How does hydraulic pressure create a mechanical advantage in a simple hydraulic jack?

to understand this answer we have to assume the following as givin fact. fluids do not compress, that out of the way, the hydraulic piston you push is a smaller diameter than the piston that does the work. for example lets say that you are using a 1 square inch piston as the one you are pressing, and you are using a 100 square inch piston as the one doing work. these numbers are greatly exaggerated but will work for the example if you put 10 pounds of pressure on the 1 inch cylinder, you will have 10 psi of pressure. when this is routed to the 100 square inch cylinder you will still have 10 psi of pressure, but now it is acting on 100 square inches (10 pounds per square inch times 100 square inches) this would calculate to 1000 pounds. it would be the same as a 1001 inch lever with the fulcrum being 1 inch in from one end, only you would exert force on the larger lever to gain a mechanical advantage. hydraulics used in this way are known as liquid levers