Session V: Drainage I

Transcription

1 Session V: Drainage I V.1 Empirical study on terminal water Velocity of drainage stack, Part 2 (1) C.L. Cheng, Dr. (2) W.J.Liao, Ms. (3) K.C. He, Dr. (4) J.L.Lin, Ms. (1) CCL@mail.ntust.edu.tw (2) D @mail.ntust.edu.tw (3) D @mail.ntust.edu.tw (4) M @mail.ntust.edu.tw (1) (2) (3) (4) National Taiwan University of Science and Technology, Department of Architecture, 43 Keelung Road Sec.4, Taipei, Taiwan, R.O.C. Abstract Due to the importance of permit flow rate regulation which is adopted in many countries, the terminal velocity in drainage stack was seen as one of the crucial issues in building drainage studies. Several theories and predictions were reported in previous researches from 1960s. An empirical study on terminal water velocity of drainage stack was explored from 1996 and reported in 2008 CIBW62 conference HK. However, the validation issues were remained and need to be further clarified. This paper would continue the methodology with empirical approach by theoretical study from air pressure distribution mechanism. Meanwhile, a technology with digital high-speed video camera and statistic tool will be used to validate the calculation result of terminal velocity of drainage stack in this research. The results confirm that the theoretical study can fit the practical sense and the validation also can response the calculation results. Accordingly, the terminal velocity of drainage stack should be reconfirmed and redefined its accurate value under the new validation evidences. Furthermore, the long term regulation and application which is according to the lower terminal velocity and permit flow rate also need to be reconsidered. Keywords terminal velocity, gravity acceleration, high-speed video camera, statistic methodology 284

2 List of symbols symbols content unit Q w Water flow rate l/s Q a Air flow rate in stack vent m 3 /s R Diameter of stack m V w Velocity of water flowing m/s Va V t Velocity of airflow Terminal velocity of water m/s m/s w The coefficient of water resistance in stack a g t The coefficient of air resistance in stack Gravity acceleration time interval m/s 2 sec Distance m SD The accumulation distance of falling water m 1. Introduction An innovation study which explored the terminal velocity in drainage stack was reported in 2008 CIBW62 annual conference HK. This research continued the remained issues regarding the experiment and validation process. A high-speed digital video camera and statistic sampling methodology were adopted to validate the previous calculation results. This report includes a summary of proposed calculation methodology and its results. Accordingly, we improved the verification by statistic sampling process to offer more accurate evidence for the validation. As the technical reviews, Hunter 1) explored the flow phenomenon of drainage stack in1940s. Afterward, Wyly 2)3) & Dawson first issued the theory of the terminal velocity at 1960s. According to these pioneer research results, the guideline of National Plumbing Code (NPC) of US was used to set the permit flow rate as the regulation of drainage system. Following initial work of the HASS 203 of Japan in 1970s, the method 285

3 of steady flow condition was merged as the provision reference and evaluation technique, hence, they conducted series researches of steady flow methodology and greatly contributed to the application of building drainage network. Due to the importance of permit flow rate regulation, the terminal velocity in drainage stack was seen as one of the crucial issues in these series researches. Several theories 4)5) and predictions were reported in previous researches. However, the validation and accuracy were still criticized so far and did not reach the persuasive results. The new evidence and validation are expected and need to be conducted nowadays. 2. Theoretical Reviews The theory of the annulated flowing in drainage stack was first reported by Wyly 2) in 1960s. Afterward, some researches tried to figure out the velocity of flowing water in stack by the experimental method and theory, however, no firm results were reported in that period. In 1980s, Tukagoshi 6) conducted electricity to the salt solution in Japan, and put the sensor of the electricity into the pipe which perpendicular to the pipe s section and divided into 1-25 points as observational points, when salt solution flowing into the vertical stack and pass through the sensor would evaluated the velocity and quantity of the water flowing. In 1994, Sakaue 7) in Japan continuously infused water into vertical stack for testing the velocity of the water flowing, and to return to original equation for evaluated the water flowing rate in the vertical stack. However, all these researches have not reached a clarified and validated conclusion on the terminal velocity of drainage stack. According to the previous researches 8)9)10) on air pressure distribution, the airflow rate (Qa) was identified as a critical parameter for a prediction model which can approximately figure out the falling water phenomenon in vertical drainage stack. The mechanism of flowing phenomenon within vertical drainage stack is now schematically understood. Air pressure in vertical drainage stack is caused by series interactions between downstream water and through-flow air in vertical pipe. Fig.1 illustrates the image of flow state and the modified interaction, thus it conducts the main parameters with air pressure, airflow rate, and resistance coefficients, and they are the essential factors for prediction model of air pressure distribution in vertical drainage stack. These researches also provided the possible viewpoint to explore the flowing velocity of air and water in drainage stack. Consequently, the innovative study on terminal velocity was restarted from Afterward, an initial study results with empirical approach was reported in 2008 CIBW62 conference HK. However, the validation issues were remained and need to be further clarified. 286

