PIPE FLOW 197 



due to eddy production and proportional to v 2 . The constants a and b in 

 the formula 



where/ = a H -- , were then determined on this assumption. 

 These values were as follows : 



Weisbach, on the other hand, assuming the first part of the resistance 



3 



proportional to v 2 , obtained the formula 



h = , where / = '00360 + ,~. (9) 



2 g m' V v 



Adopting the same formula, Bazin put/ = '00294 ( 1 + 3736 V while 

 Kutter and Ganguillet put 



(10) 



( 



-MI-. **' 



where N is a coefficient depending on the roughness of the pipe surface 

 and varying from '010 to '019, its value for clean cast-iron or asphalted 

 pipes being '013, for new riveted pipes '014, and for old pipes '019. 



These formulae, excepting that of Kutter, neglecting as they do any 

 variation in resistance produced by a variation in the physical condi- 

 tion of the pipe surface, are obviously only of value where the experi- 

 mental conditions can be reproduced. Moreover the fundamental 

 assumption in the formulae of D'Aubuisson, Prony, and Eytelwein, as to 

 the resistance depending on two powers of the velocity, has been clearly 

 demonstrated to be unsound by Reynolds. This since in every case 

 where the logarithms of the resistances and velocities have been plotted 

 these are found to lie on accurately straight lines (p. 53). 1 



1 True at all events for the range of velocities common in practice. See also Saph and 

 Schoder, Trans. Am. Soc. C.E.," VoL 51, 1903. 



