In a bottle rocket the air stores the energy, and the water is what gets thrown out. Compressed air above the water pushes on it, and the water squirts out of the nozzle. When the water is gone, the little air that is left rushes out too, but air is so light that this gives only a short, weak push.

Pressure here is measured as gauge pressure: how much it is above the pressure of the air around us. In this lab the unit is the bar: 1 bar = 100 000 pascals, about the pressure of the atmosphere. The pressure difference between inside the bottle and outside is ΔP.