4 Fig.1 Interaction mechanism of water and air in drainage stack The essential phenomenon of falling water and interaction mechanism in drainage stack was described in our last report. Fig.1 shows the image of interaction mechanism of water and air in drainage stack. The velocity of the falling water in the stack is mainly dominated by the three interaction balance including gravity force (g) and friction drag of the pipe inside and the air interaction toward the falling water which we mentioned in our last report. When the falling water in the stack reaches the terminal velocity situation, which means the interaction inside the stack reaches the condition of balance and the forces actions are totally equal and neutralized. Herein, we omitted the conduction details of theoretical process and summarized the result of terminal velocity function as equation (1). The details of the theoretical study could be referred from our last report in 2008 CIBW62 proceedings 11). V t g w..(1) 287

5 3. Experiment and observation Following the development of observation technology, this research used a digital highspeed video camera to validate the calculation model for terminal velocity. According to previous report in 2008 CIBW62 conference HK 11), an initial experiment was executed to validate the theoretical terminal velocity. The further precise verification process is necessary to be conducted in this research. Due to the phenomenon of falling water in stack is complex and random by time sequence, the improvement of accuracy is a crucial part for the reliability of validation. In order to improve the reliability of validation results, a statistic methodology of sampling conception for random observation is adopted in this report. The same as our previous report last year, Table 1 is the specification of this digital high-speed video camera which is used to observe the falling water velocity in stack. Fig.2 is the picture of experiment in observation place which shows the circumstance and condition of the operation. Table 1 Specification of the digital high speed camera MEMORY ELECTRICAL CORE COMPUTER LINKS DIAPHRAGM VIDEO CAMERA Video camera Auto Exposure Control,Color or monochrome 2,100 pictures per second full resolution Software: Acquisition, Analytical playback, Measurements, Image processing and File management 256 mg RAM,for files memory Diaphragm Adjustable diaphragm. Resolution of the screen 288

6 Fig.2 The experimental device and operation picture The pictures of the transparent pipe at each floor of the experimental tower were taken by high-speed video camera. Water discharges are all from 12 th floor with the water flow rate of 1.0 l/s, 2.0 l/s, 3.0 l/s, 4.0 l/s, meanwhile each floor divides into 3 layers so that each floor can be taken video with three times. This research totally got 128 video data from the observation of 32 layers. The experimental device includes digital high speed camera, two lamps, notebook for recording the data and high resolution image screen. Fig. 3 shows the devices of this observation. Fig.3 The experimental tower and testing device profile in NTUST 289

7 According to the visual observation by transparent pipe, the phenomenon of falling water is complex and no possible to identify its character from the picture. As we slow down the picture by the high-speed video camera, the behavior of falling water reveals its feature visually in the picture. An image of falling water picture in stack is as shown as Fig. 4. Firstly, we can see the annual water along with the surface of stack with a comparable slow velocity. The other obvious part can be identified is the chunk body of falling water with comparable high speed velocity mostly in the middle of the stack. The last obvious feature part can be seen is the drop water with various falling velocity in the picture. Fig.4 An image of falling water picture in stack According to the statistic conception for the sampling process, at least 385 observation samples are necessary for the accuracy of calculation under 95% reliable level and 5% permit inaccuracy. Therefore, 129 observation samples are picked from individual part of these three water features and totally 387 samples are taken into the calculation for one observation point. In order to catch the individual sample of water, clear black lines are set by 10 mm interval on the screen picture to trace the moving of falling water. Accordingly, the velocity of each sample can be calculated by the moving distance and time interval. The calculations include average velocity and deviation for three water features. Fig.5 shows the process flow and details of sampling method. We used the grid meshes to specify the water sample and trace its moving velocity. Fig.6 shows a case of the different time location which we pick 25 and 26 recognizable samples for tracing their moving behaviors. All the velocity of the recognizable water drops can be exactly calculated by its moving distance and time intervals for each observation point in experiment tower. As the above mentioned about experiment device, the discharge water is from 12 th floor height, and three observation points are set in each floor area. Accordingly, there are 290

