EFFECT OF ASYMMETRIC SIDE SILL ON SCOUR CHARACTERISTICS DOWNSTREAM OF SUDDEN EXPANDING STILLING...

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Int. Conf. on Hydroscience and Engineering (ICHE-2004), May 30-June 3, Brisbane, Australia 1

EFFECT OF ASYMMETRIC SIDE SILL ON SCOUR CHARACTERISTICS

DOWNSTREAM OF SUDDEN EXPANDING STILLING BASINS

Osama K. Saleh1, Abdel-Azim M. Negm

2 and Noha G. Ahmad

3

ABSTRACT

Previous investigations proved that Scour downstream of Sudden Expanding Stilling Basins (SESB)

are asymmetric due to the asymmetric flow conditions in the basin. Improving the flow pattern

inside the basin by forcing it to be symmetric will improve the resulting scour pattern downstream of

the basin. Different measures may be used to improve the flow pattern in the sudden expanding

stilling basin. One of these measures is using one or more asymmetric side sill at certain position

with particular orientation. In this paper, the effect of asymmetric side sill on the scour

characteristics represented by the maximum scour depth downstream of SESB is investigated.

Determination of the best position of the asymmetric side sill is the main objective of the present

research. The effects of such conditions on the flow patterns inside the basins are also discussed. It

is concluded that using asymmetric side sill reduces the maximum scour depth significantly,

especially when two asymmetric side sills are used. A simple prediction equation is developed for

estimating the maximum depth of scour knowing the Froude number or the upstream head ratio and

the relative position of the sill.

1. INTRODUCTION

The sudden expanding stilling basins have been attracted the researchers during the last few decades

to study its effectiveness as an energy dissipators. Basic information on such types of basins and

others may be found in Hager (1992). Graber (1982) observed and reported that the flow in

symmetric sudden expanding channels is asymmetric. This may be due to the instability of

hydrostatic forces at the beginning of the issuing jet below the outlet. Also, Breman and Hager

(1994) documented that the flow is asymmetric. They used different measures to improve the

efficiency of the basin as an energy dissipater. One of the measures that they used was the

symmetric central sill of limited length (sill length is less than the channel width). The flow behavior

was improved, the length of jump was decreased and more energy was dissipated using the central

1 Associate Professor, Dept. of Water & Water Structures Eng., Faculty of Engineering, Zagazig

University, Zagazig, Egypt, E-mails: [email protected] 2 Professor of Hydraulics, Dept. of Water & Water Structures Eng., Faculty of Engineering, Zagazig

University, Zagazig, Egypt, Email: [email protected] 3 Post-graduated student, Dept. of Water & Water Structures Eng., Faculty of Engineering, Zagazig

University, Zagazig, Egypt

mailto:[email protected]

mailto:[email protected]

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sill at a specified location. They provided design equations for the dimensions and the position of

the sill in the basin. They performed two additional experiments using movable bed of uniform

gravel of 10 mm with a thickness of 150 mm at a value of initial Frouude number, F1=7, and

expansion ratio, e=3.0. The first experiment was conducted using a smooth basin and the second

one was performed using a lateral central sill of optimized dimensions and a 2 horizontal to 1

vertical sloping end sill designed according to USBR basin III. In the former experiment, a scour

hole of depth 150 mm occurred at 500 mm and was observed after 15 minutes of operation

compared to only 20 mm scour hole in the later experiment with 30% reduction in the length of the

jump and the flow was symmetrical.

Earlier studies on the movable bed downstream sudden expansion include that of Nashta et

al. (1987). Nashta et al. (1987) investigated the effect of subcritical flow (F1=0.48 to 0.73) in sudden

expansion (e=1.5 to 4.5) on movable bed topography (sediment size is 0.28 mm). While, the effect

of supercritical flow on the scour downstream of smooth sudden expanding stilling basin was

studied by Negm et al. (2002a) and by Negm et al.(2002b) for SESB with central sill at different

positions. In the first study, they concluded that the scour patterns are asymmetric due to the

asymmetric flow patterns. The smaller expansion ratio produces shallower maximum scour depth

and vice versa. They provided the following prediction model for the maximum scour depth (Ds)

downstream the smooth SESB.

1.2

b

bBF26.0

G

D9.28

G

H59.3F13.1

G

DsG

50G

G (1)

Equation 1 has a determination coefficient of R2=0.857 and standard error of estimate, SEE =

0.4476.

