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Journal of Hydro-environment Research 2 (2008) 119e128www.elsevier.com/locate/jher

Stormwater overflow in stepped channel

Daeyoung Yu*, Joseph H.W. Lee, Colin K.C. Wong

Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China

Received 10 September 2007; revised 28 April 2008; accepted 2 May 2008

Abstract

Sharp bends in drainage channels are sometimes engineered to suit local topography, especially in densely populated cities where land islimited. A hydraulic model study of a steep urban drainage channel is carried out to investigate the causes of an overflow incident in HongKong urban area, and to develop the drainage improvement measures to prevent flooding. The stepped drainage channel has a sharp bend inthe middle and several trash racks are located along the channel. Experiments are performed on a 1:16 Froude scale model. In the first phase,experiments on a purposely built straight channel model are performed to study the bottom roughness of the stepped channel flow isolating theeffect of the bend. After the straight channel experiments, four trash rack scenarios are tested in the exact model with detailed channel features.The flow in the drainage channel is supercritical and highly aerated. Based on the theory of skimming flow in stepped channels, a hydraulicassessment suggests that the bend and trash racks may be dominant causes of the overflow. The experiments show that sharp bend causes a spiralflow leading to significant lateral overflow. The trash racks are observed to generate a serious ski-jump type overshooting flow. It is found that thestormwater overshoot and flooding can be prevented by the repositioning of appropriately sized trash racks and the containment of the spiralflow. The proposed channel improvement design has been implemented on site and found to work successfully in heavy rainstorms after instal-lation. The present study offers novel insights into the design of urban drainage works.� 2008 Published by Elsevier B.V. on behalf of International Association for Hydraulic Engineering and Research, Asia Pacific Division.

Keywords: Supercritical flow; Channel bend; Stepped channel; Trash rack; Aerated flow; Urban drainage; Physical model

1. Introduction

Sharp bends in drainage channels are sometimes engineeredto suit local topography, especially in densely populated citieswhere land is limited. In addition, trash racks for screeningdebris are sometimes put in the drainage channels to protectthe downstream drainage system. In the early morning hoursof 24 June 2005, a serious flooding incident occurred in a drain-age channel at Smithfield in Hong Kong. A large scale over-shooting of stormwater runoff from the drainage channel wasobserved. Highly aerated flow overtopped the channel andran down to the road below. The flooding channel is a 1.5 mwide rectangular stepped channel consisting of the upperchannel, lower channel and steep cascade (Figs. 1 and 2).

* Corresponding author. Tel.: þ852 2857 8470; fax: þ852 2559 5337.

E-mail addresses: daeyoung@hku.hk (D. Yu), hreclhw@hkucc.hku.hk

(J.H.W. Lee).

1570-6443/$ - see front matter � 2008 Published by Elsevier B.V. on behalf of Internatio

doi:10.1016/j.jher.2008.05.004

The total length of the channel is approximately 60 m witha 132� bend between the upper and lower channels. The Smith-field channel is located on a man-made cut-off slope, approx-imately 40 m above the street level (Fig. 2). On the day offlooding the channel was fitted with two trash racks in thelower channel in front of the entrance to the steep cascade.The flooding discharge is estimated to be 9.2 m3/s and theovershooting from the drainage channel is a potential serioushazard to traffic as well as pedestrians.

The flow can be characterized as a supercritical steppedchannel flow complicated by the presence of a sharp bendand trash racks. Stepped channels are commonly found in drain-age systems to increase bottom roughness of the channel witha roughness length of the order of the size of the steps resultingin large energy dissipation. While there have been a number ofstudies on stepped spillways, most of the studies dealt withspillways with slopes greater than 40�. These studies showedthat the Darcy-Weisbach friction factor in a stepped channelcan be as much as 0.7e1.0, compared with a typical value of

nal Association for Hydraulic Engineering and Research, Asia Pacific Division.

12.1°

23.2°

Upperchannel

Lowerchannel

Steepcoveredcascade

Streetlevel

38.7 m

a Side view

22.3 m

19.4 m 21.3 m132°

1.5 mRoof

Upper

channel Lowerchannel

Steepcoveredcascade

To downstreamdrainage sytem

b Plan view

Fig. 1. Smithfield drainage channel.

