152 On the Variation of the Critical Velocity of Water. [July 16, 



" An Experimental Determination of the Variation of the Critical 

 Telocity of Water with Temperature." By E. G. Goker, 

 M.A. (Cantab.), D.Sc, (Edin.), Assistant Professor of Civil 

 Engineering, and S. B. Clement, B.Sc, Demonstrator of Civil 

 Engineering, both of McGill University, Montreal. Commu- 

 nicated by Professor Osborne Kfa t nolds, F.R.S. Received 

 July 16 —Read November 20, 1902. 



(Abstract.) 



The change from stream-line to eddy motion in water was first 

 examined by Osborne Reynolds, who in his earlier experiments, intro- 

 duced colour-bands into a glass pipe in which water was flowing, to 

 indicate the change in the motion, and later observed the resistance 

 encountered in pipes over a great range of velocities. 



The results of these experiments, and a consideration of the equations 

 of motion, enabled him to express the laws relating to the critical 

 velocity of water in pipes by the exceedingly simple equation 



where % is the critical velocity of water, r is the radius of the pipe, fi is 

 the viscosity of the water, p is the density, and k is some constant. 



In the original experiments the range of temperature was very 

 limited, and it was pointed out that " it would be desirable to make 

 experiments at higher temperature, but there were great difficulties 

 about this, which caused me, at all events for the time, to defer the 

 attempt." It does not appear that such experiments have since been 

 made, and although the difficulties were great, it was resolved to 

 test the law through a much greater range than had hitherto been 

 attempted. 



Preliminary experiments showed that at temperatures beyond 50° G 

 the losses due to conduction and radiation were large, and that 

 elaborate arrangements would be required to obtain reliable results. It 

 was therefore decided to determine the variation of the critical velocity 

 over a range extending from about 4° C. to 50° G, which seemed to be 

 sufficient as a test of the law, and, with ordinary precautions, only 

 necessitated small corrections for the effects of conduction and radia- 

 tion. The resistance method used by Osborne Reynolds in his later 

 experiments was employed, the arrangement only differing from his in 

 details, such as the use of pressure chambers giving a continuous 

 opening at the ends of the -f-inch pipe examined, the employment of an 

 inverted U-tube for measuring the pressures, and the weighing of the 

 discharge. 



