A4 9 The Barrels

Abstract

We model Pascal’s barrel through the hydrostatic paradox. A 10 m long, 1 cm wide tube is fixed to a sealed 225 L barrel; adding 0.785 kg of water raises the head to produce 98.1 kPa gauge pressure at the lid. This pressure yields a 25.9 kN upward force on the lid despite the small added mass, illustrating that pressure depends on height and density, not container volume. The paradox is resolved by force balance: the lid exerts an equal 25.9 kN reaction on the fluid, so the barrel base must carry both the total fluid weight of 2.2 kN and this additional downward load. The results align with hydrostatics and validate the model.