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293 



LECTURE XXIV 



ON THE FRICTION OF FLUIDS. 



\V^E 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 Avith 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 laboriously 

 and judiciously investigated by the Chevalier de Buat, it was almost impossi- 

 ble to apply any part of our theoretical knowledge of hydraulics 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 in- 

 clined 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 gravita- 

 tion, and the motion is always accelerated. But the resistance to the mo- 

 tions of fluids arises princij^lly from different causes; not from the tenacity of 



