1904.] The Flow of Water through Pipes. 355 



It was found that it was possible to measure three flows : that 

 at which the flow was entirely stream-line with no tendency to form 

 eddies ; second, that at which the eddies remained in the flow without 

 the appearance of stream-lines ; and third, that at which the eddies 

 and stream-lines followed each other at regular intervals. The change 

 from one flow to the other was observed by the rate of the oscillation on 

 the thread of the thermometer. An inspection of the curves given by 

 Reynolds for the relation between velocity and pressure, above and 

 below the critical velocity, shows that no sharp line of intersection 

 exists between the curve representing stream-line and that representing 

 eddy motion, but that there is a portion over a considerable range of 

 flow where the readings are unsteady. It was in this region that the 

 three flows mentioned above were found. The first was the highest 

 limit of the stable stream-line, the second the lowest limit of the 

 stable eddy flow, and the third the point half-way between. The results 

 are given in the following table for the third point, which is the critical 

 velocity of Reynolds : 



Table IV. 

 Diameter of pipe, 0-0125 metre. 



Q. Time. 



Temp. c.c. sees. Ye. P. UL. 



6 830 30-2 0-225 0-238 0-239 



6 866 30-2 0-234 0*238 0-239 



17-2 952 45-2 0-171 0-176 0-167 



17-2 930 45-0 



18-1 951 45-1 



18-1 926 45-2 



18-1 944 45-1 0-171 0-172 0-163 



18-1 960 45-0 



18-1 923 45-2 



40-5 580 45-3 



40-5 568 45-2 0-103 0-104 0-086 



40-5 565 45-1 



The first column contains the temperature at which the critical 

 velocity was measured. The second column contains the total quantity 

 of liquid Q which was collected in the measuring glass during the time 

 given in the third column. The times were all taken on a stop-watch. 

 Under V c are given the values of the critical velocity, calculated in the 

 usual way from the area of the pipe and the flow per second. 

 P the values of the critical velocity are given, calculated by Reynolds 

 lower-limit formula. This formula reads 



V X - P 



" 278 D 



in metres per second, where P and D have the same meaning as before. 



