Abstract
Since the value of the hydraulic resistance depends on flow rate, problem of flow distribution per pipes in a gas or water distributive looped pipelines has to be solved using iterative procedure. A number of iterative methods for determining of hydraulic solution of pipeline networks, such as, Hardy Cross, Modified Hardy Cross, Node-Loop method, Modified Node method and M.M. Andrijašev method are shown in this paper. Convergence properties are compared and discussed using a simple network with three loops. In a municipal gas pipeline, natural gas can be treated as incompressible fluid. Even under this circumstance, calculation of water pipelines cannot be literary copied and applied for calculation of gas pipelines. Some diferences in calculations of networks for distribution of these two fluids, i.e. water apropos natural gas are also noted.
Similar content being viewed by others
References
Altman T, Boulos PF (1995) Convergence of Newton method in nonlinear network analysis. Math Comput Model 21(4):35–41. doi:10.1016/0895-7177(95)00004-L
Andrijašev MM (1964) Hydraulics calculation of water distribution networks. Stroizdat, Moscow (in Russian)
Aynsley RM (1997) A resistance approach to analysis of natural ventilation airflow networks. J Wind Eng Ind Aerod 67–68:711–719. doi:10.1016/S0167-6105(97)00112-8
Boulos PF, Lansey KE, Karney BW (2006) Comprehensive water distribution systems analysis handbook for engineers and planners. MWH Soft, Hardback
Brkić D (2009) An improvement of Hardy Cross method applied on looped spatial natural gas distribution networks. Appl Energ 86(7–8):1290–1300. doi:10.1016/j.apenergy.2008.10.005
Coelho PM, Pinho C (2007) Considerations about equations for steady state flow in natural gas pipelines. J Braz Soc Mech Sci Eng 29(3):262–273. doi:10.1590/S1678-58782007000300005
Colebrook CF (1939) Turbulent flow in pipes with particular reference to the transition region between the smooth and rough pipe laws. J Inst Civil Eng (London) 11(4):133–156. doi:10.1680/ijoti.1939.13150
Corfield G, Hunt BE, Ott RJ, Binder GP, Vandaveer FE (1974) Distribution design for increased demand. In: Segeler CG (ed) Gas engineers handbook. Industrial Press, New York, pp 63–83
Cross H (1936) Analysis of flow in networks of conduits or conductors. Engineering Experimental Station 286(34):3–29
Ekinci Ö, Konak H (2009) An optimization strategy for water distribution networks. Water Resour Manag 23(1):169–185. doi:10.1007/s11269-008-9270-8
Epp R, Fowler AG (1970) Efficient code for steady flows in networks. J Hydraul Div ASCE 96(1): 43–56
Farshad F, Rieke H, Garber J (2001) New developments in surface roughness measurements, characterization, and modeling fluid flow in pipe. J Petrol Sci Eng 29(2):139–150. doi:10.1016/S0920-4105(01)00096-1
Gay B, Middleton P (1971) The solution of pipe network problems. Chem Eng Sci 26(1):109–123. doi:10.1016/0009-2509(71)86084-0
Haaland SE (1983) Simple and explicit formulas for friction factor in turbulent pipe flow. J Fluid Eng T ASME 105(1):89–90. doi:10.1115/1.3240948
Hamam YM, Brameller A (1971) Hybrid method for the solution of pi** networks. Proc IEE 118(11):1607–1612. doi:10.1049/piee.1971.0292
Huddleston DH, Alarcon VJ, Chen W (2004) Water distribution network analysis using Excel. J Hydraul Eng ASCE 130(10):1033–1035. doi:10.1061/(ASCE)0733-9429(2004)
Kumar SM, Narasimhan S, Bhallamudi SM (2010) Parameter estimation in water distribution networks. Water Resour Manag 24(6):1251–1272. doi:10.1007/s11269-009-9495-1
Latišenkov AM, Lobačev VG (1956) Hydraulics. Gosstroizdat, Moscow (in Russian)
Lopes AMG (2004) Implementation of the Hardy-Cross method for the solution of pi** networks. Comput Appl Eng Educ 12(2):117–125. doi:10.1002/cae.20006
Mah RSH (1974) Pipeline network calculations using sparse computation techniques. Chem Eng Sci 29(7):1629–1638. doi:10.1016/0009-2509(74)87014-4
Mah RSH, Lin TD (1980) Comparison of modified Newton’s methods. Comput Chem Eng 4(2): 75–78. doi:10.1016/0098-1354(80)80018-4
Mah RSH, Shacham M (1978) Pipeline network design and synthesis. Adv in Chem Eng 10:125–209. doi:10.1016/S0065-2377(08)60133-7
Mathews EH, Köhler PAJ (1995) A numerical optimization procedure for complex pipe and duct network design. Int J Num Method Heat Fluid Flow 5(5):445–457. doi:10.1108/EUM0000000004072
Pretorius JJ, Malan AG, Visser JA (2008) A flow network formulation for compressible and incompressible flow. Int J Num Method Heat Fluid Flow 18(2):185–201. doi:10.1108/09615530810846338
Shamir U, Howard CDD (1968) Water distribution systems analysis. J Hydraul Div ASCE 94: 219–234
Sukharev MG, Karasevich AM, Samoilov RV, Tverskoi IV (2005) Investigation of the hydraulic resistance in polyethylene pipelines. J Eng Phys Thermophys 78(2):350–359. doi:10.1007/s10891-005-0068-8
Todini E, Pilati S (1988) A gradient method for the analysis of pipe networks. In: Computer applications for water supply and distribution, vol 1. Wiley, New York, pp 1–20
Wang Y-J, Hartman HL (1967) Computer solution of three-dimensional mine ventilation networks with multiple fans and natural ventilation. Int J Rock Mech Min Sci 4(2):129–154. doi:10.1016/0148-9062(67)90039-3
Wood DJ, Charles COA (1972) Hydraulic network analysis using linear theory. J Hydraul Div ASCE 98(7):1157–1170
Wood DJ, Rayes AG (1981) Reliability of algorithms for pipe network analysis. J Hydraul Div ASCE 107(10):1145–1161
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Brkić, D. Iterative Methods for Looped Network Pipeline Calculation. Water Resour Manage 25, 2951–2987 (2011). https://doi.org/10.1007/s11269-011-9784-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-011-9784-3