the hydraulic press
A hydraulic press is a machine that turns a small push into a huge one using a trapped liquid, usually oil. Two pistons of different sizes sit in a connected container of fluid; press gently on the small piston and the large piston lifts a car with ease. It is the fluid version of a lever, and it answers a very practical question: how can a person exert a force many times greater than they could by muscle alone?
It works directly from Pascal's principle. Pressing the small piston of area A_1 with a force F_1 raises the fluid pressure by P = F_1 / A_1, and this same pressure acts on the large piston of area A_2, producing a force F_2 = P × A_2. Combining these gives F_2 = F_1 × (A_2 / A_1): the output force is multiplied by the ratio of the piston areas. Make the big piston a hundred times the area of the small one and you multiply your force a hundredfold.
There is no free lunch, and this is the crucial honesty. Energy is conserved, so the machine cannot create work. The big piston moves a smaller distance in exact proportion: F_1 × d_1 = F_2 × d_2 for an ideal press. You gain force but lose distance, pumping the small piston through a long stroke to inch the heavy load up a little. In this the hydraulic press is exactly like a lever or a set of pulleys, a force multiplier, never an energy multiplier.
If the large piston has 50 times the area of the small one, a 200 N push on the small piston lifts F_2 = 200 × 50 = 10 000 N, enough to raise a small car, but the small piston must be pushed 50 cm to raise the load just 1 cm.
Force is multiplied by the area ratio, but distance shrinks by the same ratio, so work stays the same.
A hydraulic press multiplies force, not energy. Conservation of energy demands that the large piston moves proportionally less, so the total work in equals the work out (minus friction).