Calculate max. pressure of liquid in motion

Assuming you time your rocking motion in a way that you get a sinusoidal wave going nicely back and forth you may just add 3*2= 6 centimeter to the height of water. This is without slushing force.

For estimating rough numbers for slushing, I would consider the potential energy of a test rectangular sliver of water standing half the 3 cen at the middle of the tank width as a tide turning into kinetic energy at the wall, without friction breaking into wall of tank. Then you pick another test point along the width and the height and valume corresponding to this point.

After 3-4 trial pints you add the maximum value to the prior value you got for hydrostatic pressure.

The pressure on the walls of tank consists of a hydrostatic + dynamic component. In all cases of vertical up/down motion, the pressure on the floor of the tank will be the greatest of all the walls, because the hydrostatic pressure is greatest at the floor of the tank and the reaction of the dynamic component is also against the floor. Therefore we will calculate the pressure on the tank's floor and this sets an upper limit for the pressure on the walls.

The hydrostatic component of the pressure is related to the height of the water above the tank. Although sloshing in the tank will vary the height, to a first approximation if we assume that this change is small, the hydrostatic pressure is therefore constant with time and given by (density x gravitational constant x height).

The dynamic component of pressure is proportional to the vertical acceleration of the tank. From F = ma, PxA = rho x V x a P = rho x h x a

Where: P = change in pressure on tank's floor A = unit area on the tank's floor V = volume of water above unit area A = Ah rho = density of water a = acceleration h = height or depth of water

Therefore the total pressure acting on the floor = (rho x g x h) + (rho x h x a)

The accurate way of solving this problem is through solving the associated free-surface hydrodynamic stability problem and treating the pressure field as having a static plus perturbation components. Depending on your desire for accuracy, of course, this might be too cumbersome and a better way of calculating the wall thickness could be to calculate the wall thickness for the base of the tank (where highest hydrostatic pressure will be experienced) and multiply it by a safety factor instead.