A calculation method using a differential equation for the turbulent shear stress has been successfully applied to boundary layers with compressibility, heat transfer, three-dimensionality or unsteady flow, with an empirical input obtained almost entirely from low-speed flow at constant pressure. With numerical changes in the empirical input the method has been extended to duct flows and free shear layers. Running times are typically 5–10 sec on a CDC 6600 or five times this on an IBM 7094; programs are freely available from the authors.