During the past decade three-dimensional flow problems of turbomachinery have been solved for frictionless fluids under the assumption of an infinite number of vanes. However, the practical application of this advancement to the design of turbomachinery has not yet reached a state of acceptance commensurate with the practical importance of this theoretical development. The present paper endeavors to contribute toward such application by presenting the principles of the theory in a physically simple manner, and by illustrating its application by two examples, solving the general problem by two successive approximations. The first approximation disregards the departures of the meridional streamlines from their straight and parallel potential-flow pattern; the second approximation takes account of these departures on the basis of the first. The vorticity of the flow is assumed to be strong. The time and means required for working out each of the examples were found to fall within the practical limits of a competently staffed engineering department.