Visualization of the continuity equation. Showing how any change in mass density inside a fixed control volume is exactly balanced by the net mass flux through its boundary. Blue particle concentration represents, the green arrow represents velocity, and the orange arrows show mass entering and leaving. The density is... redistributed, but no mass is created or destroyed.show more

Nothing appears or disappears it only crosses the boundary.

Continuity would have been way easier to learn if this visual was shown to me 15 years ago when I first learned it

nice graph, powerbi? airtable??

Even though the particles are constantly moving around, the total amount of mass always stays the same unless something enters or leaves the system.

Las gallinas que entran por las que salen

Hey Super, build an interactive fluid dynamics and field theory simulation of the continuity equation (∂ρ/∂t + ∇·(ρv) = 0) based on local mass conservation principles. Users must be able to directly manipulate fluid density fields ρ(x,y), velocity fields v(x,y), and control volume boundaries (rectangular, circular, custom polygon) in a 2D interactive canvas. The first viewport must immediately load a fully working uniform flow state where blue particle mass concentration, emerald green velocity vectors, and orange boundary flux vector components display exact mass balance calculations in real-time. Include interactive velocity and density vector field controls, source/sink addition toggles, preset fluid configurations (Converging Nozzle, Vortex Flow, Dipole Source/Sink, Compressible Compression), dynamic particle spawning driven by local mass flux, and real-time computation of ∮ ρ v · n dA versus ∂/∂t ∭ ρ dV. Allow snapshot export of current boundary fluxes, divergence fields, and numerical data. Ensure exact canonical metadata, matching og:image, twitter:card=summary_large_image, clean responsive typography, touch-safe controls, and dark blue slate physics lab styling using p5.js for canvas rendering. slug: continuity-equation-mass-conservation-sim-31 canonical: og:url: og:title: Continuity Equation & Mass Conservation Visual Simulator og:description: Interactive visual physics simulator for the fluid dynamics continuity equation and boundary flux conservation. og:image: twitter:title: Continuity Equation & Mass Conservation Visual Simulator twitter:description: Interactive visual physics simulator for the fluid dynamics continuity equation and boundary flux conservation. twitter:image: twitter:card: summary_large_image