自然災害科学特別号（特別号）（177）

Study on Estimation of Inflow
Discharge to Underground Storage
System for Mitigation of Urban
Inundation Damage
Dongwoo KO ＊・Hajime NAKAGAWA ＊＊・Kenji KAWAIKE ＊＊＊・
Hao ZHANG ＊＊＊＊

Study on Estimation of Inflow Discharge to Underground Storage
System for Mitigation of Urban Inundation Damage
Dongwoo KO*, Hajime NAKAGAWA**, Kenji KAWAIKE***and Hao ZHANG****
Abstract
Underground storage systems are installed to mitigate damage of urban flooding.
Estimation of overflowing discharge into those storage systems is significant forevaluation of their mitigation effects. Such overflow happens between pressurized sewer
pipe and storage system over a side weir. The equation proposed by De Marchi toestimate overflow discharge over a side weir has been verified through several
experimental researches only for open channel flow. Therefore in this study, overflow
discharge coefficient is evaluated for pressurized flow of circular pipe throughexperiments with different side weir length. From obtained results, peculiar water headprofile over the side weir can be observed. Discharge coefficient derived fromexperimental results implies applicability of constant value to estimate overflow
discharge if mean value of integrated water head along the side weir is used, whichshould be verified through numerical simulation in the future.
Key words： Underground storage system, Side weir, Discharge coefficient

Student Member of JSNDS, Doctoral Student, Departmentof Civil and Earth Resources Engineering,
Kyoto University (Katsura Campus, Nishikyo-ku, Kyoto
615-8540, Japan)＊＊
Member of JSNDS, Prof., DPRI, Kyoto University (Yokooji, Fushimi, Kyoto 612-8235, Japan)＊＊＊＊＊＊＊＊177

Member of JSNDS, Assoc. Prof., DPRI, Kyoto
University (Yoko-oji, Fushimi, Kyoto 612-8235, Japan)
Member of JSNDS, Assist. Prof., DPRI, Kyoto
University (Yoko-oji, Fushimi, Kyoto 612-8235, Japan)

178

Study on Estimation of Inflow Discharge to Underground Storage System for Mitigation of Urban Inundation Damage

1. INTRODUCTION
Even though a large number of researches

side weir measured from upstream end of side
weir, g is the acceleration of gravity, p is the height

related to reduction of the urban inundationof the side weir, h is the flow depth at the section L,

damage have been conducted, the damage is still

Cd is the discharge coefficient of side weir. The

serious problems every year. Urban inundation hasdischarge coefficient is influenced by the following

caused immense property damage and personalparameters,

injury due to local heavy rainfall during a shorttime and extreme climate in worldwide. To mitigate
this problem, underground storage systems as aneffective countermeasure have been implemented

where D is diameter of main pipe, S is slope of main

especially in highly urbanized area. However, therechannel.

are no criteria how much mitigation effect can beSome previous theoretical analyses andexpected from installation of such undergroundexperimental researches have been reported instorage systems. In many cases, those storage

terms of flow over rectangular side weirs in circularsystems are attached to sewerage systems, andopen channel (Allen, 1957 ; Uyumaz and Muslu,

some part of stormwater within a sewerage pipe is1985 ; Vatankhah, 2012 ; Granata, 2013). Generally,

diverted over the side weir into the storage system.

The method assumes one-dimensional flow

Therefore, evaluation of mitigation effect of storage

conditions, thus neglecting the variations ofsystem requires appropriate estimation of overflow

overflow direction and the velocity distribution

discharge from sewerage system over the side

(Willi H. Hager 1987). Besides, as seen in Table 1,weir. So, the researches in terms of overflow

a lot of researches obtain the equations fordischarge over the side weir related todischarge coefficients for rectangular side weirs

underground storage systems are essential.

based on experimental results, where F is FroudeSide weirs are hydraulic structures that are

number for the upstream end of the side weir onusually used as flow dividers in urban drainage

the main channel. Those side weir discharge

systems, irrigation channels and flood protection

coef ficients ar e deter mined by var yingworks (Granata et. al. 2013). The main contributor

experimental conditions like flow state, weir length

to the understanding of hydraulic behavior of sideand height.

