DISTRIBUTION OF VELOCITY IN OPEN CHANNEL 343 



W sin 6 f /i 2 

 v = v inax -- y- I - h yi + 



Thus 



W sin h* 



.'. t'fc V = --771 - 



24 fx 



from which, b> determination of the mid-depth velocity, the mean 

 velocity may be determined. 



In general the mid-depth velocity is from r02 to 1*06 times the mean, 

 and from "94 to *98 of the maximum. 



If y be the depth at the point having a velocity equal to the mean, we 

 have, from equations (5) and (9) 



3 



+ J^~h 4~ 2 



Putting ?/i = *2 h this gives y = '62 h. 

 yi = -3 h y = '65 h. 



ART. 97. PERMISSIBLE VELOCITY IN OPEN CHANNELS; EROSION AND 

 DEPOSITION OF SILT. 



Water in motion exerts an erosive or scouring action on the bed and 

 sides of the containing channel, and the maximum permissible velocity 

 thus depends on the nature of the bed. 



Particles of matter once disturbed, may be transported either by being 

 rolled along the bed of the stream or by being carried in suspension, and 

 for each material a certain critical velocity must be attained, depending on 

 its size and specific gravity, before this is set in motion. Once in motion, 

 however, the velocity may be reduced somewhat below this critical value 

 before the material is again deposited, as is indicated (p. 344) by the 

 results of experiments by Dubuat 1 on transportation in small wooden 

 channels. 



While the erosive power of water varies as the square of its velocity, 

 its transporting power, or the power to move boulders, etc., which may 

 lie in its path, varies approximately as v 6 . This may be seen if we con- 

 sider that the force exerted by the stream on any body is equal to the 

 change of momentum produced in the stream passing the body, and since 

 the area of that portion of the stream affected is proportional to the 

 sectional area, a 2 , of the body, this force will be equal to K v 2 a 2 Ibs. 

 The force resisting motion is that of the friction of the body on the 



1 Principes (V Hydr antique, Dubuat. Paris, 1816. 



