Fun fact
In 1648, Blaise Pascal's brother-in-law carried out one of the most dramatic demonstrations in the history of physics. He fitted a long, thin vertical tube to a sealed barrel filled with water and climbed to the second floor, pouring water into the tube. Just a few litres of water in the narrow tube — weighing a couple of kilograms — was enough to burst the barrel apart. The pressure at the bottom depends only on the height of the water column, not on the total volume: ρ × g × h. This is the hydrostatic paradox. It's also why dams are built thicker at the bottom, why a diver gains roughly one atmosphere every 10 metres, and why the wall of a 30-storey building's water tank needs careful engineering.
The physics behind the barrel
Why did a few litres of water burst a full barrel?
Pressure depends only on the height of the water column above it, not on the volume of water. The thin tube reaching the second floor added roughly 6–7 metres of additional water head, so the pressure at the barrel jumped by about 0.6–0.7 bar. Barrels are held together by hoops only strong enough for a roughly 1-metre water column, so the extra head from the tube — a couple of kilograms of water — produced more force at the bottom than the entire barrel of water itself. That is the hydrostatic paradox: a small volume high up can exert enormous force at the bottom.
What is a metre of water column (mH2O)?
The pressure industry still uses the unit mH2O ("metres of water column"). One metre of water column equals about 9.81 kPa (0.0981 bar), so 10 mH2O ≈ 0.981 bar ≈ 1 kgf/cm². Pressure gauges for pumps, wells and fire hydrants are commonly marked in mH2O precisely because of this easy mental conversion — if you know the height, you know the pressure.
How deep is one atmosphere in water?
Divers gain roughly one atmosphere (1 atm ≈ 1.013 bar) of pressure for every 10 metres of descent. At 30 metres — the recreational deep-diving limit — a diver experiences 4 atmospheres of absolute pressure: 3 from the water plus 1 from the air above. Scuba regulators deliver air at ambient pressure for exactly this reason; breathing at surface pressure at depth would be impossible.
Tool usage guide
- Open the Water Pressure Calculator and pick the Hydrostatic tab.
- Enter the depth below the surface (e.g. 10 m) and choose the water type — fresh water at 20 °C, the densest 4 °C water, hot 60 °C, or seawater.
- Read the gauge pressure in bar, kPa, psi and atm instantly, plus the absolute pressure (add 1.013 bar) and the equivalent water column.
- Try the Pressure ↔ Head tab to convert a pump's pressure rating into metres of head — essential for pump selection.
These conversions matter far beyond the classroom: diving tables and dive computers are built around the ~10 m per atmosphere rule; suction pumps can lift water at most about 10 metres, because atmospheric pressure can only push the column that high; and dams and aquarium walls are engineered thicker at the bottom because the pressure there grows linearly with depth, not with total water volume.