8 totally 32 observation points and selected samples for calculation in this empirical validation study. Fig.5 The details of sampling method 291

9 time 16:42: Original image and pick 25 samples time 16:42: Original image and pick 26 samples samples pick 51 samples Fig. 6 The sampling process of water drop The experimental condition for observation is a continuing discharge and repeatable phenomena in stack. Thus, the profile of water velocity can be expressed as the distribution of air pressure in stack. As the results, the velocity of each observation point can be produced from the sampling process and Fig. 7~10 shows the holistic water velocity profile of water discharge from 12 th floor height. 292

10 Fig.7 Water velocity in stack for three water features (1.0 l/ /s) Fig.8 Water velocity in stack for three water features (2.0 l/s) Fig.9 Water velocity in stack for three water features (3.0 l/ /s) Fig.10 Water velocity in stack for three water features (4.0 l/s) 293

11 Fig.11 Water velocity and air pressure in stack (1.0 l/s) Fig.12 Water velocity and air pressure in stack (2.0 l/s) Fig.13 Water velocity and air pressure in stack (3.0 l/s) Fig.14 Water velocity and air pressure in stack (4.0 l/s) 294

12 The velocity profiles in figures are including average of individual part of these three water features which are annual water along with pipe and the chunk body of falling water and the drop water with various falling velocity in the picture. Meanwhile, the discharge flow rate are including 1.0 (l/s), 2.0 (l/s), 3.0 (l/s) and 4.0 (l/s). The results reveal that the terminal velocity increases following the water flow rate and obviously it shows 4.0 (l/s)>3.0 (l/s)>2.0 (l/s)>1.0 (l/s). Fig.11~14 shows the average velocity for each observation point and the simultaneous air pressure distribution in stack. It is seen that the terminal velocity approximately happen in C zone of the air pressure distribution. That also matches the theoretical conception and the initial assumption of this research. Namely, the results can validate the accurate terminal velocity of drainage stack by this empirical approach. 4. Validation and discussion The previous report in 2008 CIBW62 conference introduced an empirical methodology to calculate the terminal velocity in drainage stack. The calculation process and results are summarized in Chapter 2. On the other hand, the terminal velocity is concluded from the observation by high-speed video camera and statistic sampling process in chapter 3. The comparison of the results from the different approach is show in Table 2 and Fig. 15. It reveals that the results of individual water flow rate (1.0, 2.0, 3.0 and 4.0 l/s) are approximately closed and validation is reliable. We also compare the positions of maxima air pressure by calculation and observation. The position of maxima air pressure is expressed by the distance from discharge floor. The results are shown in Table 2. It also reveals that the range is approximately matched for the two approaches. Table 2.the result of the terminal velocity Water flow rate(q W ) The theoretical value (m/s) The experimental value (m/s) The theoretical value of max negative point (m) The experimental value of max negative point (m) ~ ~ ~ ~9 295

13 The theoretical value The experimental value(standard deviation) Fig15. The comparison of calculation and experiment of the terminal velocity The theory of the annulated flowing in drainage stack was first issued by Wyly 2) in 1960s as mentioned in Chapter 2. Regarding the researches of terminal velocity, Dawson (US) used the Manning equation and conducted calculation model to determine the terminal velocity by the following equation (2). V t Qw R 0.4..(2) Meanwhile, Wyly (US) continued to explore the falling water in stack and assumed the flowing mechanism to be annual membrane flow. Consequently, he amended the coefficient and proposed the calculation equation for the terminal velocity as the following equation (3). V t Qw R 0.4..(3) This paper compares the theoretical calculation results as shown as Table 3 and Fig.16. The results reveal that the calculated terminal velocity in this research is much greater than the results which were done by Wyly and Dowson. 296

