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A rocket engine uses pressure from a combustion to create thrust, while a water rocket uses water pressure to create thrust.

In both cases, the enigines have chambers filled with high pressure fluid: the rocket mixes air and fuel to create a combustion, which pushes on every side of the engine, while the water rocket compresses water to exert pressure. However, both have a hole in the back, the exhaust. Since nothing can push on this hole, there will be no pressure there, and this imbalence of pressure will push the rockets up.