120 D. Yu et al. / Journal of Hydro-environment Research 2 (2008) 119e128

around 0.03 for a smooth concrete channels (Rajaratnam, 1990;Chanson, 1993). A recent study (Ohtsu et al., 2004) has re-ported skimming flow characteristics on channels with slopesin the range of 5e20�.

Fig. 2. Smithfield drai

There are limited studies on the effect of trash racks on theflow. The headloss coefficient of trash racks of various shapesare found in Miller (1978). Abt et al. (1992) carried out an ex-perimental study on the blockage at a trash rack in a supercrit-ical flow. In their study, different blockage ratios that causeflooding for standard trash rack design are investigated. A par-abolic shape trash rack design with emphasis on safety issuesand sweeping of the floating objects was proposed by Allred-Coonrod (1994).

The objective of this study is to investigate the causes of thestormwater runoff overshoot through a physical model study.A hydraulic assessment of the channel capacity is carriedout based on the stepped channel flow theories. From the re-sults of the physical model study, improvement measures areproposed and successfully implemented.

2. Description of drainage channel andexperimental setup

2.1. Drainage channel description

The channel consists of an upper channel, a lower channeland a steep cascade. The upper channel is 22.3 m-long with bot-tom slope of 12.1�; the channel is partly stepped, with 0.3 mhigh and 1.4 m long steps (Fig. 1). The upper channel turnsthrough a 132� bend into a 19.4 m-long lower channel. Thesteeper lower channel has a bottom slope of 23.2� with 0.3 mhigh (h) and 0.7 m long (l ) steps. The upper part (8.6 m) ofthe lower channel is covered with a roof. The width and wallheight of the lower channel are 1.5 m and 1.6 m, respectively.The flow from the lower channel enters a 28 m-high coveredsteep cascade that leads to the downstream drainage system.

nage channel site.

G1G2

G5

G3G4 G6

Location of trash racks

1.5 m

1.6

m

thickness: 75 mm thickness:100 mm diameter: 25 mmspacing: 214 mm

G1, G2 G3, G4, G5 G6

0.75

m

0.45

m

0.45

m

upperchannel

lower channel steep cascade

diameter: 16 mmspacing: 125 mm diameter: 20 mm

spacing: 200 mm

Fig. 3. Location and dimension of trash racks.

121D. Yu et al. / Journal of Hydro-environment Research 2 (2008) 119e128

During the flooding of June 2005, two trash racks werelocated in the lower channel in front of the entrance to thesteep cascade (G1 and G2 in Fig. 3). After the flooding inJune 2005, the two trash racks were replaced by three trashracks (G3, G4 and G5 in Fig. 3). As shown in Fig. 3, the trashracks have relatively thick frames (75 or 100 mm) that reducethe cross-sectional area substantially. As an alternative, a trashrack without thick frame (G6) is tested in the model study.

The rainfall data of the Smithfield drainage channel (year1999e2006) are collected and analyzed. The rainfall data are5-minute precipitation records from one of the nearest raingauge stations. The 60-minute and 30-minute duration rainfallare computed from the raw data and sorted out. The rainfallanalysis has revealed that the rainfall of the June 2005 floodingis the heaviest rainfall event during the year 1999e2005.The rainfall corresponds to a 15-year return period event basedon 60-minute rainfall and a 30-year return period event for 30-minute rainfall. Furthermore, it was preceded by threesuccessive rainy days that probably have saturated the soil.

2.2. Model setup

Fig. 4. Smithfield channel model.

A 1:16 scale undistorted Froude model of the Smithfielddrainage channel was built to undertake the investigation.The model includes upper, lower channels and steep cascade.The detail of steps and trash racks in the channel are preciselyrepresented. The entire model channel was made of perspex tofacilitate flow visualization. The set up consists of an inlettank, the Smithfield drainage channel model, and an outletchannel for measurement of outflow discharge. The physicalmodel is housed in a specially designed 4 m-high, two-levelframe structure that allows efficient testing (Fig. 4).

