STUDY ON SUITABLE COEFFICIENT OF OVERFLOW DISCHARGE EQUATION UNDER PRESSURIZED FLOW CONDITION

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1 Annual Journal of Hydraulic Engineering, JSCE, Vol.59, 2014, February STUDY ON SUITABLE COEFFICIENT OF OVERFLOW DISCHARGE EQUATION UNDER PRESSURIZED FLOW CONDITION Dongwoo KO 1, Hajime NAKAGAWA 2, Kenji KAWAIKE 3, and Hao ZHANG 4 1 Student Member of JSCE, Doctoral Student, Department of Civil and Earth Resources Engineering, Kyoto University (Katsura Campus, Nishikyo-ku, Kyoto , JAPAN) 2 Fellow of JSCE, Prof., DPRI, Kyoto University (Yoko-oji, Fushimi, Kyoto , JAPAN) 3 Member of JSCE, Assoc. Prof., DPRI, Kyoto University (Yoko-oji, Fushimi, Kyoto , JAPAN) 4 Member of JSCE, Assist. Prof., DPRI, Kyoto University (Yoko-oji, Fushimi, Kyoto , JAPAN) The research regarding side weirs of stormwater storage systems which can be considered as effective hydraulic structure to mitigate the urban flooding and estimation of overflowing discharge over the side weir into those storage systems are significant. The De Marchi s equation seems appropriate for the open channel flow condition to understand hydraulic behavior of the side weir but there are no studies that identify its suitability under the pressurized flow condition. Hence in this study, the overflow discharge coefficient in the De Marchi s equation is evaluated for pressurized flow condition with different side weir length and height to verify the variation of discharge coefficient. The process of proposing discharge coefficient for each different side weir condition in circular channel is discussed through comparisons between experiment and simulation. Key words: Underground storage system, Side weir, pressurized flow, Discharge coefficient 1. INTRODUCTION Even though numerous researches related to the reduction of urban inundation damage have been conducted, such damage remains a serious problem every year. Before urbanization, there are wide permeable areas such as farming land and forest, but after urbanization, permeable area has decreased as a result of increase of roads area, construction of buildings etc. Due to this, the most of the storm water dose not infiltrate into the ground and total amount of storm water runoff has increased, which can lead to urban inundation. To mitigate this problem, underground storage systems as an effective countermeasure have been implemented especially in highly urbanized areas. However, there are no criteria on the degree of mitigation effect that can be expected from installation of such underground storage systems. In many cases, those storage systems are attached to sewerage systems, and some part of the stormwater within a sewerage pipe is diverted over the side weir into the storage system. Therefore, evaluation of the mitigation effect of storage systems requires appropriate estimation of overflow discharge from a sewerage system over the side weir. Therefore, it is essential to research overflow discharge over the side weir related to underground storage systems. Fig. 1 shows the structure of underground storage system briefly. The present study is undertaken to determine the appropriate equation to estimate diversion discharge to storage system. Some previous theoretical analyses and Fig. 1 Underground storage system

2 experimental researches have been reported in terms of flow over rectangular side weirs in circular open channel. 1)2)3) Generally, the method assumes onedimensional flow conditions, thus neglecting the variations of overflow direction and the velocity distribution. 4) The main contributor to the understanding of hydraulic behavior of side weir is De Marchi 5). He presented theory based on the assumption of constant energy head along the side weir and the overflow discharge being calculated by classical weir formula which overlooks the effect of lateral outflow direction, local velocity and type of flow (pressurized or non-pressurized) in the system. In the cases of open channel flow condition, De Marchi s equation is usually employed, and its discharge coefficient has been suggested by many researchers. However, no study has verified the suitability of this equation in pressurized flow condition, which would be often the case within sewerage systems during urban flooding. Therefore, in this study, under the assumption that De Marchi s equation is applicable to the pressurized flow condition, the numerical model is used to validate the experimental results using the discharge coefficient obtained by experiment. 2. EXPERIMENTAL SETUP The experiments have been conducted in the Ujigawa Open Laboratory of the Disaster Prevention Research Institute (DPRI), Kyoto University. The rectangular side weir in circular pipe is shown in Fig. 2, where D is the diameter of the main pipe, p is the height of side weir, and L is the length of side weir. The experimental setup consists of a side weir with two circular acrylic pipes 4m in length and 0.05m in internal diameter. There are an upstream supply tank with a recirculation pump system and a downstream collecting tank with a movable gate to adjust the downstream water level. The recirculation system can be controlled by the RPM controller which controls motor speed to supply the constant inflow discharge to the upstream tank. A flowmeter is used to measure the upstream input discharge. The water heads were measured by a total of 17 piezometer tubes placed along the lowest bottom of the pipe, as shown in Fig. 3. All of the experiments were conducted using a horizontal pipe. The experiments have been conducted with three different lengths of the side weir, 10cm, 15cm and 20cm, and three different, 3cm, 3.5cm and 4cm, side weir height in all cases, where standard of the weir elevation is the dashed line of the bottom of pipe in Fig. 2. This side weir height can be adjusted up and down easily. The fundamental length and height of the side weir model were determined according to the actual size of the pipe diameter and the side weir in Moriguchi city, which can be regarded as a typical overflow system of side weirs. The prototype and experimental model scale were assumed to be 1/ EXPERIMENTAL CONDITIONS The experiments of 63 cases in total were conducted to determine the overflow discharge coefficient keeping the steady condition with different side weir lengths and height. Seven experiments were carried out for each different side weir condition, and the discharge supplied to the upstream tank, which differed from 0.5 l/s to 1.1 l/s. The overflow discharge was captured by sampler box directly as shown in Fig.2, which later was weighted and the discharge was calculated considering time of sampling. The downstream movable gate level was set to the bottom of the main pipe. The detailed hydraulic conditions are summarized in Table 1, which contains the observed water head at the downstream end of the pipe. Each experiment under the same condition was repeated three times to consider the consistency of the overflow discharge rate. Fig. 2 Definition sketch of the rectangular side weir 4. EXPERIMENTAL RESULTS (1)Water head profile Fig. 4 shows the overtopping over the side weir of experiment. Fig. 5 shows the water surface profiles of the entire pipe system and around the side weir for the case with a weir length of 10cm in