In the second study, they concluded that the lateral central sill affects both the flow and scour

patterns. The minimum scour dimensions are function of the flow parameters as Hu/G and FG, sill

parameters as xs/Lb and hs/G, expansion ratio B/b and the ratio of mean diameter of soil particles

D50/G (Hu is the head upstream the gate, G is the gate opening, FG is the under-gate Froude number,

xs is the position of the sill from the section of the sudden expansion, Lb is the length of basin, hs is

the height of sill, B is the width of wider channel, b is the width of the narrower channel and D50 is

the mean particle diameter of the grain size). They used all the collected experimental data for

basins with and without sills and developed eq.(2) to predict the maximum relative scour depth

downstream the SESB.

687.0b

bBF25.0

L

X30.0

G

D3.17

G

h47.1

G

H042.0F27.1

G

DG

S50Su

G

S

(2)

Equation 2 has a coefficient of determination of 63.4% and standard error of estimate of 0.64.

Recently, Saleh et al. (2004) investigated the effect of using a sill at the end of the SESB to

reduce the maximum scour depth. Three expansion ratios were tested and different heights of the

end sill were used. It was concluded that the scour downstream of the SESB with end sill was

asymmetric. The extent of scour and deposition process was dependent on the Froude number, the

height of the end sill and the expansion ratio. The height of the end sill should not be more than the

dominant height of the gate to avoid the deflection of the main jet of flow just downstream of the sill

and hence a fully asymmetric and incomplete scour hole may be avoided. They stated that

practically, the use of end sill in SESB to reduce the scour depth is not recommended. However, it

may be useful to throw the scour hole away from the end of the basin increasing the safety of the

structure. The following equation was developed to estimate the maximum scour depth ratio in

terms of the flow and basin parameters.

G

D809.100

b

B702.0F375.0

H

G92.38

G

h496.0012.7

G

D 50G

u

ss (3)

Which has an R2=0.83 and SEE=0.705.

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Extensive review of the available literature indicated that almost no investigation exists on

the characteristics of the downstream scour under the effect of supercritical flow when asymmetric

side sill exists in the SESB. This paper presents the results of an experimental investigations to study

the effects of one and two asymmetric side sills with fixed height, fixed length, fixed top width and

variable position on the scour patterns and on the maximum scour downstream of sudden expanding

stilling basin. The present results are compared to those of smooth SESB (without sill) presented

previously by Saleh et al. (2004).

2. THEORETICAL BACKGROUND

Figure 1 shows a definition sketch for the phenomena under study. The maximum (max) scour depth

downstreaam of the stilling basin can be expressed as follows, Negm et al. (2002b)

)L,x,h,D,H,B,b,V,G,,,g(fDs bsS50uGs (4)

in which Ds is the maximum depth of scour, g is the acceleration due to gravity, ρ is the density of

water, ρS is the density of the movable soil and VG is the mean velocity under the gate.

Applying the Buckingham theorem with ρ, G, VG as repeating variables, eq. 3 can be written in

dimensionless form as:

s50bssu

Gs ,

G

D,

G

L,

G

x,

G

h,

G

b,

G

B,

G

H,Ff

G

D (5)

In which FG = VG /(gG)0.5

is the Froude number under the gate. The effect of the density ratio is

excluded because only one fluid and one soil are used during the course of experiments. Also, the

effect of expansion is neglected because only one expansion ratio is used. Keeping in mind the

properties of the dimensional analysis, eq. 4 could be reduced to

G

D

L

x,

G

h,

G

H,Ff

G

D 50

b

sSuG

s (6)

The validity of this equation will be checked using the collected experimental data in a forthcoming

section.

Figure 1 Definition sketch for scour downstream of sudden expanding stilling basin (SESB) with

asymmetric side sill

3. EXPERIMENTAL STUDY

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The experiments were carried out in a laboratory recirculating flume 0.30 m wide, 0.25 m deep and

3.5 m long. The discharge was measured using a pre-calibrated orifice meter installed in the feeding

pipeline. The stilling basin model was made from prespex of thickness 10 mm with a length of 1.25

m. the length of the approaching channel was 50 cm while the length of the apron of the expanding

stilling basin is 75 cm. The width of the approaching channel was kept constant to 10 cm, and the

width of expanding channel was fixed to obtain an expansion ratio of 1.54, which is close, to the one

normally used in practice.

