Easter Monday Dousing

The amount of water being pushed by the piston inside at a given moment is equal to the amount of water shooting in a stream outside. This is what the law of conservation of matter (mass) postulates. The continuity equation is the conclusion inferred from the law in question. The product of the density of water r, the surface of the piston S₁ and the velocity v₁ of the water flow in a chamber with a piston (which stands for the mass of water flowing in a unit of time) has to be equal to the product of the density of water, the surface of the muzzle S₂ and the velocity in the muzzle v₂:

As illustrated by the equation, the velocity of a jet of water is proportional to the velocity of the piston movement and it is greater by a ratio of the surface of the piston by the surface of the muzzle.

The hydraulic press operates on a similar principle (see the picture). If force F₁ is applied to a piston with S₁, surface, the force applied to the other piston will be greater by a ratio of the surface of the pistons.

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You can construct your own pneumatic press using two syringes of different diameter joined with a piece of plastic hose. Fill them with water! Air can be compressed quite easily and the press would not operate properly.