FLOW OF WATER IN CLEAN PIPES 245 



to render hopeless any direct attempt to determine its mechanical equiva- 

 lent.* It becomes necessary therefore, as in all such physical problems 

 to speculate upon a law to govern this loss if any attempt is to be made 

 to construct a theory to fit the case. In order to do this it is necessary 

 first that careful quahtative observations be made as to the form of the 

 hnes of flow so that as nearly as may be some concrete idea may be had 

 of what actually takes place in the body and near the boimdary of water 

 flowing over rigid material surfaces, then any postulate formulated must 

 be repeatedly tested quantitatively by the empirical measurements of 

 actual experiments and thus repeatedly revised and corrected. 



It can be readily observed in a channel of flowing water, by introducing 

 visible particles of about the same density as water such as various dyes, 

 particularly permanganate of potash, that the stream lines in the core of 

 the channel are more or less nearly parallel to the axis of the flow, that some- 

 what nearer to the boundary they are somewhat sinuous and quite near 

 the boimdary they are markedly sinuous. For a boundary surface that 

 is regular and uniformly heterogeneous the path of a particle near that 

 surface appears to obey the harmonic law with periodic turning points 

 and changes of curvature. Particles very near the boundary are agitated 

 into paths of short periods, appear to roll and revolve in a whirling motion 

 in vortex rings which extend along the boundary across the cross section 

 and roll wdth a relatively slow motion of translation along the bottom 

 and sides in the direction of the flow. Water appears to flow over the 

 boundary surface of its channel in ripples which in deep channels with 

 moderate velocity of mean motion are not evidenced on the free surface 

 or at a large distance from the rigid boimdary, these ripples are much 

 the same in kind differing only in degree from those that are seen in the 

 free surface of shallow chaimels. These phenomena are especially notice- 

 able in a stream after a recent shower of rain which discolors the water 

 along the banks showing plainly whirls, eddies and reversed currents 

 near the boimdarj'' extending out to the core of the main stream which 

 flows as it were in an undulating channel of hquid boundary. Water 

 flowing in the main channel thus appears to be flowing in a channel of 

 liquid boundary of much slower moving or relatively still water which 

 is a series of undulations or liquid barriers or submerged dams over which 



* From a purely physical point of view the existence of a shearing stress is neces- 

 sary as a causation in the loss of energy. While it does not occur as a measurable 

 cause of loss yet it does come into play as an agent for dissipating the lost energy 

 in heat; i. e., if there were no fluid friction there would be no going over into heat 

 and no creation of vortices. 



