Analytical methods are described that were developed to undertake the pump manifold calculations for hydraulic air compressors (HAC) where multiple pumps are installed in parallel configurations. The procedures are fast and exact and were developed for design optimisation and control tasks which, although described in the specific context of HACs, are also applicable to more general pumping systems. The proposed method uses a recursive / iterative procedure to establish the pump curve equivalent to the pump combination, so that the design performance of the system can be assessed for any value of externally attached hydraulic resistance. The technique is verified against a numerical method applied to the same problem, but where the external hydraulic resistance must be completely specified for a solution. Losses at convergent and divergent wyes, which are required to create the parallel pump manifold arrangements, are found to be significant factors in establishing the overall energy efficiency of the pumping system. With efficient pump manifold arrangements designed, a so-called binary pumping scheme is explained, where individual pumps in the manifold can be activated (1) or deactivated (0), so that the pumping system discharge can be reduced with good turn-down ratios while ensuring that the best efficiency point (BEP) efficiency of the system is maintained (exemplified with 4:1 or 25%).