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I've been looking into how hydraulic lifts work and i don't quite understand yet how Pressure and Forces relate. Let's assume the water is on equal level on both sides and i apply a force to The smaller Area A is amplified by a factor B/A on the other side at Area B, But when do these forces equal out? Because assuming the Pipes are long enough at some point the Force Applied on A will be canceled out by the weight of all the water on the otherside at B.

hi

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2 Answers 2

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Assuming that the system was in equilibrium to begin with, the weight of the water column B was already compensated by the the weight of the water column A. (Although the water column B is heavier, it is distributed over a larger area, as compared to A.)

Any external force applied anywhere in the fluid, will not have to cancel any weight elsewhere, because that has already been taken care of (since the system was in static equilibrium to begin with).

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  • $\begingroup$ But when a force is applied how does that force cancel out? Is it when the water on the side of b has reached a gravity force of the same size as the force A applies on B? $\endgroup$
    – Kais
    May 13, 2020 at 12:58
  • $\begingroup$ @Kais Nothing cancels the force. If it were to be cancelled, you wouldn't see the system change. You can keep applying the force for as long as want. $\endgroup$
    – Arjun
    May 13, 2020 at 13:02
  • $\begingroup$ So the Area A would continue to go down aslong as a force is applied to it? No matter how much water is moved to the side of b? $\endgroup$
    – Kais
    May 13, 2020 at 13:06
  • $\begingroup$ @Kais Yep....... $\endgroup$
    – Arjun
    May 13, 2020 at 13:12
  • $\begingroup$ Is there any intuitive explanation for this?, because this feels rather intuitive to me. $\endgroup$
    – Kais
    May 13, 2020 at 14:34
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Arjun has already answered your question, but I thought I would add this.

The relationship between force and pressure is something like the relation between mass and density. Density tells you how mass is spread out. If you integrate density over a volume, it adds up to the total mass. Or you can integrate over a part of the total volume to find out how much mass is in that volume.

A liquid exterts a force on the surface of the container. Pressure is force per unit area. You integrate over the surface A or B to find the total force on A or B.

There is also a difference between pressure/Force and density/mass. For a given object, the total mass is always the same. But total force on a surface can change.

Consider another container with just a piston A on the bottom. If the container is a cylinder like the left arm, the piston would cover the whole bottom of the container. The total force on the piston would be the weight of the fluid.

Now put the same fluid in another container the size of arm B. Because the diameter is larger, the fluid does fill it to the same level. The total force on the bottom is the same, the weight of the fluid. Piston A in the bottom of this larger container occupies only a fraction of the bottom, and therefore only has a fraction of the weight.

This also tells you the pressure is higher on the bottom of the tall thin container.

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