172 SEWER DESIGN 



down-stream affects the shape of the parabola, bringing the 

 axis nearly to the surface, so that the surface velocity is the 

 maximum velocity, while an up-stream wind drops the axis 

 below the mid-depth. In the last case the bottom and top 

 velocities were about the same, while the up-stream wind 

 reduced the bottom velocity to about 85 per cent of that at 

 the surface. 



It is to be noticed that before the construction of the 

 Kutter formula the most advanced development of the primi- 

 tive formula v = cVRS was embodied in the formula of M. 

 Bazin, who made the coefficient c vary with (i) the degree of 

 roughness of the wetted perimeter, decreasing with the increase 

 of roughness; (2) the value of the hydraulic mean radius, increas- 

 ing with its increase; and (3) the slope, decreasing with its 

 increase in large channels and increasing with its increase 

 in small channels. 



It remained for Ganguillet and Kutter to combine all 

 these variables into one algebraic expression for the value of 

 c, a discussion of which follows in logical order. 



Before taking up the discussion of the Kutter formula, 

 however, the two latest English formulae may well be noticed. 

 The first, by Henry Robinson, was arrived at, says the author, 

 by Mr. Edgar Thrupp, the author's chief assistant, and is 

 said to be based on the results of direct experiments in sewers, 

 made by himself and by a great many other observers during 

 the last forty years and up to the present time. 



The formula is 



R x 



cVs' 



where v is the velocity in feet per second ; 

 R is the hydraulic radius; 



5 is the length of sewer in which it falls one foot; 

 C is a coefficient of roughness; and 

 x and n constants. 