3 Fig. 3 Experimental arrangement Fig. 4 Photo of overflowing water weir height of 4cm. As the upstream discharge increases, the hydraulic gradient becomes steeper in comparison with the results under smaller discharge cases. This same situation is presented for all the cases. Generally, the surface profile on the side weir showed by previous researches also rises toward the downstream end of side weir. But, rate of rise in pressurized flow condition is bigger than that in open channel condition. The high water head at the downstream end of the side weir has an effect on the water heads of the downstream pipe. The reason for this may be the strength of lateral flow under pressurized flow conditions. This result shows the difference between open channel flow and pressurized flow conditions. 6) (2)Discharge Coefficient The discharge coefficient can be derived from by De Marchi s equation as Eq.(1) C d = 3 2 Q out 2gL(h p) 1.5 (1) This discharge coefficient depends on the hydraulic conditions that are weir length, weir height, and water head on the side weir and overflow discharge. As the upstream discharge increases, the overflow rate also increases in comparison with the results under the low discharge conditions. The Table 2 shows the overflow discharge along the different weir length and height, which is increased in accordance with lower height and longer length of side weir. The Seven discharge coefficients were derived using the above hydraulic conditions for each different weir condition. Actually, the water head is the most important parameter to derive the discharge coefficient in this study. According to some previous studies, the water head at the upstream end of the side weir is used for the discharge coefficient. However, I have already mentioned above that there is larger variation in the water heads on the side weir excessively compared with those of previous studies on characteristic of pressurized flow. From this perspective, the averaged water head along the entire side weir Fig. 5 Water surface profile

4 Table 1 Experimental conditions Weir length(cm) Weir height(cm) Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Upstream discharge(l/s) 10, 15, 20 3, 3.5, Water depth at the downstream end of the pipe(cm) length is adopted, which was derived from the side weir length and water head integrated along the side weir. Uyumaz et al. 7) also reported that the water head was not constant on the side weir. The mean of upstream and downstream water heads on the side weir did not produce satisfactory solutions. Calculating the average of several intermediate heads provided more satisfactory results. In this study, the discharge coefficients remain almost constant if the averaged water head is taken in place of only water head at upstream end of the side weir. In particular, these coefficient values become close to the constant value even though the upstream discharge increases, which implies the applicability of a constant coefficient value. Fig. 6 shows one of cases with weir length of 10cm in weir height of 4cm for the discharge coefficient distribution along the different water head on the side weir. Fig. 6 Discharge coefficient distribution along the different water head on the side weir 5. NUMERICAL SIMULATION MODEL (1)1D sewer model The rainwater in the sewer pipe is dynamically calculated based on the following 1D continuity (2) and momentum (3) equations using Leap-Frog method. A = q t x (2) Q = ga H Q Q t x x R 4/3 A (3) where A is cross sectional area of flow, Q is discharge, q is overflow discharge per unit length over the side weir, u is flow velocity, R is hydraulic radius, H is piezometric head(h = z + h), z is bottom elevation of pipe, h is water depth in pipe measured from the bottom, which is calculated as follows (4), f(a) (A A p ) h = { B` + A A p (4) (A > A B p ) s where f is a function that expressing a relation between flow cross section area and water depth in circular pipe, the case of A A p is open-channel flow condition and that of A > A p is pressurized flow condition, B` is height of pipe ceiling, A p is cross sectional area of pipe and B s is slot width, which is calculated as follows (5), B s = ga (5) a 2 Where a is pressure propagation velocity for pipe and 5 m/s was used. The value of the roughness coefficient is uniformly In other to treat both open-channel and pressurized flow conditions, the slot model 8), which considers the sewer pipe with a hypothetical narrow slot on its ceiling, is introduced in this study. (2)Overtopping equation The De Marchi s equation was adopted to calculate the overflow discharge in this model, which is as follows (6), q = dq out = 2 C dl 3 d 2g(h p) 1.5 (6) where C d is discharge coefficient obtained by experiment along the each different side weir condition. The grid generated depends upon length of side weir on model. That is to say, weir length is reflected on the grid size.