14 Table 3 the terminal velocity of water flowing in stack Water flow rate Q w Previous researches Wyly type Dowson type This study (the experimental value) 1.0 l/s l/s l/s l/s Wyly Dawson The experimental value(standard deviation) Fig.16 Comparison of terminal velocity values It is obviously that the major reason for the different terminal velocity between present research and previous documents is the calculation assumption. Wyly and Dowson s researches assumed that water flow in stack is similar to the open channel with annual membrane flow in stack and adopted the Manning equation to estimate the terminal velocity. However, the visual observation significantly shows that the real flow in drainage stack is more complex and dynamic than annual flow assumption. Meanwhile, according to the visual observation and the calculated velocity in this research, it is noticed that even the annual flow along the stack has greater value than previous researches. Fig.17 shows the comparison of the annual flow velocity. Namely, the terminal velocity in drainage stack should be reconfirmed nowadays and need to 297

15 redefine its accurate value under the new validation results. Furthermore, the long term regulation and application which is according to the lower terminal velocity and permit flow rate are also necessary to be reconsidered Wyly Dawson annular water(standard deviation) Fig.17 Comparison of the annual flow velocity 5. Conclusion According to the importance of permit flow rate regulation, the terminal velocity in drainage stack was seen as one of the crucial issues in building drainage researches. This paper introduces a calculation method with empirical approach for terminal velocity by theoretical study from air pressure distribution mechanism. An observation technology with digital high-speed video camera was used to validate the prediction of terminal velocity of drainage stack in this report. The theoretical study reveals that the practical sense and the validation approximately responses to the calculation results. The guideline of National Plumbing Code (NPC) of US was used to set the permit flow rate as the regulation of drainage system. Following initial work of the HASS 203 of Japan in 1970s, the method of steady flow condition was merged as the provision reference and evaluation technique. As the results of this research, the terminal velocity in drainage stack should be reconfirmed nowadays and need to redefine its accurate value under the new validation results. Furthermore, the long term regulation and 298

16 application which is according to the lower terminal velocity and permit flow rate are also necessary to be reconsidered. Acknowledgements The authors would like to thank the Architecture & Building Research Institute of the Ministry of the Interior of Taiwan (ABRI) and the National Science Council of the Republic of China (NSC E )for financially supporting this research. 7. Reference 1) Roy.B.Hunter;BMS 79 Water Distributing System for Building, (1941) 2)R.S.Wyly and H.N.Eaton;Capacities of Plumbing Stack in Building,BMS Repoet,132(1952) 3) R.S. Wyly and H.N. Eaton : Capacities of Stacks in Sanitary Drainage System for Building, N.B.S. Monograph 31, (1961) 4)B.J.Pink;A Study of Water Flow in Vertical Drainage Stacks by Means of a Probe,CIB-W62 Semminar,(1973) 5) Yoshiharu Asano;The basic research of the specific of the velocity in vertical stack---terminal velocity, the report of the architectural institute of Japan, 278(1979) 6) Tukagoshi;The experimental research method of the specific of the vertical stack,transactions of the Society of Heating, Air-Conditioning and Sanitary Engineers of Japan (1977) 7) Sakaue: The analysis of the variation of the pressure in vertical stack, Transactions of the Society of Heating, Air-Conditioning and Sanitary Engineers of Japan (1979) 8) Cheng, C. L., Kamata, M., Kurabuchi, T., Sakaue, K., Tanaka, T., A Prediction Method of Air Pressure Distribution of Drainage Stack System in Case of Single- Point Steady Discharge, Journal of Archit. Plann. Environ. Eng., No.481, pp (1996). 9) Cheng, C. L., Kamata, M., Kurabuchi, T., Sakaue, K., Study on Pressure Distribution of Drainage Stack System in High-Rise Apartment Houses, Journal of Graduate School and Faculty of Engineering the University of Tokyo (B), Vol. XLIII, No.4, pp (1996, EI) 299

17 10) C.L. Cheng, Lu, W. H., Shen, M.D., An Empirical Approach: Prediction Method of Air Pressure Distribution on Building Vertical Drainage Stack, Journal of the Chinese Institute of Engineers, Vol 28.(2004) 11) C.L. Cheng, K.C. He, C. J. Yen, W.J. Liao, Empirical study on terminal water velocity of drainage stack, CIB-W62 International Symposium, Hong Kong ( ). Presentation of Author Cheng-Li Cheng is the Professor at National Taiwan University of Science and Technology, and ex-chairman of Department of Architecture. He is a researcher and published widely on a range of water supply and drainage in building. He has published extensively on a range of sustainable issues, including the water and energy conservation for green building. Currently he also acts as referee and member of Taiwan Green Building Evaluation Committee and National Building Code Review Committee. 300