weir is De Marchi(1934). He presented theory

All of the above researches have been conductedbased on the assumption of constant energy head

under open channel flow conditions, and the De

along the side weir and the overflow discharge

Marchiʼs approach seems appropriate for the open

being calculated by classical weir formula whichchannel flow condition. However, there is no study

overlooks the effect of lateral outflow direction,that verify the De Marchi equationʼs suitability inlocal velocity and type of flow (pressurized or non-the pressurized flow condition. Thinking ofpressurized) in the system. The equation is as

overflow from sewerage system during urban

follows,

flooding, pressurized flow condition would often
happen and De March equationʼs applicability mustbe also verified in that condition. Hence in thisresearch, the experimental set up is proposed with

where q is discharge per unit length of side weir,pressurized circular channel with different side

Qout is overflow discharge, L is distance along theweir length so that the effectiveness of the use of

自然災害科学特別号（179）

Table 1 Side weir discharge coefficient equations

the above equation can be discussed.
The aim of this experiment is to determine thedischarge coefficient for pressurized flow incircular channel with different side weir length sothat effective conclusions can be made regarding
suitability of the De Marchi equation also for thesecases and such experimental data can beextensively used to validate future numerical model
estimating effects of underground storage systems.
Fig. 1 Photo of the experimental setup

2. EXPERIMENTAL SETUP
The experiments were carried out in the Ujigawa
Open Laboratory of the Disaster Prevention
Research Institute (DPRI), Kyoto University.
Experimental setup, side weir and sectional view ofa rectangular side weir are shown in Fig. 1, Fig. 2and Fig. 3.
The model and proto type scale are assumed tobe 1/22. Experimental setup consisting of side weirFig. 2 Photo of the side weirwith the two circular acrylic pipes of 4m long and
0.05m internal diameter. There are upstream
supply tank with the recirculation pump system anddownstream collecting tank with a movable gate toadjust the downstream water level. The
recirculation system can be controlled by the RPMcontroller. A flowmeter was used to measure theFig. 3 Sketch of the rectangular side weir in a circularpipe

upstream input discharge. The flow heads havebeen measured by total seventeen piezometer5, the three different lengths of side weir, 10cm,

tubes placed along the lowest bottom of pipe, as

15cm and 20cm, have been used. Experiments

shown in Fig. 4. All of the experiments werewere conducted for steady flow condition. The weircarried out by the horizontal pipe. As seen in Fig.

height was set as 4cm in all the cases. The length180

Study on Estimation of Inflow Discharge to Underground Storage System for Mitigation of Urban Inundation Damage

Fig. 4 Experimental arrangementout for each different side weir, and supplieddischarge at upstream tank differs from 0.5 l/s to
1.5 l/s. The downstream movable gate level is set tothe bottom of main pipe. The detailed hydraulicconditions were summarized in Table 2, whichcontains the obser ved water level at thedownstream tank. Each case of experiment wasrepeated three times to consider consistency ofoverflow discharge rate.

Fig. 5 The three different length of side weir

4. EXPERIMENTALDISCUSSIONRESULTSAND

and height of side weir model were determined(1) WATER HEAD PROFILE

according to real size of the pipe diameter and theThe water surface profiles of whole pipe systemside weir in Moriguchi city, which can be regardedof the case with 10cm weir length and those aroundas a typical overflow system of side weir.

the side weir of all the cases are described in Fig.
6. Fig.

3. EXPERIMENTAL CONDITIONS

7 shows the overflowing water ofexperiment of the case with 10cm weir length. OnThe experimental condition here is considered

the whole, the water head at the upstream end ofsteady. Although, in reality, the phenomenon isthe side weir is lower than that at the downstream

unsteady, but for simplification of the problem, theend of the side weir, as shown in Fig. 6. The samesteady-state condition is chosen and unsteady also

results were observed in all previous experimental

will be analyzed as an advancement of the research.

studies. The water head slightly decreases at theThe experiments of 33 cases in total weremiddle of side weir for small discharge cases.

