192 



COEFFICIENT OF FRICTION FOR PIPES. 



in which a 1 and 8 denote constants to be determined by 

 experiment 



In order to determine these constants, these authors 

 availed themselves of 51 experiments made at different times 

 by Couplet, Bossut, and du Buat upon the flow of water 

 through long pipes. From these 51 experiments, the fol- 

 lowing numerical values were obtained : 



Prony obtained, l = 0.0000693, 

 Eytelwein, x = 0.0000894, 



D'Aubuisson,* t = 0.0000753, 



8 = 0.0013932. 

 2 = 0.0011213. 

 8 = 0.0013700. 



Taking the value of h lt and substituting it in (2) of Art. 

 104, instead of the value of h i as given in (1) of Art 103, 

 we have 



,) (3) 



(4) 



Putting - - = 5, and reducing, (3) becomes 



lid 



from which the value of v may be found. But the follow- 

 ing method of approximating to the value of v is more 

 convenient. From (4) we have 



hd 



bd 



Expanding the first member by the binomial theorem, 

 and neglecting all the terms of the expansion after the sec- 

 ond, since 8 is considerably greater than j, we have 



+ 



2 (Id + 8 v 



hd 



bd 



* Weisbach's Mechs., p. 866. 



