A curved flume bed-load experiment

(1)

I

t

I

-I

I

l!:

~i

TU

Delft

Delft University of Technology

Facuhy of Civil Engineering

(2)

I

_{part of:}

I

STW-project;

I

A curved flume bed-load experiment.

A.M.Talmon E.R.A.Marsman

report no. 4-88, June 1988

River bend morphology with suspended sediment.

Delft University of Technology Faculty of Civil Engineering Hydraulic Engineering Division

(3)

I

2

I

SUMMARY

I

In this report the results of a bed-load experiment in a curved flume are presented. The experiments have been carried out in the Laboratory of Fluid Mechanics (L.F.M.) at the Delft University of Technology. The main object of the experiments is to develop and to test data-acquisition procedures for future suspended-load experiments. At the same time data were acquired which apply to the case of bed-load only. In this report the experimental data are presented.

The bed-topography in the bend shows an harmonie oscillation of the lateral bed-slope.

The reported results apply to the stationary bed topography under steady flow conditions.

I

(4)

I

3 CONTENTS page SUMMARY 2 LIST OF FIGURES 4 LIST OF SYMBOLS 4 1. Introduction 5 2. Model features 6 3. Resu1ts 8

3.1 Relevant experimenta1 parameters 8

3.2 Flow veloeities 9

3.3 Bed topography 9

4.0 Conc1usions 10

References 10

(5)

I

4

I

LIST OF FIGURES

1. Layout, Laboratory of Fluid Mechanics curved flume 2. Sieve curve of bed material

I

4.3.

5. 6.

Velocity measurements 15 mm below water level Contour lines of the relative water depth a/aO Water depth in cross-direction

Longitudinal profile of the water depth

I

LIST OF SYMBOLS

I

a water depth

aO mean water depth of cross-section 1 W width of the flume

C Chézy coefficient; C = ü/JaOi Dso median grain size

Fr Froude number

i water surface slope L arc length of the bend

c

Q discharge

R radius of curvature ofaxis of flume c

I

u depth averaged mean flow velocity Shields number; 0 - aOi/(~ D90)

relative density of the sediment; ~ 1. 65

I

(6)

I

5

I

1. Introduction

I

A mathematica1 river bend model hes been deve10ped, 01esen 1987, in which the type of sediment transport was 1imited to bed-10ad only. The project at hand is directed towards the extension of this model by

inc1uding suspended-10ad a1so. To this purpose laboratory experiments

are necessary. To deve10p and to test data-acquisition procedures, which

wi11 be used in future suspended-10ad experiments, a bed-1oad experiment has been performed. The resu1ts of this experiment can be used to verify

the existing model.

I

This research is a part of the project: 'River bend morpho10gy with

suspended sediment', project no. DCT55.0842. The project is supported by

the Netherlands Technology Foundation (STW).

I

(7)

I

6

I

2. Model features

I

The layout of the L.F.M. curved flume is shown in figure 1. Water is pumped from an underground basin to an elevated head tank and led to the model. The water discharge is controlled by a valve in the supply

circuit and is measured using an orifice plate.

Af ter passing the weir at the end of the flume, by which the water level is adjusted, the water poures into a settling reservoir. Af ter passing this recervoir the water flows back into the underground bas in.

The dimensions of the flume are:

I

inflow section length outflow section length arc length of the bend radius of the bend width of the flume depth of the flume The bottom of the flume

11.00 m 6.70 m L = 12.88 m c R= 4.10 m c W 0.50 m H = 0.30 m

is made of glass and the side walls are made of

I

perspex.

I

The flume is filled up with sand. The height of the sand bed at the entrance of the flume is about 0.1 m, at the exit the bed height is about 0.06 m. The sieve curve of the sand is given in figure 2.

The sand is supplied to the model 2 m downstream of the entrance of the flume. The supp1y is effected by a constant discharge of dry sand from small holes in the bottom of a container. The sand discharge is measured every day.

The sand settled down in the settling reservoir is gathered every day and weighted under water. The results are converted to equivalent

weights of dry sand. The amounts of sand supplied and gathered from the settling reservoir are compared.

The water surface slope in longitudinal direction is measured every day. Af ter about 450 hours of flow, to establish equilibrium conditions, the measurements of the bed topography have been started. At that stage no significant changes of the water surface slope and differences between

in and outflow of sand were measured. It is thus assumed that an equilibrium state has been reached.

