The Velocity Potential PDE in an Orthogonal Curvilinear Coordinate System

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Abstract: This work studies and clarifies some local physical phenomena in fluid mechanics, in the form of an intrinsic analytic study, regarding the PDEs of the velocity potential and (especially) 2-D “quasi-potential” (their simpler and special forms), over the “isentropic” or the 3-D (V, Ω) surfaces and along the “isentropic & isotachic” space curves, written for any potential and even rotational flow of an inviscid compressible fluid for both steady and unsteady motions. 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 flow. Applying the advantages offered by the special virtual surfaces (“isentropic” and “polytropic”) and space curves (intersection lines of these surfaces) introduced in the previous works, a simpler PDE of the 2nd order in only two variables, and more, a Laplace’s PDE (for any rotational “pseudo-flow”, using a new smart intrinsic coordinate system), instead of the general PDE (Steichen, 1909, for plane potential supersonic flows only) of the 2nd order in three variables. So far, this equation was known as being written for potential flows only. A model extension for rotational flows of a viscous compressible fluid was given.

WSEAS Transactions on Fluid Mechanics, ISSN / E-ISSN: 1790-5087 / 2224-347X, Volume 9, 2014, Art. #6

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Richard Selescu, "The Velocity Potential PDE in an Orthogonal Curvilinear Coordinate System," WSEAS Transactions on Fluid Mechanics, vol. 9, pp. 58-77, 2014, DOI:
Richard Selescu. The Velocity Potential PDE in an Orthogonal Curvilinear Coordinate System. WSEAS Transactions on Fluid Mechanics. 2014;9:58-77.
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