Optimization of Dead End Water Distribution Systems

A single dead end system with multiple withdrawals has been synthesized. Dead end water distribution systems are frequently encountered in rural water supply systems. Their optimal design is reduced to a nonlinear objective function with a nonlinear constraint. A closed form solution of the problem has been obtained by the Lagrangian multiplier method. The solution is presented in a form directly usable by the design engineer providing optimal pipe diameters, pumping head, hydraulic gradient line, and the minimal cost. The solution has been generalized for a continuous withdrawal of discharge. The case of two withdrawals is depictable in graphical form and provides a clear insight into the variation of the various parameters. Substantial saving can be achieved by designing the water distribution facilities at minimal costs.