I

(8)

I

7

I

The measurements of the bottom and water level are performed with an electronic indicator (PROVO). This device is traversed in

cross-sectional direction. In each cross-section 9 equidistant measuring

points are used. The carriage in which the PROVO is mounted is also

traversed in longitudinal direction. In longitudinal direction 49 cross-sections are situated, they are indicated in figure 4. The distance

between these cross-sections at the flume axis is 0.32 m . The profile

indicator is continously moved in cross-sectional direction, this is

achieved by specially developed electronic hardware. The position of the

profile indicator is measured electronically. The carriage is moved by hand in longitudinal direction.

I

In one measuring session the water level and the bottom topography of

the 49 cross-sections were measured. The data were digitized and stored

at alocal data-acquisition system which uses a HP 1000 mini computer.

Next, the data are processed by a central main frame IBM computer of the

Delft University.

I

(9)

From a theoretical point of view the choice of model parameters was influenced by the following arguments:

The sediment transport rate in the whole channel should be sufficient to prevent locations with no transport at all. Such locations are not

modelled in the morphological model, and therefore should be avoided.

A large width/depth ratio is desired to correspond with the validity of

the flow model and realistic prototype conditions.

From a practical point of view the flow conditions are controlled by;

the volume flux of water, the mass flux of sediment and the height of the weir at the downstream end of the flume.

Also a minimal water depth of 0.02 m at the inner side of the bend is desired in order to be able to use the PROVO at these locations.

I

3.

I

8 Results

By careful adjustment of controls an equilibrium state has been reached.

The flow conditions of the equilibrium state are a çompromise between the theoretical and practical considerations. The condition of

sufficient transport was judged by eye. The width/depth ratio was

chosen such that the PROVO could be used at nearly all locations in the flume. Only at the location of the point-bar the PROVO could not be used.

I

3.1

I

Relevant experimental parameters

The relevant parameters of the experiment are:

I

u

I

[m] 0.07 3 [m Is] 0.0115 [mlo 0.5 [mis] 0.32 [ - ] 1.0

*

10 -3 [mm] 0.780 [-] 7.14 [-] 0.018 [mO.s/s] 39

(10)

I

9

I

8 [-] 0.053

I

Although no locations with absence of sediment transport were seen, it should be realized that the overall Shields number is close to

initiation of motion of the sediment. The critical value is 8 . =0.047.

cr1t

I

3.2 Flow velocities

I

Also a few velocity measurements are carried out to check the magnitudeof the flow velocities. The measurements are taken 15 mm below water level at the beginning of the bend where the bed topography is almost smooth.

The relative flow velocity u/u. fl_1n _ow is shown in figure 3.

I

₃_.₃ _{Bed topography}

I

The bed topography has been obtained by ensemble averaging of 18 independent measuring sessions. Each session consists of 49

cross-sectional traverses. Within a cross-section 9 measuring points are used. By ensemble averaging the stationary part of the bend is determined. The bed topography is shown in the figures 4 - 6.

Figure 4 shows the ensemble averaged contour line map of the relative water depth. (normalized with the mean water depth of cross-section 1)

The contour lines are drawn at intervals of ~a/aO = 0.2.

The figures 5A-L show the ensemble mean relative water depths of each cross-section. At each measuring point the a interval is also indicated. These intervals are based on 18 data points.

Figure 6 shows three longitudinal profiles of the relative water depth,

one left and one right of the axis at a distance of 0.3W from the side walls and one along the axis of the flume.

At the bend entrance the bed is relatively smooth, downstream of traverse 15, approximately, the bed consists of elongated undulations

(z 1 a 1.5 m length, z 0.05 m height at crest.) moving downstream, which resemble the alternating bar type but are only present in the outer part of the bend.

I

(11)

I

10

I

Figures 5 and 6 show that at the bend entrance the bed is nearly horizontal.

The bed topography displays a pronounced harmonie oscillation of the lateral bed-slope. In the 180 0 bend one point-bar at traverse 12 and three pools at traverses 12,26 and 39 are present, see figure 4.

