Lessons · Engineering · Pascal's principle and the hydraulic jack
Pascal's principle: the same pressure everywhere, so area multiplies force
Pressure in a confined fluid is the same at every point, so F_1 / A_1 = F_2 / A_2. A small push on a small piston becomes a big push on a big one.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A two-tonne car goes up on a jack a person works by hand. Nothing is free: the small piston travels many times farther than the big one. Sizing the ram and the pump comes down to this one ratio.
How to think about it
Find the pressure from the side you know, force over area. Apply that same pressure to the other area. If the problem gives diameters, square them: doubling a diameter quadruples the area and the force.
Worked example
Pressure is the same everywhere in a confined fluid, so F_1 / A_1 = F_2 / A_2The principle, written as the equation you will use.
Jack: small piston 4 cm², large piston 100 cm², effort 80 NThe setup.
p = 80 / 4 = 20 N/cm²; F_2 = 20 × 100 = 2000 NPressure from the small side, force on the large side.
The trade: the small piston moves 25 times as far as the large oneForce is multiplied by 25 and distance divided by 25. Work is not multiplied at all.
Your turn
Areas 3 cm² and 60 cm², effort 50 N. Write the lift.
F_2 = 50 × 60 / = 1000 N
Solve one, graded on the server
The trap
Using diameters as though they were areas. A ram twice the diameter has four times the area; the multiplication is by the square of the diameter ratio, not the ratio itself.