A control sluice gate is made from the same prespex and is used to control the upstream

depth and the gate opening. The gate is installed 5 cm upstream the sudden expansion section. The

rest of the flume (2.5 m) is covered by sediment consisting of 7.5 cm sand layer of medium

diameter, D50 = 1.77 mm. The tail gate at the end of the flume is used to control the tailwater depth.

During the course of the experiments, the tailgate is kept unchanged such that the tailwater depth

was about 5 cm

A vertical side sill of length 7.35 cm, top width of 0.8cm and height of 1.5 cm is fixed on one

of the stilling basin sides laterally at particular position. The dimensions of the sill were selected

based on the previous investigations, Bremen and Hager (1994), Negm et al. (2002a) and Saleh et al.

(2004). Different positions of single side sill at 0.15Lb, 0.25Lb and 0.5Lb are tested. Two additional

models are tested such that each one is consisted of two side sills fixed in staggered way opposite to

each other’s. The pair of the first sills are fixed at 0.25Lb and 0.5Lb while the second pair of side

sills are fixed at 0.5Lb and at 0.75Lb. The positions of sills were selected based on the observed

lengths of the deflected main jet of flow to hit the bank of the basin in case of no sill. It was found

that the length of deflection varies between 20 cm and 45 cm depending upon the value of the

Froude number. Smaller deflection length is corresponding to low Froude numbers and vice versa.

Range of discharges and gate openings were used such that the Froude number under the gate

ranged from 1.20 to about 3.9. A total of about 45 runs were performed. The data for smooth SESB

from, Saleh et al. (2004) were used in the present study for comparison purposes. The time of each

run was chosen to be 45 min based on previous studies, Negm et al. (2002a,b) and Saleh et al.

(2004). A typical run consisting of leveling the movable soil, allowing a particular fixed tailwater

depth in the downstream channel with the control gate in close position. The discharge was adjusted

to the desired value and the gate was opened to the desired opening to obtain the required under gate

Froude number. During each run the flow pattern was observed and sketched. The deflection of the

supercritical jet was recorded. After about 20 minutes, the water surface profile is recorded and its

direction is noticed. After 45 minutes, the control gate was closed and the pump was switched off.

The topography of the movable bed was measured at each 5 cm in the direction of the flow (x

direction) and in the widthwise direction or lateral direction (y direction) to enable the study of the

scour pattern.

4. ANALYSIS AND DISCUSSIONS OF EXPERIMENTAL RESULTS

4.1 Maximum Scour Depth

Figure 2 presents the relationship between Ds/G and FG for different xs/Lb. Generally, the relative

maximum scour depth Ds/G increases with the increase of Froude number at particular xs/Lb. The

same result is observed for no sill case , Negm et al. (2002a) and Saleh et al. (2004). At particular

FG, the Ds/G has its maximum value when no sill exists in the basin and has its minimum value

when two side sills are used and placed at staggered way. The two side sills are fixed such that

xs/Lb=0.25 & 0.50 or xs/Lb=0.5 & 0.75. Specifically, at relatively high Froude number, FG>2.25, the

second system produces lower values of relative maximum depth of scour (few data points are being

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excluded from the fitting, one point from the first system at FG=3.9 and two points from the second

at FG=3.7 and 3.9). At low FG, the system xs/Lb=(0.25 & 0.5) produces a lower values of Ds/G but

not significantly different from those produced by the second system of xs/Lb=(0.5 & 0.75).

However, if all points are included in the fitting, both systems of using double staggered sills will

produce equivalent relative maximum depth of scour at higher FG>3.0 while the first produces lower

values at FG<3.0. Using a single side sill at 15%Lb, 25%Lb or 50%Lb reduces the relative maximum

scour depth at the same Froude number compared to the case of no sill but still the relative

maximum depth of scour is higher than those produced by the system of using double staggered side

sills.