I

4.0 Conelusions

I

been determinedEnsemble mean water depths of a curved flume bed-load experiment have. Also some velocity data have been obtained. The experiment is characterized by a Shields number near initiation of sediment motion. Consequently the bed at the entrance of the bend is relatively smooth.

In the bend large bed forms develop which resembie the alternating bar type.

By ensemble averaging the stationary part of the bed topography is

,

determined. The topography displays an harmonie oscillation of the transverse bed-slope.

The numerical computation of the experiment by the bed-load model of Olesen is beyond the scope of this report and will be reported

separately.

I

References

I

Olesen, K.W. 1987

Bed topography in shallow river bends

Dissertation: Lab. Fluid Mech.,Dept. Civil Engrg. ,Delft Univ. also as: Communications on Hydraulics and Geotechnical Engineering 87-1, Dept. Civil Engrg., Delft Univ.

I

(12)

I

11

I

Appendix A: Ensemble averaged water depths.

I

In this appendix the ensemble averaged re1ative water depths of the 18

I

measurements are tabulated.

I

Discharge .0115 m /s3 Sediment transport 2.3 kgfh dry sand.

I

from re1ative mean water depth a/aO aO = 0.07 m. inner side

I

of bend eS01 eS02 eS03 eS04 eS05 eS06 eS07

I

00.10.05 .97.90 .88.92 .91.96 .91.97 .97.91 ..9097 ..9081 0.15 l.01 .95 .98 l.00 l.01 1.01 .97

I

0.20 .99 .94 .98 .98 l.00 .99 .98 0.25 l.02 .97 l.02 l.00 l.01 1.01 .98 0.30 l.03 1.00 1.03 1.01 l.02 1.02 1.02

I

0.35 1.01 .97 1.00 .99 1.00 1.00 1.02 0.40 1.02 .99 1.02 1.01 1.02 1.03 1.08

I

0.45 1.03 .99 1.00 l.00 1.01 1.02 1.12

I

from re1ative mean water depth a/aO aO = 0.07 m. inner side

I

of bend eS08 eS09 eS10

csn

eS12 eS13 eS14 0.05 .70 .58 .49 .29* .29* .29* .60

I

_0.10 _.78 .68 .58 .29* .29* .29* .78 0.15 .88 .79 .67 .29* .29* .29* .81

I

00.20.25 .93.93 .90.94 .89.80 .64.75 .54.70 ..5789 .80.95 0.30 1.00 1.02 .96 .88 1.08 1.27 1.24

I

0.35 1.05 l.11 1.13 1.26 1.57 1.64 1.55 0.40 1.17 l.29 1.50 1.77 1.98 1. 95 1.80

I

0.45 1.31 1.58 1.89 2.10 2.23 2.14 1.95

I

(13)

I

12

I

Discharge .0115 m /s3 Sediment transport 2.3 kgfh dry sand.

I

from re1ative mean water depth a/aO a = 0.07 m. 0

I

of bendinner side eS15 eS16 eS17 eS18 eS19 eS20 eS21

I

0.05 .88 .86 .86 .86 .84 .83 .70 0.10 .82 .83 .84 .84 .79 .76 .71

I

00.20.15 .78.94 ..8782 ..9488 ..8490 .80.86 .77.84 .75.81 0.25 1.01 .98 .93 .98 .94 .93 .89

I

0.30 1.13 1.17 1.05 1.04 1.03 1.02 1.01 0.35 1.34 1.32 1.21 1.16 1.17 1.15 1.17

I

00.45.40 1.551.69 1.481.58 1.391.51 1.301.43 1.421.30 1.461. 31 1.351.50

I

from re1ative mean water depth a/aO aO = 0.07 m.

I

of bendinner side CS22 eS23 CS24 eS25 CS26 eS27 CS28

I

0.05 .67 .79 .52 .59 .56 .64 1.98 0.10 .64 .66 .58 .71 .66 .79 .65 0.15 .68 .63 .67 .78 .90 .92 .76

I

0.20 .76 .71 .78 .85 1.04 .94 .88 0.25 .87 .85 .95 1.06 1.18 1.11 1.00

I

0.30 1.01 1.07 1.18 1.26 1.44 1.11 1.33 0.35 1.20 1.30 1.46 1.57 1.71 1. 39 1.50 0.40 1.39 1.54 1.69 1.82 1.90 1.65 1.65

I

0.45 1.55 1.71 1.83 1.94 2.02 1.84 1.75

I

(14)

I

13

I

Discharge .0115 m /s3 Sediment transport 2.3 kgjh dry sand.

