Design of Multistage Pumping Main

Long-distance pipelines transporting fluids against gravity and frictional resistance involve multistage pumping. Equations for the optimal diameter and the pumping head for a single-stage pumping main are available. However, in the case of multistage pumping, the optimal number of pumping stages are worked out by an enumeration process. Such a process does not indicate functional dependence of input parameters on the design variables. In this paper, the multistage pumping main design is formulated as a geometric programming problem having a single degree of difficulty. The constant friction factor case of the problem yielded a closed-form solution for a long pipeline with relatively flat topography. The variation of the friction factor with diameter has been accounted for iteratively.