In addition to the exact model of Smithfield drainagechannel, a 1:16 Froude-scale straight channel model was built,covering the whole upper and lower channels and the upstreamone third of the steep cascade. The configuration of thestraight channel has the same stepped channel characteristicsas the exact model except for the absence of 132� bend(Fig. 5). The main objective of the straight model experiments

is to study the bottom roughness of the stepped channel isolat-ing the effect of the bend on the flow characteristics.

All the model experiments are carried out at steady flowcondition. The inflow discharge is measured by a calibratedultrasonic flowmeter (Controlotron System 1010) with an accu-racy of 1e2%. The outflow from the cascade (i.e. at the modeldischarge point) is measured by a specially designed receivingtank fitted with a V-notch weir; the overflow can then be deter-mined from the difference between the measured inflow andoutflow.

Fig. 5. Straight channel model.

122 D. Yu et al. / Journal of Hydro-environment Research 2 (2008) 119e128

The formation of overshooting is determined using digitalimage processing e a digital image of overshooting is re-corded together with a reference frame and digitally analyzed.The water depth is measured in the upper channel; depth mea-surement in the lower channel is not meaningful due to thefluctuating and non-uniform nature of the aerated flow. Inthe straight channel experiments, the water depth is measuredat a number of points along the full length of the channel.

2.3. Experimental procedure

The flow conditions in the drainage tunnel together withthe corresponding rainfall characteristics are summarized inTable 1. This study is carried out in three phases. In the firstphase, experiments are carried out in the straight channelmodel. The variation of the water depth along the channel is

Table 1

Rainfall events and discharges for Smithfield drainage channel

Rainfall event Flow (m3/s)

2005-08-13 3.2

1 in 5 year 5.6

1 in 10 year 8.3

2005-06-24 9.2

1 in 20 year 10.2

1 in 50 year 10.4

1 in 100 year 12.0

1 in 200 year 12.7

Extreme 14.7

measured for discharges of 2e12 m3/s (prototype scale). Inthe second phase, experiments of four alternative trash rackarrangements are performed on the exact model of the Smith-field drainage channel. The blockage by debris at trash racksare not considered. For each test scenario, experiments arecarried out for discharges corresponding to 1 in 5, 10 and200 year return period rainfall events. The flooding on 24June 2005 and on 13 August 2005 are also studied usingthe trash rack configurations of those days. The matrix ofmodel test scenarios is shown in Table 2.

In the third phase, the channel improvement measures areproposed; the Smithfield channel model is modified accord-ingly. Several series of experiments are carried out to studythe effectiveness of the proposed channel modification, andto ascertain the relative importance of the trash grille, sidewallheight and inlet geometry.

3. Hydraulic assessment of drainage channel

In order to unravel the causes of stormwater runoff over-shoot in June 2005, the flow capacity of a straight steppedchannel with the same characteristics was evaluated. Of thetwo reaches of the Smithfield channel e the upper and lowerchannels, only the key features of the lower channel flow arepresented below because the flow capacity is determined bythe straight lower reach before entering the steep cascade(Fig. 1).

For a stepped channel with a bottom slope in the range ofq¼ 19e55�, the onset of skimming flow occurs at (Ohtsuet al., 2004):

h

dc

¼ 7

6ðtan qÞ1=6 ð1Þ

where h¼ step height, dc ¼ ðq2=gÞ1=3 ¼ the critical depth,q¼ bottom slope, q¼Q/B¼ unit discharge, Q¼ discharge,B¼ channel width, and g¼ gravitational acceleration. Forthe lower channel of Smithfield channel with q¼ 23.2�,h¼ 0.3 m, and B¼ 1.5 m, Eq. 1 gives h/dc¼ 1.013, orQ¼ 0.757 m3/s at the onset of skimming flow. For the flowdischarge of interest, Q¼ 2 e 12 m3/s, the flow on theSmithfield stepped channel can be categorized as a skimmingflow.

