:

, 2015.

:

:

.

1

1. ................................................................................................................................... 2

2. ....................................................................................................... 5

2.1. .................................................................................................... 6

2.2. ......................................................................................................... 9

3.

............................................................................................................ 15

3.1. Boes, Hager 2003a, 2003b .......................................................................................... 16

3.2. Hunt et al. 2008 ........................................................................................................... 18

3.3. Hunt et al. 2012 ........................................................................................................... 20

3.4. Wadhai et al. 2015 ....................................................................................................... 25

3.5. .................................................................. 25

3.5.1. ........................................................................... 25

3.5.2. .......................................................................................... 27

3.5.3. ................................................................ 28

4.

..................................................................................................................... 31

5. ............................................... 44

5.1. ......................................................................... 45

5.2. ....................................................................................... 46

5.3. USBR III ........................................................................................................... 47

6. ............................................................................................ 49

6.1. ....................................................................................... 50

6.2. USBR III ........................................................................................................... 52

7. ...................................................................................................................... 54

8. .......................................................................................................... 56

9. ........................................................................................ 60

10. 1 .................................................................................................. 65

11. 2 .................................................................................................... 75

12. ................................................................................................................. 81

13. .................................................................................................. 83

1.

3

,

.

,

, .

.

(RCC Roller-Compacted Concrete) 80- 20. .

.

( RCC , ),

.

1.1

,

,

(Gonzalez, Chanson 2007).

2018. 5500

50 ,

(Woolbright, 2008).

,

, .

,

.

.

4

1.2

: ,

; ,

.

,

, . .

,

.

.

(Boes, Hager 2003a, 2003b; Hunt

2008; Hunt, Kadavy 2005-2012,)

.

.

,

.

2.

6

2.1.

. ,

.

( ),

.

2.1

, .

.

, = / ( [m3/s] , [m] ) , ( 2009):

- ( 2.2), ,

;

- ( 2.2b),

.

7

2.2

.

Chanson- ( 2009), :

[m] , [m] ( 2.2).

11 52, / 0,2 1,3. ,

30%. , > 1,3 ,

, < 0,7 (, [m] ,

, [m] , [m]

(2.1)) ( 2011).

Boes Hager (2003b):

[rad] .

:

: [m3/s], [m], a = 9,81 m/s2.

(2.3) ,

.

(2.1)

= 3 (2.3)

1,057 0,465

(2.2)

0,91 0,14

8

( 2009).

,

. ,

, .

(RCC) , .

.

.

( )

.

.

, (

) . ,

, . .

,

, ,

.

, , ,

.

,

( 2.4).

.

,

.

( 2.3).

,

.

, ,

. Vischer- Hager- (1998),

:

: - ( ) [rad], [-].

= +1

(2.4)

9

2.3

2.2.

()

, .

, .

,

.

. ,

(

)

.

0,1% 1%, .

1% .

,

1,

1 1 ( 2.4).

( 2009):

1 2 = 2 1 (2.5)

10

2.4 ( 2009)

1 2 [N] 1 2, 1 2 1 2 ,

1 2:

:

: (1) 1 2

, (2)

(56 2), (3) 1 2 (4) , .

.

:

- ,

( ) ,

;

-

( 2.4),

-

( 3.1). ,

.

USBR ,

11 = 22 (2.6)

21

=1

2(81 + 1 1)

(2.7)

11

.

USBR III , 2.5.

2.5 USBR III (Peterka 1978)

, USBR III (

). , , , ( ), , , , , ( 2009):

: [m] , [m] [m/s] .

70%

. ( 2.7):

:

[m] .

B/2 ( 2.6), :

=

2

2=

2

2

(2.8)

1 2 = 2 1

(2.9)

1

2

2+ 1

2

2=

22

2+ 1

(2.10)

12

2+

12

1

1

4

2

=

22

2+

22

2

(2.11)

12

2.6 ( 2009)

(2.11) .

,

, . , .

, ,

, , ,

. ,

USBR III = 4 5 2, 2,7 2.

: USBR III

?.

.

2.7

/2 USBR III . ( 0,7:1)

= 2,7 2.

Boes Hager (2003b) , (

) ( )

, ,

( ).

, Cardoso (2007)

/2 , H:V=0,75:1 ( 2.8). , /2 : 2,7 USBR III , 4,0

.

13

2.7 /2 , ;

USBR III

(Peterka 1978)

2.8

: Peterka , Cardoso et al. (2007)

14

Frizell, Kubitchek Matos (2009),

, ,

USBR III

.

,

( 2.9). ,

15m , .

2.9 .

e = 74m3/s , (Frizell et al. 2009).

a a (

11,0m/s), 49% .

21,2, 60,8.

, ,

USBR III ( (2.11)),

.

USBR III

,

, ,

, . /2 USBR- (2,52,7) .

, ,

!

3.

16

2,

3 ( 3.1):

- , ,

, ()

, , - , .

.

3.1

3.2

.

Boes Hager (2003a, 2003b).

3.1. Boes, Hager 2003a, 2003b

,

(

) ,, .

,

17

( 3.1).

(Boes, Hager 2003a):

: [m], [rad], [m].

3.3 (Boes, Hager 2003b)

(Boes, Hager 2003b):

, 90,, (Boes, Hager 2003b):

[-] , s (Boes, Hager 2003b):

=5,90

6/5

()7/51/5

(3.1)

, = 0,215 2/3

(3.2)

90, = 0,5 (0,1 +0,5)

(3.3)

=

3

(3.4)

18

.

(Boes, Hager 2003b):

(

, hw,u), ,

. (Boes, Hager 2003b),

, Hdam,u,

, hc, :

( )

(3.6),

( (3.32) 2009; 2011).

:

[m] , (Khatsuria 2005):

.

3.2. Hunt et al. 2008

.

(. standing wave, oblique standing wave, shock wave)

2.1. ,

( 3.2). ,

2 (Hunt et al. 2008, 2012):

,

.

