If two pistons with different areas are connected by hydraulic fluid, how does displacement relate?

If two pistons with different areas are connected by hydraulic fluid, how does displacement relate?

• A. Displacement is independent of area and depends only on pressure.
• B. The smaller piston travels farther, with distance proportional to the ratio of larger to smaller area.
• C. The smaller piston travels the same distance as the larger piston.
• D. The larger piston travels farther than the smaller piston by the same distance.

Answer: (B)

In a connected hydraulic system with an incompressible fluid, the same volume of fluid must move on both sides. The displacement on each piston relates to its area because the volume is area times travel distance. So the relationship is A_large × d_large = A_small × d_small. Since A_large is bigger, d_large is smaller and d_small must be larger to move the same volume. The smaller piston's distance is proportional to the ratio of the larger area to the smaller area: d_small = (A_large / A_small) × d_large. This means the smaller piston travels farther when the pistons have different areas, matching the area ratio.

In a connected hydraulic system with an incompressible fluid, the same volume of fluid must move on both sides. The displacement on each piston relates to its area because the volume is area times travel distance. So the relationship is A_large × d_large = A_small × d_small. Since A_large is bigger, d_large is smaller and d_small must be larger to move the same volume. The smaller piston's distance is proportional to the ratio of the larger area to the smaller area: d_small = (A_large / A_small) × d_large. This means the smaller piston travels farther when the pistons have different areas, matching the area ratio.