This article objectively assesses, the hypothesis of the streamline's shape theory and its formulated equation. The deduction of proof uses algebra rather than first-order partial differential equations to address the specific hypothesis of "Streamline's shape theory" from the fundamental perspective of applied mathematics and scientifically derives mathematical relations of the axioms and corollaries in the field of fluid dynamics. The algebraic methods employed provide progressively more distinct and precise solutions compared to first-order partial differential equations. The foremost objective of this work is to evaluate if the formulations of the streamline's shape theory can have solutions for inviscid-incompressible and viscid-compressible flows of Newtonian fluids and to identify their nature. Secondly, to understand how the topology of the body and the free-stream conditions affect these solutions with due regards to the shape and size of the body interacting with the fluid flow. Finally, to explore the possibility of this theory to develop a CFD solver for streamline simulation to reduce the experimentation in the analysis of flow-structure interactions of Newtonian fluids and also to identify its scope of applications and limitations.

This article attempts to formulate a mathematical model for a potential explanation regarding the unavoidable impact of a rigid body's peculiar shape on the seamless flow over it. The solid body completely immersed in a Newtonian fluid and respectively has a relative open circuit flow on it will typically experience various observable phenomena like flow separation, flow transition, down-wash, stalling at the higher angle of attack, stalling velocity and how cambered airfoil can typically generate lift at a zero incidence angle. This article respectively represents an understanding of the laminar flow over a rigid body's external surface with due respect to its distinctive shape and size. This working paper formulates a more realistic and simplified mathematical model for open circuit laminar flow over a body, based on the historical data of aerodynamics and theoretical mechanics. This is intended to properly estimate forces on the continuous surface of the body in a laminar flow, to properly explain, understand and predict mentioned phenomena. Most of all the mechanism of streamline formation and its deformation with due regards to flow, shape and size of the body in an open-circuit laminar are formulated mathematically to enhance better design theory which can reduce experimentation while designing a streamlined body.