= 1 ,90,

(3.5)

, = 24 ()2/3 (3.6)

=1/6

26

(3.7)

=

(3.8)

2 = (, , , )

(3.9)

19

2008. (Hunt et al.)

.

1:22, H:V=3:1 ( = 18,43) 15, 30 52, . / ( , .), .

3.4 (Hunt et al. 2008)

3.5.

15, 30 52,

1,0, 1,75 3,0.

( = 18,43), , . ,

(PMF)

.

20

3.5 ,

(Hunt et al. 2008)

3.3. Hunt et al. 2012

2012. ,

( , ). 2008. , .

3.6 (Hunt et al. 2012)

21

3.4 :

: 2 , [m/s],

[kg/m3], C-C [m2].

(3.11)

, -, .

.

3.7:

, , , .

:

- ( 3.8) :

-.

3.7 -

=

22

(3.11)

= sin() + 0 + cos()

(3.12)

= cos() + 0 ()

(3.13)

= cos() sin() + cos() cos() + ()

(3.14)

22

3.8 -

3.8 -:

( -, . ) :

2 , B-B ( 3.9).

3.9 B-B

,

. ,

, :

2 ,

. , :

= sin() + cos() + 0

(3.15)

= cos(2) cos() + cos(2) sin() sin(2)

(3.16)

= 2

2 cos(2) 2

(3.17)

= 1

2 cos() 2

(3.18)

23

1 , . :

[m3] .

.

(Hunt, Kadavy 2006), :

:

:

1 [m/s] A-A. 2 ( 3.4), :

(3.23) 2 :

1 [-] -:

(3.24)

.

, (3.24)

=

(3.19)

= 2

2 sin()

2

(3.20)

= 12( )

(3.21)

= 121[cos() cos() sin() + 0 sin() sin()]

(3.22)

2)

2

2 cos(2) cos()

2

22 ()

2

= 1

2 cos()

2+ 1

21[cos() cos() sin() + sin() sin()]2

(3.23)

21

= cos() + 21 [cos() cos() sin() + sin() sin()]2

cos(2) cos() sin() (3.24)

1 =1

2

1 (3.25)

24

.

, -:

1:22

H:V=3:1. 3.1.

3.1 (Hunt 2012)

[] ,/,

[-]

(1 ,/,) [%]

/

0 1,00 0 -

15 0,97 3

30 0,90 10

52 0,94 6

70 1,28 -28

70,

.

10%. 2%, .

,/, = 0,98.

(Hunt 2008), .

(), . = 0,46 = 1,37. , :

(3.24):

(1 , , )

13%.

2

=1

cos(2) (3.26)

= 0,46 2

2 sin() 1,37()

2

(3.27)

21

= cos() + 21 [cos() cos() sin() + sin() sin()]2

cos(2) cos() 0,46 sin() 1,37() (3.28)

25

3.4. Wadhai et al. 2015

Wadhai et al. 2015. ( = 45, =45) Hunt (2008, 2012) :

-

3.5, ,

- : Hunt 2008

50% 23 ( ), Hunt 2012

40% 1% ( ),

- = {10, 20, 40, 80}, = 40, = 80, .

3.5.

3.5.1.

(Bouzina Dam)

.

.

1045mnm, a 1320m3/s 4,03m

1049mnm. ,

H:V=8:9 ( = 48,37).

1:40. 3

: 12,0, 18,8, 22,6, 55m,

40m 30m. :

- ,

- ,

(EC )

(EC

),

- , ,

- , .

EC

. 3.3 3.11

, , ( , ). .

26

3.10

3.11 ( )

27

3.5.2.

, , .

:

:

: , , ,

, , ,

, , .

:

:

,

.

3.2.

3.2 ,

[m]

= 40

[s]

=//

=

= 1/2 6,32

[m/s]

= 1/2 6,32

[m3/s]

= (

)2

= 5/2 10119

[N]

= (

)3 []

[]= 3 64000

[Pa]

=

(

)2

=3

2= 40

[m-1/3s]

= (

)1/6

= 1/6 1,85

3.2 = 130,4 l/s.

= (3.29)

=

(3.30)

1 =

= 1 40 (3.31)

28

3.5.3.

10 11.

3.12

3.13

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0.4 0.5 0.6 0.7 0.8 0.9 1.0

/h

c[-

]

x/L [-]

=22.6

=18.8

=12.0

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

50 55 60 65 70 75

/h

c[-

]

Fr [-]

=22.6

=18.8

=12.0

29

3.13 (Boes, Hager 2003b):

: = /, [-],

0 = = /,

[-],

= / [-], [m],

= 3 (,

2 sin ) [m]

10/3 [-].

,

= , 2%. (3.32) (3.6).

ln ( 1

0 1

0

) = (3.32)

30

3.14 = 12, = 1320m3/s,

4.

32

.

.

, 3,

[(4.1), (4.3), (4.4)]. ,

:

1. ,

2.

(

),

3. ,

4. ( 4.2).

4.1

:

:

: [m],

= 2 [m],

[m], 1 [m], 1 [m/s].

,

4.2, :

: 2 [m], 2 [m/s].

1 = ( 2)11

(4.2)

2 =(1 + 2)

22 (4.3)

1 = 11 (4.1)

33

4.1 -

4.2

:

(4.2) (4.3) (4.4),

:

, = = 11:

= 1 + 22 (4.4)

= 11

(1 + 2)2 211 (4.5)

=( )

(1 + 2)2 2 (4.6)

34

:

4 ,

, , 1, . (. Boes, Hager 2003a, 2003b; Hunt 2012).

(3.38) (3.39) .

, :

1 [-] . ,

. :

, [m] ( = 80m), 3.11.

