A historical review of the various turbomachine theories is given. The Lorenz channel theory is developed for the analysis of riscous flows through turbomachines. Both the infinitesimally and the finitely spaced blades are considered. Firsts the incompressible, viscous and then the compressible viscous flows are treated. The method of analysis consists of an iteration procedure in which the first step is the eraluation of an equivalent axially symmetric turbomachine stage with infinitesimally spaced blades. The results of this first step in the analysis are used as the first terms of infinite series for the veloci¬ties and pressure, when the transition to finitely spaced blades is made. These infinite series are written in powers of the tangential coordinate and the coeffi-cients are functions of the radial as well as the axial coordinates.nThere are a number of boundary conditions which must be satisfied by the solution of the finitely spaced blade analysis. These are: 1. Along the frozen streamline surfaces, the values of the flow variables have been prescribed to be those of the infinitesimally spaced blade analysis. 2. Along the new and corrected streamline surfaces forming the actual blade surfaces in the finitely spaced blade analysis, the resultant velocity should be zero (non-slip condition).
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