Microsoft Word - cet-01.docx Research on the Planning of Municipal Pipe in Tibet Bayi Town Center Area Based on Fractal Yongchen Zong*, Guangdong Lu, Zhu He, Jianli Jin Agriculture and Animal Husbandry College,Tibet University, 860000, China. zyc_2001@sohu.com In this paper, to achieve rational distribution of municipal pipe network in Bayi Town Centre Area, Box dimension and Rank dimension are used to carry out evaluation studies on the planning of water supply network and drainage network in Bayi Town. The results show that Box dimension and Optimization dimension of Water supply network are roughly equal and water supply network planning is reasonable. The Rank dimension of drainage network meets the law of optimization, so there is no problem that drainage network can achieve its basic functions, but the Length ratio and Branch ratio of it are small. Combining the pipeline network with actual situation and analyzing the causes, we find that drainage network planning has a large space for optimization. 1. Introduction At present, the urbanization in Tibet has been 17 years, and the cumulative investment of it has been reached to tens of billions. The layout of Lhasa as the center, town as sub-centers, the county town and key port as Level 3 towns has been initially formed. In the process of the urbanization, many questions have been exposed such as unreasonable municipal pipe network layout and imperfect infrastructure. Bayi town is now divided into three areas which are the central area, northwest area and Yongjiu area, Specific conditions of three areas is showed in Table 1. Table 1: Specific condition of three areas Area Feature Number of the population(Ten thousand) Area (Km2) central area Administrative, commercial, cultural, commercial, Tibetan medicine 7 12.38 northwest area Science, life 0.8 13.63 Yongjiu area Public services, logistics 0.2 12.18 The studied area is central area of Bayi Town, which now has a population of 70 thousand. Existing water supply network was built in the 1990s and from 2002 to 2005, the main problems at this stage are that the diameter of pipe is too small, and the pressure of some regional is too low, and pipe leakag e is serious, and the layout of pipeline is irrational. 2. The theory of fractal Li Fengdao, Zhu Jinzao and Zhu Qingke (2002) reported, Fractal is a science of nonlinear systems, which was proposed by Benoit Mandelbrot in 1973 at the College de France for the first time. In 1977, Mandelbrot put forward the measures of fractal—dimension. Cui Lingzhou, Xiao Xuenian and Li Zhanbin (2004) reported the classic method of calculating the fractal dimension is Box dimension. This is a common method of calculating the fractal dimension, its approach is to take a different side length of a square box on covering graphics and covering graphics length (l) changes CHEMICAL ENGINEERING TRANSACTIONS VOL. 46, 2015 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Peiyu Ren, Yancang Li, Huiping Song Copyright © 2015, AIDIC Servizi S.r.l., ISBN 978-88-95608-37-2; ISSN 2283-9216 DOI: 10.3303/CET1546125 Please cite this article as: Zong Y.C., Lu G.D., He Z., Jin J.L., 2015, Research on the planning of municipal pipe in tibet bayi town center area based on fractal, Chemical Engineering Transactions, 46, 745-750 DOI:10.3303/CET1546125 745 when the number of boxes (N(l)) also change accordingly, La, Barbera, P., Rosso, R (1989) reported, the following formulas (1) can be given on the basis of fractal theory. N(l) ∝ l−D (1) Chen Jianan (1999) reported, when the length of the boxes were l1, l2, l3,…, lk,r1 the number of boxes were N(l1), N(l2), N(l3),…N(lk) N(r1),after Logarithmic obtained we can get the following formula: lgN(l) = −Dlgl + A (2) Wherein, A is the constant to be determined, and D is Box dimension or absolute value of slope. Also with least square method and one-variable linear regression, the estimated value of dimension D can be available 3. Study on planning of the water supply network Planning of Population in Bayi town center area is 90 thousand, and planning map is shown in Figure 1. Figure 1: Planning map of Water supply network 3.1 Box dimension of the water supply network Hu Lifeng (2010) reported, the method of Box dimension was used to calculate Fractal of water supply network, and the process is shown in table 2. Table 2: Statistics box of Water supply network Decile Length(L) Ln(L) Number of box(N) Ln(N) 2 13426.00 9.5049 3 1.0986 4 6713.00 8.8118 9 2.1972 8 3356.50 8.1187 24 3.1781 16 1678.25 7.4255 70 4.2485 32 839.13 6.7324 217 5.3799 64 419.56 6.0392 497 6.2086 Using the data in Table 2, Fig. 2 is fitted with Ln (L)LN(L) for x-axis and Ln(N) for y-axis. 746 Figure 2: Fitting a straight line on box dimension of Water supply network After the function fitting, Box dimension of Water Supply Network in Bayi Town Center Area is 1.4909. 3.2 Analysis and discussion Zhao Peng and Zhang Hongwei (2007) reported the fractal properties of the water supply network, and thought that water supply network as the lifeline of the city and other network systems have an optimized structure and dimension of the water supply network have the relationship with the area of water supply and a population following relationship after a large study. D = 1.51- 0.72 S2.33 + 0.1( Q S ) 0.92 (3) In the formula, DO is the dimension of water supply network, S is the area of water supply, and Q is a population. When S equals to 12.38 km2 and Q equals to 90000, we can get that D is 1.5825. We find that the value of DO is the same as the value of Box dimension. The absolute difference is only 0.0916, and the relative difference is 5.78%. So we have reason to believe the planning of water supply network in Bayi Town center stage Area is almost optimal, and it is reasonable. 