The apparent volumetric displacement of digital displacement pumps and motors is reduced with increasing fluid pressure. So-called pump shrinkage has been documented in previous publications, where fluid compressibility effects were assumed to affect input and output power equally. In this paper, the authors derive the torque and flow rate of an ideal digital displacement pump. It is shown that the output power shrinks slightly more than the input. The difference between input and output shrinkage is counted as a power loss according to the accepted definition of total efficiency. New equations are presented for calculating mechanical and volumetric efficiencies which are up to 2% more accurate than the previous method (which assumes equal shrinkage) and up to 5% more accurate than conventional equations (which assume no shrinkage). Compressibility effects may be even more significant depending on pump design parameters, fluid properties, flow control algorithms and operating conditions. Calculations of partial pump efficiencies require a derived displacement volume to be known. The derived displacement volume of digital displacement pumps is considered for the first time in this paper. The contributions of this work are instructive for understanding the unique characteristics of digital displacement pumps as well as check-valve type pumps in general.

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