I

of bendinner side CS29 CS30 CS31 CS32 CS33 CS34 CS35

I

0.05 .86 1.07 .93 .96 .96 .87 .74 0.10 .79 .95 1.02 1.06 1.03 .96 .84

I

0.150.20 .91.98 .98.95 .99.97 .93.90 .92.93 .94.93 .93.89 0.25 1.14 1.01 1.04 .97 .96 .97 .98

I

0.30 1. 33 1.14 1.08 1.06 1.02 1.00 1.03 0.35 1.49 1.27 1.13 1.13 1.08 1.06 1.10

I

0.400.45 1.611.70 1.361.46 1.211.29 1.211.28 1.181.27 1. 301.18 1.221.34

I

inner side

I

of bend CS36 CS37 CS38 CS39 CS40 CS41 CS42

I

0.05 .63 .57 .53 .51 .52 .61 .68 0.10 .75 .64 .59 .56 .60 .68 .82 0.15 .81

.

72

.66 .64 .73 .87 1.03

I

0.20 .88 .82 .77 .78 .86 .94 1.01 0.25 .99 .95 .92 .98 .98 1. 09 1.10

I

0.300.35 1.061.19 1.101.28 1.141.41 1.251.54 1.281.56 1. 321. 54 1.311.49 0.40 1.33 1.45 1.67 1.78 1. 76 1. 74 1.66

I

0.45 1.46 1.62 1.82 1.91 1.87 1. 83 1.77

I

(15)

I

14

Discharge .O1l5 m /s3 Sediment transport 2.3 kgjh dry sand.

I

inner side of bend CS43 CS44 CS45 CS46 CS47 CS48 CS49 0.05 .78 .88 .90 .91 .92 l.00 l.05 0.10 .97 .93 .96 .98 l.00 l.07 l.06 0.15 .98 .92 .93 .98 l.05 l.07 l.06 0.20 .98 .92 .92 .97 .97 .99 1.02 0.25 1.14 1.01 1.01 1.05 1.03 l.04 1.04 0.30 1.37 1.22 l.14 1.13 1.11 l.08 1.04 0.35 1.51 1.42 1.29 1.24 1.15 l.10 1.06 0.40 1.66 1.57 1.43 1.33 1.18 l.10 1.06 0.45 1.77 1.68 1.52 1.39 1.19 1.10 1.08

I

(16)

I

"

I

---,---

-

---

---E o

3 _o

E

c---c.ó

W: 0.50

m

E

o

(") d

:

' '

,

: '

,'

'

s'on'd:

',,'

, '

."

'

;

',

.

'. '. . " '

FIG. 1

LAYOUT,

LFM

'

CURVED

FLUME

DELFT UNIVERSITY OF TECHNOLOGY

--

-

_

'

-o

.x: C C1

....

0'1 C

(17)

I

,

.

I

99.99 99.'> 99

11

11 95 90 ~ ₅₀

..

S

..

'-" 0 c

..

v

..

a.

r

10 5

I

2

7

1 I 0.1

/

QOl 0.1 0.2 0.5 1.0 2.0 groin s iz e in rnrn

SIEVE

CURVE

OF

BED

MATERlAL

FIG.

2

(18)

I

'

I

Uinllow

=

0.363 mIs.

DELFT UNIVERSITY OF TECHNOLOGY

FIG.

3 MODEL OF RIVER BEND

BED LOAD TRANSPORT

(19)

11 MODEL OF RIVER BENO. BEO-LaAD EXPERIMENT

ENSEMBLE MEAN OF 18 LONGITUDINAL

TRAVERS ES

I

"

I

CONTOUR

LINES

OF

RELRTIVE

WRT

ER

OEP

T

H

R

/

RD

RT

INTERVRLS

OF

ó

R

/

RO

=

0.