0,4. , = () (2 = 0,9991):

4.1 , = 12,022,6

/ * 1

[-] [-] [-] [-] [-] [-] [-]

1,0 72,22 1,334

0,4

1,226 1,403 8,07

0,9 70,77 1,305 1,203 1,373 7,77

0,8 68,63 1,260 1,180 1,352 7,32

0,7 65,50 1,177 1,125 1,265 7,50

0,6 61,00 1,008 0,953 1,069 6,04

0,5 54,64 0,859 0,822 0,910 5,92

* - ,

2 =( + 2)

(1 + 2) (4.7)

= (, 1, ) (4.8)

= () (4.9)

= 1,092 104 3 + 2,075 102 2 1,279 + 26,609 (4.10)

35

4.3

= 8,07%,

(4.9):

1,1.

:

, ,

:

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

50 55 60 65 70 75

a [

-]

Fr [-]

(4.10)

= 0,4() (4.11)

1 = 11 = 121( 2) (4.12)

2 = 22 cos() = 22

(1 + 2)

2 cos() (4.13)

36

,

,

:

[N] ,

:

(4.14) :

(4.16)

. 4.4. ,

Boes Hager (2003a, 2003b), (3.28).

4.2 , , = 1320m3/s, o Boes Hager 2003a, 2003b

[m3/s] 1320

[m] 80

[m] 4,00

[m] 3,03

[m] 0,90

[rad] 0,844

[m] 64,00

(3.4) [-] 7,137

, [m] 0,717

90, [m] 1,500

[-] 0,522

1 [m] 0,727

1 [m/s] 22,70

1 [-] 72,22

=1 + 22

(4.14)

= 1 = 121

(4.15)

= (, ) =1

21( 2) + 22(1 + 2) cos()

121

(4.16)

37

4.3 ,

, = 1320m3/s, Hunt 2012.

1 2 2/1 2 [rad] [-] [] [rad] [] [rad] [rad] [-] [m]

0,844 76,02

0,2 0,003 0,22 0,004 0,844 1,00 0,729

5,0 0,087 5,60 0,098 0,842 2,07 1,507

12 0,209 13,16 0,230 0,833 4,52 3,288

18,8 0,328 19,93 0,348 0,817 6,94 5,043

22,6 0,394 23,38 0,408 0,804 8,32 6,051

25 0,436 25,43 0,444 0,795 9,22 6,702

30 0,524 29,36 0,512 0,772 11,16 8,115

4.4 , ,

= 1320m3/s

/ 2 1 2 1 + 22

[] [-] [m] [m/s] [MN] [MN] [MN] [MN] [-]

0,2 0,139 0,462 32,76 29,46 0,36 30,18

29,96

1,01

5,0 0,503 1,677 60,24 24,84 6,77 38,33 1,28

12,0 0,718 2,391 51,32 18,77 12,37 42,97 1,43

18,8 0,867 2,887 45,51 12,75 16,33 43,67 1,46

22,6 0,940 3,129 43,08 9,22 18,17 42,77 1,43

25,0 0,983 3,274 41,77 6,90 19,23 41,75 1,39

30,0 1,071 3,566 39,38 1,78 21,18 38,45 1,28

( ) (

) :

.

,

.

.

. ,

. ( 4.5).

= 2( + 1) = 36,34/ (4.17)

38

4.5 , ,

= 1320m3/s, = 36,34m/s

2 1 2 1 + 22

[] [m] [m/s] [MN] [MN] [MN] [MN] [-]

0,2 0,341

36,34

29,55 0,33 30,20

29,96

1,01

5,0 3,534 23,45 5,19 33,79 1,13

12,0 3,665 17,82 9,51 36,42 1,22

18,8 3,752 12,11 13,53 37,72 1,26

22,6 3,800 8,72 15,70 37,70 1,26

25,0 3,831 6,48 17,03 37,36 1,25

30.0 3,899 1,53 19,71 35,67 1,19

4.5 4.4,

. ,

; ,

,

,

. ,

, .

4.4,

.

.

4.4 ,

, = 1320m3/s, = 80m

1.00

1.05

1.10

1.15

1.20

1.25

1.30

0 5 10 15 20 25 30

I[-

]

[]

39

10 11.

.

( ).

, , :

[Pa], [m2]. = /2, = , (4.18) :

, (4.19)

:

:

:

(4.22) (4.19),

:

:

=

(4.18)

=1

2 2

2

1

(4.19)

1 = 1

2

2

(4.20)

1 = 1

2

2( 2) (4.21)

() =1 2

+ 2, [0, ] (4.22)

2 =1

2 (

1 2

+ 2)2

=

=0

(4.23)

(4.24) 2 =1

2

[(1 2) + 2]3

3(1 2)2 |

=0

=

40

, :

:

4.6,

.

T 4.6 , ,

= 1320m3/s

1 2 1 2 + /

[] [MN] [MN] [MN] [MN] [MN] [MN] [MN] [-]

0,2 29,55 0,33 30,20 0,205 0,001 0,206 30,41 0,007

5,0 23,45 5,19 33,79 0,162 0,023 0,207 34,00 0,006

12,0 17,82 9,51 36,42 0,123 0,082 0,288 36,70 0,008

18,8 12,11 13,53 37,72 0,084 0,182 0,447 38,17 0,012

22,6 8,72 15,70 37,70 0,060 0,258 0,577 38,28 0,015

25,0 6,48 17,03 37,36 0,045 0,315 0,675 38,04 0,018

30,0 1,53 19,71 35,67 0,011 0,461 0,932 36,60 0,026

4.5

(2.7)

( ), . ,

,

(4.25) 2 =1

6(1

2 + 12 + 22)

(4.26) = 1 + 22

41

? (2.7)

( 4.5) ( 2009):

,

, , (4.27) :

1 = 12 (1) =

2 () , :

, :

:

, (4.30)

(2.7).

, 4.7.

