Why does the bubble speed up as it rises?

Lower pressure lets the bubble expand at roughly constant gas mass, increasing displaced volume and buoyant force; drag also grows with radius and speed, so velocity approaches a balance rather than increasing forever.

Rising Bubble (Archimedes)

A spherical air bubble rises through a liquid column. Hydrostatic pressure decreases toward the free surface, so an isothermal ideal-gas bubble expands as it rises (V ∝ 1/p). Buoyancy ρgV increases with volume while the gas mass is fixed, so the net upward force grows until Stokes viscous drag balances it. The model ignores surface tension, bubble shape oscillations, and wake dynamics.

Who it's for: Fluid statics plus ideal gas law plus Newton’s law; contrast with the static Buoyancy simulator.

Key terms

Archimedes’ principle
hydrostatic pressure
isothermal expansion
Stokes drag

Live graphs

How it works

A tiny air bubble is released at depth y₀ with radius r₀. Hydrostatic pressure p(y) = p_atm + ρgy decreases as the bubble rises, so isothermal ideal gas expands: V(y) = nRT/p(y). Buoyancy ρgV grows while the gas mass stays fixed, so upward acceleration tends to increase (until drag balances). Stokes drag 6πμrv is a rough model for laminar flow; real bubbles wobble and may oscillate.

Key equations

p(y) = p_atm + ρgy, V = nRT/p(y) ⇒ V grows as y ↓ (toward surface)

m v̇ = mg − ρgV − 6πμrv (depth y downward, v = ẏ)

Frequently asked questions

Why does the bubble speed up as it rises?: Lower pressure lets the bubble expand at roughly constant gas mass, increasing displaced volume and buoyant force; drag also grows with radius and speed, so velocity approaches a balance rather than increasing forever.