How do you compute the effective piston area on the rod side of a cylinder?

How do you compute the effective piston area on the rod side of a cylinder?

• A. A_eff = A_piston
• B. A_eff = A_piston − A_rod, with A_rod = π(d_rod^2)/4
• C. A_eff = A_piston + A_rod
• D. A_eff = A_piston − 0.5 × A_rod

Answer: (B)

On the rod side, the rod itself blocks part of the piston face, so the fluid can only push on the annular area around the rod. That means the effective area isn’t the full piston face area, but the piston area minus the rod’s cross-sectional area. Compute each cross-sectional area with A = πd^2/4, where d is the diameter. So the effective area is A_piston minus A_rod: A_eff = A_piston − A_rod = π(D_piston^2)/4 − π(d_rod^2)/4. This A_eff is what you use to find the hydraulic force on the rod side: F = P × A_eff. For reference, the piston side (no rod blocking area) uses the full piston area, F = P × A_piston. Example: if the piston diameter is 100 mm and the rod diameter is 40 mm, A_piston ≈ 7854 mm^2 and A_rod ≈ 1257 mm^2, giving A_eff ≈ 6597 mm^2.

On the rod side, the rod itself blocks part of the piston face, so the fluid can only push on the annular area around the rod. That means the effective area isn’t the full piston face area, but the piston area minus the rod’s cross-sectional area. Compute each cross-sectional area with A = πd^2/4, where d is the diameter.

So the effective area is A_piston minus A_rod:

A_eff = A_piston − A_rod = π(D_piston^2)/4 − π(d_rod^2)/4.

This A_eff is what you use to find the hydraulic force on the rod side: F = P × A_eff. For reference, the piston side (no rod blocking area) uses the full piston area, F = P × A_piston.

Example: if the piston diameter is 100 mm and the rod diameter is 40 mm, A_piston ≈ 7854 mm^2 and A_rod ≈ 1257 mm^2, giving A_eff ≈ 6597 mm^2.