212 DIFFERENT VELOCITIES IN A CROSS-SECTION. 



114. Different Velocities in a Cross-Section. The 



velocity of the water is not uniform in all points of the 

 same transverse section. In all actual streams the different 

 fluid filaments have different velocities. The adhesion of 

 the water to the bed of the channel, and the cohesion of the 

 molecules of water cause the particles of water nearest to 

 the sides and bed of the channel to be most hindered in 

 their motion. For this reason, the velocity is much less at 

 the bottom and sides than it is at the surface and centre. 

 According to some authors, the maximum velocity in a 

 straight river is generally found in the middle of its sur- 

 face, or in that part of the surface where the water is the 

 deepest.* Theoretically we should expect this, but practi- 

 cally it is often very different. 



The theory adopted by most modern writers is the fol- 

 lowing: The motion of the water being caused solely by the 

 slope of 'the surface, the velocity in all parts of any trans- 

 verse section of the river would be equal, were it not for the 

 retarding influence of the bed. The layer of elementary 

 particles next to the bed adheres firmly to it by virtue of 

 the force of adhesion. The next layer is retarded partly by 

 the cohesion existing between it and the first, partly by the 

 friction, and partly by the loss of kinetic energy arising from 

 constant collision with the irregularities which correspond 

 to those of the bed. The next layer is retarded in the same 

 manner, but in a less degree. Thus, according to this 

 theory, the effect of the resistances is diminished as the 

 distance from the bed is increased ; and assuming, as is 

 usually done, that no sensible resistance is experienced from 

 the air, the maximum velocity should be found in the sur- 

 face filament situated at the greatest distance from the bed. 

 The many experiments, however, which have been made to 

 determine the actual variation in velocity at different 

 depths, and upon the surface, at different distances from the 

 banks, give very different results. 



* Weisbach's Mechs., p. 956 ; also Tate's Wech. PJiil., p. 308, 





