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Abstract
This paper shows how it is possible to represent the link between the leakage from a pipe and the internal pipe pressure by relying on the classical Torricelli equation, which is valid for a thin-walled orifice with complete contraction, provided that a correction is introduced to take account both of the potential deformation of the leak opening and hydraulic factors which alter the coefficient of discharge. The quantities that contribute to determining this correction coefficient and its form are identified by means of the Buckingum π theorem combined with an evolutionary technique. The Buckingum π theorem enables the dimensionless outflow to be placed in relation with potential quantities describing the material, the leak size and shape, etc., all of which are dimensionless so as to lend the relationship general validity. The evolutionary technique used to define the form, or equation, of this corrective coefficient is the Evolutionary Polynomial Regression (EPR), which enables the form and parameters of the equation searched for to be defined simultaneously. The data necessary for the study were drawn from laboratory tests using two different elastic materials (steel and u-PVC), two diameters and two different leak shapes, each with different dimensions. The results obtained confirm the validity of the theoretical approach and support the possibility of writing a single Q-h relationship that is valid for varying materials, diameters and leak shapes and sizes.
Acknowledgements
The authors are grateful to the two anonymous reviewers for their very helpful comments which help us to improve our paper. The research reported in this paper was founded by PRIN-2012 “Tools and procedures for an advanced and sustainable management of water distribution systems”.