4.7 ,

= 1320m3/s, (4.30)

[] [m] [m] [m/s] [-]

0,2 79,6 8,408 1,973 0,047

5,0 69,7 9,551 1,984 0,042

12,0 54,9 11,164 2,153 0,042

18,8 39,8 13,274 2,497 0,048

22,6 30,9 14,967 2,856 0,056

25,0 25,0 16,441 3,215 0,064

30,0 11,9 22,356 4,973 0,113

(4.27)

2

2

2

2 =

2 2

(4.28) 112 =

2

2+

2

(4.29) 121 =

2 (1

2+ )

(4.30) = 1

1

+12

(4.31) =

42

, ( = 80m), (2.7), = 8,382m.

(

2009 2011),

6% 10% = 12,022,6 ( 4.8, 4.6).

4.8 (2011),

(2009) (*), , = 1320m3/s.

4.6

* [] [m] [m] [m] [%]

0,2 79,6 8,408 8,485 -0,94

5,0 69,7 9,551 9,158 4,11

12,0 54,9 11,164 10,041 10,06

18,8 39,8 13,274 12,175 8,28

22,6 30,9 14,967 14,051 6,12

25,0 25,0 16,441 15,775 4,05

30,0 11,9 22,356 22,911 -2,48

4.6

.

.

5

10

15

20

25

0 5 10 15 20 25 30

hn

iz[m

]

[]

(4.30)

2011.

43

,

( 4.4). ,

.

(. (4.10)).

(4.16) , ( = 2 tan(), ). (, ) ( /). , .

5.

45

5.1. 1

,

, ,

.

, ,

.

, .

:

1. , 40m,

2. , 40m ( )

30m ( ).

.

0,1% = 653,02m3/s.

= = 418,00mnm. .

12,40m, 1,40m,

37,20m. 4,10m.

.

0,45m, 0,90m.

, 5,00m.

,

,

.

, ,

:

1. ,

I,

2. USBR III II.

,

1% = 477,64m3/s

8,73m. I 35m, II 23,6m.

1 . RCC : , 2014.

46

5.2.

3 4,

.

( 2014) = 5,02.

5.1 , ,

Boes Hager 2003a, 2003b, 1% = 477,64m3/s

= 1% [m3/s] 477,64

[m] 40

[m] 4,10

[m] 2,44

[m] 0,90

[rad] 0,785

[m] 53,70

(3.4) [-] 5,310

, [m] 0,589

90, [m] 1,225

[-] 0,519

1 [m] 0,595

1 [m/s] 20,08

[-] 69,12

5.2 ,

, 1% = 477,64m3/s, Hunt (2012),

1% = 477,64m3/s

2 2/1 2 [rad] [-] [] [rad] [] [rad] [rad] [-] [m]

0,785 69,12 5,02 0,088 5,00 0,087 0,786 2,00 1,190

5.3 , ,

1% = 477,64m3/s

/ 2 1 2 1 + 22

[] [-] [m] [m/s] [MN] [MN] [MN] [MN] [-]

5,02 0,479 1,285 64,39 6,63 4,74 16,06 9,59 1,67

47

= 33,50m/s, .

5.4 , ,

1% = 477,64m3/s, = 33,50m/s

2 1 2 1 + 22

[] [m] [m/s] [MN] [MN] [MN] [MN] [-]

5,02 3,257 33,50 5,68 3,25 12,15 9,59 1,27

5.5 ,

1% = 447,64m3/s

(4.30) 2011.

[] [m] [m] [m/s] [-] [m] [%]

30,0 11,9 8,73 1,812 0,038 7,67 12,13

5.4 4

.

(4.30),

( 5.5).

5.6 I2

[m] 8,73

[m] 30

[m] 9,20

[m] 35

5.3. USBR III

USBR III

. USBR III

. ,

2,7 (Peterka 1978). .

, .

2 2009.

48

5.7 II3

USBR III

[m] 8,73

[m] 30

[m] 9,20

[m] 23,60

[m] 2,00

[m] 1,50

[-] 10

3 USBR III 2009.

6.

50

6.1.

. .

[m3; kg] [/m3; /kg] []

m3 54 225 7,5 406 688

m3 21 139 7,5 158 543

m3 15 856 7,5 118 923

91 220 684 153

m3 96 876 45 4 359 420

m3 74 875 100 7 487 500

m3 9 322 120 1 118 640

181 073 12 965 560

kg 932 200 1,2 1 118 640

14 768 353

m3 3 778 18 68 004

m3 7 669 55 421 795

m3 2 637 18 47 466

537 265

m3 3 566 140 499 240

kg 356 600 1,2 427 920

1 464 425

m3 2 745 7,2 19 764

m3 16 893 8,0 135 144

154 908

51

. .

[m3; kg] [/m3; /kg] []

m3 1 120 7,2 8 064

m3 2 720 8,0 21 760

29 824

kg 5 000 8,5 42 500

kg 13 000 8,5 110 500

Howel-Bunger kg 4 000 8,5 34 000

kg 7 500 6,8 51 000

kg 36 172 8,5 307 462

545 462

:

= 16 962 972 x 1,3 = 22 051 863

52

6.2. USBR III

. .

[m3; kg] [/m3; /kg] []

m3 54 225 7,5 406 688

m3 21 139 7,5 158 543

m3 10 733 7,5 80 496

86 097 645 726

m3 96 876 45 4 359 420

m3 74 875 100 7 487 500

m3 8 172 120 980 640

179 923 12 827 560

kg 817 200 1,2 980 640

14 453 926

m3 3 778 18 68 004

m3 7 669 55 421 795

m3 2 637 18 47 466

537 265

m3 3 566 140 499 240

kg 356 600 1,2 427 920

1 464 425

m3 2 745 7,2 19 764

m3 16 893 8,0 135 144

154 908

53

. .

[m3; kg] [/m3; /kg] []

m3 1 120 7,2 8 064

m3 2 720 8,0 21 760

29 824

kg 5 000 8,5 42 500

kg 13 000 8,5 110 500

Howel-Bunger kg 4 000 8,5 34 000

kg 7 500 6,8 51 000

kg 36 172 8,5 307 462

545 462

:

= 16 648 545 1,3 = 21 643 109

7.

55

.

