VELOCITY NEAE WALLS 215 



cent, from its mean value 0'921. The radius of mean velocity in these 

 experiments was '80 of the pipe radius. 



Surface Velocity. Since the Pitot tube, with which velocities are 

 invariably measured, cannot be used to determine velocities at points 

 nearer to the wall than the radius of its orifice, the manner in which the 

 velocity varies at points very near the wall is difficult to determine with 

 any degree of accuracy. By producing the curve obtained by plotting 

 velocities across the pipe, the earlier experimenters concluded that the 

 surface velocity was approximately one-half the maximum velocity. 

 More recent experiments by Morrow on a pipe 2 inches in diameter, and 

 by Stanton 1 on the flow of air through pipes of 5 and 7*4 cmm. 

 diameter, however, indicate that the velocity of the film in actual contact 

 with the wall is zero, even with sinuous flow, and that the velocity 

 at first increases very rapidly as the centre of the pipe is approached. 

 The film of fluid in the immediate neighbourhood of the wall appears 

 to be moving with steady viscous flow, this state of viscous flow merging 

 almost imperceptibly into that of sinuous flow, the thickness of the film 

 undergoing rectilinear motion being extremely small. 



In the latter experiments a Pitot tube having an orifice only 

 25 millimetre deep was used. In rough pipes (resistance proportional 

 to v 2 ) the velocity curve was found to be similar from the centre to within 

 3 millimetres of the walls, for all velocities, and to be a parabola, having 

 the equation 



v = V C -A r 2 . 



For smooth pipes the curve was also parabolic up to a radius of 0*8 a. 

 For exact similarity of the curves over the whole range of radii, it is 

 necessary that the central velocities should be inversely proportional to 

 the pipe diameters. Fig. 98 shows velocity curves obtained in these 

 experiments. 2 



ART. 67 A. MIXING OF ADJACENT LAYERS DURING FLOW OF LIQUID 



IN PIPES. 



From the fact that the velocity near the centre of a pipe is much 

 greater than near the walls, it is evident that there must be a continual 

 admixture of the faster moving liquid with those more slowly moving 

 particles nearer the walls ahead of it. Thus the particles of a column of 

 the fluid, originally of unit length, will, at any subsequent time, be 



1 " Proc. Roy. Society," A., vol. 85, 1911, p. 366. 



2 In the above formula V c is the velocity at the centre of the pipe. 



