WSEAS Transactions on Fluid Mechanics
Print ISSN: 1790-5087, E-ISSN: 2224-347XVolume 9, 2014
New First Integrals for the Continuity, Vorticity and Related Equations
Author:
Abstract: This work studies and clarifies some local phenomena in fluid mechanics, in the form of an intrinsic analytic study, regarding the continuity equation, its first integral (the flow rate equation), for inviscid compressible fluids, and the vorticity equation, for viscous incompressible fluids, finding new first integrals. It continues a series of works presented at some conferences and a congress during 2006 – 2012, representing a real deep insight into the still hidden theory of the isoenergetic rotational flow. Several new functions, surfaces and vectors were introduced: 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 for the steady flow in a thick stream tube admits the same first integral as for the flow in a thin one, and whose envelope sheets are the sections of uniform flow), for the flow rate equation; the 3-D stream function vector, allowing new local and global forms of continuity equation (the global one similar to Helmholtz’ 2nd theorem about vortices in an ideal fluid); Selescu’s incompressible roto-viscous vector and the zero-work surfaces (for some non-conservative vectors), for the vorticity equation. The dependence “2-D velocity quasipotential <-> 2-D quasi-stream function” was established. The unsteady flow’s continuity equation was analytically integrated.
Keywords: rotational flows, steady and unsteady flows, inviscid and viscous fluids, compressible fluids, isentropic or (V, Ω) surfaces, Selescu’s 3-D stream function vector, surfaces of iso-normal mass flux density, roto-viscous vector and zero-work surfaces
Pages: 34-48
WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #4