Abstract
The relationship between the functioning conditions of pipe systems and the leakage, or leak law, can be used at two different scales. At a local scale, i.e. for a single leak, it is derived from the classical orifice equation and, basing on experimental data, is modified to take into account all the relevant parameters it depends on (e.g., leak shape, pipe material and thickness, …). At a global scale, for a whole district or a part of a pressurized pipe system with several leaks, the same relationship is often used, basing on the assumption that the combination of local leak laws produces a similar global leak law.
In this paper the effects of the spatial variation of the leak law parameters at the local scale on the leak law at a global scale are analyzed. Two leak laws derived from the orifice equation, the power law and the linear law, are considered. Results suggest that the global leak law exponent is larger than the corresponding mean local leak law exponent since it takes into account the spatial variability of the quantities affecting leakage.
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References
Bajura RA (1971) A model for flow distribution in manifolds. J Eng Power 93(1):7–12
Bajura RA, Jones E (1976) Flow distribution manifolds. J Fluids Eng-Trans Asme 52(12):654–666
Berardi L, Giustolisi O, Todini E (2010) Accounting for uniformly distributed pipe demand in WDN analysis: enhanced GGA. Urban Water J 7(4):243–255
Brunone B, Ferrante M (2001) Detecting leaks in pressurised pipes by means of transients. J Hydraul Res IAHR 39(5):539–547
Cassa A.M, van Zyl JE, Laubscher R (2010) A numerical investigation into the effect of pressure on holes and cracks in water supply pipes. Urban Water J 7(2):109–120
Collins R, Boxall J (2013) The influence of ground conditions on intrusion flows through apertures in distribution pipes. J Hydraulic Eng ASCE 139(10):1052–1071
Ferrante M (2012) Experimental investigation of the effects of pipe material on the leak head-discharge relationship. J Hydraul Eng ASCE 138(8):736–743
Ferrante M, Brunone B, Meniconi S (2009a) Leak detection in branched pipe systems coupling wavelet analysis and a Lagrangian model. J Water Supply: Res Technol -AQUA 58(2):95–106
Ferrante M, Brunone B, Meniconi S (2009b) Leak-edge detection. J Hydraul Res IAHR 47(2):233–241
Ferrante M, Massari C, Brunone B, Meniconi S (2011) Experimental evidence of hysteresis in the head-discharge relationship for a leak in a polyethylene pipe. J Hydraul Eng ASCE 137(7):775–780
Ferrante M, Massari C, Todini E, Brunone B, Meniconi S (2013) Experimental investigation of leak hydraulics. J Hydroinformatics 15(3):666–675
Ferrante M, Todini E, Massari C, Brunone B, Meniconi S (2012) Equivalent hydraulic resistance to simulate pipes subject to diffuse outflows. J Hydroinformatics 14(1):65–74
Greyvenstein B, van Zyl JE (2007) An experimental investigation into the pressure - leakage relationship of some failed water pipes. J Water Supply: Res Technol- AQUA 56(2):117–124
Jaumouillé E, Piller O, van Zyl JE (2007) A hydraulic model for water distribution systems incorporating both inertia and leakage. Proc Int Conf Comput Control Water Ind 129–135
Karadirek IE, Kara S, Yilmaz G, Muhammetoglu A, Muhammetoglu H (2012) Implementation of hydraulic modelling for water-loss reduction through pressure management. Water Resour Manag 26(9):2555–2568
Lambert A (2001) What Do We know about pressure/leakage relationships in distribution systems.” Proc. IWA Specialised Conference: System Approach to Leakage Control and Water Distribution Systems Management. Brno, Czech Republic, pp 89–96
Massari C, Ferrante M, Brunone B, Meniconi S (2012) Is the leak head–discharge relationship in polyethylene pipes a bijective function?. J Hydraul Res IAHR 50(4):409–417
May J (1994) Pressure dependent leakage. World Water Environmental Engineering, (October), 10.
Meniconi S, Brunone B, Ferrante M, Massari C (2011) Small amplitude sharp pressure waves to diagnose pipe systems. Water Resour Manag 25(1):79–96
Osterwalder J, Wirth C (1985) Experimental investigations of discharge behaviour of crack-like fractures in pipes. J Hydraul Res IAHR 23(3):255–272
Rossman L (1994) EPANET 2 Users Manual. Water Supply and Water Resources Division National Risk Management Research Laboratory Cincinnati, OH 45268
Tabesh M, Yekta AHA, Burrows R (2008) An integrated model to evaluate losses in water distribution systems. Water Resour Manag 23 (3): 477–492
Thornton J, Lambert A (2005) Progress in practical prediction of pressure: leakage, pressure: burst frequency and pressure: consumption relationships Proc of IWA Special Conference ’Leakage 2005’. Halifax, Canada
van Zyl JE, Cassa AM (2013) Modeling elastically deforming leaks in water distribution pipes. J Hydraul Eng ASCE 140(2):182–189
van Zyl JE, Clayton C (2007) The effect of pressure on leakage in water distribution systems. Proc Inst Civil Eng: Water Manag 160(2):109–114
Walski T, Bezts W, Posluszny E, Weir M (2006) Modeling leakage reduction: through pressure control. J A Water Works A 98(4):147–155
Yang Y, Zhang T, Zhu DZ (2014) Influence of porous media on intrusion rate into water distribution pipes. J Water Supply: Res Technol - AQUA 63(1):43–50
Acknowledgements
This research has been supported by the Italian Ministry of Education, University and Research (MIUR) under the Projects of Relevant National Interest “Advanced analysis tools for the management of water losses in urban aqueducts”, “Tools and procedures for an advanced and sustainable management of water distribution systems” and Fondazione Cassa Risparmio Perugia under the project “Hydraulic characterization of innovative pipe materials (no. 2013.0050.021)”.
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Ferrante, M., Meniconi, S. & Brunone, B. Local and Global Leak Laws. Water Resour Manage 28, 3761–3782 (2014). https://doi.org/10.1007/s11269-014-0708-x
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DOI: https://doi.org/10.1007/s11269-014-0708-x