, ,

.

,

.

, .

,

.

,

,

( 4).

, ,

.

3 4

,

.

( )

. ,

.

.

,

.

, ,

4

( 12%).

,

.

As our circle of knowledge expands, so does the circumference of darkness surrounding it

.

8.

57

[m2],

[m2],

, (4.9) [-],

[m],

[m],

[m],

USBR III [m],

[-] [%],

[-] [%],

USBR III [-],

USBR III [m],

[N],

, (3.18) [N],

(3.17) [N],

, (3.19) [N],

1 [-],

, , [-],

, 4.5 [-],

[-],

(3.4) [-],

USBR III [N],

= 9,81m/s2,

[m],

, [m],

[m],

,

[m],

1 ; (2.5 2.11) [m],

2 ; (2.5 2.11) [m],

[m],

58

, Boes, Hager 2003a, 2003b [m],

90, Boes, Hager 2003a, 2003b [m],

, 4.5 [m],

, 4.5 [m],

* , [m],

, [m],

[m],

,

[m],

,

[m],

, , , [-],

1 [N],

2 [N],

[N],

[m],

[-],

[mnm],

[m],

, [m],

[m],

[m],

[m],

, , [m],

[m-1/3s],

USBR III [-],

, , , , 3.7 3.9,

[-],

[N],

[Pa],

1 ; (2.5 2.9) [N],

59

2 ; (2.5 2.9) [N],

[m3/s],

= / , [m3/s/m],

1 [m3/s],

2 [m3/s],

[m],

1 ; (2.5 2.11) [m/s],

2 ; (2.5 2.11) [m/s],

, , [m/s],

[m/s],

, 4.5 [m/s],

USBR III [m/s],

, 4.5 [m/s],

(3.19) [m3],

[m],

= / [-],

[m],

= 3 (,

2 sin ) [m],

[-],

0 = [-],

; [rad],

[rad],

[-],

[kg/m3],

10/3 [-],

[rad],

3.8 [rad],

2 3.9 [rad],

[-],

[m],

[m].

9.

61

3.

3.1

(Hunt 2012)

3.2 ,

4.

4.1 , = 12 22,6

4.2 , , = 1320m3/s, Boes Hager 2003a, 2003b

4.3 ,

, = 1320m3/s, Hunt 2012.

4.4 ,

, = 1320m3/s

4.5 ,

, = 1320m3/s, = 36,34m/s

4.6 , ,

= 1320m3/s

4.7 ,

= 1320m3/s, (4.30)

4.8 (2011),

(2009) (*), , = 1320m3/s.

4.6

5.

5.1 , ,

Boes Hager 2003a, 2003b, 1% = 477,64m3/s

5.2 ,

, 1% = 477,64m3/s, Hunt (2012)

1% = 477,64m3/s

5.3 ,

, 1% = 477,64m3/s

5.4 ,

, 1% = 477,64m3/s, = 33,50m/s

5.5 ,

1% = 447,64m3/s

5.6 I

5.7 II

62

10. 1 -

10.1 ,

, 12 ( 1,38m)

10.2 ,

, 18,8 ( 1,00m)

10.3 ,

, 22,6 ( 0,75m)

10.4 ,

= 1320m3/s

10.5

1.

1.1

1.2

2.

2.1

2.2

2.3

2.4 ( 2009)

2.5 USBR III (Peterka 1978)

2.6 ( 2009)

2.7 /2 ,

; USBR III

(Peterka 1978)

2.8

: Peterka , Cardoso et al. (2007)

2.9 .

e = 74m3/s , (Frizell et al. 2009).

3.

3.1

3.2

3.3 (Boes, Hager 2003b)

63

3.4 (Hunt et al. 2008)

3.5 ,

(Hunt et al. 2008)

3.6 (Hunt et al. 2012)

3.7 -

3.8 -

3.9 B-B

3.10

3.11 ( )

3.12

3.13

3.14 = 12, = 1320m3/s,

4.

4.1

4.2

4.3

4.4 , = 1320m3/s, = 80m

4.5

4.6

11. 2

11.1 ,

= 130,4 l s , = 12

11.2

, = 130,4 l s , = 12

11.3 ,

= 130,4 l s , = 18,8

11.4

, = 130,4 l s , = 18,8

64

11.5 ,

= 130,4 l s , = 22,6

11.6

, = 130,4 l s , = 22,6

11.7 ,

= 130,4 l s

10. 1 -

1 -

66

10.1 ,

, 12 ( 1,38m)

[mm] [mm] [m/s] [%] [mm] [mm] [m/s] [%]

10 5 3,935 8,08 30 25 3,660 15,98

10 10 3,890 8,46 30 30 3,810 16,87

10 15 4,104 9,93 30 35 3,909 19,11

10 20 4,121 10,04 30 40 4,114 20,30

10 25 4,190 10,20 30 45 4,312 23,21

10 30 4,273 9,12 30 50 4,391 30,77

10 35 4,334 10,30 30 55 4,536 41,83

10 40 4,334 11,65 30 60 4,675 67,88

10 45 4,554 11,71 30 65 4,741 84,77

10 50 4,615 11,04 30 70 4,885 92,48

10 55 4,615 12,01 30 75 4,780 94,68

10 60 4,761 13,56 40 5 2,520 10,94

10 65 4,868 15,89 40 10 2,651 11,99

10 70 5,043 25,37 40 15 2,956 13,28

10 75 5,309 57,21 40 20 3,224 14,64

10 80 5,325 83,28 40 25 3,415 16,32

10 85 5,338 93,50 40 30 3,600 17,99

20 5 3,437 10,01 40 35 3,750 21,01

20 10 3,418 10,71 40 40 3,977 24,46

20 15 3,690 11,32 40 45 4,114 32,57

20 20 3,909 12,36 40 50 4,312 45,72

20 25 4,046 13,03 40 55 4,352 62,30

20 30 4,114 15,17 40 60 4,457 79,07

20 35 4,193 15,40 40 65 4,512 90,25

20 40 4,312 15,17 40 70 4,794 93,60

20 45 4,431 15,70 40 75 4,880 94,58

20 50 4,569 18,62 50 5 2,235 11,71

20 55 4,917 29,89 50 10 2,425 11,92

20 60 5,018 55,63 50 15 2,654 13,44

20 65 5,018 80,18 50 20 2,967 14,29

20 70 5,037 92,22 50 25 3,222 16,48

20 75 5,149 94,66 50 30 3,418 18,58

30 5 2,837 10,90 50 35 3,613 22,29

30 10 2,956 12,43 50 40 3,739 27,72

30 15 3,294 12,00 50 45 3,929 39,42

30 20 3,547 13,61 50 50 4,179 56,05

1 -

67

10.1 ()