5 Table 2 Experimental and simulated results (overflow discharge) Weir length(cm) Weir height(cm) method Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Comparisons between experiment and simulation-overflow discharge(l/s) 10 3 Exp Sim Exp Sim Exp Sim Exp Sim Exp Sim Exp Sim Exp Sim Exp Sim Exp Sim MODEL VERIFICATION Numerical simulation was carried out to verify the suitability of the discharge coefficient obtained by experiment. First, those discharge coefficients for each different weir condition were applied to numerical simulation. Secondly, the each overflow discharge simulated was compared with overflow discharge data obtained by experiment, as shown in Table 2. Consequently, the overflow discharge simulated could reproduce the experimental results though there are still small different on the whole. The small difference is caused by inevitable measuring error of sampling method. This reproduction implies the applicability of De Marchi s equation to pressurized flow. To apply the overflow discharge coefficient to actual field, the constant coefficient value would be easy to handle. So, the suitable coefficient was determined within the limited of the experimental results for each weir length and height. As a result, the suitable coefficients were suggested from 0.57 to And, empirical correlation to predict discharge coefficient was developed for the ratio of weir height to length using the suitable coefficients, as shown in Fig. 7. The resulting correlation is given in Eq. (7), C d = p (7) L where deterministic coefficient( R 2 ) is Previous C d empirical correlation is not applicable in my study because each experiment is carried out along the different experimental conditions like open channel, weir scale. Applicability of h or F on equation of C d is limited due to limited input discharge range in my experiment in comparison with some previous research. So in this study, I decide to use function of p/l since p and L are already fixed. Those suitable values were selected within the range of the lowest and the highest coefficients in experimental results along the weir condition, which was determined through the least square method, where triangle is the lowest coefficient, circle is the highest coefficient, cross is the suitable coefficient, as shown in Fig. 8. Fig. 7 Discharge Coefficient for p/l values 7. CONCLUSIONS The present study investigated the variation of the discharge coefficient for pressurized flow in a circular channel with different side weir conditions. The suitability of the De Marchi s equation in

6 Fig. 8 Suitable discharge coefficient along each different weir condition. pressurized flow condition was also validated using numerical model. Finally, the suitable discharges coefficient for each different weir condition and empirical correlation were suggested through the comparison between experimental and simulated results. However this study is limited to the steady condition only for simplicity. Next step will be to verify the numerical model under unsteady condition, which would enable to estimate the overflow discharge from sewerage to storage systems and the mitigation effect of those storage systems. ACKNOWLEDGMENT: This experiment is supported from Mr. Oomoto (Master s course student in Kyoto University). REFERENCES 1) Allen, J.W.: The discharge of water over side weir in circular pipes, ICE Proc, Vol.6, No.2, pp , ) Vatankhah, A.R.: New solution method for water surface profile along a side weir in a circle channel, J. Irrigation and Drainage Eng.Vol.138, No.10, pp , ) Granata, F., Marinis, G.D., Gargano, R., Tricarico, C.: Novel approach for side weir in supercritical Flow, J. Irrigation and Drainage Eng. Vol. 139, No.8, pp , ) Hager, W.H.: Lateral outflow over side weirs, J. Hydraulic Eng. Vol. 113, No.4, ) De Marchi, G.: Saggio di teoria del funzionamento degli stramazzi laterali, L Energia Elettrica, Vol.11, No.11, pp (in Italian), ) Ko, D. W., Nakagawa, H., Kawaike, K., and Zhang, H.: Study on estimation of inflow discharge to underground storage system for mitigation of urban inundation damage, J. Japan Society for Natural Disaster Science. Vol. 33, pp , ) Uyumaz, A., and Muslu, Y.: Flow over side weirs in circular channels, J. Hydraulic Eng. Vol. 111, No.1, pp , ) Chaudhry, M. H.: Applied Hydraulic Transients, Van Nostrand Reinold, (Received September 30, 2014)