>fi HYDRAULICS AND ITS APPLICATIONS 



The exact effect of altering this inclination is still unknown, except that 

 increasing the angle of divergence rapidly diminishes the stability, while 

 in converging tubes stability of motion rapidly increases with the angle 

 of convergence. At all ordinary velocities in fact, the motion in tubes or 

 nozzles having more than a few degrees of convergence may be considered 

 as being steady. Experiments by the author l on pipes having sides con- 

 verging uniformly at an angle 6 gave the following results. The critical 

 velocities were obtained in the usual way, by plotting the logarithmic 

 homologues of loss of head and of velocity at the contracted section, 

 noting the point at which the index of v suddenly changes. As the 

 motion at the entrance to the larger pipe was in every case unsteady, 

 owing to the bends and irregularities in the supply pipe, these values 

 mark the lower critical velocity at which eddy motion settles down 

 into non-sinuous or stream-line motion. 



The temperature of the water in these experiments was 57j F. 

 The lower critical velocity in a parallel pipe of the same mean diameter 

 (2J inches) at this temperature is 0'133 feet per second, while in a 3-inch 

 and a IJ-inch pipe it is respectively 010 and 0'20 feet per second, the 

 higher critical velocities being respectively 0'86, 0*65, and 1*29 feet per 

 second. Should the ratio of higher to lower critical velocities have the same 

 value in a conical pipe as in a parallel pipe, this would mean that in the 

 case of a IJ-inch jet discharged from a converging nozzle with steady 

 flow in the supply pipe, the critical velocity would have the following 

 values 



and this would explain the glassy appearance of the high velocity jet, 

 leaving the nozzle of a Pelton wheel. Further experiments are, however, 



1 " Proceedings, Roy. Soc. B.," vol. 83, 1910, p. 376. 



