ON THE FRICTION OF FLU"lDS. 293 



the fluids, which, where it exists, is a force nearly uniform, like that of 

 friction, but principally from the irregular motions and mutual collisions of 

 their particles ; and in this case, according to the laws of mechanics, it must 

 vary nearly in proportion to the square of the velocity. For when a body 

 is moving in a line of a certain curvature, the centrifugal force is always as 

 the square of the velocity; and the particles of water in contact with the sides 

 and bottom of a river or pipe, must be deflected, in consequence of the 

 minute irregularities of the surfaces on which they slide, into nearly the same, 

 curvilinear paths, whatever their velocity may be, so that the resistance, which 

 is in great measure occasioned by this centrifugal force, must also vary as the 

 square of the velocity. Thus also the curvature assumed by the outline of a 

 stream of water issuing from a simple orifice, which constitutes the contrac- 

 tion already described, is very nearly the same, whatever the velocity may 

 be: nor does the friction increase with the pressure, as is demonstrated by 

 an experiment of Professor Robison on the oscillations of a fluid through a 

 bent tube, terminated by two bulbs, which were performed in the same time, 

 whether the tube w^as in a horizontal or in a vertical position. Mr. Coulomb 

 has also proved the same fact by experiments on the vibrations of bodies 

 .immersed in fluids, and suspended by twisted wires; he finds that precisely 

 at the surface, the friction is somewhat greater than at any depth below it: 

 he also considers a certain part of the friction as simply proportional to the 

 velocity, and a very small portion only, in common fluids, as perfectly inde- 

 pendent of it. 



It is obvious that wherever the friction varies as the square of the velocity, 

 or even when it increases in any degree with the velocity, there must always 

 be a limit, which the velocity can never exceed, by means of any constant 

 force, and this limit must be the velocity at which the resistance would be- 

 come equal to the force. It is for this reason that a light body, descending- 

 through the air, soon acquires a velocity nearly uniform ; and if it be caused, 

 by any external force, to move for a time more rapidly, it will again be speed- 

 ily retarded, until its velocity be restored very nearly to its original state. 

 In the same manner the weight of the water in a river, which has once ac- 

 quired a stationary velocity, is wholly employed in overcoming the friction 

 produced by the bottom and the banks. - . 



