584 



type lias been chosen: tlie motion of a fluid between two parallel 

 walls, one of wlucli lias a translalional motion in its own plane with 

 the velocity V with respect to the otiier, while the distance between 

 the two walls has the constant value / (comp. fig. 1). To ensure 

 this motion forces of niagnilnde 5 per unit of area must be applied 



Fig. 1. 



to the walls in opposite directions. The tangential force between 

 any two adjacent layers of the fluid has the same value S. The 

 law of resistance will be written : 



S-CqV' (1) 



The coefficient C is a function of Reynolds' number: 



R = —^ (2) 



ft 



For small values of R the motion is laminar, and the value of 

 C is easily seen to be : 



' = 'r <" 



If the value of R is high, the motion becomes turbulent, and C 

 decreases much slower. There do not exist any direct measure- 

 ments for this case of motion; however, the arrangement of the 

 experiments made by Coüktte comes very near to it '). According 

 to this author we may expect a formula of the following type: 



C = c, + c, i?-i (4a) 



Investigations by von Karman on the law of decrease of the 

 mean motion in the neighbourhood of a smooth wall') point to: 



C = 0.008 R-'U (U) 



1) M. GouETTE, Ann. de Chitn. et de Phys. (6) 21, p. 457, 1890. 



2) Th. von Kaeman, ZS. fur angew. Math. u. Mechanik, I.e. 



I 



