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Pascal law says, conceptually, that exerted pressure is transmitted equally to all points on a fluid.

The so called example of hydraulics, where force gets amplified, is an application of the principle.

Below is what I'm referring to:

img

Is there any graphical way to see how force gets amplified/diminished according to the areas? I mean, avoiding everything about pressure, just seeing forces.

The puntual question is:

Can we see, using only Newton laws, how force gets amplified in the named hydraulic system?

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    $\begingroup$ That is a horrible graphic, because the large piston should move through a shorter distance than the small one by the same factor that the force is magnified. $\endgroup$ – dmckee May 10 '18 at 1:24
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You can't avoid talking about static pressure in this system because that is the mechanism of force multiplication.

On the other hand, they system is quite equivalent to a lever with a long arm (length $L_l$) and a short arm (length $L_s$). The side with the small piston is equivalent to the long arm and the side with the large piston is equivalent to the short arm.

For the level, the force $F_s$ exerted on the short side is related to that on the long side $F_l$ by $$ F_s = \frac{L_l}{L_s} F_l \;,$$ while the distance traveled is proportional to the length of the arm, so that the work on the two side is equal $$ F_s (L_s \, \Delta\theta) = F_l (L_l \, \Delta\theta) \;.$$

For the hydraulic system The force on each piston is proportional to it's area, but the distance traveled is inversely proportional to the area because a volume $V$ of fluid is transferred from one side of the apparatus to the other. As a result the work done on each side is equal in magnitude.

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  • $\begingroup$ I understand all you say, but the problem is on your first sentence, I can't really see why we can't use newtons law directly -of course it might not be possible as you say. $\endgroup$ – santimirandarp May 10 '18 at 18:46
  • $\begingroup$ I suppose there should be some deduction in differential form, from One to another, something like that. And as an aside question, is something like pressure in 3 dimensions ? $\endgroup$ – santimirandarp May 10 '18 at 18:48
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    $\begingroup$ In kinetic theory pressure is explained in terms of Newton's laws, but it is very difficult to work the details of kinetic theory with non-trivial models, and pressure was an empirical observation long before Maxwell and Boltzmann got kinetic theory off the ground. $\endgroup$ – dmckee May 10 '18 at 19:44
  • $\begingroup$ That's very interesting. Can it be applied to liquids? $\endgroup$ – santimirandarp May 11 '18 at 0:51
  • $\begingroup$ It would be nice if you can add something about kinetic T to the post. Anyway, accepted $\endgroup$ – santimirandarp May 11 '18 at 0:52
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lets say the surface area of the pump side is one square centimetre and the surface area of the platform is one square meter.

You apply 2 kilogram pressure at the pump side. All the walls and pipes and the platform feel the same pressure, 2 kilograms/centimetre. (1)

the platform bed now has a total force of 10000 centimetres times 2 = tons.

However you need to pump ten thousand cc of water before the platform moves up one centimetre!

(1) If your tanker is too deep the pressure on the walls will increase proportional to the water or fluid's $ gh\rho. $

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