Direct measurements (3): ballistics
vgas
=
d2 (rliq - rgas) g
18 m
Bubble rise in a magma:
Basalt: a bubble of 1 mm in diameter (d)  takes 6 months to rise 1 km
particle in gas jet:
vpart2
=
2 p d (rliq - rgas) g
3 Cd rair
Remark: Stromboli; crystal settling: d = 1 mm; vcryst = 56 m/s
ballistics
vpart = 50 m/s : particle velocity
Vgas = 100 m/s : gas velocity
Apparent velocity: w = vgas - vpart
balance between  viscous resistance in magma and bubble buoyancy
balance between friction in air and particle weight
m: viscosity (Pa.s);
liq and rgas  liquid and gas density (kg/m3);
Cd: drag coefficient (turbulent) = 1.18