UNIVERSITY OF VIRGINIA PUBLICATIONS 



BULLETIN OF THE PHILOSOPHICAL SOCIETY 



SCIENTIFIC SECTION 



Vol. I, No. 5, pp. 127-186 June, 1910 



ON THE FLOW OF WATER IN PIPES, CONDUITS AND OPEN 

 CHANNELS AND THE LOSSES OF ENERGY DUE TO ITS 

 MOTION.* 



BY 



WILLIAM H. ECHOLS. 



I. THEOEETICAL CONSIDEKATIONS. 



1. One of the most interesting chapters in the history of engineering, 

 considered theoretically as well as practically, is that which relates to the 

 flow of water. Its importance from the economic point of view is un- 

 questioned and it has demanded the serious attention of the ablest engineers 

 of every age. The difficulties which beset the problem have long been the 

 despair of the theoretical investigator and the solution has been regarded 

 as well near hopeless by the practical engineer. So many invalid empirical 

 formulae have been proposed to express the loss of energy due to the effect 

 of the so-called "fluid friction" that the engineer in practice turns aside 

 with impatient irritation at the suggestion of a new one. Almost without 

 exception these formulae have been essentially and purely empirical, 

 designed without regard for the fundamental mechanical principles in- 

 volved and which must form the basis of any really serviceable formula. 

 They are, as a rule, mere interpolations designed to fit certain experiments 

 the range of whose data is too limited to give them a dignity of importance 

 above that of mere thumb rule confessedly and grossly approximate save 

 for the narrow range for which they were designed. They serve the purpose 

 of providing provisional estimates in special cases but lack the precision 

 and generality necessary to provide the engineer with a working rule 

 which he can apply with confidence and with a knowledge of the limits of 

 probable error involved. The best formula that has been designed in point 

 of generality is that of Kutter, which is an empirical elaboration of a 

 formula previously given by Darcy, who in his turn generalized one 

 originally due to Chezy. These engineers based their designs upon elaborate 



*Read before the Scientific Section of the University of Virginia Philosophical 

 Society at its regular meeting on March 12, 1910. 



