140 HYDEAULICS AND ITS APPLICATIONS 



d + a 



-).,- log '-^ 



' (1 



Let r a = n d 



Then Q = b J 2 g (H - a) . n d log f I + i 



(r b \* (v a \* H-a 



And since ( - - = ( - 



. 



a & H a d 



, ,., yfi |- ^ I [Jg^p ,,(,+!)] 



But for permanence of regime the flow will adjust itself until the dis- 

 charge is a maximum, and in this case-^ = o. 



(jt) 72- 



On differentiating 2 this gives -^ ^ = log e (l + - j 

 or n = '8814 (log (1 + i ) ='7581^ 



7/0^ '8814 X 2'7628 1 



/. Q = b ^ 2 g (H ay . 2 - y 



Taking a-i- II = '13 this becomes 



Q = -423 6 * 



= 3-39 6 H% G ' s ' 

 a value in very close agreement with results experimentally. 



H - a 



~H -a-d 



i)) 



+ 1) 4 



) 1 



; I 



.-. 2 n + 1 = log (l +-} \(n + 1) (4 n + 1) - 2 n (2 + 1)}. 

 \ w/ \ ' 



