Turbulent Flow in Pipes and Channels. 335 



over the cross-section, and F some function of the variable 

 UD/y. This principle was fully confirmed in its application 

 to pipes of widely different diameters for fluids differing in 

 density and viscosity to the extent represented by air and 

 water. The value of UD/y corresponding to "critical"" 

 changes in the character of the motion is not very sharply 

 defined, but leads to a value of Reynolds's Constant in the 

 neighbourhood of K=2500. It does not appear to the 

 writer that the theory of the mode of breakdown from 

 stream-line to turbulent motion, suggested in the previous 

 section as depending on transverse modes of compressional 

 vibrations, is in contradiction with the principles just 

 discussed, except that the form of the function F(UD/i/), 

 and especially the value of UD/V corresponding to a change 

 in the type of motion, would depend on the form of the cross- 

 section of the tube, but would probably remain the same for 

 geometrically similar shapes as in the particular case covered 

 by existing experiments on circular cross-sections. For 

 this reason it would seem highly desirable to obtain the 

 corresponding data on two-dimensional channels or cross- 

 sections having an elongated elliptical form ; it would be 

 expected thai the appearance of the " critical " flow would 

 occur at a higher velocity than that given by the usual 

 Reynolds's Criterion, owing to the high degree of determin- 

 ateness of the transverse modes. 



Mention should be made of numerous experiments by 

 Sorkau 36 on the flow of water and of various organic liquids 

 through a short capillary tube (diameter 0*423 mm. : length 

 about 5 cm.). Observations were made of total flow against 

 pressure ; although, as has already been pointed out, such 

 observations are not suitable for revealing discontinuities of 

 flow unless they are well marked, the experiments of Sorkau 

 indicate the existence of three distinct regimes of turbulent 

 flow occurring at velocities considerably less than that given 

 by Reynolds's Criterion. Quoting from the last-mentioned 

 reference given below, the value of K for water varies from 

 K=413'4 at 4° C. to 410-5 at 25° C. Above 25° C. the 

 three turbulent regimes are well-marked. Similar results 

 were obtained in the case of various pure organic liquids. 



(ii.) Gases. — Accurate observations on the flow of gases 

 with reference to a study of the turbulent regime have only 

 comparatively recently been carried out ; in such cases the 



36 Sorkau, W., Phys. Zeit. xii. pp. 582-595 (1911); xiii. p. 805 

 (1912) ; xiv. pp. 147 et seq., 759-766, 828-831 (1913) ; xv. pp. 582-587, 

 768-772 (1914) ; xvi. pp. 97-102 (1915). 



