Hydraulic jack and pascal's law When using the hyraulic jack , I am totally convinced that the pressure at the initial phase must be the same in the interconnecting liquid and both surfaces where force is applied (pascal's law) , But the question is about the end state , as long as one area surface will move downward and the other is upward , so there will be difference in height .. therefore there is delta p :
Delta p = density . g . Delta h
This is mathimatically , but physically i  still somehow FEEL it must be the same pressure ..
So is it the same , or different , and why?! And am I understanding the pascal's law correctly!
 A: With a hydraulic jack, the weight of the object being lifted is usually much greater than the weight of the working liquid. Therefore the difference in pressure in the working liquid due to different heights will be much smaller than its absolute pressure, and may be difficult to measure.
To expand my answer, in a hydraulic jack you apply a relatively small force $F_1$ to a small surfaces area $A_1$ which produces a larger force $F_2$ on a larger surface area $A_2$. The relationship is usually stated as
$\displaystyle \frac {F_1}{A_1} = \frac {F_2}{A_2}$
but this assume the surfaces are at the same height. If the second surface is at a height $h$ above the first surface then the correct relationship is
$\displaystyle \frac {F_1}{A_1} = \frac {F_2+W}{A_2}$
where $W$ is the weight of the working fluid in a column of area $A_2$ and height $h$. Since $W= \rho A_2 g h$ we get
$\displaystyle \frac {F_1}{A_1} = \frac {F_2}{A_2}+ \rho g h$
but usually the correcting term $\rho g h$ is small compared with the other pressure terms.
A: A jack with hydraulic oil in it will have a very slight pressure difference from the top to the bottom due to pressure increasing with depth. This is negligible to the operation of the jack. For instance, a typical hydraulic jack with a load on it may have around 1800 psi at the top of the cylinder, and around 1800.4 psi at the bottom, depending on its height. Some hydraulic jacks are made to operate horizontally so the pump height and pressure could be nearly the same as the head height and pressure.