1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50

FG

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

Ds/

G

NO SILL CASE [7]

xs/Lb=0.25

xs/Lb=0.15

xs/Lb=0.5

xs/Lb=(0.25 & 0.5)

xs/Lb=(0.5 & 0.75)

Figure 2. Relationship between maximum relative scour depth Ds/G versus Froude number, FG for

different xs/Lb

4.2 Scour Patterns

Figures 3 and 4 present the scour patterns for typical cases. Figure 3 presents two samples of scour

patterns at small value of FG =1.7 for two different positions of the sill side, single and double

systems while Fig. 4 presents the same for high value of FG=3.9. In the first case, a limited length

downstream of the basin is affected by the scouring and deposition processes (Figure 3a and Figure

3b) while in the second case, the scouring and deposition processes are extended to about 1.5 times

the length of the basin (Figure 4a). However, using double side sills at (0.25 & 0.5) or at (0.50 &

0.75) as in Fig. 4b reduces greatly the extent of scouring and deposition process to about one times

the length of the basin (in the first system, not presented) or even less (2/3 Lb in the second system).

It is also observed that sometimes the maximum scour depth is reduced and sometimes it is

increased by using the double side sills based on the behavior of the flow in the basin over the solid

apron before reaching the movable soil. If both sills affect the main jet of flow, the scour depth is

reduced and is increased if only the coming flow is affected by only one of the two side sills based

on the direction of issuing jet and the length of deflected jet (distance from the section of sudden

expansion to the point where the jet hits the wall of the basin).

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0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00

Distance from apron (cm)

0.00

10.00

20.00

Wid

th o

f ch

ann

el (

cm)

(a) xs=0.5 Lb, FG=1.7, G=1.8cm

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00


0.00

10.00

20.00

Wid

th o

f ch

ann

el (

cm)

(b)xs=(0.5 & 0.75) Lb, FG=1.7, G=1.8cm Figure 3. Typical scour patterns at low FG =1.70 for (a) single side sill at xs/Lb=0.50 and (b) double

asymmetric side sill at xs/Lb =(0.5 & 0.75)

Analyzing all the observed scour patterns indicated that most of the maximum scour and the

maximum deposition depths occur at the left or at the right of the central line of the channel and in

very few cases they may be formed near to the center line of the channel. This means that the scour

patterns in sudden expanding stilling basins are asymmetric even if one or two side sills are used to

improve the scour pattern and to reduce the maximum depth of scour downstream the basin. The

results indicated that the side sill is effectively reducing the maximum scour depth specially if two

opposite asymmetric side sills are used. However, at high Froude number, FG 3.7, there is no

grantee that the double side sills will be better than one side sill because one of them may be

inactive (Figure 4b). Sometimes, both sills are inactive when the jet hits the opposite bank

downstream of the first side sill and then changed its direction downstream of the second sill. In this

case, the values of the maximum scour depth approaches the values when only a smooth SESB is

used. In the present study, one run from the sill model xs/Lb=(0.25 & 0.5) occurred at FG=3.9 and

two runs at FG=3.7 and FG=3.9 behaves similarly when the model xs/Lb=0.50 & 0.75 is used. For

this reason, these three runs will be excluded from the analysis when trying to find a suitable

prediction equation for the maximum scour depth downstream SESB. This is because their inclusion

in the regression model will reduce significantly the correlation coefficient and the explained

variation by the model. Extensive experimental work is thus needed to collect more similar data in

order to be able to build a suitable prediction model for these type of data resulting when the sills are

partially or fully inactive.

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0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0


0.0

10.0

20.0

Wid

th o

f ch

ann

el (

cm)

(a) xs=0.5 Lb, FG=3.9, G=1.0 cm

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0


0.0

10.0

20.0

Wid

th o

f ch

ann

el (

cm)

(b) xs=(0.5 & 0.75) Lb, FG=3.9, G=1.0 cm Figure 4. Typical scour patterns at high FG =3.9 for (a) single side sill at xs/Lb=0.50 and (b) double

asymmetric side sill at xs/Lb =(0.5 & 0.75)

4.3 Flow Patterns

It was observed that the flow pattern over the solid apron in the SESB is a function of the Froude

number and the position of the asymmetric side sill at particular expansion ratio. The behavior of the

main jet of flow in both cases of xs/Lb=0.15 and 0.25 are mostly similar. At low Froude numbers up

to 2, the gate becomes partially submerged due to the back flow created by the presence of sill. A

vortex flow is formed in front of the sill downstream the sudden expansion with a longer length of

vortex flow on the opposite side of the sill (towards the other bank). The water surface was mostly

wavey and the main jet is slightly symmetric just downstream the gate and its direction was changed

to the opposite direction of the sill due to the instability of the hydrostatic pressure created by the sill

at the sudden expansion. At higher Froude numbers, a part of jet hit the sill forming high

fluctuations in the water surface then changed its direction to flow parallel to the bank in the

opposite side of the sill. It is also observed that the flow issued from the gate initially as two jets

which, meet each other at some distance downstream the expansion and upstream the sill forming

one jet which is directed to flow parallel to the bank in the opposite side of the sill. No deflection of

the jet was observed and a reversed flow was observed in case of single side sill at xs/Lb=0.25 which

was not observed at xs/Lb=0.15. The maximum scour was reduced by using the sill at any of the two

positions compared to the case of no sill but the scour pattern was asymmetric since the flow in the

basin was also asymmetric.

