GRADES AND SELF-CLEANSING VELOCITIES 155 



just given are summed up by Mr. Hooker with the state- 

 ment that the suspension of sediment in flowing water may be 

 attributed to three causes acting together, or in rare cases 

 separately: 



" First. The resultant upward thrust due to eddies, con- 

 ditioned upon the fact that the earth's (bed of stream) pro- 

 file offers more rugosities than the air profile, and the effort 

 exerted by a current upon a solid varies as the square of the 

 relative velocities. 



" Second. The resultant upward motion of solids due to the 

 fact that an immersed body tends to move faster than the 

 mean velocity of the displaced water, and in such motion tends 

 to follow the line of least resistance. 



" Third. The viscosity of the water." 



The law of Airy, that the transporting power of flowing 

 water varies as the sixth power of the velocity, Mr. Hooker 

 passes over without comment, but he gives curves showing the 

 increase of suspending power with velocity. 



By these laws as given, it is evident that a certain velocity 

 and depth are necessary to keep material from sedimentation. 

 The exact relation between velocity and depth to secure the 

 best transporting power is not known. In the case of sewers 

 it is generally assumed that for a given quantity of water the 

 maximum transporting power is secured with the maximum 

 velocity, and that therefore a sewer section in which the vol- 

 ume of flow is variable should be designed so as to keep the 

 velocity of flow for all depths equal, or as nearly equal as pos- 

 sible, to that obtainable from the section most favorable for 

 that quantity if considered alone. Since the maximum velocity 

 for a constant quantity is obtained when area divided by 

 wetted perimeter is a minimum, the section generally used as 

 giving the greatest velocity is circular, and in sewers of vary- 

 ing flow the section is egg-shaped as being the best possible. 

 Should it, however, be found that the depth of flow is more 

 important as a function of the transporting power than is now 

 thought, the maximum velocity will be no longer sought, since 



