Terminal Velocity (Falling Through a Fluid)
Release a sphere into a tall column of fluid — adjust its size, density, and the fluid's density and viscosity to see it asymptote to a terminal speed, or float, depending on which is denser.
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What you can adjust
- Fluid density (ρ_fluid)
- 1 – 13600 kg/m³
- Fluid viscosity (μ)
- 0.001 – 1.5 Pa·s
- Ball radius (r)
- 0.001 – 0.05 m
- Ball density (ρ_ball)
- 200 – 22600 kg/m³
- Start position
- 0 – 1
~1 for air, ~1000 for water, ~1400 for glycerol, ~13600 for liquid mercury.
~0.001 for water, ~1-1.5 for glycerol/honey-ish fluids. Higher viscosity means more drag and a lower terminal speed.
Larger balls have more weight (volume) but proportionally less drag, so they reach a higher terminal speed.
~2700 for aluminium, ~22600 for osmium (the densest natural element). If this is LESS than the fluid density, the ball floats/rises instead of sinking.
Above the liquid: the ball drops in from the air. Below: it's released resting on the container floor and rises (if buoyant).
About this simulation
What it shows
A sphere is released into a tall column of liquid, either dropped in from above or released from the bottom. It speeds up, then settles at a steady speed or floats.
The key idea
Weight pulls down while buoyancy and viscous drag push up. The drag grows with speed until the forces balance, which gives a steady terminal speed of 2r²(ρ_ball − ρ_fluid)g / (9μ). A ball less dense than the fluid rises and floats.
Try this
Set Ball density (ρ_ball) to 600 kg/m³ with Fluid density (ρ_fluid) at 1000: the ball no longer sinks, it floats at the surface.
Drag follows Stokes' law, which is accurate for slow, smooth flow. A large, fast ball in a thin fluid would feel more drag in real life.