128 UNIVERSITY OF VIRGINIA PUBLICATIONS 



series of experiments and have furnished the profession with final formulae 

 which express the flow of water with a certain considerable degree of 

 accuracy. Much quantitative measurement of the flow of water has been 

 made since Kutter designed his formula for the flow of water in open 

 channels, and the investigator has to-day at his command a much larger 

 and more varied list of experimental determinations on which to base his 

 enquiry. If one seeks extreme precision in the testing of any proposed 

 theory one is discouraged at the start by a careful tabulation of the experi- 

 mental data. Two presumably careful experimenters will diifer in the 

 final velocity of discharge of two cast iron pipes of equal lengths, diameters 

 and pressures, frequently from five to ten per cent. The facts in the case 

 are, as every engineer knows, no two pipes, conduits or channels are 

 exactly alike as to roughness of surface and the results show this within 

 certain limits always. 



If one seeks a law for the loss of energy in an actual and real flow, 

 one should consider what takes place in a flow under the most perfect of 

 obtaiaable conditions in a real flow, in order to eliminate complications 

 and the perturbations of all unknown causes of irregularity which obscure 

 the fundamental facts and mislead as to the nature of the causes. Then 

 proceed from the simple to the more complex, knowing that what is true 

 under the best conditions must be true mutatis mutandis under more 

 complex ones. The best condition for investigation is that which takes 

 place in the flow of water in a straight cylindrical pipe whose interior 

 surface is as smooth as possible without joints, and under a constant 

 pressure head. The law of the losses for the rougher surfaces and under 

 less favorable conditions whether in conduits or open channels should 

 differ from these in degree rather than in kind when the surfaces are 

 fairly, regular. 



2. If we speculate upon what takes place in the course of the flow of 

 water in a straight pipe under constant head, the mean velocity of discharge 

 is constant and we usually consider that after a limited time the flow is in 

 a state of steady motion in which the stream lines are assumed as being 

 parallel to the axis of the pipe. It is now known that this condition is far 

 from the truth, save in very smooth tubes of extremely small diameter. 

 The liquid is not in a condition of steady motion but ia ordinarily clean 

 pipes is in a condition of more or less stationary motion such that about 

 the mean velocity at a given point that of a particle oscillates within certain 

 limits. The lines of flow are not parallel to the axis of the cylindrical 

 pipe but are perturbed and oscillatory with respect to that fixed position. 



