Design of high-rise pumping mains

For urban water supplies, many a times water often has to be conveyed to great heights over a relatively short distance. On account of development of large pressure heads, pumping cannot be done in a single stage, and one has to resort to multistage pumping. In the present design practice the number of pumping stages are decided on an ad hoc basis and the pumping main in the intervening stages is designed as a single pumping main. Such a design is a suboptimal design. Presented herein are the explicit equations for the optimal number of pumping stages, the pumping main diameter, and the corresponding cost. It is hoped that the equations are useful to a design engineer.