DISTKIBUTION OF VELOCITY IN OPEN CHANNEL 841 



If v 8 = surface velocity, i.e., where y = 0, C = v a 



W sin ( ' By \ 2 B 2 p 



2 fx \ ^ " " W 7 sin / " *~ 2 JF sin 

 7?V TT sin (9 / _ _Bj/_\ 2 g , 



^" ' 2 PF sin d ~ 2 n* \ ^ " " IF sin (9 / 

 the equation to a parabola having a horizontal axis at a depth 



a . 

 Since 



JFsin 

 d v W sin 



y ~ n W sin 



we have = 0, i.e., the velocity is a maximum where 

 dy 



r 2 W sin d 

 _ v 4. ^ sin g 2 /4) 



/. from (2) and (4) we have r^ - v = W * m dji - ?/) 2 . (5) 



If v b = bottom velocity, where y = h 



*W*-.T* 



Vh i; W sin 



Bh- W sin e /i 2 from (2) 

 2 //, 



B = 



/A 



?L..E!L(fcy_^. (6) 



Also - t-j = S (y - ft) + < (^ - ?/ 2 ) 



(7) 



While different observers have deduced different forms for the vertical 

 velocity curve, the parabola with its vertex either in or below the surface 

 appears to fit the majority of cases fairly well. 



The foregoing analysis is therefore interesting, as giving the correct 

 form of curve. 