Table 2

Run parameters for test scenarios of second phase experiments

Test scenario 1 2 3 4

Trash rack

arrangement

G1, G2

(2005-06-24

condition)

G3, G4, G5

(2005-08-13

condition)

G4, G5, G6 G4, G5

Flow (prototype

scale, m3/s)

3.2

5.6 5.6 5.6 5.6

8.3 8.3 8.3 8.3

9.2 10.4

12.7 12.7 12.7 12.7

123D. Yu et al. / Journal of Hydro-environment Research 2 (2008) 119e128

For a steady uniform flow, the bottom shear stress to can berelated to the bottom slope, So¼ tan q¼ h/l, hydraulic radius,R, and mean velocity, V as:

to ¼ rgRSo ¼f

8rV2 ð2Þ

where r¼ fluid density, f¼Darcy-Weisbach friction factor,and V¼ cross-sectional average velocity. For a uniform step-ped channel flow, if the flow depth and channel velocity abovethe pseudo-bottom are measured, the hydraulic radius and thefriction factor can then be determined:

f ¼ 4to

12rV2

ð3Þ

Since the velocity is given by the Manning’s equation as:

V ¼ 1

nR

23S

12o ð4Þ

it can be shown that the Manning’s n and the friction factor arerelated as

n¼ffiffiffiffiffif

8g

sR

16 ð5Þ

For a bottom slope of q¼ 19e55�, the friction factor in a skim-ming flow can be estimated from the discharge and step heightas (Ohtsu et al., 2004):

f ¼ fmax � a�

0:5� hdc

�2

; 0:1< h=dc < 0:5

¼ fmax 0:5� h=dc

ð6Þ

where a¼ 0.452, and fmax¼ 2.32� 10e5q2 e 2.75� 10e3

qþ 0.231 (q in degrees). The friction factor for each flowcan first be estimated from Eq. 6 based on an assumed depth(e.g. critical depth); the uniform depth can then be obtainedfrom the Manning’s equation, from which a revised estimateof the friction factor (or Manning’s n) can be obtained. The ap-propriate roughness can typically be obtained in a few iterativecalculations. It can be shown that the friction factor is in therange of f¼ 0.13 e 0.18, and the Manning’s n¼ 0.034 e0.037 for Q¼ 2 e 12 m3/s. This is more than twice theManning’s n of a smooth concrete channel (n¼ 0.016). Thepredicted flow depths in the straight Smithfield model basedon the above Manning’s n are shown in Table 3.

A series of experiments has been carried out at steady uni-form flow for nominal discharges of Q¼ 2, 4, 6, 8, 10, 12 m3/s

Table 3

Predicted flow characteristics of straight Smithfield stepped channel

Flow Q (m3/s) h/dc Clearwater depth yw (m) Velocity V (m/s) Frictio

2 0.530 0.228 5.85 0.180

4 0.334 0.364 7.32 0.170

6 0.255 0.484 8.27 0.153

8 0.210 0.595 8.96 0.210

10 0.181 0.701 9.51 0.134

12 0.161 0.804 9.95 0.128

(prototype scale) in the straight channel model. For each dis-charge, the water depth (normal to the free surface), y wasmeasured at a number of locations along the channel. In themodel, there is no air entrainment, and the measured flowdepth can be assumed to be that of the clearwater depth (seediscussion below). The measurements (Fig. 6) indicate thatuniform depth on the stepped channel is attained in the midreach of the lower channel. It can be seen the data supportthe predicted bottom roughness of the Smithfield steppedchannel (in the absence of air entrainment) rather well (Fig. 7).

The measured water depth and velocity are summarized inTable 4 together with the Reynolds number and Weber num-ber. Aeration is not found in the model because of the scaleeffects. For modeling of aeration in a stepped channel, Rey-nolds number and Weber number should be large enough toavoid the scale effects. The experimental results of the straightSmithfield channel show that Reynolds number is in the rangeof 2.1� 104e1.3� 105 and Weber number of 4.1� 102e4.6� 103, which are smaller than the minimum criteria ofthe stepped channel aeration modeling (Boes and Hager,2003).

