Deep Insight into the still Hidden Theory of Isoenergetic Flow (Part Two)

摘要

This work studies and clarifies some local physical phenomena in fluid mechanics, in the form of an intrinsic analytic study, regarding the motion, continuity, flow rate and velocity potential equations (for inviscid compressible fluids), and the vortex equation (for viscous incompressible fluids), and finds new first integrals. It continues a series of works presented at some conferences and at a congress during 2008 - 2010, representing a real deep insight into the still hidden theory of isoenergetic flow (a real "physiology of the fluid medium"). Several new functions, surfaces and vectors were introduced: the polytropic integral surfaces, for the motion equation; Selescu's incompressible roto-viscous vector, for the vortex equation; the 2-D "quasi-stream" function on the 3-D (V, Ω) surfaces, for the continuity equation; the surfaces of iso-normal mass flux density (over which the continuity equation of the steady flow of a compressible fluid in a thick stream tube admits a first integral - the same as for this flow in a thin tube, and whose envelope sheets are just the sections of uniform flow, if they exist), for the flow rate equation; the 3-D stream function vector, allowing new local and global forms for the continuity equation; Selescu's "quasi-incompressible quasi-potential" (Laplace) lines of a "quasi-uniform" rotational flow of an inviscid compressible fluid, for the velocity (quasi-)potential equation (Steichen). A case of first integrability for the system of equations (motion and continuity) for the steady flow of an inviscid compressible fluid was also considered.