Savchenko Problem 4.1.10
Physics · mechanics · fluid-mechanics
Problem
A hydraulic press filled with water has pistons that have cross-sections of 100 and 10 cm2 A weight of 80 kg is placed on the larger piston. To what height will the small piston then rise?Intuitive explanation
Pascal's principle tells us that pressure applied to a confined fluid spreads equally everywhere—so the force on the large piston creates the same pressure throughout the water. The key insight is that while pressure stays constant, force and distance trade off: the smaller piston experiences less force but must move farther to conserve the volume of incompressible water. Set up the pressure equation, then use volume conservation to relate how far each piston moves.
Intuitive explanation
Pascal's principle tells us that pressure applied to a confined fluid spreads equally everywhere—so the force on the large piston creates the same pressure throughout the water. The key insight is that while pressure stays constant, force and distance trade off: the smaller piston experiences less force but must move farther to conserve the volume of incompressible water. Set up the pressure equation, then use volume conservation to relate how far each piston moves.