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Consider a hydraulic jack with massless pistons as follows.

enter image description here

The famous equation for this system is

$$ \frac{F_1}{A_1}=\frac{F_2}{A_2} $$

My question is why isn't the equation as follows?

$$ \frac{F_1}{A_1}=\frac{F_2}{A_2} + \rho g h $$

It is based on my understanding that any points in the same horizontal line have the same pressure.

Could you spot my misconception?

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    $\begingroup$ This is a good exercise to learn a bit of thinking like a physicist. You've done the "be careful and pedantic in deciding what the physics is" part. Now do the "figure out what contributions we can safely ignore" part... $\endgroup$ – dmckee --- ex-moderator kitten Mar 11 '14 at 16:04
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Your second equation is correct. The $\rho gh$ term is small compare to the force needed to lift a car for example in a real jacking situation, however.

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Your second equation is correct when there is a piston height difference.this equation is derived from pascal law.law states the initial difference remains same.it only talks what happens when you apply a force on one end and how the pressure of incompressible liquid transmit that force to the other end.

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