The preliminary sizing and design of a centrifugal compressor for a 10 MWe waste heat recovery supercritical carbon dioxide (S-CO2) Brayton power plant is presented. Modelling and achieving proper convergence at the design point is challenging due to the proximity to the critical point. To overcome this challenge dimensional analysis was used. Three independent non-dimensional parameters were used to perform the scaling between the design point and a partially dynamically and geometrically similar operating point, which lies in the supercritical ideal gas region of carbon dioxide. The investigation found that the compressor characteristic map can be expressed as a single map referred to as the Generalized Map. The map is expressed in terms of the Enthalpy Rise coefficient and the Flow Coefficient for a set of constant speed lines. From the Generalized Map, the designer can project the characteristic map corresponding to another operating point.