When the side sill was placed at xs/Lb=0.5, the deflection length for most values of the

Froude number (FG<3.4) are less than 0.5Lb. Consequently, the flow behaves as in the case of no sill

with the exception that lower maximum depth of scour was observed when the direction of the main

jet was in the direction of the sill and vice versa. At higher values of FG, the sill forces the jet to the

other direction to flow parallel to the bank and causing scour which is less than that of the no sill

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case. Also, it was observed that a slight portion of flow is revered on the apron of the basin due to

the formation of mound downstream of the SESB. In all cases of flow conditions, the observed scour

patterns were asymmetric because the main jet of flow was also asymmetric. The results of testing

the sill leads to avoid further testing of other single side sills at positions beyond the 50% of the

basin length but combinations of the discussed cases were tested, i.e. side sills at (0.25 & 0.50) and

(0.50 & 0.75).

When two asymmetric side sills were fixed in staggered way at positions 0.25 and 0.5 of the

basin length, the scour was greatly reduced if compared with the case of using only one of these two

sills. In this case, both sills affected the flow because the first sill forced the flow to the other side,

hence, the flow was affected by the other sill. At very low FG, the flow is symmetric and causing

little scour depth, which tends to be symmetric. Increasing the Froude number, causing the main jet

of flow to be in the direction of the faraway sill passing over it and flows parallel to the bank in the

direction of the second side sill. At higher FG=3.9, the main jet of flow was mostly symmetric up to

the second sill then slightly diverted to the bank in the same direction of the second sill and flows

parallel to the same bank. In all cases, the flow at the gate is partially submerged and two vortices

were formed, one in front of the each side sill.

If the sill at 0.25Lb was moved to 0.75Lb, the second system of two side sills at (0.50 & 0.75)

was obtained. In this system of sills, the flow is mostly similar and behaves as the no sill for

FG 2.0. For FG greater than 2 up to 3.4 as the flow hits the bank upstream of the first sill and then

was deflected to pass over the second sill and hence more energy was dissipated leading to a

reduction in the maximum scour depth. However, the main jet of flow may hit the bank in the

direction of the faraway sill then may pass over the sill or may be deflected to flow beyond the zone

of the effect of both sills leading to high scour depth but less than that formed by the no sill case

specially at higher FG of 3.7 and 3.9.

5. ESTIMATION OF MAXIMUM SCOUR DEPTH RATIO Ds/G

Using the linear regression analysis both simple and multiple, several models were proposed and

their coefficients were estimated using the experimental data.

The first model has the form:

)G/h(664.4)L/x(980.0)G/H(0462.0)F(288.2555.0G

DsbsuG

s (7)

With determination coefficient equals to R2=0.915, standard error of estimate equals to, SEE=0.372

and correlation coefficient of the residuals equals to, Rres=0.00042

The second model has the form:

)G/D(860.38)L/x(980.0)G/H(0462.0)F(288.2555.0G

D50bsuG

s (8)

with R2=0.915, SEE=0.372 and Rres=0.0042

Removing hs/G from eq. 7 or D50/G from eq. 8 reduces the R2 from 0.915 to 0.886 and SEE

is increased from 0.337 to 0.427. The regression coefficient will be –0.276, 0.249, 0.0936 and –

0.980 respectively. It should be note that both of hs and D50 were kept constant in the study.

Therefore, the inclusion of hs/G and D50/G disable the model building process. Moreover, since

both FG and Hu/G represent flow parameters, one of them could be removed. This leads to eq. 9 in

which R2 is reduced from 0.886 to 0.877 and SEE is is increased from 0.427 to 0.438. The

correlation coefficient of the residuals is 0.000047.

