Potenzialfluss

Potenzialfluss, a German term translating to "potential flow," refers to a simplified model in fluid dynamics. It assumes that the fluid is ideal, meaning it is incompressible and inviscid (non-viscous). In potential flow, the fluid motion can be described by a scalar velocity potential function, often denoted by $\phi$. The velocity vector $\vec{v}$ is then the gradient of this potential: $\vec{v} = \nabla \phi$.

The key characteristic of potential flow is that the velocity field is irrotational, meaning the curl of the velocity is zero ($\nabla \times \vec{v} = \vec{0}$). This irrotationality is a direct consequence of the existence of the velocity potential. For incompressible fluids, the continuity equation ($\nabla \cdot \vec{v} = \vec{0}$) combined with the irrotationality condition leads to Laplace's equation for the velocity potential: $\nabla^2 \phi = \vec{0}$.

Solving Laplace's equation with appropriate boundary conditions allows for the determination of the velocity field and thus the behavior of the fluid. Potential flow theory is particularly useful for analyzing the flow around streamlined bodies at low Reynolds numbers where viscous effects are negligible, or as a starting point for more complex flow analyses. It provides a framework for understanding phenomena like lift generation on airfoils and the flow patterns around submerged objects. Despite its idealizations, potential flow offers valuable qualitative insights and can yield quantitative results for certain flow regimes.