, , 12 ( 1,38m)

[mm] [mm] [m/s] [%]

50 55 4,257 75,43

50 60 4,334 88,04

50 65 4,515 92,96

50 70 4,658 94,87

60 5 2,027 12,36

60 10 2,231 13,49

60 15 2,508 14,46

60 20 2,509 15,94

60 25 2,797 18,40

60 30 3,103 20,28

60 35 3,264 23,31

60 40 3,491 28,53

60 45 3,759 39,96

60 50 4,058 67,43

60 55 4,270 83,34

60 60 4,349 90,43

60 65 4,425 94,58

70 5 1,841 12,30

70 10 2,138 12,72

70 15 2,410 14,62

70 20 2,523 15,88

70 25 2,722 19,24

70 30 2,763 21,21

70 35 3,284 24,40

70 40 3,515 29,62

70 45 3,760 44,23

70 50 4,012 70,42

70 55 4,219 86,46

70 60 4,352 92,27

1 -

68

10.2 ,

, 18,8 ( 1,00m)

[mm] [mm] [m/s] [%] [mm] [mm] [m/s] [%]

10 5 4,370 8,48 30 5 4,023 10,15

10 10 4,174 10,54 30 10 3,519 10,14

10 15 4,023 11,66 30 15 3,529 10,11

10 20 4,069 11,95 30 20 3,680 10,98

10 25 4,069 11,29 30 25 3,680 10,49

10 30 4,114 11,08 30 30 3,720 12,52

10 35 4,069 12,00 30 35 3,720 13,61

10 40 4,273 12,32 30 40 3,806 13,76

10 45 4,273 12,10 30 45 3,977 15,25

10 50 4,273 14,02 30 50 4,135 18,11

10 55 4,396 16,05 30 55 4,457 21,71

10 60 4,615 14,80 30 60 4,457 28,58

10 65 4,615 16,07 30 65 4,615 31,45

10 70 4,615 15,50 30 70 4,554 32,57

10 75 4,688 14,90 30 75 4,431 33,60

10 80 5,043 24,29 30 80 4,677 44,09

10 85 5,363 41,37 30 85 4,890 59,77

10 90 5,387 76,82 30 90 5,149 84,66

10 95 5,498 89,54 30 95 5,198 89,11

10 100 5,498 94,78 30 100 5,265 92,72

20 5 4,150 9,43 30 105 6,400 93,89

20 10 3,720 11,21 30 110 6,933 95,60

20 15 3,846 10,42 30 115 6,933 95,66

20 20 3,886 11,90 40 5 3,573 8,82

20 25 3,840 11,49 40 10 3,213 10,83

20 30 3,886 12,37 40 15 3,392 11,22

20 35 3,931 13,23 40 20 3,424 10,65

20 40 3,977 12,92 40 25 3,424 11,87

20 45 4,076 13,68 40 30 3,605 12,81

20 50 4,273 14,50 40 35 3,720 13,71

20 55 4,396 16,55 40 40 3,857 16,28

20 60 4,510 18,69 40 45 4,135 18,63

20 65 4,615 19,15 40 50 4,350 26,92

20 70 4,615 19,54 40 55 4,457 37,52

20 75 4,677 21,18 40 60 4,457 48,55

20 80 4,800 32,96 40 65 4,615 51,84

20 85 5,018 56,04 40 70 4,615 48,90

20 90 5,280 83,34 40 75 4,615 52,63

20 95 5,353 91,83 40 80 4,615 61,35

20 100 5,425 94,29 40 85 4,761 70,70

1 -

69

10.2 ()

, , 18,8 ( 1,00m)

[mm] [mm] [m/s] [%] [mm] [mm] [m/s] [%]

