311] SKIN-RESISTANCE. 575 



For example, putting */ = '018, w = 300 [o. s.], /='005, we obtain 

 / = '024cm.* The smallness of this result suggests that in the 

 turbulent flow of a fluid through a pipe of not too small diameter 

 the value of w is nearly uniform over the section, falling rapidly 

 to zero within a very minute distance of the walls ~K 



Applied to pipes of sufficient width, the formula (2) gives 



Tra 2 f %7raR = Trfpawf, 

 (Lz 



-!&=/*' (4). 



p dz a 



The form of the relation which was found to hold by Reynolds, in 

 his experiments, was 



1 d/p v*- m w m 



pdz* a s ~ m ' 

 where m = 1723. 



The increased resistance, for velocities above a certain limit, 

 represented by the formula (2) or (4), is no doubt due to the action 

 of the eddies in continually bringing fresh fluid, moving with a 

 considerable relative velocity, close up to the boundary, and so 

 increasing the distortion -rate (dw/dn) greatly beyond that which 

 would obtain in regular ' laminar ' motion J. 



The frictional or ' skin-resistance ' experienced by a solid of 

 ' easy ' shape moving through a liquid is to be accounted for on the 

 same principles. The circumstances are however more complicated 

 than in the case of a pipe. The friction appears to vary roughly 

 as the square of the velocity ; but it is different in different parts 

 of the wetted area, for a reason given by W. Froude, to whom the 

 most exact observations || on the subject are due. 



* Cf. Sir W. Thomson, Phil. Mag., Sept. 1887. 



t This was in fact found experimentally by Darcy, I. c. The author is indebted 

 for this reference to Prof. Eeynolds. 



J Stokes, Math, and Phys. Papers, t. i., p. 99. 



So called by writers on naval architecture, to distinguish it from the wave- 

 resistance' referred to in Arts. 221, 228. 



|| "Experiments on the Surface-friction experienced by a Plane moving through 

 Water," Brit. Ass. Rep., 1872, p. 118. 



" The portion of the surface that goes first in the line of motion, in experiencing 

 resistance from the water, must in turn communicate to the water motion, in the 

 direction in which it is itself travelling. Consequently the portion of the water 

 which succeeds the first will be rubbing, not against stationary water, but against 

 water partially moving in its own direction, and cannot therefore experience as 

 much resistance from it." 



