How is pascal's law applied while the fluid moves in a hydraulic lift example? I think I have some misconception for Pascal's law. My knowledge is that Pascal's law is applied while the fluid at rest and thus the pressure transmission is equal and act at all directions. But what's really confusing me is the hydraulic lift example. Since the fluid is pushed down by a piston 1 and moves upwards pushing piston 2, then how can we still talk about Pascal's law while the fluid is moving (i.e dynamic pressure would be in presence and thus the pressure is not really equal at pistons based on Bernoulli's principle)?
 A: 
Since the fluid is pushed down by a piston 1 and moves upwards pushing piston 2, then how can we still talk about Pascal's law while the fluid is moving (i.e dynamic pressure would be in presence and thus the pressure is not really equal at pistons based on Bernoulli's principle)?

Strictly speaking, you are absolutely correct. Technically while the lift is moving the fluid is flowing and Pascal's law is not applicable. However, if the lift is rising slowly then the deviations from Pascal's law are small and the example is valid.
In physics, everything is an approximation to some degree or another. So we cannot avoid them and indeed we need to embrace approximations. Even our most fundamental laws are probably approximations. But it is important to always recognize the approximations we are making and consider their impact.
Approximations are useful insofar as they simplify the math, and clarify the major effects. Approximations are problematic insofar as they produce errors that exceed our desired level of accuracy.
For example, I recently re-worked the hydraulics on my tractor to add a grapple for moving farm debris easily. If I wanted to determine how tightly my grapple could grip a load, I could simply take my hydraulic pump specified pressure, the diameter of the cylinder, and the lever arm of the grapple itself. This would give me a good approximation of the grapple's strength using Pascal's law. I only need to know that strength to within 100 lb force or so, and the tractor's hydraulic flow is slow.  So the difference between Pascal's law alone and a full fluid dynamic analysis is negligible for my needs. Pascal's law is completely valid for determining if I can grab a specific log.
A: After doing some basic research on hydraulic lifts, I've found out that hydraulic lifts work by pushing a smaller surface of liquid (say a 1 square meter circle being shoved 1 meter down a cylinder full of water). The structure containing the liquid also has another, larger moving part which get's moved by the increased pressure in the water (continuing our arbitrary example, if this moving part is 2 square meters, it will get moved a half meter outward). The advantage of a hydraulic press is that it applies mechanical advantage (in our example, 2:1), however the liquid in the system pushes outwards with the same constant force, just over a greater area.