40 90 5,018 81,62 60 70 4,738 76,69

40 95 5,044 87,30 60 75 4,800 79,63

40 100 5,105 92,03 60 80 4,873 82,66

40 105 5,193 94,09 60 85 4,945 86,66

40 110 5,178 95,09 60 90 5,018 89,83

50 5 3,040 10,85 60 95 5,018 93,17

50 10 2,964 9,92 60 100 5,131 93,98

50 15 3,144 10,12 70 5 2,857 11,47

50 20 3,231 10,73 70 10 3,147 12,15

50 25 3,294 12,72 70 15 3,329 12,91

50 30 3,534 13,26 70 20 3,400 12,93

50 35 3,720 14,09 70 25 3,400 13,72

50 40 3,857 17,40 70 30 3,614 15,45

50 45 4,135 23,67 70 35 3,766 19,31

50 50 4,457 36,43 70 40 3,977 27,16

50 55 4,457 52,20 70 45 4,135 44,19

50 60 4,728 64,15 70 50 4,457 63,76

50 65 4,530 68,10 70 55 4,457 76,37

50 70 4,615 66,11 70 60 4,615 81,39

50 75 4,677 68,28 70 65 4,677 83,10

50 80 4,800 73,05 70 70 4,800 84,83

50 85 4,873 78,10 70 75 4,873 87,18

50 90 5,018 84,99 70 80 4,945 89,90

50 95 5,018 88,73 70 85 5,018 91,86

50 100 5,018 92,82 70 90 5,018 93,73

50 105 5,193 94,50 70 95 5,105 93,92

50 110 5,338 94,57 80 5 2,455 9,18

60 5 2,959 9,59 80 10 2,643 11,45

60 10 2,922 9,30 80 15 2,860 13,09

60 15 3,009 11,27 80 20 3,179 13,82

60 20 3,116 10,49 80 25 3,329 14,22

60 25 3,365 11,56 80 30 3,534 17,13

60 30 3,574 14,34 80 35 3,766 22,89

60 35 3,766 17,03 80 40 3,937 30,96

60 40 3,977 20,82 80 45 4,135 48,83

60 45 4,135 31,83 80 50 4,457 67,47

60 50 4,457 50,34 80 55 4,563 80,36

60 55 4,530 68,68 80 60 4,615 86,19

60 60 4,781 73,80 80 65 4,800 88,88

60 65 4,761 78,45 80 70 4,873 90,73

1 -

70

10.2 ()

, , 18,8 ( 1,00m)

[mm] [mm] [m/s] [%]

80 75 4,945 91,69

80 80 4,945 92,36

80 85 5,018 93,31

80 90 5,018 94,05

80 95 5,018 94,48

90 5 2,423 12,85

90 10 2,561 11,93

90 15 2,834 13,00

90 20 3,116 13,23

90 25 3,294 15,76

90 30 3,494 20,02

90 35 3,649 25,45

90 40 3,857 36,30

90 45 4,135 55,36

90 50 4,411 73,26

90 55 4,510 84,82

90 60 4,615 90,35

90 65 4,800 92,90

90 70 4,945 94,05

90 75 5,018 94,22

90 80 5,164 94,82

100 5 2,473 12,12

100 10 2,487 12,97

100 15 2,814 13,52

100 20 3,088 14,90

100 25 3,294 18,15

100 30 3,463 21,80

100 35 3,614 28,86

100 40 3,910 41,10

100 45 4,135 59,44

100 50 4,320 77,70

100 55 4,603 87,47

100 60 4,834 91,97

100 65 5,018 93,96

100 70 5,018 94,41

100 75 5,236 94,73

1 -

71

10.3 ,

, 22,6 ( 0,75m)

[mm] [mm] [m/s] [%] [mm] [mm] [m/s] [%]

10 5 3,600 9,12 30 95 5,164 74,21

10 15 3,937 11,67 30 100 5,091 85,07

10 25 3,977 13,77 30 105 5,164 91,83

10 35 4,135 14,71 40 5 3,220 11,70

10 45 4,350 18,39 40 15 3,388 12,97

10 55 4,615 25,44 40 25 3,565 15,80

10 65 4,615 27,73 40 35 3,720 22,22

10 75 4,615 22,12 40 45 4,135 25,86

10 85 4,615 14,97 40 55 4,510 30,78

10 95 4,834 15,54 40 65 4,615 31,35

10 100 5,524 19,65 40 75 4,800 38,48

10 105 5,657 39,62 40 80 4,800 49,20

10 110 5,524 70,33 40 85 5,018 62,36

10 115 5,496 89,61 40 90 5,018 77,42

20 5 3,494 11,19 40 95 5,018 84,23

20 15 3,565 11,31 40 100 5,018 89,70

20 25 3,760 12,74 40 105 5,018 92,22

20 35 3,977 15,75 50 5 3,195 11,03

20 45 4,334 20,97 50 15 3,200 12,89

20 55 4,688 29,44 50 25 3,388 16,99

20 65 4,834 37,15 50 35 3,720 22,01

20 75 4,615 32,31 50 45 3,977 28,09

20 85 4,615 20,35 50 55 4,334 35,56

20 90 4,688 17,86 50 65 4,615 41,71

20 95 4,834 19,92 50 70 4,615 45,99

20 100 5,280 30,91 50 75 4,800 52,54

20 105 5,425 58,30 50 80 4,800 61,89

20 110 5,498 77,84 50 85 5,018 71,31

20 115 5,236 89,78 50 90 5,018 78,57

20 120 5,236 94,74 50 95 5,018 85,53

30 5 3,298 11,97 50 100 5,018 89,02

30 15 3,494 12,34 60 5 3,069 10,30

30 25 3,680 15,19 60 15 3,032 12,61

30 35 3,977 20,06 60 25 3,294 17,37

30 45 4,273 25,41 60 35 3,529 23,13

30 55 4,635 30,21 60 45 3,897 31,43

30 65 4,834 29,43 60 55 4,396 44,40

30 75 4,834 25,33 60 65 4,615 54,60

30 85 4,945 36,10 60 70 4,615 58,51

30 90 5,018 52,16 60 75 4,800 63,51

1 -

72

10.3 ()

, , 22,6 ( 0,75m)

[mm] [mm] [m/s] [%] [mm] [mm] [m/s] [%]

