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δ x V A A V V + x x δ A + x x δ x A V Q AV A+ δx V + δx V A A V AV + A δx+ V δx+ δx V A A δx+ V δx V A A + V ( ) ( AV ) AV Constant Q

1 Text 7.1 ( ) P1 7 7.P8 5 D v g z x + x 1 v ( v+ x ) g + x z z + x L

v z 1 v z + + + z+ x+ + x+ v+ x g g + x v v v v + v x+ x v + v x x v z+ + + g v z + + + g Constant

v z + + + g Constant D L

v z+ + + g z i, I f : v + i + + I f g v I f i I g e :

Cezy I f v CR Manning I f nv R 4 v i+ + + I f g

Cezy Manning v v i + + + g C R v n v i + + + 4 g R

Q Q Av v A v Q 1 Q A Q A g g A g A ga Q A Q A A B + ga ga B v v + i + + g C R Q A A B v i + + + ga B C R Q A Q A B Q 1 i + ga ga B C A R

Cezy Q A B Q i + Q A 1 ga ga B x C A R Manning Q A B n Q i + ga B A R Q A 1 ga 4/

B A A B, R,, B Q A B Q i + CB A Q 1 B ga gb ga B x C A R q g Manning Cezy q 1 i ic q 1 g nq B 1/ Manning nq 1 i i q 1 g 1/ Cezy q Ci Manning 1 nq i

Cezy Manning 1 1 i 1 i 1 i 1 i 1 1 ϕ ϕ B z z ay y

Cezy q q Ci g Manning i g C 1 1 nq q i g g i 1 9 ng q 9 1 9 nq q i g q g 9 1 9

i < i q q g i Ci gci i i< i 1 i 1 > i (Mild Slope Cannel) i< i > i > i q q g i Ci gci i i > i 1 i 1 < i (Steep Slope Cannel) i > i <

4 i< i > > > i > > > > > > > > > x > M 1 (Bak Water) i< i

i 1/ 5, q 1. (m / s) n.5 1 nq i q g 46.7m 7.54m downstram 84.6 (m)

> > i < > < > x M S i< i i > i

i 1/ 5, q 1. (m / s) n.5 1 nq i q g 46.7m 7.54m downstram 56.4 (m)

> > i < < > x < M1 M i< i

5 i > i > > > i > > > > > > > > > > x S1 i > i

> > i > < < < x S i > i

i 1/5, q 1. (m / s) n.5 1 nq i q g 46.7m 5.4m upstream 4.4 (m)

M S i< i i > i

i 1/ 5, i 1/ 5, q 1. (m / s) n.5 1 1 nq nq 7.54m 5.4m i i q 46.7m g

i 1/ 5, i 1/ 5, q 1. (m / s) n.5 1 1 nq nq 7.54m 5.4m i i q 46.7m g

> > i < < > < x S1 i > i S S

i 1/5, q 1. (m / s) n.5 1 nq i q g 46.7m 5.4m upstream 4.8 (m)

M M i< i M1 S1 S S i > i

> Critial Slope Cannel i i > > > i i i i > x i ix + C x L HH i L+ C C H i L i ( x L) + H L x x' H i x' C1 x ' i x L i i i

< i i i i > < x i ix + C x HH C i x+ H i H C i i x i

i Q A B Q i + Q A 1 ga ga B x C A R Q i CB Q 1 gb Q i CB Q CB q q ( ) d dx ( ) d dx C C 1 4 q x+ K 1 4 4 C x H K H H 4 q x H H C 4 1 ( 4 4 ) ( ) (4)

> Q CB < > < q x H H C 4 1 ( 4 4 ) ( ) H H x x

< Q CB < < > q x H H C 4 1 ( 4 4 ) ( ) H H x x

i < > < Q i CB < > < A i <

< < Q i CB < < > A i <

S S1 M M i > i M S i< i i > i

1 Cezy 1 i 1 Manning 1 i 1 1 Text( )p9 Manning

z v n v + + + 4 g R Q Av, A B, R z Q n Q + + + 1 B gb z, B, n, g, Q

Q n Q z+ + + 1 gb B 1, Q Q 1 z+ + z + + gb gb x 1 1 x x 1 nq nq + + 1 1 B 1 B

Q Q 1 z+ + z + + gb gb x 1 1 nq nq + + 1 1 B 1 B Q Q 1 z + + z 1 1 gb gb1 1 x nq 1 1 + + 1 1 B1 1 B Q Q n Q x 1 1 z z 1 + + 1 + + 1 1 gb gb1 1 B1 1 B 1, or 1 1

1 Q Q n Q x 1 1 z z 1 + + 1 + + 1 1 gb gb1 1 B1 1 B Q n Q x Q n Q x 1 1 1 1 1 gb1 1 gb B1 1 B f( ) + z + z 1 1 X 1 f ( X ) X + α X + β X + γ f( X ) X Q n Q x α, β gb B 1 1 Q n Q x 1 1 gb B γ z + z

Y f( X) X Y X Y f( X) X X Newton f( X ) X f( X + X) 1 f X + f X X + f X X +! ( ) '( ) ''( ) X f( X ) + f '( X ) X X f '( X ) f( X )

X f '( X ) f( X ) 1 f( X) X + α X + βx + γ 1 f '( X) 1 αx βx 1 1 f( X ) X + α X + βx + γ 1 f '( X ) 1 X X 1 α β X No f( X ) f ( X), f '( X) X f '( X) f( X ) END Yes Newton X + X X

Manning n., i1/1, B1(m) Q(m /s) (1) 1 1 9 9 ng. 9.8 i.4 9 9 q 1 () i 1/1.1< i.4 () 1 1 nq. ( /1) 1.15(m) i 1/1 q g ( /1) 9.8.74(m)

(4) A.9(m) A A 5mB. B A 1.15(m).74(m) 1? M.9(m) x 5(m) < < M

1 f( X) X + α X + βx + γ Q α.4 gb 9.8 1 1 nq x. 5 β.4 B 1 1 Q n Q x. 5 ε z + z.5.9 1.159 1 1 1 gb 9.8 1.9 B 1.9 z 1 1/1 5m z z1 z 5 /1.5 1 f( X) X +.4X.4X 1.159 1 f '( X) 1.48X +.1X

X.9m X.9, f( X ).67, f '( X ).656 X.9785 X.998 X.998, f( X ).74, f '( X ).748 X.517 X.99 X.99, f( X ).87, f '( X ).74 X.11 X.99 X.99 1.99(m) 1.15(m).74(m) C 1? x 5(m) B M 1.99(m) x 5(m) A.9(m)

(5) 5m ( ) M

(6) 1.5m M1 ( )