On the geometry of a steady two dimensional potential flow and its physics

The paper studies the geometrical aspects of steady, two-dimensional potential flows and their relation to the physics that governs them. To achieve this, the streamline curvature of a flow is determined when the vector velocity field describing it, is known. Two methods, which allow the calculation of streamline curvature at every point of a flow field, are developed: the ‘Method of Rotation’ and the ‘Method of Directional Derivative’. Especially the first method reveals an interesting feature of curvature, allowing it to be interpreted kinematically. Furthermore, an attempt has been made towards the formulation of a potential theory from a geometrical perspective. For this reason the concept of ‘Global Curvature’ is introduced, being a measure of both stream and potential line curvature. It has been proven that it contains all the information needed to determine the physical quantities of velocity and static pressure throughout a potential flow, thus depicting the strong link between geometry and physics.