How to play Pascal's Barrel
- Choose a test and read the lid, the tube, and the height or the push on the card.
- The water in the tube adds Δp = ρ·g·h under the lid, and Pascal's principle passes that same Δp to every part of the barrel.
- A force is the pressure times the area it acts on: F = Δp·A. Type your prediction and press Start.
- Watch the bars: the force that goes in stays tiny while the force on the lid or the bottom grows huge.
How can a cupful of water burst a barrel?
Squeeze a closed liquid anywhere and the extra pressure reaches every part of it, pushing out on every wall at right angles: that is Pascal's principle. A thin tube standing on a sealed, full barrel shows how far it goes. Water h metres up the tube adds a pressure ρ·g·h under the lid, about 10 kPa for every metre, however thin the tube is. That pressure pushes on the whole lid, so a lid of 0.5 m² feels about 5 kN for every metre of water in the tube, even if the tube holds only a cupful. The story goes that Pascal burst a barrel this way. What matters is the height of the water, not its amount: a wider tube needs more water but the same height. The bottom is deeper still, so it feels the tube's pressure plus its own water's. A push works the same way: a cork forced into a full bottle passes its pressure, F ÷ A_cork, to the bottom, where a larger area turns it into a larger force. The hydraulic lift is the same idea at work.
A focused learning model
The barrel is rigid, full, and sealed except for the tube, and water doesn't compress. Water is poured steadily into the tube for 2 s; the extra pressure under the lid is ρ·g·h, and it reaches every wall, the lid, and the bottom at once (the bottom also feels the barrel's own water, ρ·g·H). A lid pops the moment ρ·g·h·A_lid reaches its strength (within 0.05% still pops) and is drawn lifting off for 1 s. The cork is pushed with a force that grows steadily for 2 s, adding F ÷ A_cork everywhere. Tube heights are to scale; the barrel and the bottle are not. A height is right if it pops the lid with at most 2% to spare; a force within 2%. g = 9.8 m/s²; water is 1000 kg/m³. Plays in real time.