Compressors and booster pumps constitute the "heart" of the supercritical carbon dioxide transport pipeline network because they consume most of the required energy input. In other words, most of the operating expenditure for the transport pipeline goes to the running of compressors and pumps. The long-term economic feasibility of running such pipeline networks is achievable only if operating costs linked to the energy consumption of both machines can be kept as low as possible. Energy consumption can be kept as low as possible by sizing compressors and booster pumps optimally to ensure that power losses in both machines are minimized. In this study, a quasi-dimensional model based on the laws of conservation was developed, validated with available experimental data and then used for a detailed investigation of the effect of various impurities on the performance of a centrifugal machine handling supercritical carbon dioxide of varying purity. Results of the study show that discharge pressure, power requirement and efficiency of a centrifugal machine are strongly dependent on certain key parameters; namely, the size and speed of its impeller rotor as well as the composition of the impure CO2 stream. More importantly, this study also demonstrates that the quasi-dimensional model can be used as a tool for appropriate selection and sizing of centrifugal compressors and booster pumps installed on a supercritical carbon dioxide transport pipeline.