In the prototype, the high speed supercritical flow will beaerated. In the uniform stepped channel flow, the average airconcentration, C, depends on the channel slope, q, and the rel-ative step height, h/dc. An estimate of the mean air concentra-tion can be obtained from the recent experiments of Ohtsuet al. (2004):

C¼ d� 0:3exp

�� 5

�h

dc

�2

�4

�h

dc

��for q¼ 19� 55+ ð7Þ

where C¼mean air concentration, and d¼�2.0� 10e4

q2þ 2.14� 10e2q e 0.0357 (q in degrees). In the presenceof air entrainment, the bulked depth of the air-water flow, yb,is related to the clear water depth, yw, by:

yb ¼yw

1�Cð8Þ

For the Smithfield channel, the clear water depth, velocity,mean air concentration, and bulked depth are computed foreach discharge (Table 3). The flow on the stepped channel isfound to be supercritical, with clear water depths in the rangeof 0.2e0.8 m, and velocities in the order of 6e10 m/s. TheFroude number (not shown) is in the range of 3.5e3.9. Themean air concentration varies in the range of 0.21e0.34.The air entrainment can lead to significant bulking of theflow. For the flood flow of 24 June 2005, with an estimated

n factor ( f ) Manning’s n Air concentration (C ) Bulked depth yb (m)

0.036 0.344 0.348

0.037 0.308 0.526

0.036 0.275 0.667

0.035 0.249 0.793

0.035 0.230 0.911

0.034 0.214 1.020

−2 0 2 4 6 8 10 12 14 16

−6

−4

−2

0

2

x (m)

y (m

)

Q = 12 m3/sQ = 10 m3/sQ = 8 m3/sQ = 6 m3/sQ = 4 m3/sQ = 2 m3/s

Fig. 6. Observed water surface profile in lower part of straight channel model (prototype scale).

124 D. Yu et al. / Journal of Hydro-environment Research 2 (2008) 119e128

flow of around 10 m3/s, the bulked water depth (above thepseudo-bottom joining the corners of the steps) is approxi-mately 0.9 m. Accounting for a step height of 0.3 m, theflow should be contained within the 1.6 m high channel atthis flow. The presence of air can also have a cushioning effecton the bottom resistance, thereby reducing the friction factor.Based on the bottom friction reduction factors for self-aeratedflow on spillways (Wood, 1991), the effect of air concentrationon the Manning’s roughness is judged to be not significant forthe Smithfield problem.

From the analysis of the hydraulic characteristics of theSmithfield stepped channel flow, it is found that the Smithfieldstepped channel flow is a skimming flow, with an estimatedbulked depth of around 0.9 m for a discharge of Q¼ 10 m3/s.The analysis suggests that in the absence of a sharp bendand trash racks, the straight stepped channel can cater the

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

measured depth (m)

pred

icted

d

ep

th

(m

)

Fig. 7. Comparison of measured and predicted water depth in straight stepped

channel model (prototype scale; Q¼ 2, 4, 6, 8, 10, 12 m3/s).

stormwater flow of 24 June 2005. This in turn implies thatthe sharp bend and the blocking due to the trash racks mayplay an important role in the observed overshooting of thestormwater flow in June 2005.

4. Experimental results

4.1. Condition of flooding on 24 June 2005(test scenario 1)

The test scenario 1 (with trash racks G1 and G2 in the lowerchannel; Fig. 3) represents the Smithfield drainage channelcondition of the flooding on 24 June 2005. In the test scenario1, four discharges are tested including 9.2 m3/s which corre-sponds to the discharge of flooding of June 2005 (Table 2).

The flow in the upper channel is smooth and uniform formore than half of its length. The flow is supercritical withthe water surface profile following a typical S2 curve(Fig. 8). In accordance with theory (Eq. 1), skimming flowsare observed for all the discharges tested. No aeration is ob-served in the upper channel even for the largest test discharge(12.7 m3/s). The flow feature in the upper channel is found tobe the same for all the test scenarios regardless of the presenceof trash racks in the upper channel.

The sharp change in direction of the supercritical flow leadsto the flow impingement, resulting in a disintegrated and

Table 4

Measured flow characteristics of straight Smithfield stepped channel (model

scale)

Flow Q (m3/s) Depth y

(m)

Velocity V

(m/s)

Reynolds

number Re

Weber number W

0.002 0.015 1.40 2.1Eþ04 4.1Eþ02

0.004 0.020 2.10 4.3Eþ04 1.2Eþ03

0.006 0.030 2.13 6.4Eþ04 1.9Eþ03

0.008 0.037 2.31 8.5Eþ04 2.7Eþ03

0.010 0.042 2.52 1.1Eþ05 3.7Eþ03

0.012 0.049 2.60 1.3Eþ05 4.6Eþ03

Re¼ q/n, where q¼ unit discharge, and n¼ kinematic viscosity.