conducted to determine overflow discharge

These results are influenced by entrance effect atcoefficient keeping steady-state condition withthe upstream end of the side weir and lateral flow

different side weir length. The 11 cases are carriedon the side weir. As the upstream discharge

自然災害科学特別号（181）

Table 2 Experimental conditions (10cm, 15cm, 20cm)
Weir length (cm)Case1

Case 2

Case3

Case4

Case5

Case6

Case7

Case8

Case9

Case10

Case11

1.0

1.1

1.2

1.3

1.4

1.5

0.73

0.80

0.87

0.95

1.02

1.09

Upstream discharge (l/s)
10, 15, 20

0.5

0.60.70.8

0.9
Froude number

10, 15, 20

0.36

0.44

0.51

10

1.1

1.1

1.2

1.3

1.4

1.4

1.5

1.6

1.7

1.8

1.8

15

1.1

1.1

1.2

1.2

1.3

1.4

1.4

1.5

1.5

1.6

1.7

20

1.1

1.1

1.2

1.2

1.3

1.4

1.4

1.4

1.5

1.6

1.7

0.58

0.65

Water level at the downstream tank (cm)Fig. 6 The water surface profile

increases, the hydraulic gradient becomes steeper
in comparison with the results under smaller
discharge cases. The high water head at thedownstream end of the side weir have an effect onwater heads of the downstream pipe. The reason
for this maybe the strength of lateral flow under thelarge discharge conditions. This result shows thedifference between this study and previous studies.
(2) DISCHARGE COEFFICIENT
The discharge coefficient was calculated by DeFig. 7 Photo of overflowing water of experiment

182

Study on Estimation of Inflow Discharge to Underground Storage System for Mitigation of Urban Inundation Damage

Marchiʼs equation as follows,

view, the averaged water head along the side weir
adopted, which was derived from the side weirlength and water head integrated along the sideweir.
Uyumaz (1985) also reported that water headThis discharge coef ficient depends on thewas not constant on the side weir. Using the mean

hydraulic conditions that are weir length, weirof upstream and downstream water heads on theheight, water head on the side weir and overflow

side weir did not produce satisfactory solutions.

discharge. Under the low discharge conditions,

Calculating the mean of several intermediate heads

water heads are nearly constant but lateral flow isproved more satisfactory results. Fig. 8 shows thenot constant. Under the large discharge conditions,coefficient value increases gradually if the water

both water head and lateral flow are not constant.

head at the upstream end of the side weir was

As the upstream discharge increases, the lateralused. On the other hand, the discharge coefficient

flow rate also increases in comparison with results

remains almost constant if the mean value of

under the low discharge conditions. According tointegral heads was adopted instead of water head atsome previous studies, water head at the upstream

the upstream end of the side weir. In particular,

end of the side weir is used for parameter ofthese coefficient values become close to constantdischarge coefficient. However, as seen in thevalue although upstream discharge increases,

surface profile of Fig. 6, there is lager variation inwhich implies applicability of constant coefficientwater heads on the side weir excessively comparedvalue. Table 3 shows the experimental results ofwith those of previous studies. With this point of

overflow discharge rate and calculated mean ofFig. 8 The discharge coefficient distribution along the different water head on the side weir

自然災害科学特別号（183）

Table 3 Experimental results (10cm, 15cm, 20cm)
Overflow discharge (l/s)
Weirlength(cm)Case1

