CRITICAL VELOCITY 55 



Thus when t = 32 F. = C. . . P = 1. 



* = 62 F. = 16J C. . '. . P = -616. 

 t = 100 F. = 37| C. . . . P = '385. 

 t = 212 F. = 100 C. . . . P = '1523. 

 If the unit of length is 1 metre . . . . b = 43'79. 

 Ifoot . 6= 4-06. 



This gives the higher C. V. at which steady becomes eddy motion. 

 Exactly the same formula, but with a different numerical coefficient, 

 was found to hold for the lower (true) C. V. at which eddy becomes 

 steady motion. 1 



Here if the unit of length is 1 metre . . . . b = 278. 

 ,, n Ifoot .... 6=25-8. 



E.g., with water at 10 C. 50 F. 



Motion is steady if v d < '029 



unstable if v d > '^ 

 <C *182 



turbulent if v d > '182 

 the unit of length being 1 foot. 



More recent experiments, 2 carried out on glass tubes by the colour band 

 method, show that by taking the greatest care to eliminate all disturbance at 

 entry to the tube, values of the higher critical velocity considerably greater 

 than (up to 3'66 times as great as) those given by the above formula may 

 be obtained. The probability is, in fact, that there is no definite higher 

 critical velocity, but that this velocity always increases with decreasing 

 disturbances. It is very doubtful, moreover, whether the Reynolds law is 

 strictly true for diameters much in excess of those (up to about 2 inches) 

 covered by his experiments. 



ART. 18. CRITICAL VELOCITY IN A CONVERGING TUBE. 



The numerical constants involved in the case of the stability of motion 

 in flow through a parallel tube have been accurately determined, but not 

 in the case of a converging or a diverging tube. At sufficiently low 

 velocities we know that the motion is steady in any case, but in con- 

 verging or diverging tubes the angle of inclination of the sides has a 

 great influence on the velocity at which stable becomes unstable motion. 



1 " Phil. Trans. Roy. Soc.," 1883. Also " Scientific Papers," Osborne Reynolds, vol. 2, pp. 

 51 103. This coefficient was obtained from experiments in which the resistance to flow at 

 different velocities was measured. 



2 Ekrnan, " Arkiv. for Matematic, Ast. och Fys," 1910. Band 6, No. 12. 