2 WRTER

OEPTH

RT

BENO

ENT

R

RNCE

RO

~ 0

.07

M

FLOW

w ~ 7 ~ N

o 0 0 0 0 0

DELFT UNIVERSITY OF TECHNOLOGY

(20)

,I

I

'

I

,

I

1

"

I

0.5 ₀_.5 I

J-J-I-I--J--~

_I

J-t--I--I--r-I--f--J--I

1.5 ₁_.₅ 2 ₂ 2.51 _2.5 0.8 D.G D.~ 0.2 0 1 0.8 O.G o,~ 0.2 0

CRCJSS-SECTION

1 CRCJSS

-

SECTIDN

2

0,5 _O_._S Cl

-I-J-f-+-l-~

I

r-+-l-r----r-'

a: I ₁ ~t-- "-a: ::x: l-a, LLI 1.5 ₁_.₅ Cl a: LLI l-a: 2 3: 2 2.51 _Z_.₅₁ 0.8 0.6 O.~ 0.2 0 0.8 U.G O,~ o.z 0

DISTANCE fAOM INNEASIDE BEND Y/W

CROSS-SEC

TIO

N

3 CR

O

S

-

S

EC

TION

4 W

=

0 .

5 M

AD

=

0 .

0

7 M

I

± a of 18 measurements

-WATER DEPTH IN CROSS-DIRECTION

FIG.

5

R

DELFT UNIVERSITY OF TECHNOLOGY

(21)

I

'

I

- -o.~ O,S

,

Jl-t-I--I--I--l-r--r-I

,

--'_f-r-I-f-~

i.s I.~ 2 2 2.5, 2.5 U,8 U.G U.~ u.z 0 I 0.8 O.G O,~ ,U." 0

CRlJSS

-

SE

C

T

IlJ

N

5 _C

_RlJSS-SECTIO

_N

₆

O.S O.S

r

l

r--'

0

r-I--r-r-a:

,

_{___}

I--I-I-J-r-I <,

V--r-a: :I: ~ t-Q.. W i.s 1.5 0 cr: W t-a: 2 ::z ₂ Z.S, Z.S, 0.8 O.G U.~ c.z U O.H O.G U.~ ₀_._" 0

OISTANCE fROM INNERSIOE BENO Y/W

CRlJSS-SEC

TIlJ

N

₇

_CRlJ

_SS-SEC

_TIlJN

₈

W

₌

0 .

5

M

RO

z:

_0.

₀

₇

_M

I

± 6

of

16

measurements

WATER DEPTH IN CROSS-DIAECTION

FIG.

5

B

DELFT UNIVERSITY OF TECHNOLOGY

(22)

I

'

I

0.5

~.

0.5

~.---r-~~

r-r-r

I

,/r---r-

I

;Î

1.5

/

I.~ 2 2 2.51 2.5 0.8 O.G U•• u.e 0 I O.b U.G U., u.z U

C

ROSS-S

E

CTION

9 CROS

S

-SECTION

10 -_

.

---0.5

~(

0.5

y--./

0 ~

(!

a: I I <, a: ::c ~ n, W I.S I.S Cl. a:

({

w ~ a: 2 2 :3: 2,SI 2,SI

0.8 O.G U., O.l 0 u.e U.G U•• - u.z U

DI STANCE FAOM INNEASIDE BEND Y/W

CROSS

-

SECTION

1 1

CRO

S

S-SECTION

1 2

W

₌

0 .

5 M

RO

=

0.07 M

r

± a of

18

measurements

WATER

DEP TH

IN

CROSS-DIRECTION

FIG. 5 C

(23)

I

'

I

"

I

,

I

.'

-_.

e.s

r(

c.s • •

v!-f-~

(i

(v

•,5 _'_.₅ Z

rr

2.

r(

2.5. U.8 U.& U., U,~ U 2.5. U.8 U.6 U,. U.l U

CROSS-SECTION

13 CROSS-SECTION

14

0.5 U,~ 0

rr~

r+c-I--t

a: _•

,

<, a:

r

:I:

r--(

(

r~r

I-a, LU I.~ 1.5 0 a: LU l-a: :J: 2 2 2.5. _U_._U _u_._c _u_,_. _u_._z _U 2.5, _u_._e U.G U,. _u_._z U

OISTnNCE FROM INNERSIOE BENO Y/W

CROSS-SECTION

15 CROSS-SECTION

16 W

=

0.5 M

RO

._

0 .07

M

I

±

a of

18

measurements

WATER DEP

TH IN

CROSS-DIREC

T

IO

N

FIG. 50

(24)

