Pumping mains are pipelines in which the flow is maintained by pumping. The present design equations are based on the Hazen-Williams equation or the constant friction factor in the Darcy-Weisbach equation. Considering the variability of the friction factor, the pumping main design is formulated as a constrained geometric programming problem having a single degree of difficulty. The solution yielded equations for the minimal cost, the optimal diameter, and the pumping head. These design equations provide insight about the functional dependence of the input variables on the optimal design.
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Prabhata K. Swamee (2001) studied this question.
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