328 Prof. L. Vessot King on 



flames 14 . Osborne Reynolds's experimental work on the 

 subject in 1883 marks an important point in the history o£ 

 the subject 15 . By studying the nature of the flow by means 

 of colour-bands, it was shown that at a certain " critical " 

 mean velocity the stream-like flow broke up into violently 

 •eddying motion; it was also shown from the theory of: 

 dimensions that the criterion of breakdown should depend 

 on the ratio DU/)///, only, D being the diameter of the tube, 

 U the mean velocity of the fluid, p its density, and //, its 

 coefficient of viscosity, all these quantities being measured 

 in C.Gr.S. units. The passage from laminar to turbulent 

 flow was indicated both by the colour-band method, as well 

 as by a change in the law of resistance as observed from 

 the discontinuity in the curve connecting the total flow and 

 the pressure- gradient, and was shown to take place for a 

 value of U given by the relation 



DU»=K, (20) 



which will be referred to as "Reynolds's Criterion/' while 

 the number K will be referred to as "Reynolds's Constant." 

 In the case of water Reynolds found, both from his colour- 

 band method as well as from a study of his own experiments 

 and those of Poiseuille 16 and Darcy 17 on the laws of fluid 

 resistance in pipes, that K had a value in the neighbourhood of 

 K = 1900 to 2000. According to theory K should have the 

 same value for all viscous incompressible fluids. Several 

 series of observations, carried out since that date by various 

 observers on liquids and gases, when examined by the same 

 methods as those employed by Reynolds, agree in assigning 

 fairly consistent values to the constant K; these are discussed 

 in further detail in the next section. 



Reynolds's observations gave rise to a series of theoretical 

 contributions, among the first of which were papers due to 

 Kelvin 18 and Rayleigh 14 . Kelvin examined the types of 

 flow discussed in Sections 3 and 4 from the point of view 

 of stability, and came to the conclusion " that the steady 

 motion is wholly stable for infinitesimal disturbances, 

 whatever may be the value of the viscosity (fi) ; but that 

 when the disturbances are finite the limits of stability 



14 Rayleigh, Various papers between 1879 and 1914 ; Collected Works, 

 Arts. 58, 66, 144, 194, 216, 217 ; also Phil. Mag. vol. xxviii. p. 609, 

 Oct. 1914. 



15 Reynolds, O., Phil. Trans, vol. clxxiv. p. 935 (1833); Collected 

 Works, vol. ii. p. 51. 



16 Poiseuille, Comptes Rendus, vols. xi. & xii. (1840-1). 



17 Darcy, Comptes Rendu.*, vol. xxxviii. 



18 Kelvin, Phil. Mag. vol. xxiv. pp. 188, 459, 529 (1887). 



