In 1939, Bagnold  introduced a very simple model to describe the pressure in a gas pocket entrapped between the liquid and the wall during sloshing events. This model takes only into account the compressibility of the gas and the initial relative velocity with respect to the wall of the liquid which is modeled as a solid piston. As shown by Bagnold, this models (and therefore the pressure in the pocket) is completely described by two dimensionless numbers, the impact number S_B and the adiabatic constant of the gas gamma_g.

In this work, we generalize this model in two directions. First we introduce the effect of a constant (in time) acceleration and then we take into account the compressibility of the liquid. We  provide for these generalizations analytical models and analytic formulas for the maximum pressure on the wall the rise time and the period of oscillations of the gas pocket as functions of the dimensionless numbers. This is done for general equations of state for both fluids. Particularizing these equations of state (namely perfect gas for the gas and stiffened gas for the liquid) we can graphically represent the aforementioned quantities of interest.