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The classical hodograph equation for the study of the irrotational compressible flow of an ideal gas is here extended to the rotational case in which an entropy gradient normal to the streamlines is present. The formulation is in terms of Crocco's stream function and leads to an equation differing from that valid for the irrotational case because of an additional nonlinear tp m. In spite of this nonlinearity an exact solution can be found, describing a clas? of rotational vortices. Moreover,doi:10.1090/qam/1012274 fatcat:6veszhjcprhpdpbrdmjj4kwiky