W¼ ryV2/s, where r¼ density of water, y¼water depth, V¼ velocity, and

s¼water surface tension.

Fig. 8. Water surface profile in upper channel model (test scenario 1, Q¼ 9.2 m3/s e prototype scale).

125D. Yu et al. / Journal of Hydro-environment Research 2 (2008) 119e128

highly aerated flow and side spillover (Fig. 9a). The developedsupercritical flow from the upper channel impinges on thesidewall at the bend much like a jet. This flow impingementagainst the wall results in a strong spiral-type flow down thechannel winding over the entire channel cross-section. Asthe upstream part of the lower channel is roofed, the spiralflow continues to swirl until the channel cover ends. At theend of the channel cover, a significant portion of the spiralflow spills over the channel wall. The supercritical flow im-pingement and spiral flow across the channel cross-sectionare illustrated in Fig. 9b.

The main overshooting is observed at the upstream trashrack (G2) for all the discharges tested. For an estimated flow

impingementspiral flow

Upper ChannelLower Channel

Covered channel section Bend

supercritical flow

side overspill

a

b

Observed spiral flow downstream of bend (test scenario

1, Q = 12.7 m3/s – prototype scale)

Flow impingement at bend and spiral flow

Fig. 9. Spiral Flow in lower channel.

of around Q¼ 9 m3/s, the clearwater and bulked depths areabout 0.65 m and 0.85 m respectively. As shown in Fig. 3,the top of the rack is at around 0.75 m above the channelbottom. This suggests that the approach supercritical flowdepth is of the same order as the height of the trash rack.The top of the main water stream strikes the top 75 mm thickframe of the rack at a velocity of the order of 9 m/s; the flowis obstructed and split by the trash rack frame into (i) a ski-jump type overshooting flow, and (ii) an underflow. Theobserved overshooting and mechanism of flow splitting at thetrash rack are illustrated in Fig. 10. The relatively thick(75 mm) frame is found to play a dominant role in causingthe overshooting. There is also significant obstruction by theside frame with the same thickness. The overshooting flowfrom trash rack G2 runs over the top of steep cascade to theground level. It is found that the effect of the trash rack G1which is located downstream of G2 is negligible.

The flow enters the steep cascade in the form of a jet thatseparates from the channel bottom at the sharp edge wherethe cascade step starts. The jet flow impinges on the oppositewall; the flow is disintegrated resulting in significant airentrainment. Most of the flow appears to stay attached to theopposite wall instead of skimming over the steps (Fig. 11).The same flow pattern is found for the other test scenarios.

4.2. Test scenarios 2, 3, 4

Six trash grilles (G1 to G6) with different bar thickness andspacing are modelled (Fig. 3). In each test scenario, a combina-tion of two or three of the grilles are placed at differentlocations along the channel (Table 2 and Fig. 3).

4.2.1. Test scenario 2The three trash racks (G3, G4 and G5) used in test scenario

2 are shorter in height than G1 and G2 of test scenario 1(0.45 m vs. 0.75 m) and has wider spacing with a thickerframe. G3 is placed in the lower channel near the locationof G2 (for test scenario 1); G4 and G5 are placed at thebend and at the entrance of the upper channel respectively(Fig. 3). G5 (at the entrance to the upper channel) is fully

Fig. 11. Flow in lower part of steep cascade model (test scenario 1,

Q¼ 9.2 m3/s e prototype scale).

Table 5

Measured overflow (prototype scale)

Qi (m3/s) Qs (m3/s) Rs (%)

Test scenario 1 5.60 0.59 10.5

8.29 0.69 8.3

9.20 0.83 9.0

12.70 1.13 8.9

Test scenario 2 3.17 0.33 10.4

5.73 0.25 4.4

8.30 0.86 10.4

12.49 2.18 17.5

Test scenario 3 5.60 0.00 0.0

8.30 0.08 1.0

12.40 0.40 3.2

Test scenario 4 5.60 0.08 1.4

8.33 0.00 0.0

10.41 0.32 3.1

11.98 0.40 3.3

Qi¼ inflow discharge, Qs¼ overflow discharge, Rs(¼Qs/Qi)¼ overflow ratio.

supercritical flow

overshooting flow

trash rack

Observed overshooting at trash rack (test scenario

1, Q = 9.2 m3/s – prototype scale)

a

b Flow splitting by trash rack

Fig. 10. Overshooting at trash rack.

