JCARM Journal of Contemporary Academic Research and Methodologies JCARM 3139-7247 Ivory and Finch Publishers 10.5281/zenodo.21300022 JCARM_JUN_26_054 Original Research Article Analysis of Potential Fluid Flow,Harmonic Function and its Application ThankGod Eteng Apih Department of Mathematics, Faculty of physical Science. University of Cross River State. apihthankgod2017@gmail.com N Tanu Obi Department of Electrical Electronics Department, Federal Polytechnic Ugep Obono Ofem. Daniel department of Chemistry, School of Physical Science; University of cross river state Mustapha Musa Ekpelu, Department of Science and Laboratory Technology, Federal Polytechnic Ugep Edache Elijah Ehoche https://orcid.org/0000-0002-7821-3220 Department of Science and Laboratory Technology, Federal Polytechnic Ugep Dorcas Elijah Odifioyi Department of Electrical Electronics Engineering, School of Engineering, Federal University of Technology Minna 10 07 2026 1 5

This project is aimed at showing the application of potential flow in fluid mechanics. It has been shown so far in this project that for an incompressible irrotational and inviscid flow that the vorticity vector is the curl of the flow velocity it gives in a potential kind of flow. It was also demonstrated in this project that the harmonic function is a solution of the Laplace equation it gives in fluid mechanics to the potential kind of flow which is also called the irrotational flow. The irrotationality of a potential flow is due to the curl of the gradient of a scala, always being equal to zero. The flow described by this model are potential fields, the velocity potential function and the determination of the velocity component from it’s scalar function. i.e. by differentiating the stream function with respect to the given coordinates are described in this project. A description of the reduction of the equations of motion for “ideal” (irrotational incompressible and inviscid) flow to a single equation. Viz the laplace equation is provided in some details.

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