13G UNIVEESITT OF VIRGINIA PUBLICATIONS 



Whence the velocity of discharge 



4/ 1.5 + m ~ 



^9 



• ^/Jr, (23) 



/V m + 1.5^ 



wherein J = E/L is termed the static grade or slope in contra-distinction 

 to 



— A 



*'"" L 



which is called the hydraulic grade or slope, h being the head lost by 

 resistance. If, as is the case in all long pipes, conduits and open channels, 

 l.hr/L is so small as to be negligible with respect to m, then J can be 

 taken as equal to s and we write 



y = c yl7; (24) 



where 



c = Jt, (25) 



' m 



is called the coefficient of velocity. 



7. Fixing the attention on the equations (20) and (24), when the 



constants in (20) have been determined and H, L, r are known, the 



solution of the two equations (20) and (24) furnishes the velocity of 



discharge. This solution may be, and is generally, effected by choosing a 



provisional value of V and using it in (20) to compute a provisional value 



of m, which value substituted in (24) furnishes an approximate value of 



V. This value of V when used in (20) gives a closer value of m. which in 



(24) gives a value of V which may be taken as final. Otherwise, on the 



elimination of m the equations (20) and (24) furnish a quadratic equation 



in V, the solution of which is easily obtained in a form suitable for 



logarithmic computation by the ordinary well-known process of solution 



by means of circular functions. It is, however, preferable to eliminate T' 



between (20) and (24) and determine m from the resulting quadratic 



equation. The solution is 



m = , ,\ . tan=^®, (26) 



1 + 6rP 