126 D. Yu et al. / Journal of Hydro-environment Research 2 (2008) 119e128

submerged even for the smallest discharge tested (3.2 m3/s); itshows no influence on the flow. As the flow is found to start toswirl around the cross-section, and to become disintegrated atthe bend where G4 is located, the effect of G4 on the flow ishardly noticeable. The spiral flow downstream of the bend isobserved to be the same as the test scenario 1.

For small discharges (3.2 and 5.7 m3/s), the approach flowis split by the frame of G3 trash rack frame following the samemechanism as test scenario 1. The overflow discharge, how-ever, is smaller than that of test scenario 1 (Table 5) becausepart of the overshooting flow by the short trash rack fallsback in the channel instead of overtopping the cascade cover.

As the water depth becomes larger than the height of G3with the increase of discharge, the side contraction playsdominant role in inducing the overshooting. The side framedeflects the flow to the center of the channel, causing signifi-cant air entrainment and consequent bulking of flow. Thedepth of the converged and aerated flow becomes much largerthan the approach flow depth, resulting in overflow at thecascade entry. Overall, the flow feature of test scenario 2 isqualitatively similar to that of test scenario 1 as shown inFigs. 9 and 10.

4.2.2. Test scenario 3In test scenario 3, the same trash rack arrangement as test

scenario 2 is used except that G3 is replaced with G6(Fig. 3). G6 has wider spacing with a thin frame, and is in-clined at 35� to horizontal. No overshooting by this trashrack is found (Fig. 12a). The side overflow due to the spiralflow at the bend is the same as test scenario 1 and 2.

4.2.3. Test scenario 4In test scenario 4, only two trash racks, G4 and G5, are used

(Fig. 3). Without a trash rack in the lower channel, no over-shooting is observed (Fig. 12b). As with test scenario 3,only the side overflow by the spiral flow occurs.

Fig. 12. Overflow of test scenario 3 and 4 (Q¼ 12.7 m3/s e prototype scale).

127D. Yu et al. / Journal of Hydro-environment Research 2 (2008) 119e128

4.3. Overflow discharge

Modifiedcurved invert

Original invert

Extended cover

Fig. 13. Modified channel.

The experimental results clearly show that the cause of theoverflow is the sharp bend between the upper and lower chan-nels and the trash rack in the lower channel. In particular, thepresence of the trash rack is the main cause of the overflow;the thick frame of the trash rack generates ski-jump type over-shooting (test scenario 1) or excessive side contraction (testscenario 2). With a slender trash rack (test scenario 3) or notrash rack (test scenario 4), no overshooting takes place. Theside overflow that is produced by the spiral flow generatedat the sharp bend is observed for all four test scenarios.

The overflow discharges are summarized in Table 5. Fortest scenario 1 and 2 where the overflow by the trash rack isdominant, the overflow discharge increases with the channeldischarge; the overflow ratio (the ratio of overflow dischargeto the total discharge) is approximately 8e10%. As an extremecase, the overflow ratio of test scenario 2 with Q¼ 12.5 m3/srises up to 17.5%. On the contrary, for the test scenario 3and 4 where only the side overflow by the bend is observed,the overflow discharge is very small with the maximumoverflow ratio of around 3%.

Compared to test scenario 3 or 4 in which there is no over-flow by a trash rack, the ratio of overshooting by the trash rack

(test scenarios 1 and 2) to the total overflow for high dischargecan be inferred as approximately 64e72% which revealssignificant portion of overflow occurs over the sidewall. Forlower discharge (5.6 m3/s), the overshooting at a trash rackmarks around 84% of the total overflow.

It should be pointed out that the experimental results onoverflow discharge can be underestimated. As shown in Table3, the air concentration can be as much as 25% for the largerflows in the Smithfield channel. Since the air entrainment can-not be properly modelled in the present model, the flow bulk-ing due to air entrainment in the prototype is expected to begreater than that in the model.

