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. Translational inertia uses an effective mass m_gas plus liquid added mass ½ρV (potential-flow sphere); using only m_gas would make the rise unrealistically violent. 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). Motion uses effective inertia m_gas + ½ρV (added mass of the liquid), not gas mass alone. 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_eff v̇ = mg − ρgV − 6πμrv, m_eff = m_gas + ½ρV (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.