FluidOne

### Analytic Fluid Mechanics Lab & Flow Field Visualizer Explore classic analytical solutions of fluid dynamics in a clean, focused Apple-native workspace. FluidOne provides 36 closed-form flow and wave models from foundational fluid mechanics textbooks across 6 major families: steady viscous and rotating flows, unsteady viscous diffusion, potential flow, vortex dynamics, boundary layers and low-Reynolds creeping flows, and surface/interface waves. Features instantaneous parameter updates, streamline and vector rendering, physical point probing, governing equation references, and scientific CSV, high-resolution PNG, and vector PDF exports. #### 【6 Core Families · 36 Textbook Fluid Models】 - **Steady Viscous & Rotating Flows (6 Models)**: Parallel plates (Couette-Poiseuille), circular pipe (Hagen-Poiseuille), annular pressure flow, rectangular duct, elliptical duct, circular Couette flow between concentric cylinders, gravity-driven inclined film, and Ekman boundary layer spiral. - **Unsteady Viscous Flows (4 Models)**: Stokes' first problem (impulsively started plate), Stokes' second problem (oscillating plate), starting channel flow, and starting circular Couette flow. - **Potential Flow Theory (9 Models)**: Flow past a cylinder (with and without circulation), planar stagnation flow, line source and sink, line doublet, Rankine half-body, Rankine oval, elliptical cylinder at an angle of attack, Joukowski cusped airfoil with Kutta circulation, and 3D potential flow past a sphere. - **Vortex Dynamics (6 Models)**: Rankine vortex (rigid core + potential exterior), Burgers vortex (axial strain balance), Kirchhoff rotating elliptical vortex patch, Lamb-Oseen diffusing vortex, point vortex dipole pair (co-rotation and translation), vortex near a slip wall, and Kármán vortex street. - **Boundary Layers & Low Re (4 Models)**: Falkner-Skan boundary layer family (with Blasius flat plate and Hiemenz stagnation presets), von Kármán rotating disk boundary layer, round laminar submerged jet (Landau-Squire solution), and creeping flow past a sphere or fluid drop (Stokes drag and Hadamard-Rybczynski internal circulation). - **Surface & Interface Waves (4 Models)**: Capillary-gravity travelling waves in finite depth, finite-tank standing wave normal modes, two-fluid interfacial waves (Kelvin-Helmholtz shear stability), and nonlinear cnoidal and solitary shallow-water waves. #### 【Interactive Features & Scientific Exports】 - **72-Hour Full-Featured Free Trial**: Starts automatically on first launch without subscriptions or account logins. Enjoy unrestricted access to all 36 models, solvers, and exports for 72 hours, with an optional one-time non-consumable full unlock. Existing paid customers receive automatic permanent lifetime access. - **Scientific Color Palettes**: Switch effortlessly between Ocean (classic hydrodynamic cyan-blue), Thermal (high-contrast warm scalar ramp), and Schlieren (monochromatic optical contrast gradient). - **High-Resolution PNG & Vector PDF Export**: Export publication-grade 1200×760 @2.0x PNG field snapshots and vector PDF figures with streamlines, velocity vectors, and legends via native file pickers, in addition to structured 81×51 CSV grids. - **Governing Equations & Regime Notes**: Expandable header cards reveal governing PDEs, dimensionless scaling parameters, and modeling assumptions with direct links to matching chapters in the bundled 365-page PDF theory textbook. - **8 Interface Languages**: Instantly switch between English, Simplified Chinese, Traditional Chinese, Japanese, French, German, Russian, and Spanish.