1904.] The Flow of Water through Pipes. 351 



We observed that by opening the valve, and increasing the flow, the 

 stream-lines appeared to re-form. This was shown by a return of the 

 thread of colour. It was not until we reached a velocity of 2'97 metres 

 per second that the thread again disappeared. By altering the flow a 

 little at this point we could make the thread of colour disappear, or 

 obtain it clearly defined. We repeated this several times, and found 

 that the definite nature of this point was remarkable, the thread of 

 colour appearing in almost as sudden a manner as it disappeared. 



The diameter of the pipe plays an important part in obtaining the 

 higher stream-line flow, for we found that with a pipe T05 cms. in 

 diameter we could not pass the upper limit, nor cause a re-formation of 

 stream-lines. We made some experiments with a brass-pipe, 5*41 cms. 

 in diameter, and 1-5 metres long, by the method of colour bands, and 

 found that we could carry the stream-line flow up to velocities of 

 1 metre per second, which was the highest flow we could measure. 

 To obtain this flow we were obliged to arrange a much larger measure 

 to handle the water discharged. The upper limit for a pipe of this 

 size, according to the formula, amounts to about O24 metre per second 

 at 20 C. We, therefore, exceeded this by four times, as far as we 

 could see, without the formation of eddies. There was a tendency to 

 flash at the highest point, but no definite critical velocity, and the 

 thread of colour could be seen very distinctly. 



We cannot enter into a discussion of the influence of the diameter of 

 the pipe on the attainment of the second stream-line flow, but it 

 appears to us obvious that we were able to obtain these higher readings 

 only by paying the strictest attention to the steadiness of the water in 

 the tank. The magnitude of our tank, and the volume of water at our 

 disposal, made this comparatively easy. The inverse diameter law has 

 been shown by Reynolds to be true both for the upper and lower 

 limits, and our experiments show the same where the water has not 

 become perfectly steady ; but it is probable that, as the diameter of the 

 pipe becomes larger, the disturbing influence of the walls becomes less 

 effective in causing a breaking up of the stream-lines. In the jet 

 experiments, where there is no directing pipe, stream-line is the stable 

 flow for all velocities, providing the water has become absolutely quiet. 

 For pipes of small diameter, under J inch, or 1 cm., the steadiness of 

 the water probably becomes less important, compared with the influence 

 of the walls of the pipe. It is probable that for absolutely quiet water 

 the inverse diameter law holds up to 1 cm., beyond which the critical 

 velocity apparently increases with increasing diameter, until for large 

 pipes we approach the jet. The higher critical velocity may be a 

 second critical velocity, but we have not decided this point. 