)L/x(980.0)F(193.1149.1G

DbsG

s (9)

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Analyzing the outputs of the eqs. 7 to 9 indicated that none of these equation could predict

the relative maximum scour depth accurately because the resulting errors are very high in most of

the cases and the MRE may be more than 80%.. In this case, the simple linear regression model may

be better. One of two models may be used as given by eqs. 10 and 11.

)F(baG

DG

s (10)

)G/H(baG

Du

s (11)

Where a and b in both equations are regression coefficients. Their values depend only on the value

of xs/Lb as shown in Table 1.

The estimated Ds/G from eqs. 7 to 11 are plotted against the measured ones in Figure 5 and the

line of equality is shown on the figure. Clearly, fair agreement was obtained for both eqs. 10 and 11.

These two equations are equally attracted in most of the cases. Obviously, the three excluded data

points are out of the prediction domain of the models numbers 10 and 11. The models

underestimated their values. In fact, this is true for any empirical model since they should b only

applied within their applicable limitations. Equations 10 and 11 are applicable for the ranges of the

experimental study.

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50

Measured Ds/G

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

Pre

dic

ted

Ds/

G

Eq.(7)

Eq.(8)

Eq.(9)

Eq.(10)

Eq.(11)

Line of equality

Figure 5 Comparison of estimated Ds/G and measured ones for basin with asymmetric side sills

using different regression models.

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Table 1. Values of the coefficient a and b of eqs. 10 and 11

Eq.(10) Eq.(11)

xs/Lb a B R2 SEE a b R

2 SEE

0.15 -1.700 1.323 0.975 0.222 -0.423 0.128 0.942 0.341

0.25 -1.807 1.462 0.981 0.216 -0.434 0.144 0.979 0.225

0.50 -1.280 1.117 0.957 0.252 -0.251 0.111 0.977 0.186

0.375* -1.224 0.889 0.938 0.226 -0.408 0.089 0.944 0.215

0.625**

-0.1797 0.415 0.899 0.122 0.191 0.850 0.850 0.147 * 0.375 is the average of (0.25 & 0.50) and ** 0.625 is the average of (0.50 & 0.75).

From eqs. 7 to 11, it could be stated that eq. 6 should become

b

sG

s

L

x,Ff

G

D Or

b

sus

L

x,

G

Hf

G

D (12)

6. CONCLUSIONS

An experimental investigation was conducted to study the effect of using asymmetric side sill both

single and double side sills on the maximum scour depth downstream sudden expanding stilling

basin (SESB). Five different positions of asymmetric side sills were tested. Three of them were

tested using a single side sill while the rest were tested using double side sills fixed in staggered

arrangement. The maximum scour depth is significantly reduced using a single or double side sills.

The effect of using double asymmetric side sills on reduction of the maximum scour depth was more

than using a single side sill. No matter at which side the sill should be fixed because the flow

direction in not exactly known. When the main jet of flow hits the bank upstream of a single side

sill, the scour is highly reduced specially at the high values of Froude numbers and if not, little effect

was observed on the scour depth. It was observed that the flow patterns in most of the cases were

asymmetric and the resulting scour and deposition were also asymmetric. Simple prediction

equations are developed to estimate the maximum relative scour depth downstream SESB with

asymmetric one or two side sills. It is observed that the maximum scour depth is high when the two

asymmetric side sills are partially inactive. The study highlights the need of further research to

investigate the different sides of this important subject. Also, testing the effect of more other

measures in improving the scour patters are highly needed.

7. REFERENCES

Bremen, R.& Hager, W.H. (1994). “Expanding Stilling Basin”, Proc. Instn Civ.Engrs Wat., Marit. &

Energy, Vol. 106, No. 9, pp. 215-228.

Graber, S.D. (1982). “Asymmetric Flow in Symmetric Expansion”, Journal of Hydraulics Div.,

Proc. ASCE, Vol. 135, No. 10, pp. 1082-1101.

Hager, W.H. (1992). Energy Dissipators and Hydraulic Jumps. Kluwer Academic Publications,

Dordrecht, The Netherlands.

Nashta, C.F.& Swamee, P.K., and Garde, R.J. (1987). “Subcritical Flow in Open Channel

Expansions with Movable Bed”, Journal of Hyd. Research, Vol. 25, No. 1, pp. 89-102.

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EFFECT OF ASYMMETRIC SIDE SILL ON SCOUR CHARACTERISTICS DOWNSTREAM OF SUDDEN EXPANDING STILLING...

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