Fluid Mechanics · Interactive

Viscosity & Terminal Velocity

Drop a sphere into a viscous fluid and watch it settle to a steady terminal speed. At first gravity wins and it accelerates; but viscous drag grows with speed until it exactly cancels the sphere's net weight — from then on the sphere falls at a constant terminal velocity.

→ Velocity ↓ Weight ↑ Buoyancy ↑ Drag v–t graph on the right

Setup

Sphere radius r 2.0 mm
Fluid viscosity η 1.000 Pa·s
Sphere density ρ 7800 kg/m³
Fluid density σ 1000 kg/m³
terminal velocity 0.059 m/s
Steady falling speed
0.06
v terminal (m/s)
0.00
current v (m/s)
2.2
weight−buoy (mN)
0.0
drag at v (mN)
v_t = 2r²(ρ−σ)g / 9η drag = 6πηrv v_t ∝ r²

Playback

Try this: double the radius and the terminal speed jumps roughly 4× (v_t ∝ r²). Switch the fluid from water-thin to honey-thick (higher η) and the sphere falls far slower, easing into terminal speed more gently.