166 SEWER DESIGN 



1. The force which sets the water in motion is derived 

 solely from the inclination of the water-surface. 



2. When the motion is uniform the resistance which the water 

 meets, or the retarding force, is equal to the accelerating force. 



He also showed that the resistance is independent of the 

 weight or pressure of the water, so that its friction upon the walls 

 of pipes and channels is entirely different in its nature from 

 that existing between solid bodies. 



Coulomb's investigations, a little later, indicated that the 

 resistance offered by the perimeter of a channel is represented 

 by two values, the first of which is proportional to the velocity, 

 and the second to the square of the same. Upon this principle, 

 de Prony based his formula 



in which a and b are constants to be derived from experi- 

 ments. From thirty measurements by Dubuat and one by 

 Chezy, de Prony found, for metric measures, that a equals 

 0.000,044 and b equals 0.000,309. Somewhat later, Eytel- 

 wein, after comparing the above thirty-one experiments with 

 fifty-five others by German hydraulicians, suggested that a 

 should equal 0.000,024 and b equal 0.000,366. 



This formula of Eytelwein is a familiar one, and reference 

 is made to Proc. Inst. C. E., Vol. XCIII, p. 383, for extensive 

 tables on sewer design, based upon it. 



Many authorities, seeking to simplify the expression, held 

 that it would be permissible to shorten the formula by neglect- 

 ing the term aXv, which is very small for large streams espe- 

 cially, reducing the form to that of the Chezy formula again. 



For this modified formula the value of b is given as 0.0004, 

 later taken by Eytelwein as 0.000,386, and it has been much 

 used in Germany and Switzerland until recently. It gives 

 in metric units 



v = $o.<)\ / R-S, 

 and in English units 



