From Wikipedia: "Pascal's law, or the Principle of transmission of fluid-pressure, states that "Pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid, such that the pressure ratio remains the same."
For brakes or hydraulic lifts, the idea is simple. Apply a force (F1) through a small area (A1) and the pressure (P) is given by F1/A1.
The pressure is transmitted through the fluid equally. The pressure on the other side, onto another piston (area A2) will generate a force (F2). P = F2/A2
Since the pressures are constant:
F1/A1 = F2/A2
Some interesting pages to view:
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