Turbulent Floic in Pipes and Channels. 333 



flow in tubes o£ large diameter, the Telocity-distribution 

 over a particular cross-section is nearly always un symmetrical 

 with respect to the axis. Then again, if the curves 29 ' 

 connecting the total flow with pressure-gradient be carefully 

 examined, it will be noticed that slight discontinuous changes 

 of slope can be detected some time before the "critical 

 flow " is reached ; the effect in this case is probably due to. 

 sudden changes of velocity-distributions resulting from a 

 number of symmetrical transverse modes being brought into, 

 existence before the first indeterminate mode leading to a 

 complete breakdown of stream-line flow. If this is the- 

 correct interpretation of Reynolds's condition of " sinuous 

 flow," it would seem capable of mathematical formulation- 

 leading to a more satisfactory explanation of the experimental! 

 constant K. Such an investigation would hardly be profit- 

 able in the present state of experimental knowledge until- 

 the much simpler and more determinate cases of two-dimen- 

 sional flow have been thoroughly worked out, both experi- 

 mentally and theoretically. 



Section 6. Discussion of Experimental Results on the 

 Flow of Viscous Fluids. 



(i.) Liquids. — Reynolds's original experiments on the- 

 subject have already been reviewed in the preceding section, 

 and a possible explanation of several features of the pheno- 

 menon discussed. Further experiments along the same lines 

 by Barnes and Choker 30 give additional support to the view 

 that the passage from stream-line to turbulent flow depends 

 on the determinateness of the transverse modes of the 

 compressional vibrations rather than on the instability of 

 steady viscous flow, as generally understood in theoretical 

 investigations on the subject. The observers just mentioned, 

 by exercising extreme care in preventing the formation of 

 eddies in the tank previous to the entrance of the liquid into 

 the flow-tube, were able to obtain stream-line motion for 

 velocities as much as four times as high as that given by 

 Reynolds's Criterion. In some cases, after passing through 

 a state of turbulent flow, stream-lines reformed at higlier 

 velocities ; in such cases a sharp rap on the tube sufficed to 

 break down the motion, which immediately became stable 



29 Such, for instance, as the curves for air obtained by Ivohlrausch, 

 "K. W. F., Annalen der Physik, xliv. p. 297 (1914) ; and more especially 

 those obtained bv Sorkau for water and various organic liquids. (Foot 

 note 36.) 



30 Barnes, H. T., & Coker, F. G., llov. Soc. Proc. vol. lxxiv. p. 341 

 (1904). 



