196 HYDRAULICS AND ITS APPLICATIONS 



obtained the law 



f where d diameter of pipe in feet. 

 v = velocity in feet per second. 



( h = head loss expressed in feet of water. 



Assuming, with Darcy, that the loss is proportional to the kinetic 

 energy of the stream, and replacing d by its value 4 m, the above 

 becomes 



^~ (5) 



f where/ = ^ J, in which form the equation is often stated. 



Darcy's experiments, carried out on C. I. pipes, gave, in round numbers, 

 the following values of the coefficient/. 



(For clean and bare metal surfaces . . . f = -005. 

 (For old and incrusted ...... / = '010. 



Hag en (1854) deduced from experiments by Bossut, Couplet, and 

 Dubuat the formula 



(6) 



but did not discover any law of variation of these indices or of the 

 coefficient/ with the surface or diameter of the pipe. Most of the other 

 formulae deduced by the earlier experimentalists are merely modifications 

 of the formula 



h-S lv * 



H -p: - 



2 g m 

 or, to put it in the form adopted by De Chezy 



v = C \f^. (7) 



The more important of these are stated below, and for ease of compari- 

 son have been reduced, where possible, to one of these forms. Where the 

 original formula did not contain the factor 2 g, in introducing this the 

 value 64*4 has been adopted, and other numerical factors altered 

 correspondingly. Dimensions throughout are in feet. 



Thus, D'Aubuisson, Prony, and Eytelwein assumed that the resistance 

 to motion is composed of two parts, one due to simple frictional resist- 

 ance at the boundaries and proportional to the velocity, and the second 



