'ption of n, the factor representing the retarding influences. 

 There is a wide range of values which may ])e assigned to tliis factor, 

 the friction becoming greater in passing from smooth, planed boards 

 through a list of such materials as concretes, masonry, and earth in 

 good c(jri(lition to channels clK^ked with grass, moss, and detritus. 



1 E. OanjcuJIIet and W. R. Kutter, translated by Rudolph IlerlnR and John C. Trautwlne, jr. A G«i«ral 

 Formula (or the Uniform Flow of Water In Rivers and other Channola. Nuw York, 1907, 2d od. 