Case 2

Case3

Case4

Case5

Case6

Case7

Case8

Case9

Case10

Case11

10

0.063

0.113

0.168

0.233

0.279

0.324

0.366

0.416

0.468

0.519

0.569

150.065

0.122

0.179

0.246

0.304

0.377

0.430

0.480

0.574

0.607

0.656

200.069

0.130

0.199

0.253

0.330

0.407

0.468

0.529

0.589

0.632

0.700

Mean of integral heads on the side weir (cm)Weirlength(cm)Case1

Case 2

Case3

Case4

Case5

Case6

Case7

Case8

Case9

Case10

Case11

10

4.73

4.78

4.93

5.10

5.28

5.38

5.55

5.65

5.85

5.95

6.08

15

4.58

4.7

4.80

4.95

5.08

5.20

5.25

5.33

5.50

5.55

5.65

20

4.55

4.68

4.75

4.82

4.93

5.03

5.13

5.23

5.28

5.35

5.45

Discharge coefficient
Weirlength(cm)Case1

Case 2

Case3

Case4

Case5

Case6

Case7

Case8

Case9

Case10

Case11

Averagevalue of Cd100.346

0.561

0.639

0.684

0.656

0.681

0.642

0.665

0.630

0.645

0.645

0.618

15

0.337

0.470

0.565

0.600

0.616

0.647

0.695

0.711

0.705

0.710

0.699

0.614

20

0.286

0.397

0.519

0.572

0.628

0.664

0.664

0.661

0.693

0.682

0.679

0.586

integral heads on the side weir. The discharge

water head on the side weir.

coefficients for each case are also shown in Table

Finally, the next step will be to find out the3, which are derived from experimental data. As

suitable discharge coefficient within the limit ofweir length increases, the mean of coefficient

above experimental results for each weir length

values decreases.

and experimental condition and to reproduce theIn application to actual estimation of overflow

overflow discharge obtained from experiment bydischarge, the constant coefficient value would beusing numerical model. That numerical model

easy to handle. Therefore, as the next step,

verified in that way would enable to estimate

applicability of constant value derived from theseoverflow discharge from sewerage to storage

experiments will be investigated by using

system and mitigation effect of those storage

numerical model. And this time, my study is limitedsystems.

to steady condition only for simplicity. In futurework, I will consider the unsteady condition also.

ACKNOWLEDGMENT: This research is
supported by ʻGrant-in-Aid for young Scientists (A)5. SUMMARY(23681038 Kenji Kawaike)ʼ.

The present study has investigated the variationof discharge coefficient for pressurized flow incircular channel with different side weir length. A
detailed work is also presented for flow surface
profile along the side weir and the dischargecoefficient of the side weir. The suitable dischargecoefficient is essential to estimate the model
validation through the experimental data and theREFERENCES
Allen, J.W.(1957). “The discharge of water over side
weir in circular pipes.” ICE Proc, Vol.6, No.2, pp.
270-287
Borghei, M., Jalili, M.R., Ghodsian, M.(1999).
“Discharge coefficient for sharp-crested side weirin subcritical flow. ASCE Journal of HydraulicEngineering Vol. 125, No.10, pp. 1051-1056

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Study on Estimation of Inflow Discharge to Underground Storage System for Mitigation of Urban Inundation Damage

Cheong, H.F.(1991). “Discharge coefficient of lateraldiversion from trapezoidal channel.” ASCE
Journal of Irrigation and Drainage Engineering.
Vol.117, No.4, pp. 321-333
De Marchi, G.(1934). “Saggio di teoria delfunzionamento degli stramazzi laterali.” LʼEnergia
Elettrica, Vol.11, No.11, pp. 849–860 (in Italian)
Granata, F., Marinis, G.D., Gargano, R., Tricarico,C.(2013). "Novel approach for side weir insupercritical Flow"
J. Irrigation and Dranage Eng. Vol. 139, No.8, pp. 672679
Hager, W.H.(1987). "Lateral outflow over side weirs." J.
Hydraulic Eng. Vol. 113, No.4.
Subramanya, K., Awasthy, S.C.(1972). “Spatially varied
flow over side weirs.” ASCE Journal of theHydraulics Division. Vol. 98, No.1, pp. 1–10
Uyumaz, A., and Muslu, Y.(1985). "Flow over sideweirs in circular channels." J. Hydraulic Eng. Vol.
111, No.1, pp. 144-160
Vatankhah, A.R.(2012) “New solution method forwater surface profile along a side weir in a circlechannel.”
J. Irrigation and Drainage Eng.Vol.138, No.10, pp. 948954
Yu-Tech, L.(1972). “Discussion of spatially varied flow
over side weir.” ASCE Journal of the Hydraulics
Division, Vol. 98, No.11, pp. 2046-2048（投稿受理：平成 26 年 4 月 18 日）