84 



Mr. 0. Reynolds. 



[Mar. 15, 



III. 44 An Experimental Investigation of the Circumstances which 

 Determine whether the Motion of Water shall be Direct or 

 Sinuous, and of the Law of Resistance in Parallel Chan- 

 nels/' By Osborne Reynolds, F.R.S. Received March 7 y 

 1883. 



(Abstract.) 



1. Objects and Results of the Investigation. — The results of this, 

 investigation have both a practical and a philosophical aspect. 



In their practical aspect they relate to the laws of resistance to the 

 motion of water in pipes, which appears in a new form, the law for 

 all velocities and all diameters being represented by an equation of 

 two terms. 



In their philosophical aspect these results relate to the fundamental 

 principles of fluid motion ; inasmuch as they afford for the case of 

 pipes a definite verification of two principles, which are that the 

 general character of the motion of fluids in contact with solid surfaces 

 depends on the relation (1) between the dimensions of the space occupied 

 by the fluid and a linear physical constant of the fluid; (2) between the 

 velocity and a physical velocity constant of the fluid. 



The results as viewed in their philosophical aspect were the primary 

 object of the investigation. 



As regards the practical aspect of the results, it is not necessary to 

 say anything by way of introduction; but in order to render the 

 philosophical scop e and purpose of the investigation intelligible, it is 

 necessary to describe shortly the line of reasoning which determined 

 the order of investigation. 



2. The Leading Features of the Motion of Actual Fluids. — 

 Although in most ways the exact manner in which water moves is 

 difficult to perceive, and still more difficult to define, as are also the 

 forces attending such motion, certain general features both of the 

 forces and motions stand prominently forth as if to invite or defy 

 theoretical treatment. 



The relations between the resistance encountered by, and the 

 velocity of a solid body moving steadily through a fluid in which it is 

 completely immersed, or of water moving through a tube, present 

 themselves mostly in one or other of two simple forms. The resistance- 

 is generally proportional to the square of the velocity, and when this is 

 not the case it takes a simpler form, and is proportional to the velocity. 



Again, the internal motion of water assumes one or other of two 

 broadly distinguishable forms — either the elements of the fluid follow 

 one another along lines of motion which lead in the most direct 

 manner to th eir destination, or they eddy about in sinuous paths, the 

 most indirect possible. 



