You probably noticed that the smaller syringe plunger was much easier to push than the larger one, yet traveled a much greater distance in the process.
This phenomenon arises as a direct result of Pascal’s principle, a cornerstone of hydraulics, the use of fluids to transmit forces. Pascal’s principle says that a change in pressure in any part of an enclosed fluid is transmitted undiminished to all parts of the fluid. Pushing on the plunger applies pressure on the water inside, and the transmitted pressure causes the plunger in the other syringe to move.
Though the pressure on the water is equal everywhere, the force on the two plungers is not. The force on a surface is equal to the pressure times the area of the surface.
force = pressure x area
Since the base of the smaller syringe plunger has a significantly smaller surface area, it takes much less force to get it to move.
The good news with the small syringe is that you’ve obtained a force advantage; the bad news is that you’re paying for it with a distance penalty and have to push the plunger further. Mechanical work is the product of force times the distance the force moves through.
work = force x distance
The work done by one plunger must equal the work put into the other—so what you gain in increased force you lose in decreased distance.
Hydraulic systems like the one you just made are common in countless applications: lifts and jacks for servicing cars, brake systems, airplane wing flaps and landing gear, mechanical arms on garbage trucks, and so on.