4. Study on planning of drainage network The planning of drainage network is separate drainage system. Panning map is shown in Fig. 3. 4.1 Box dimension of drainage network The method of Box dimension was used to calculate Fractal of drainage network which was confirmed (Cheng Yongqian, Zhang Yue and Song Qianwu (2012)), and the process is shown in table 3. Figure 3: The planning of drainage network 747 Table 3: Statistics box of drainage network Decile Length (L) Ln (L) Number of box (N) Ln (N) 2 13426.00 9.5049 3 1.0986 4 6713.00 8.8118 9 2.1972 8 3356.50 8.1187 22 3.0910 16 1678.25 7.4255 72 4.2767 32 839.13 6.7324 202 5.3083 64 419.56 6.0392 466 6.1442 Using the data in Table 3, Fig. 4 is fitted with Ln (L)LN(L) for x-axis and Ln (N) for y-axis. Figure 4: Fitting a straight line on box dimension of drainage network After the function fitting, Box dimension of drainage network in Bayi Town Center Area is 1.4735. Cheng Yongqian, Song Qianwu and Zhang Yue (2011) reported, So planning of drainage network is reasonable because there is no big difference between water supply network and drainage network, the absolute difference is only 1.2%, comparing with water supply network in that area. 4.2 Rank dimension of drainage network Rank dimension is based on which both the drainage network and rivers belong to the gravity flow, and river systems can meet level of law, so it can be considered the drainage network is tree system and meet the level of law which was confirmed (He Longhua and ZhaoHong (1996)). There are three laws of Branch Ratio, length ratio, and Rank dimension in the law of aqueous. The law of Branch Ratio: rb = Nm−1 Nm (4) In the formula, rb is Branch Ratio, Nm is the number of m-level drains. The law of length ratio: rL = Lm−1 Lm (5) In the formula, rL is length ratio, Lm is the length of m-level drains. Rank dimension 748 D = lnrb lnrL (6) In the formula, DR is Rank dimension. In order to research on Rank dimension of drainage network, we use which was confirmed (Feng Jinliang and Zhang Wen (1999)) Classification scheme to analyze branch-off drainage network. We don’t draw classification of FIG. 3 in order to sake of brevity, and the number of m-level drains Nm Nm and the length of m-level drains LmLm are shown in table 4 and 5. Table 4: Statistics of branching ratio on network m 1 2 3 𝑁𝑚 82 23 12 ln𝑁𝑚 4.4067 3.1355 2.4849 Table 5: Statistics of length ratio on network m 1 2 3 𝐿𝑚 292.6098 500.2174 614.5833 ln𝐿𝑚 5.6788 6.2150 6.42094 Figure 5: Linear fitting of Branch ratio Figure 6: Linear fitting of Rank ratio From the Fig. 5 and Fig. 6, we find that LnrLlnrL is 0.3711 and Lnrb lnrb is 0.9609, and Rank dimension of drainage network DR is 2.589, and Branch Ratio rb is 2.614 and length ratio rL is 1.449. 4.3 Analysis and discussion Chen Yanguang and Liu Jisheng (2001) reported, It is well known that Branch Ratio of river is 3~5 and length ratio of river is 1.5~3 and Rank dimension of river is 2~3. Zhang Mingsheng (2010) reported it is found that Branch Ratio and length ratio of drainage network is less than Branch Ratio and length ratio of river. According to Rank dimension, we also find that the planning of drainage network is close to the laws of nature fractal optimization and the structure of planning is within optimization theory. In other words, the function of drainage network can be realized in the water of gravity. Meanwhile, Rank dimension is almost the same with Box dimension of drainage network as well as dimension of the water supply network, but drainage network isn’t improved and economic enough because Branch ratio and Length ratio is small. Analyzing Fig. 3, we can find that Drainage network are constrained because Tibet Bayi town is surrounded by 318 national Road, mountains, and Niyang river. And so Branch Ratio is small. The second reason is that different levels of length pipeline have not yet reached to mix a more ideal state. This is also the main cause of low length ratio. 749 5. Conclusions In this paper, Box dimension D and Rank dimension DR are used to research on planning of water supply network and drainage network in Bayi Town Center Area, the findings show that planning of water supply network is reasonable because Box dimension D and Optimization dimension D O of Water Supply Network in Bayi Town Center Area are almost equal, and that planning of drainage network may meet the functional of own weight flow because Rank dimension DR of drainage network meet the relevant requirements, but drainage network can be continued to optimize because Branch ratio rb and Length ratio rL are not big enough. Acknowledgments This research is supported by the Natural Science Fund Project in Tibet for 2015(Research of wastewater treatment technology and countermeasure under the influence of high altitude), the Talent Program in Snowy Plateaus of Agricultural and Animal Husbandry college of Tibet University (Research of Investigation and Safety Evaluation on Drinking water of Niyang River-basin, Water environment protection of the plateau river) ,and High-level personnel launch scientific research projects (RC201503). References Barbera P.L., Rosso R., 1989, On the Fractal Dimension of Stream Networks. Water Resources Research. DOI: 10.1029/W R025i004p00735 Chen J.N., 1999, Define and measurement method of the fractal dimension [J]. Electronics Technology, 4: 44- 46. 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