Canon Moseley on the steady Flow of a Liquid. 185 



two gauges. This head of water is that designated in the fol- 

 lowing paper by the symbol h. 



Besides determining the efflux under different conditions, M. 

 Darcy determined also the velocities of the water at different 

 distances from the axis of certain of the pipes on which he experi- 

 mented; and with reference to the theory of the flow of liquids, 

 this was the most interesting feature of his experiments. He 

 effected it by means of the instrument well known as Pitot's tube, 

 into the construction and use of which he introduced some ad- 

 mirable improvements, for the particulars of which the reader is 

 referred to his work. The results he arrived at are stated at 

 length in Table I. of the following paper. 



A film in a liquid flowing through a pipe, in the sense in 

 which the word is used in the following paper, is a continuous 

 portion of the liquid, every molecule in which flows with the 

 same velocity. A filament is an exceedingly narrow film. To 

 the surface of the pipe a film of the liquid is supposed to adhere 

 and to remain at rest. The film adjacent to it moves over this 

 fixed film, the third over the second, the fourth over the third, 

 &c. with continually increasing velocities; the film nearer to 

 the surface moving always slower than that more remote. This 

 is proved by the experiments of MM. Darcy and Bazin. 



The resistance opposed by the surface of the pipe to the flow 

 of the liquid immediately in contact with it is represented by the 

 formula 



P= / t I + X l V», (1) 



where P is the resistance per unit of surface, V the velocity of 

 the flow, \ a constant, and fi x a term as to which there is a dif- 

 ference of opinion whether it is constant or increases with the 

 velocity. 



This formula is founded on experiment*. The first term in it 

 is considered to represent that part of the resistance which is 

 due to the adherence of the liquid to the surface of the pipe, and 

 which is of the nature of that which in solid bodies is opposed 

 to shearing. 



The second term is understood to represent the resistance 

 caused by the impacts of the molecules of the flowing liquid on 

 those of the film of liquid fixed to the surface of the pipe, and 

 on the eminences of the solid surface of the pipe which project 

 through that film. 



Let the steady flow of a liquid in a horizontal circular pipe of 

 uniform dimensions and roughness of surface be supposed to be 

 maintained by the pressure of the liquid in a reservoir whose 

 surface is always on the same level ; let 



* See Poncelet, Introduction a la Mecanique Industrielle, art. 387, 388. 



