1904.] The Flow of Water through Pipes. 349 



the temperature, which was found to be the formula obtained by 

 Poiseuille for the change in flow of water in capillary tubes. 



P then equals 



(1 + 0-03368 T + 0-000221 T 2 )- 1 . 

 Calculating the upper limit for this pipe we find : 



v 0-0228 7 



0-0195x1 -59 



This value comes out 0-734 metre per second instead of 1-15, as we 

 observed it. The higher limit obtained in our measurements is 

 undoubtedly due to the steadiness of the water at the mouth of our pipe. 



We convinced ourselves in these experiments that we had not 

 exceeded the upper limit, for the valve controlling the flow was moved 

 very slowly as the point was reached, and stopped instantly the jump 

 took place. It was possible to obtain the stream-lines again by slightly 

 closing the valve. For a velocity of 0*7 metre we had perfectly steady 

 stream-lines. For our smaller pipe, 1-05 cm. in diameter, we found a 

 close agreement with the formula of Reynolds, but that above this, for 

 pipes of larger diameters, the deviations became larger the larger the 

 pipe. 



If we tried the experiments too soon after filling the tank, before 

 the water had become perfectly steady, the upper limit came much 

 lower, and, as the water became more settled, a higher limit was 

 indicated by a tendency to form stream-lines, followed by a breaking- 

 up, giving rise to the phenomenon described by Reynolds as " flashing." 

 The flashes became less frequent until, finally, the water being 

 perfectly steady, the higher limit was reached. It was possible to 

 obtain the higher limit as soon as the flashes started, since it was 

 only necessary to increase the flow until the flashing ceased. The 

 flashes showed themselves by an oscillation on the thread of the 

 thermometer. 



It was not, therefore, really necessary to have absolutely quiet water 

 to obtain the upper limit, since we were able to satisfy ourselves by 

 experiment that the flashes indicated a disturbance in the tank, which, 

 if removed, would enable us to reach the upper point without their 

 appearance at all. Hence, flashing was taken to indicate a tendency to 

 form stream-lines, and if they appeared, the upper limit was obtained 

 by increasing the flow until the permanent reading on the thermometer 

 indicated that eddy motion was the steady flow. 



StrewmrLine Flow at High Velocities. 



The 1-8 metre length of our brass pipe had remained attached to the 

 tank for several days under an 8-foot head, after completing our 

 experiments, to test the influence of length. On returning to this pipe, 



2 D 2 