60 80 4,800 70,78 90 25 3,116 16,14

60 85 4,800 76,78 90 35 3,494 22,76

60 90 5,018 83,30 90 45 3,857 35,57

60 95 5,018 88,25 90 50 4,135 46,30

60 100 5,018 90,85 90 55 4,197 62,18

70 5 2,903 10,05 90 60 4,457 74,82

70 15 2,956 12,51 90 65 4,615 81,44

70 25 3,231 16,39 90 70 4,615 86,98

70 35 3,494 24,13 90 75 4,800 89,12

70 45 3,811 32,32 90 80 4,800 91,20

70 55 4,334 53,23 90 85 5,018 92,56

70 60 4,457 62,16 90 90 5,018 94,10

70 65 4,615 66,75 90 95 5,018 94,79

70 70 4,615 69,73 100 5 2,580 10,61

70 75 4,800 75,24 100 15 2,701 13,91

70 80 4,800 80,04 100 25 3,060 17,12

70 85 4,873 84,40 100 35 3,463 22,43

70 90 4,873 88,40 100 45 3,857 32,62

70 95 5,018 92,30 100 50 4,135 47,72

70 100 5,018 93,80 100 55 4,320 64,50

70 105 5,018 95,17 100 60 4,457 77,64

70 110 5,265 95,52 100 65 4,615 86,22

80 5 2,674 10,69 100 70 4,677 90,52

80 15 2,834 13,56 100 75 4,945 92,58

80 25 3,200 16,24 100 80 4,800 94,14

80 35 3,494 22,32 100 85 5,164 94,30

80 45 3,857 33,93 100 90 5,091 94,18

80 50 4,135 45,19 110 5 2,358 12,63

80 55 4,181 59,05 110 15 2,599 13,31

80 60 4,457 70,71 110 25 3,088 17,64

80 65 4,615 77,04 110 35 3,427 22,13

80 70 4,615 81,54 110 45 3,857 35,58

80 75 4,800 84,25 110 50 4,135 46,40

80 80 4,800 87,08 110 55 4,258 65,40

80 85 4,800 90,28 110 60 4,457 80,81

80 90 5,018 92,74 110 65 4,761 88,65

80 95 5,018 93,91 110 70 4,895 92,65

80 100 5,018 94,72 110 75 4,945 94,10

90 5 2,601 10,07 120 5 2,225 12,46

90 15 2,768 13,87 120 15 2,542 13,75

1 -

73

10.3 ()

, , 22,6 ( 0,75m)

[mm] [mm] [m/s] [%]

120 25 3,032 17,28

120 35 3,463 22,55

120 45 3,857 34,81

120 50 4,135 48,51

120 55 4,366 66,32

120 60 4,457 81,98

120 65 4,781 90,41

120 70 4,834 93,77

120 75 5,105 94,48

10.4 ,

= 1320m3/s

/ [-] [-] [m] [m] [-] [-]

4,221 0 3,028 0,00 1,00 0,00

4,000 0,005 2,869 0,37 1,17 0,00

3,500 0,020 2,511 1,43 1,75 0,02

3,000 0,041 2,152 2,92 2,78 0,03

2,500 0,072 1,793 5,21 4,81 0,06

2,000 0,127 1,435 9,15 9,40 0,10

1,500 0,248 1,076 17,93 22,28 0,20

1,300 0,359 0,932 25,90 34,23 0,30

1,200 0,456 0,861 32,94 43,52 0,38

1,178 0,485 0,845 35,04 45,97 0,40

1,112 0,607 0,798 43,80 54,64 0,50

1,072 0,728 0,769 52,55 61,00 0,60

1,047 0,849 0,751 61,31 65,50 0,70

1,031 0,971 0,739 70,07 68,63 0,80

1,020 1,092 0,732 78,83 70,77 0,90

1,014 1,214 0,727 87,61 72,22 1,00

1 -

74

10.5

/ /*

[-] [] [-] [-] [m] [-] [-] [-] [%]

1,0

12,0

72,22

0,739 0,056

0,40

1,373

1,334 8,07 18,8 0,797 0,060 1,226

22,6 0,988 0,075 1,403

0,9

12,0

70,77

0,720 0,055

0,40

1,338

1,305 7,77 18,8 0,782 0,059 1,203

22,6 0,967 0,073 1,373

0,8

12,0

68,63

0,671 0,051

0,40

1,247

1,260 7,32 18,8 0,767 0,058 1,180

22,6 0,952 0,072 1,352

0,7

12,0

65,50

0,614 0,046

0,40

1,141

1,177 7,50 18,8 0,731 0,055 1,125

22,6 0,891 0,067 1,265

0,6

12,0

61,00

0,54 0,041

0,40

1,003

1,008 6,04 18,8 0,619 0,047 0,953

22,6 0,753 0,057 1,069

0,5

12,0

54,64

0,49 0,037

0,40

0,910

0,859 5,92 18,8 0,534 0,040 0,822

22,6 0,596 0,045 0,846

* - ( , 11.7)

11. 2 -

2 -

76

11.1 ,

= 130,4 , = 12

11.2

, = 130,4 , = 12

[m/s]

0 - 0,5

0,5 - 1,0

1,0 - 1,5

1,5 - 2,0

2,0 - 2,5

2,5 - 3,0

3,0 - 3,5

3,5 - 4,0

4,0 - 4,5

4,5 5,0

5,0 5,5

[%]

0 10

10 20

20 30

30 40

40 50

50 60

60 70

70 80

80 90

90 100

2 -

77

11.3 ,

= 130,4 , = 18,8

11.4

, = 130,4 , = 18,8

[m/s]

0 - 0,5

0,5 - 1,0

1,0 - 1,5

1,5 - 2,0

2,0 - 2,5

2,5 - 3,0

3,0 - 3,5

3,5 - 4,0

4,0 - 4,5

4,5 5,0

5,0 5,5

5,5 6,0

6,0 6,5

6,5 7,0

[%]

0 10

10 20

20 30

30 40

40 50

50 60

60 70

70 80

80 90

90 100

2 -

78

11.5 ,

= 130,4 , = 22,6

[m/s]

0 - 0,5

0,5 - 1,0

1,0 - 1,5

1,5 - 2,0

2,0 - 2,5

2,5 - 3,0

3,0 - 3,5

3,5 - 4,0

4,0 - 4,5

4,5 5,0

5,0 5,5

5,5 6,0

2 -

79

11.6

, = 130,4 , = 22,6

[%]

0 10

10 20

20 30

30 40

40 50

50 60

60 70

70 80

80 90

90 100

2 -

80

11.7 ,

= 130,4

12.

82

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[12] , , , , , 2011.

[13] , , :

, , 2014.

[14] , . , , ,

, 2009.

[15] , ., , ., , ., ...,

, ,

, 2013.

13.

84

:

/00 ( = 55m),

/01 .

I :

I / 00 ,

I / 01 ,

I / 02 ,

I / 03 .

II USBR III :

II / 00 ,

II / 01 ,

II / 02 ,

II / 03 .