I

0.5 . 0.5 I

r-+--rt-I

I

rr+-+-+-

I

r~

f/rr-1.5 ~~ . 1.5 2 2 2.51 2.51 0.8 O.G O.~ 0.2 0 0.8 O.G O.~ o.a 0

CR055

-

5ECTION

1

7 CR055-

5 E

C

T

IDN

1

8

O.S O.S

r---r--r-t-!

r---rh,

0

r"----a: I

~r-

I <,

r~

a: :c ~~ t-a,

r

W 1.5 1.5 Cl a: W t-a: 2 :z 2 2.51 _0.8 2.51 0.6 O.~ 0.2 0 0.8 O.G O.~ o.z 0

DJSTANCE FROH INNERSJDE BEND Y/W

CR055

-

SECTION

19 C

R

O

S

-SECT

IO

N

2

0

W

₌

0.

5 M

A

D

₌

0 .

07 M

1 ± a of

18

measurements

WATER DEPTH IN CROSS-DIRECT ION

FIG.

5

E

(25)

I

'

1 I

I

-

I

· J

I

0.5 0.5

r-+--r-J-«

~~I

,

~r

,

r~

1.5

r~

1.5

r

[/

2 . ₂

2.5_,'----::--':0.8:---~O~.G ---::-O.'::-~ --::'":O.2:---~0

CROSS-SECTION

21 CROSS-SECTION

22

0.5

rr-~

0.5

...--1

~r

Cl

rr

a:

,

rr

,

<, a: :z:

I-rrr

Cl..

r~

W '.5 '.5 0 cr: W l-a: :::r: z 2 2.5, ₀_.₈ _O.G _O_._~ ₀_.₂ ₀ 2.5, _0.8 _O_._C O.~ 0.2 0

OISTANCE FR OM INNERSIOE BENO Y/W

CROSS-SECTION

23 CROSS

-

SECTION

24 W

=

0.5 M

RO

=

0.07M

r

±

6 of 18 lIeasurements

WATER DEPTH IN CROSS-DIRECTION

FIG.5 F

(26)

I

1 .'-I

I

1

0.5

.

~r++~

0.5 ~ I I

rr-r

r

1.5

rrr

1.5 2 2 2.51 2.51 0.8 0.& O.~ 0.2 0 0.8 0.& O.~ O.l 0

CROSS-SECTION

25 CROSS

-

SEC

TICl

N

26

0.5

I

0

rr-~

a: I' <, a: :x: l-Q.. W 1.5 0 eI: W l-a: :3: 2 2.51 0.8 0.& O.~ 0.2 0 0.5

DISTANCE FAOM INNEASIDE BENO YIW

CROSS

-

SECT

I

ON

27 CROSS-SEC

TION

28 w

=

0.5 M

RO

=

0 .

07 M

1 ± a of

18

measurements

WATER DEPTH IN CROSS-DIRECTION

FJG.

5

G

(27)

I

'

I

'

I

,I

I

1 I

0.5 2.5"'---::-':-0,8-~O.&~-O"'_.~ --::-'::O.l-__jO

CROS

S

-SE

CT

ION

29

0.5

O.S

2 '

2.5.,'---::-':-0.8---::-0.':-& -::-'::-o.~--::-':o.z:---:!o

CROSS-SECT

I

ON

3

0 ~ , I_+_+-+-r-f-~

w ,.S Cl cr: W l-a: :J: 2' 2.5,,'---::-':-0.8-~O.-:--G ----'O:-':--.~-::-'::0.2,---__jO

OJSTANCE FADM JNNERSJOE BENO Y/W

CROSS-SEC

TI

ON

3

1 W

=

0.

5 M

RO

=

0 .

07 M

0.5 Z.51''---::-':-0.8---::-0.':-& -::-':0-~--::-':0. O.Z:---:!O

C

R

OS

S-SECTI

ON

3

2

1

:t 6 0f 18 measurements

WATER OEPTH IN CROSS-OIAECTION

ti

DELFT UNIVERSITY OF TECHNOLOGY

1

(28)

I

'

I

,

J

I

'

I

. 0.5 0.5 1

rrr+--r-I-t---I---1

_•

r

+-

I-

l-

t-r

,1.5 r.S

r

'

2 2

2.5. 0,8 0.& O.~ O,~ 0 2.5. 0,8 0,& 0,' o.z 0

CRO

S

S-

SE

CTION

3

3 CROSS-SECTION

34

c.s o.s 0

r-r-r-~

r--~

a: _• •

r--r--r--...

rrr+--a: J:

rr

l-Q... W ••S I.S 0 a: w l-a: :z 2 2 2.S. 0.8 0.6 o.~ c.z 0 2.5. 0,8 0.6 a,. 0.2 a

DJSTANCE FR DH INNERSIDE BEND Y/W

CRO

S

S-S

E

CTION

3

5 _CROS

_S

_-

_SECTION

36 W

₌

0 .

