222 



LECTURE XXIV. 



ON THE FRICTION OF FLUIDS. 



WE have hitherto considered the motions of fluids independently of the 

 resistance which they undergo from the vessels containing them and from 

 the surfaces in contact with them, as well as from the interference of the 

 neighbouring particles with each other ; there is, however, a variety of 

 cases of very common occurrence, in which these frictions most materially 

 affect the results of our calculations ; so that before this subject was labo- 

 riously and judiciously investigated by the Chevalier du Buat,* it was 

 almost impossible to apply any part of our theoretical knowledge of hy- 

 draulics to practical purposes. 



The effect of friction is particularly exemplified by the motions of rivers, 

 in which almost the whole force of gravity is employed in overcoming it. 

 When the inclination and the dimensions of a river continue uniform, the 

 velocity is also every where equal ; for otherwise the depth would become 

 unequal : here, therefore, the force of gravitation must be an exact counter- 

 poise to the resistance which is to be overcome, in order that the water may 

 flow with its actual velocity : this velocity having been originally derived 

 from the effect of a greater inclination near the origin of the river. When 

 the river is thus proceeding, with an equable motion, it is said to be in train ; 

 and it is obvious that no increase of its length will produce any alteration 

 in its velocity. There is, therefore, a very material difference between the 

 course of a river, and the descent' of a body, with an accelerated motion, 

 along an inclined surface. For when a solid body is placed on an inclined 

 plane, the force of friction is either great enough to overpower its relative 

 weight, and to retain it at rest, or else the friction is constantly less than 

 the gravitation, and the motion is always accelerated. But the resistance 

 to the motions of fluids arises principally from different causes ; not from 

 the tenacity of 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 curva- 

 ture assumed by the outline of a stream of water issuing from a simple 

 orifice which constitutes the contraction already described, is very nearly 



* Principes d'Hydraulique, 1786, and Svols. 1816. 



