AI Tutor
When you step gently on a car's brake pedal, your foot exerts barely enough force to squash a soda can — yet it instantly stops a 4,000-pound vehicle traveling at highway speed.
To see how fluids magnify your strength, we start with pressure, which measures how much force is spread across a surface: P=FAP = \frac{F}{A}, where FF is force in newtons (N) and AA is surface area in square meters (m2\text{m}^2).
What happens when that pressure isn't pushing on an open floor, but on a trapped liquid inside sealed pipes?

Pascal's Principle

In 1653, French scientist Blaise Pascal discovered that any change in pressure applied to a completely enclosed, stationary fluid transmits equally in all directions throughout the entire fluid.
Because liquids like oil and water are essentially incompressible (their volume cannot be squeezed smaller), the fluid cannot absorb the squeeze — it simply pushes against every square millimeter of its container with identical pressure.
Because the pressure at the input piston (P1P_1) must equal the pressure at the output piston (P2P_2), we can set their pressure ratios equal to each other.
F1A1=F2A2  ⟹  F2=F1⋅(A2A1)\frac{F_1}{A_1} = \frac{F_2}{A_2} \implies F_2 = F_1 \cdot \left(\frac{A_2}{A_1}\right)
If the output area A2A_2 is 1010 times bigger than the input area A1A_1, the output force F2F_2 is automatically multiplied by 1010.
How do we put this formula to work in a real garage lift?

Calculating Hydraulic Lift Force