An inlet transition section and an inlet bowl entry can be designed to reduce a number of turbomachine casing designs. Using relationships between flow properties, distances between elements, crossover/supply pipe diameter, ideal cross sectional area, aspect ratio, and inlet bowl entry size, a transition from circular cross section to substantially polygonal cross section can be made while enabling adoption of a single size of substantially polygonal inlet bowl entry for a plurality of turbine sizes and/or crossover/supply pipe sizes with minimal losses.