Unlike gases like air, liquids like water and hydraulic oil tend to not change their overall size (volume) that easily.
When you have a lot of gas squished in one container, it’s as if you had a rubber band stretched out, ready to go flying when released. Since liquids can’t be squished as easily, when more liquid gets added in it just tries to push everything else out of the way, which is what happens in a hydraulic press. When nothing is in its way then it has nothing to push against, which is why it can stop itself rather easily simply by stopping more liquid flow in, whereas compressed gas has to get all the gas out in order to have all its energy released.
Normal flow:
Imagine being in a hallway that loops around in a circle and there’s no way out. The hallway is packed with people, everyone is shoulder to shoulder and the only way to move is for everyone to work together and walk in one direction. Everyone in the hallway, including you, represents the hydraulic fluid in the hydraulic press system flowing freely. The rate in which the hydraulic fluid moves is determined by how fast the pump is going, or in this case how fast everyone in the hallway decides to move together.
The load:
When the press meets the object it’s trying to push, you can imagine that as a thin wooden wall suddenly appearing in front of you and cutting your row of people off from the other row of people directly in front of you. If no one was told to stop moving in that initial direction, everyone would be applying pressure to the person in front of them and eventually to that thin wooden wall that you’re being crushed into. The pump is still running which causes pressure to rise in the system because the fluid being pumped has nowhere to go but one direction.
The hydraulic press wins:
Everyone has been pushing the person in front of them and eventually the thin wooden wall collapses, letting you through! Only for a fraction of a second do you feel free, as you come crashing into the row that was directly in front of you before the wall appeared. Now everyone can resume walking in unison around the hallway at the same speed it was going before the thin wall appeared. When there has been enough force generated from the pressure of the hydraulic fluid acting on the hydraulic press cylinder, then the cylinder will break through the object being pressed. There’s a small moment during that where a vacuum is created from the sudden release of pressure, but is filled very quickly by the fluid already in the system.
The press doesn’t run away after the break because it’s a closed system. Just as you crash back to the person in front of you and couldn’t keep going, the cylinder is prevented from running off at high speed due to the fluid still in the system.
There is hardly any momentum because the thing is barely moving. Momentum depends on mass and speed, and speed is basically zero.
I guess what you’re really asking why it doesn’t slam down when there is presumably something pushing it very hard. But the thing isn’t pushing the way you think it is. It’s pushed by increasing fluid pressure. When the thing preventing motion is removed or breaks, the press will only move as far as it can before that pressure is equalized with (something, don’t really know what; either atmosphere or some internal reference pressure I guess). There will be some overshoot and rebound but the distance will be very small, because even a small movement of the press will result in a huge change in pressure.
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