Consideration of the energy equation for a flowing compressible fluid shows that the so-called modified Bernoulli equation, commonly used to relate ejects velocity to pre-explosion pressure in vulcanian-style volcanic explosions, is inadequate in almost all circumstances because of its neglect of the detailed role of volatiles in explosive eruptions. The physical differences between three common types of explosive volcanic activity, typified by plinian, strombolian and vulcanian events, are reviewed and simple mathematical models are proposed for them. The models relate velocities of ejects to initial pressures at the start of an explosive phase and to mass fractions of volatiles (generally taken to be water) in the explosion products. When fitted to observed ejects velocities (or velocities deduced from the dispersal of debris) up to 500 m/s the models predict pressures up to 300 bars — almost always much lower than those deduced in earlier treatments.