Volcano Magma Chamber & Conduit Dynamics (2D)

Conduit & Chamber

Magma supply rate 4.0 m³/s

Conduit radius 15 m

Magma viscosity 50 ×10³ Pa·s

Gas / volatile content 3.0 wt%

Live Readout

Chamber overpressure

0.0 MPa

Vent exit velocity

0 m/s

Mass eruption rate

0 kg/s

Plume height

0.0 km

VEI estimate

Gas-slug period

-- s

How it works

A magma chamber of fixed volume fills from below at the supply rate you set and drains through a cylindrical conduit to the vent. Overpressure ΔP above lithostatic evolves from mass balance and drains out under Hagen–Poiseuille flow through the conduit:

Q_out = (π r⁴ ΔP) / (8 μ L)
d(ΔP)/dt = β·(Q_in − Q_out) / V_chamber

Rising gas bubbles coalesce into Taylor slugs that ascend the conduit at a speed set by their buoyancy (Taylor bubble rise-velocity relation, v = 0.35√(gD)); each slug arrival briefly collapses conduit resistance and drives a Strombolian burst of ejecta and ash, with the vent exit speed from the pressure drop via Torricelli/Bernoulli:

v_slug = 0.35√(g·2r)     v_exit = √(2ΔP/ρ)

Column height and explosivity are read from the resulting mass eruption rate (MER, kg/s) with the empirical Sparks/Mastin plume-height relation and mapped onto the Newhall–Self Volcanic Explosivity Index:

MER = 140 · Hᴸ⋅¹⁵   (H in km)  →  H = (MER / 140)^(1/4.15)

Higher supply / narrower conduit / higher viscosity — steeper pressure buildup, higher exit velocity when it releases.
More gas — shorter slug period (more frequent bursts) and a taller, more explosive plume for the same magma flux.
Wider conduit / lower viscosity — magma drains as fast as it arrives, so pressure barely builds and the eruption stays effusive.

Lava / embers Ash plume Chamber pressure trace