Potenzialströmungen

Potenzialströmungen, also known as irrotational flows, are a type of fluid flow where the curl of the velocity field is zero everywhere. This mathematical condition implies that the fluid parcels do not rotate as they move. In a potential flow, the velocity vector can be expressed as the gradient of a scalar function called the velocity potential, denoted by $\phi$. This means $\vec{v} = \nabla \phi$.

The key property of potential flows is that they are governed by Laplace's equation. If the fluid is incompressible, then the divergence of the velocity field is also zero ($\nabla \cdot \vec{v} = 0$). Substituting $\vec{v} = \nabla \phi$ into this equation, we get $\nabla \cdot (\nabla \phi) = 0$, which simplifies to $\nabla^2 \phi = 0$. This is Laplace's equation, and its solutions, the velocity potentials, describe the flow field.

Potential flows are a simplification and are often used in fluid dynamics to approximate real flows under certain conditions. They are particularly useful for analyzing inviscid and irrotational flows, such as those around streamlined bodies at low speeds or in the outer regions of more complex flows. While they neglect viscosity and vorticity, potential flow theory provides valuable insights into phenomena like lift generation and pressure distribution. However, it cannot accurately describe flows near boundaries where viscous effects become dominant or flows involving significant turbulence.