Hydraulic Press: Trade Force for Distance

See why a stronger output push travels a shorter distance.

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For an ideal liquid with no compression or leaks, area times piston travel is equal on each side. Four times the output area means one quarter the output travel. This is a paper model, not an experiment. Use diagrams and calculations only; never build or operate a press for this activity.

Worked example

Input area 2 cm^2 moves 8 cm, displacing 16 cm^3. Output area 8 cm^2 moves 2 cm and displaces the same 16 cm^3.

The input face has area 2 square centimeters and travels 8 centimeters. The output face has area 8 square centimeters and travels 2 centimeters. Both displace 16 cubic centimeters of liquid.

Would you believe it?

Many powered hydraulic machines use a motor-driven pump to supply energy. A large output force is not free energy; force and travel must both be counted.

OpenStax: hydraulic work and energy

Question 1 What volume is displaced by 2 cm^2 moving 8 cm? 10 cm^3 4 cm^3 16 cm^3

Question 2 How far does an 8 cm^2 output move with that volume? 16 cm 2 cm 8 cm

Question 3 Which piston travels farther? The small input piston The large output piston Both travel the same distance

Question 4 If input travel becomes 4 cm, output travel becomes what? 4 cm 16 cm 1 cm

Question 5 What stays equal in this ideal model? Piston area Displaced liquid volume Piston travel

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