A GENERAL METHOD FOR TREATING

Abstract

A model of a certain flow of an inviscid fluid is introduced, in order to establish a simpler form of general PDE of the velocity “quasi-potential” for the isoenergetic flows. This model consists mainly in using a new three-orthogonal system of curvilinear coordinates (one of them being tied to the local specific entropy value). The choice of this new orthogonal curvilinear coordinate system (with two coordinate curves lying on the “isentropic” surfaces) presents the advantage of enabling the treatment of any 3-D flow (even rotational) as a “quasi-potential” 2-D one, on the respective “isentropic” rigid surfaces (having different constant values of the specific entropy) - analogous to the “D. Bernoulli’s” ones (in the case of a barotropic fluid) - introducing a 2-D velocity “quasi-potential”, specific to any isentropic surface. On these surfaces the streamlines are orthogonal paths of a family of lines of equal velocity “quasi-potential”. The work deals with the steady as well as unsteady flows, in both cases giving first integrals for the equation of motion.