376 Scientific Proceedings, Royal Dublin Society. 



These experiments were coufirined by somewhat ditlerent metlioils by 

 Barnes and Coker.' Tliey also found that it was possible to maintain 

 linear flow at speeds much above tlie lowest critical velocity, provided 

 that the conditions were " steady." If the water in the supply 

 reservoir were allowed time to become perfectly steady, and if the tube 

 were very uniform, straigbt-line flow persisted much beyond the point 

 found in otlier circumstances. Tlie motion would then be unstable. 



Some investigations have been made on the flow of air in pipes. Almost 

 all that liave a bearing on the subject of the present paper are referred 

 to in a paper by Gibson,' on the resistance to the flow of air tlirough 

 a pipe. The object of tlie paper was not to determine the critical velocity, 

 but it is possible to estimate from tlie ciu'ves given that for a tube of diameter 

 ■0104 feet, the critical velocity would be about 34"6 feet per second, tlie 

 pressure being about 16'7 pounds per square inch. 



Consequently the critical velocity for the tube in question is 

 ■f 34-6 X 30-5 or 1050 cms. per second. 

 The diameter {d) is -0104 x 30-5 or -317 cms. 



From Reynolds' formula the product Vc x d sliould be independent of 

 the size of the tube, lu tliis case 



Vc>^ d = 334 . . ., (A) 



where we have not allowed for the variation of density from the average 

 atmospheric density. 



More recently in an investigation of the value of the Pitot constant, 

 Fry and Tyudall,^ using a tube about 2 inches in diameter (5 cms.), found 

 indications that stream-line motion gave way to turbulence somewhere below 

 a velocity of 76 cms. per second. Tliey did not attempt to determine tlie 

 exact critical point. 



Here the product, V^ x d, would be :j> 76 x 5 or ^ 380 . . . (B) 



The comparatively good agreement of these two estimated critical 

 velocities with Reynolds' law is remarkable, considering the widely different 

 diameters of the tubes. It seems interesting, therefore, to pursue the 

 problem furtlier. 



Possibly the reason wliy the problem has not been hitherto attacked 

 is its peculiar nature. To work with tubes of wide bore requires the 

 measurement of large volumes of air and of small-pressure slopes. The 

 flow of air can be measured readily enough by some form of air meter; 



' Barnes and Coker, Phil. Trans., Roy. Soc, vol. lx.\iv, 1904. 



- Gibson, Phil. Mag., vol. svii (1909). 



3 Fry and Tyndall, Phil. Mag., vol. xxi, 1911, 



