According to Pascal's law, how is force multiplication achieved in a hydraulic system?

According to Pascal's law, how is force multiplication achieved in a hydraulic system?

• A. Force is not affected by hydraulic systems; output equals input.
• B. Pressure is amplified by larger piston areas, increasing output pressure.
• C. Pressure is transmitted undiminished; force multiplies with larger piston area, F_out = P*A_out.
• D. Output force is independent of piston areas.

Answer: (C)

Pascal's law says that when you apply pressure to a confined fluid, that pressure is transmitted undiminished throughout the fluid. The same pressure acts on every piston in the system, so the force on a piston is the product of that pressure and the piston’s area: F = P × A. If you push on a small piston with area A_in and create pressure P, then P = F_in / A_in. The same P acts on the larger piston with area A_out, giving F_out = P × A_out = (F_in / A_in) × A_out. As a result, the output force increases in proportion to the ratio of the output area to the input area. That’s how force is multiplied in a hydraulic system without increasing the pressure beyond what you apply. So the idea isn’t that pressure gets bigger with bigger piston areas; pressure stays the same, and larger output area converts that same pressure into a greater force. The other statements imply no change in force or pressure behavior that doesn’t match this relationship, which is why the correct understanding is that force multiplies with the output piston area when pressure is transmitted undiminished.

Pascal's law says that when you apply pressure to a confined fluid, that pressure is transmitted undiminished throughout the fluid. The same pressure acts on every piston in the system, so the force on a piston is the product of that pressure and the piston’s area: F = P × A.

If you push on a small piston with area A_in and create pressure P, then P = F_in / A_in. The same P acts on the larger piston with area A_out, giving F_out = P × A_out = (F_in / A_in) × A_out. As a result, the output force increases in proportion to the ratio of the output area to the input area. That’s how force is multiplied in a hydraulic system without increasing the pressure beyond what you apply.

So the idea isn’t that pressure gets bigger with bigger piston areas; pressure stays the same, and larger output area converts that same pressure into a greater force. The other statements imply no change in force or pressure behavior that doesn’t match this relationship, which is why the correct understanding is that force multiplies with the output piston area when pressure is transmitted undiminished.