🎬Visualizing the Incompressibility and Vorticity of a Steady Helical Flow

This analysis and visualization ( 3 demos )demonstrate that the fluid flow is a steady, incompressible, and rotational helical motion. The flow's incompressibility ( $\nabla \cdot v=0$ ) guarantees that the volume of any fluid element remains constant, while the constant, non-zero vorticity ( $\omega=\frac{2 v_{ n }}{L} e_z$ ) confirms its rotational nature, driving the fluid elements in a path of rigid-body rotation without shearing. This flow behavior is further quantified and visualized by the simulation's Core Features, which include a 3D visualization of particle paths and a Real-Time Mass Flux Calculation ( $\Phi$ ) capability. Users can interactively switch between three critical surfaces-the Disc, the Cylinder Wall, and the Phi Slice-to see how the mass flux values are derived from the velocity field, allowing them to visually connect the theoretical calculations (like the zero flux through the Cylinder Wall) to the flow's dynamic interaction with each boundary.

🎬Narrated Video

🧵Related Derivation

🧄Total Mass Flux Through Cylindrical Surfaces (TMF-CS)

⚒️Compound Page

Visualizing the Incompressibility and Vorticity of a Steady Helical Flow | Resulmationviadean on Notion