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ÿþE n e r g y E q u a t i o n f o r S t e a d y O p e n - C h a n n e l F l o w h t t p : / / e d u g e n . w i l e y . c o m / e d u g e n / c o u r s e s / c r s 2 4 3 6 / c r o w e 9 7 7 1 / c r o w e 9 7 7 1 . . . 1 5 . 2 E n e r g y E q u a t i o n f o r S t e a d y O p e n - C h a n n e l F l o w T o d e r i v e t h e e n e r g y e q u a t i o n f o r f l o w i n a n o p e n c h a n n e l , b e g i n w i t h E q . ( 7 . 2 9 ) a n d l e t t h e p u m p h e a d a n d t u r b i n e h e a d e q u a l z e r o : h p = h t = 0 . E q u a t i o n ( 7 . 2 9 ) b e c o m e s ( 1 5 . 6 ) U s e F i g . 1 5 . 3 t o s h o w t h a t w h e r e S 0 i s t h e s l o p e o f t h e c h a n n e l b o t t o m , a n d y i s t h e d e p t h o f f l o w . A s s u m e t h e f l o w i n t h e c h a n n e l i s t u r b u l e n t , s o ±1 = ±2 H" 1 . 0 . E q u a t i o n ( 1 5 . 6 ) b e c o m e s ( 1 5 . 7 ) I n a d d i t i o n t o t h e f o r e g o i n g a s s u m p t i o n s , E q . ( 1 5 . 7 ) a l s o r e q u i r e s t h a t t h e c h a n n e l h a v e a u n i f o r m c r o s s s e c t i o n , a n d t h e f l o w b e s t e a d y . F i g u r e 1 5 . 3 D e f i n i t i o n s k e t c h f o r f l o w i n o p e n c h a n n e l s . C o p y r i g h t © 2 0 0 9 J o h n W i l e y & S o n s , I n c . A l l r i g h t s r e s e r v e d . 1 o f 1 1 / 1 5 / 2 0 0 9 1 : 3 0 A M
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