244 UNIVERSITY OF ^aRGINIA PUBLICATIONS 



tables of Fanning and of Smith appear to have been constructed for 4- 

 foot pipes and larger sizes on the basis of the Stearns experiment and 

 which undoubtedly leads to erroneously high velocities for large pipes. 



When one takes into consideration the chaotic appearance of the data 

 in the experiments on pipes there is not so large a difference in the results 

 for pipes of large size and of different construction as we are lead to believe 

 by the authorities. The different kinds of pipes of all sizes can be brought 

 under the law of a common formula with quite a satisfactorj' degree of 

 precision if the degree of that precision be compared with the degree of 

 agreement among the various experiments themselves. 



In the previous paper, as referred to, an expression for ?«, the coeffici- 

 ent of resistance was given as a fmiction of the velocity T' and the mean 

 radius r, which expression may be considered as carrying Darcy's formula 

 to the next degree of approximation. In the present paper this expression 

 for m will be carried to a still further degree of approximation which is 

 undoubtedly more nearly the truth. There are two distinct features in 

 the design of such a formula to be considered. In the first place in order 

 to have a proper generality it is necessary to form some idea as nearly 

 as possible of the form of the fimction of V and r which represents m 

 and this must be done through a theoretical speculation. In the second 

 place the constants or parameters in this function must be determined 

 from actual experiments, this is a problem of great difficulty owing to 

 the scattered experiments and the chaotic nature of their disagreements. 

 It is necessary to consider the data from a large variety of pipes and mass 

 their results in order to fLx the law governing the constants. 



2. Very httle is kno-rni of the laws of the so-called fluid friction. It 

 is known however quite definitely that viscosity, in the case of ordinary 

 water, or that property which admits a shearing stress has but little 

 influence in causing a loss of energy in its motion, so little in fact that 

 it may be practically ignored. The principal cause of the loss of energy 

 appears to be that due to cross currents, eddies and vortices caused by 

 particles of water impinging against the rough surface of the channel 

 boundarj^ and by reaction sent back into the body of the liquid in direc- 

 tions transverse to the direction of mean flow thus compounding their 

 velocities with those of other particles with the result of reducing the 

 velocity in the direction of mean flow and thus causing a corresponding 

 loss of effective energy of discharge. This lost energy which disappears 

 under the interference of particles striking each other with transverse 

 velocities and the distruction of motion is undoubtedly dissipated in the 

 production of heat which is conducted away in so elusive a manner as 



