Optimal operation of water distribution systems is a well explored problem defined as finding the scheduling of pumping units over time which minimize cost while maintaining flow, pressure, and tank water levels constraints. One of its major complexities is the inherent non linearity and non-smoothness relationship of the headloss equation (e.g., the Hazen Williams or Darcy Weisbach formulas). This study suggests a method for the linearization of the Hazen-Williams headloss equation which enables the non-linear hydraulic problem to be addressed and solved as a linear programming scheme. The methodology is demonstrated on a small illustrative example.
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