Hydraulic Press: Account for the Piston Rod

Calculate the effective annular area on the rod side.

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For a double-acting cylinder, cap-side area is pi D^2/4. Rod-side area is pi(D^2-d^2)/4. Net extension force is p_cap A_cap - p_rod A_annulus, using gauge pressures and neglecting friction and inertia. Diagrams and calculations only. Use diagrams and calculations only; never build or operate a press for this activity.

Worked example

If piston diameter D is 4 cm and rod diameter d is 2 cm, cap area is 4pi cm^2 and annular area is 3pi cm^2. Equal pressure on both sides does not give zero net force.

End-on views show a full circular cap-side face and a rod-side annular face with its central rod excluded. Outer diameter 4 centimeters, rod diameter 2 centimeters: areas 4 pi and 3 pi square centimeters.

Would you believe it?

Two points in still liquid can have different pressures if they are at different depths. Transmitting a pressure change does not make all pressure readings identical.

OpenStax: pressure and depth

Question 1 What is the cap-side area for D = 4 cm? 16pi cm^2 4pi cm^2 2pi cm^2

Question 2 What is rod-side annular area for D = 4 cm and d = 2 cm? 3pi cm^2 4pi cm^2 12pi cm^2

Question 3 What fraction of cap area is the annular area? 1/2 1/4 3/4

Question 4 Cap area 0.004 m^2 at 100 kPa, rod area 0.003 m^2 at 20 kPa: net extension force? 400 N 340 N 460 N

Question 5 At equal nonzero gauge pressure on both sides, net fluid force points which way? Toward extension Toward retraction There is always zero force

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