A pitot-tube jet-pump (PTJ pump) has been considerably modified and extended in order to continuously separate and transport liquids of different densities. As a first application, an oil–water mixture is considered in this work. The modified PTJ pump could be used as a primary separator for oil-polluted water (e.g., around off-shore platforms, after oil spills from ships), while additionally being able to transport the resulting fluid to further heaters, exchangers, centrifuges, distillation columns, etc., without necessitating additional machinery. The performance behavior of the separating PTJ pump (abbreviated SPP in what follows) has been first investigated with computational fluid dynamics (CFD), and then validated by comparison with experimental data acquired on a small-scale prototype. Based on these observations, a design tool has been developed to (i) predict performance and (ii) support proper device scaling. This tool is based on dimensionless parameters that are already employed for classical turbomachinery, similar to the Cordier chart. However, since the SPP works at an extremely low specific speed, its operating points lie outside the standard Cordier chart. To verify the accuracy of the design tool, a scale-up test has been conducted and validated by CFD, delivering a good agreement. A separation efficiency better than 99% has been obtained in the experiments for suitable operation conditions, while the numerical scale-up test reveals a head of 15.1 m and an oil content below 0.2% in the purified water at the high-pressure outlet.