5. Drainage improvement and model tests

Based on the foregoing hydraulic assessment and the modelstudy, the channel modifications are proposed to improve thedrainage of the stormwater. The modification consists of: (i)repositioning of trash racks (e. g. test scenario 4); (ii) raisingthe lower channel sidewall or extended cover in the lowerchannel; and (iii) modification of the stepped inlet to the steepcascade to a smooth ‘‘spillway like’’ curved inlet. Severalseries of experiments are systematically carried out to studythe effectiveness of the channel modifications and also tofurther ascertain the main cause of the flooding in the originalSmithfield channel.

Since the trash rack with a thick frame in the lower channelis found to cause the serious overshooting of the stormwater,the lower channel trash rack is removed while the upper chan-nel trash racks are retained for the screening of debris (test sce-nario 4). The sidewall that is added to the existing wall on eachside of lower channel (8.4 m long by 1.5 m high) is proved tobe effective in stopping the overflow at the channel side. Asan alternative to the raised sidewall, the extended cover thatis stretched from the original cover at the upstream of lowerchannel by 4.4 m in triangular shape, is proposed and testedwith the modified inlet (Fig. 13). The extended cover effec-tively prevents the spiral flow from spilling over the channelwall resulting in no overflow over the whole discharge range.

128 D. Yu et al. / Journal of Hydro-environment Research 2 (2008) 119e128

The downstream end of the channel is modified to generatestreamlined flow to the cascade inlet for the purpose of mini-mizing the overshooting (Fig. 13). Provided there is no trashrack in the modified channel, the inflow to the steep cascadeenters the inlet smoothly with a larger clearance from theroof (due to the lowered curved channel invert at the inlet),and no overflow is observed. The final modified lower channelwith curved channel invert, extended cover and removal oftrash rack is illustrated in Fig. 13.

6. Conclusion

The cause and preventive measures of the potential hazard-ous urban flooding from a complex drainage channel config-uration are investigated. A hydraulic model study of theextensive flooding on a steep urban drainage channel iscarried out on a 1:16 Froude scale model. The drainagechannel at Smithfield in Hong Kong is characterized as steepstepped channel (slope of 12.1e23.2�) with a sharp bend inthe middle and thick trash racks. Based on the theory of skim-ming flow in stepped channels, a hydraulic assessment of theflow capacity of the Smithfield channel has been made. Theestimated Manning’s roughness of the stepped channel basedon the skimming flow theories is validated by the straightstepped channel experiments. The hydraulic assessment sug-gests that the sharp bend and trash racks may be the dominantcause of the flooding.

Unlike the previous studies on trash racks in supercriticalflow, the present study reveals significant flooding can occureven in the absence of any debris blockage. It is found thatthe overshooting flooding flow of June 2005 is caused byboth the channel bend and more importantly the particular de-sign and location of trash racks. The sharp bend causes a highlyaerated spiral flow down the channel, leading to side overflowover the channel wall. In addition, the thick-frame trash racksin the lower channel cause a flow splitting and a serious ski-jump type overshooting flow over the covered cascade. Modeltests show that for high discharges the overshooting flowcaused by the trash rack accounts for about 70% of the totaloverflow. It should be pointed out, however, that due to flowbulking caused by air entrainment (which cannot be properly

modelled in the laboratory), the prototype overflow is expectedto be greater than predicted by the model.

Several channel improvement measures are proposed andtested. The channel improvement work consisting of reposi-tion of properly designed trash racks, smooth curved invertand extended cover was implemented on site in early 2006.The improvement work was successful without overflow dur-ing the heavy rainfall in July 2006, which recorded a greater60-minute rainfall than that of June 2005.

Two main lessons can be learned from this unusual storm-water overflow incident. First, sharp bends caused by realign-ment of a steep drainage channel can result in significantchange in the supercritical flow, leading to a spiral overflow.Second, trash racks need to be appropriately designed andpositioned in relation to the design flow and the channel sizein order to avoid a ski-jump type overshooting flood. Thenovel insight gained in this study can be beneficial in the urbandrainage designs of populated cities.

Acknowledgement

The support of Drainage Service Department of Hong KongSpecial Administrative Region, China, is acknowledged.

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