Pressure inside water: depth and density
Liquids and gases are fluids because they can flow. Gases are easily compressed, but liquids hardly change their volume. At a point inside a liquid at rest, the pressure equals the weight of the column of liquid above it, acting on each unit of area, and the force on a submerged surface acts at right angles to it. The force is F = P × A, with P in N/m² and A in m². Water pressure grows with depth, because there is more water above, and with density, so at the same depth it is greater in sea water than in a fresh water lake. At the surface the pressure is the atmospheric pressure Pa, where 1 atm = 1.013 × 10⁵ N/m². Water adds about 1 atm for every 10 m of depth, so the total pressure is P = Pa + Pwater. At 100 m the water adds about 10 atm and the total is about 11 atm. Doubling the depth doubles the water pressure, but not the total. As an extra check, ρgh = 1000 × 9.8 × 10 ≈ 9.8 × 10⁴ N/m² for 10 m of water, close to 1 atm.
| Depth | Water adds | Total pressure |
|---|---|---|
| 0 m | 0 atm | 1 atm |
| 10 m | 1 atm | 2 atm |
| 20 m | 2 atm | 3 atm |
| 30 m | 3 atm | 4 atm |
| 100 m | 10 atm | 11 atm |
Column of books, and jets. (1) Stack ten equal books and think: the bottom book carries the weight of nine above it. Compare it with the top book and say how this is like water pressure with depth. (2) With a grown-up: the adult pierces three small holes at different heights in a plastic bottle beforehand and tapes them shut. Over a sink, fill the bottle and peel the tape off. Describe which jet shoots furthest and explain.