5 M

RO

₌

0 .

07 M

I

± ~ of 18 measurements

WATER DEPTH IN CROSS-DIRECT ION

FIG. 5 I

(29)

I

,

I

,

I

'

I

J

I

0.5

r--'

0.5

r---

r--I

~

r--

_~_~ \

~}/'

\ ~ \.5

r~~

\.5

rrr

2 2 2.5\ ₀_.₈ _O_._G _D_._~ _U_.₂ _U 2.5_I _u_._e _U_.₆ _U.~ _u_.z _U

CRDSS-SECTIDN

37 CRDSS-SECTIDN

38

0.5

~r-0

D.S

r----

I

rr("

0 ~ a: \ I <, a: J: t-a, ~ 1.5 1.5 a::: W t-a: 2 :z 2 2.5\ 2.5 0.8 U.6 U.~ 0.1 U I 0.e U.G U.~ u.z U

OJSTANCE FRDM INNERSIOE BENO T/H

CRDSS-SECTIDN

39 CRDSS-SECTIDN

40 W

=

0.5 M

RO

₌

0 .

0 7 M

1 ±

6

of

18 measu

r

emen

t

s

WATER DEP

TH

IN CROSS-DIREC

T

ION

FIG.

5

J

(30)

I

,

I

'

I

'

I

.

I

. 0.5 0.5

.

rr+

--

r

~ I I

rr+-r

1.5

rrr

1.5

rrr

2 2 2.5, 2.5, 0,8 0.6 O.~ 0.2 0 0.8 O.G O.~ 0.2 0

CRCJSS-SECTICJN

41 CRCJSS-SECTI(JN

4

2

0.5 0.5 0

r

rt-

t-~

r-~l-

t-t

cr: I I <, cr:

rrr~

J:

0-rr

r

Q... W 1.5 1.5 0 a: w 0-cr: :J: 2 2

Z.s.

2.5, 0.8 0.6 O.~ 0.2 0 0.8 O.G O.~ 0.2 0

DISTRNCE FROM INNERSIDE BEND Y/W

CRCJSS-SECTICJN

4

3 CR

CJ

SS-SE

CTICJ

N

4

4 W

=

0 .

5 M

RO

=

0 .

07 M

I

±

6

of

18

m

easurements

WATER DEPTH IN CROSS-DIRECTION

FJG.

5

K

(31)

I

,

1 \

I

'

I

"

I

f

I

'

0.5

CROSS-SECTION

45

0.5

! '

t_++-

r

r--

t

-+-0

Q.. LU 1.5 '0 cr: LU ... a: ::J: Z

Z.SI·L..__---::-,::-O8 ---=-'0.6:---:0:-'::-.. ij---;;-':O.Z:---:!O

DJSTANCE FROH JNNERSJDE BEND I/W

CROSS-SECTION

47 W

=

0.5 M

RO

=

0.07M

0.5

,:

r+--r-rrt--+-~

2.S1,1---="::-0.--::'08 .':-.. ~O;-';:-.~--::':O.Z-~O

CROSS-SECTION

46

0.5 I'

f-f-t-f-f-t--l-r--I

1.5 2' 2.51''---::-'::-0----:-O.8 .'::-~ -O::-'::-.~---:-'";:0.2---:!O

CROSS-SECTION

48

1 ± ~ of

18

measurements

WATER DEPTH IN CROSS-DIRECTION

(32)

I

'

I

:1

I

1 .6 1. G R E

h

1.~ T I V E ₁_.₂ lol A 1 E R 0 E p _O_. ₆ T H A I _O_._G A 0 0.4 I bend ~ O. 20 ₄ 12 16 32 0lSlANCElWI01H