The Hydrostatic Paradox (Pascal's Vases)

Settled in 1586 by Simon Stevin's hydrostatic pressure law; demonstrated experimentally by Blaise Pascal (~1648) with his 'vases communicants' apparatus.

Simon Stevin first proved the correct hydrostatic pressure law rigorously in 1586, showing pressure at depth depends only on the height of fluid above, not the container's shape. Blaise Pascal popularized the counter-intuitive consequence roughly six decades later with his famous 'vases communicants' (communicating vessels) demonstrations, and the effect has been known as the 'hydrostatic paradox' or 'Pascal's paradox' ever since. It is one of the most frequently anthologized classic physics paradoxes and appears in essentially every popular-paradox collection, Lange's included, as a Chapter 3 ('Equilibrium of Forces') problem.

A tiny amount of water in a cleverly shaped vessel can exert as much force on its base as a much larger amount in a straight-walled tub — pressure, not total weight, is what matters at the bottom.

Explanations that circulated

• Assuming the downward force on a container's base must equal the total weight of liquid inside the container, as if hydrostatic pressure worked like a scale weighing everything poured in above it.
• Ignoring that in a vessel with slanted walls, part of the liquid's weight is supported by (or adds an extra downward component onto) the slanted walls themselves rather than the base, so the force on the base is set purely by depth via P = ρgh times base area — independent of the container's total volume or shape.

References

• Hydrostatic paradox, Wikipedia contributors, Wikipedia, 2024
• Fluid Mechanics, Frank M. White, McGraw-Hill, 2011